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.572 .216 r F P p .59803 .65204 m .57815 .62475 L .65054 .64511 L .796 .577 .604 r F P p .57815 .62475 m .55152 .5882 L .58234 .60591 L .796 .577 .604 r F P p .002 w .59971 .52793 m .65054 .64511 L p .61008 .58179 L .94 .572 .216 r F P s P p .58621 .59107 m .61008 .58179 L .59079 .56965 L .623 .34 .467 r F P p .61008 .58179 m .80956 .50427 L .60682 .56486 L .623 .34 .467 r F P p .61008 .58179 m .60682 .56486 L .59079 .56965 L .623 .34 .467 r F P p .5886 .6751 m .60277 .65278 L .65054 .64511 L .846 .943 .885 r F P p .002 w .65054 .64511 m .73528 .84043 L p .60799 .66571 L .796 .577 .604 r F P s P p .002 w .65054 .64511 m .73528 .84043 L p .63561 .6491 L .94 .572 .216 r F P s P p .73528 .84043 m .63135 .65025 L .63561 .6491 L .94 .572 .216 r F P p .63135 .65025 m .60277 .65278 L .65054 .64511 L .014 0 0 r F P p .60277 .65278 m .57128 .65558 L .65054 .64511 L .014 0 0 r F P p .48895 .66645 m .55249 .73195 L .48425 .63069 L .949 .596 .288 r F P p .50567 .66248 m .53255 .61192 L .48425 .63069 L .759 .677 .771 r F P p .51381 .69208 m .50567 .66248 L .53674 .70021 L .465 .321 .6 r F P p .50567 .66248 m .57815 .62475 L .55543 .61836 L .759 .677 .771 r F P p .58621 .59107 m .59079 .56965 L .55868 .57924 L .623 .34 .467 r F P p .58621 .59107 m .58421 .59754 L .57072 .57807 L .191 .512 .913 r F P p .54139 .55367 m .53444 .56882 L .59971 .52793 L .846 .922 .882 r F P p .53002 .55869 m .53444 .56882 L .55114 .53242 L .846 .922 .882 r F P p .55868 .57924 m .53444 .56882 L .53002 .55869 L .191 .512 .913 r F P p .57815 .62475 m .4979 .57287 L .53002 .55869 L .796 .577 .604 r F P p .59079 .56965 m .60682 .56486 L .59971 .52793 L .623 .34 .467 r F P p .60682 .56486 m .80956 .50427 L .59971 .52793 L .623 .34 .467 r F P p .61008 .58179 m .59433 .55713 L .59971 .52793 L .94 .572 .216 r F P p .61464 .52516 m .59971 .52793 L .80956 .50427 L .112 .665 .737 r F P p .60165 .52655 m .80956 .50427 L .62105 .44546 L .759 .677 .771 r F P p .60242 .526 m .59971 .52793 L .62608 .52304 L .112 .665 .737 r F P p .002 w .59971 .52793 m .62105 .44546 L p .59433 .55713 L 0 0 0 r F P s P p .48246 .48241 m .54069 .46689 L .51982 .34379 L .614 .32 .447 r F P p .54069 .46689 m .62105 .44546 L .51982 .34379 L .614 .32 .447 r F P p .5118 .48701 m .54215 .47547 L .48246 .48241 L .614 .32 .447 r F P p .54215 .47547 m .62105 .44546 L .54069 .46689 L .614 .32 .447 r F P p .54215 .47547 m .54069 .46689 L .48246 .48241 L .614 .32 .447 r F P p .58621 .59107 m .59971 .52793 L .59433 .55713 L 0 0 0 r F P p .48489 .47341 m .49855 .40724 L .51982 .34379 L .763 .754 .239 r F P p .002 w .49855 .40724 m .51982 .34379 L p .54215 .47547 L .94 .572 .216 r F P s P p .55847 .50102 m .59971 .52793 L .62105 .44546 L .846 .922 .882 r F P p .54445 .53268 m .59971 .52793 L .57651 .52925 L .112 .665 .737 r F P p .55114 .53242 m .54139 .55367 L .59971 .52793 L .846 .922 .882 r F P p .55868 .57924 m .53002 .55869 L .59971 .52793 L .796 .577 .604 r F P p .59433 .55713 m .57651 .52925 L .59971 .52793 L .94 .572 .216 r F P p .57651 .52925 m .59971 .52793 L .60165 .52655 L .112 .665 .737 r F P p .55678 .56636 m .80956 .50427 L .57651 .52925 L .759 .677 .771 r F P p .58458 .55566 m .56608 .54886 L .57651 .52925 L .465 .321 .6 r F P p .56608 .54886 m .54435 .54088 L .57651 .52925 L .465 .321 .6 r F P p .54435 .54088 m .52891 .53521 L .55114 .53242 L .465 .321 .6 r F P p .54435 .54088 m .55114 .53242 L .57651 .52925 L .465 .321 .6 r F P p .51982 .53532 m .52891 .53521 L .55114 .53242 L .112 .665 .737 r F P p .51044 .5367 m .52891 .53521 L .51982 .53532 L .112 .665 .737 r F P p .54435 .54088 m .53002 .55869 L .52891 .53521 L .465 .321 .6 r F P p .58458 .55566 m .53002 .55869 L .54435 .54088 L .465 .321 .6 r F P p .58421 .59754 m .58128 .59544 L .58167 .59509 L .191 .512 .913 r F P p .55868 .57924 m .59079 .56965 L .57017 .56487 L .623 .34 .467 r F P p .58128 .59544 m .53002 .55869 L .58167 .59509 L .191 .512 .913 r F P p .60787 .60927 m .80956 .50427 L .55678 .56636 L .759 .677 .771 r F P p .59025 .57419 m .59433 .55713 L .5903 .57436 L 0 0 0 r F P p .58421 .59754 m .58167 .59509 L .58219 .59463 L .191 .512 .913 r F P p .58072 .61398 m .60787 .60927 L .58621 .59107 L .759 .677 .771 r F P p .57815 .62475 m .60787 .60927 L .55543 .61836 L .759 .677 .771 r F P p .65054 .64511 m .58621 .59107 L .61419 .6031 L .191 .512 .913 r F P p .61568 .61084 m .61419 .6031 L .65054 .64511 L .94 .572 .216 r F P p .61419 .6031 m .61008 .58179 L .65054 .64511 L .94 .572 .216 r F P p .002 w .65054 .64511 m .80956 .50427 L p .62271 .60155 L .759 .677 .771 r F P s P p .65054 .64511 m .61419 .6031 L .63962 .61403 L .191 .512 .913 r F P p .60277 .65278 m .61888 .62743 L .65054 .64511 L .846 .943 .885 r F P p .63561 .6491 m .62655 .63171 L .65054 .64511 L .94 .572 .216 r F P p .62655 .63171 m .61568 .61084 L .65054 .64511 L .94 .572 .216 r F P p .63561 .6491 m .61888 .62743 L .61568 .61084 L .94 .572 .216 r F P p .002 w .80956 .50427 m .65054 .64511 L p .61888 .62743 L .846 .943 .885 r F P s P p .65032 .60712 m .80956 .50427 L .61008 .58179 L .623 .34 .467 r F P p .61419 .6031 m .61008 .58179 L .58621 .59107 L .623 .34 .467 r F P p .70804 .64344 m .61008 .58179 L .61419 .6031 L .623 .34 .467 r F P p .59309 .59403 m .58621 .59107 L .58752 .58682 L .191 .512 .913 r F P p .59309 .59403 m .58752 .58682 L .59083 .57611 L .191 .512 .913 r F P p .61419 .6031 m .59309 .59403 L .59083 .57611 L .191 .512 .913 r F P p .61419 .6031 m .58621 .59107 L .61888 .62743 L .623 .34 .467 r F P p .58621 .59107 m .58434 .59978 L .61888 .62743 L .623 .34 .467 r F P p .58434 .59978 m .58291 .60648 L .57128 .65558 L 0 0 0 r F P p .55543 .61836 m .58072 .61398 L .58621 .59107 L .759 .677 .771 r F P p .58167 .59509 m .5499 .56439 L .58219 .59463 L .191 .512 .913 r F P p .5499 .56439 m .5506 .56459 L .58219 .59463 L .191 .512 .913 r F P p .50567 .66248 m .55761 .61643 L .53255 .61192 L .759 .677 .771 r F P p .59433 .55713 m .59015 .57591 L .58999 .57587 L 0 0 0 r F P p .59433 .55713 m .59337 .5623 L .59015 .57591 L 0 0 0 r F P p .61888 .62743 m .58434 .59978 L .57993 .62043 L .623 .34 .467 r F P p .59433 .55713 m .58291 .60648 L .58434 .59978 L 0 0 0 r F P p .58987 .57583 m .58994 .57586 L .58434 .59978 L 0 0 0 r F P p .59025 .57419 m .58994 .57586 L .58987 .57583 L 0 0 0 r F P p .59025 .57419 m .5903 .57436 L .58994 .57586 L 0 0 0 r F P p .58621 .59107 m .59025 .57419 L .58434 .59978 L 0 0 0 r F P p .61419 .6031 m .59283 .56526 L .61008 .58179 L .94 .572 .216 r F P p .57128 .65558 m .59337 .5623 L .59083 .57611 L 0 0 0 r F P p .59283 .56526 m .58124 .54473 L .59367 .5607 L .94 .572 .216 r F P p .59283 .56526 m .59367 .5607 L .61008 .58179 L .94 .572 .216 r F P p .6078 .59572 m .5926 .56653 L .61419 .6031 L .94 .572 .216 r F P p .5926 .56653 m .58124 .54473 L .59283 .56526 L .94 .572 .216 r F P p .5926 .56653 m .59283 .56526 L .61419 .6031 L .94 .572 .216 r F P p .58124 .54473 m .57651 .52925 L .61008 .58179 L .94 .572 .216 r F P p .6078 .59572 m .59083 .57611 L .5926 .56653 L .94 .572 .216 r F P p .61568 .61084 m .59083 .57611 L .6078 .59572 L .94 .572 .216 r F P p .59083 .57611 m .53002 .55869 L .58458 .55566 L .465 .321 .6 r F P p .51982 .53532 m .53002 .55869 L .55114 .53242 L .846 .922 .882 r F P p .58697 .50957 m .57651 .52925 L .57022 .50869 L .465 .321 .6 r F P p .60563 .51055 m .62105 .44546 L .60599 .51057 L 0 0 0 r F P p .60563 .51055 m .60599 .51057 L .59083 .57611 L 0 0 0 r F P p .59337 .5623 m .60563 .51055 L .59083 .57611 L 0 0 0 r F P p .57651 .52925 m .60165 .52655 L .60538 .51096 L .759 .677 .771 r F P p .58697 .50957 m .60548 .51054 L .62105 .44546 L .759 .677 .771 r F P p .59433 .55713 m .62105 .44546 L .59337 .5623 L 0 0 0 r F P p .60599 .51057 m .57651 .52925 L .58697 .50957 L .465 .321 .6 r F P p .50567 .66248 m .51461 .64567 L .52098 .66138 L .465 .321 .6 r F P p .50567 .66248 m .52098 .66138 L .53674 .70021 L .465 .321 .6 r F P p .53674 .70021 m .51461 .64567 L .53255 .61192 L .465 .321 .6 r F P p .53485 .66039 m .48895 .66645 L .50567 .66248 L .014 0 0 r F P p .57128 .65558 m .54026 .65833 L .57099 .65465 L .014 0 0 r F P p .57128 .65558 m .54026 .65833 L .53255 .61192 L .584 .556 .789 r F P p .57128 .65558 m .48895 .66645 L .53255 .61192 L .796 .577 .604 r F P p .5886 .6751 m .48895 .66645 L .57128 .65558 L .796 .577 .604 r F P p .55249 .73195 m .53674 .70021 L .54644 .69551 L .846 .943 .885 r F P p .55249 .73195 m .54644 .69551 L .56431 .68686 L .846 .943 .885 r F P p .73528 .84043 m .558 .71522 L .5886 .6751 L .796 .577 .604 r F P p .558 .71522 m .55249 .73195 L .56431 .68686 L 0 0 0 r F P p .002 w .55249 .73195 m .73528 .84043 L p .55626 .72051 L .104 .474 .894 r F P s P p .558 .71522 m .53674 .70021 L .56431 .68686 L .796 .577 .604 r F P p .558 .71522 m .56431 .68686 L .5886 .6751 L .796 .577 .604 r F P p .53674 .70021 m .48895 .66645 L .5886 .6751 L .796 .577 .604 r F P p .63962 .61403 m .61419 .6031 L .61299 .58884 L .191 .512 .913 r F P p .63962 .61403 m .61299 .58884 L .63526 .60163 L .191 .512 .913 r F P p .58219 .59463 m .51982 .53532 L .57072 .57807 L .191 .512 .913 r F P p .58167 .59509 m .53002 .55869 L .5499 .56439 L .191 .512 .913 r F P p .57798 .59837 m .58621 .59107 L .57763 .59441 L .759 .677 .771 r F P p .57973 .61815 m .58621 .59107 L .57978 .61882 L 0 0 0 r F P p .57973 .61815 m .57978 .61882 L .57128 .65558 L 0 0 0 r F P p .57815 .62475 m .57973 .61815 L .57128 .65558 L 0 0 0 r F P p .58621 .59107 m .58434 .59978 L .57128 .65558 L 0 0 0 r F P p .57993 .62043 m .57763 .59441 L .53255 .61192 L .623 .34 .467 r F P p .58434 .59978 m .57763 .59441 L .57993 .62043 L .623 .34 .467 r F P p .58999 .57587 m .59015 .57591 L .58291 .60648 L 0 0 0 r F P p .57763 .59441 m .55868 .57924 L .53255 .61192 L .623 .34 .467 r F P p .62294 .59455 m .59083 .57611 L .62804 .55324 L .584 .556 .789 r F P p .63526 .60163 m .62804 .55324 L .65015 .57817 L .584 .556 .789 r F P p .63962 .61403 m .63526 .60163 L .80956 .50427 L .846 .943 .885 r F P p .70804 .64344 m .65054 .64511 L .63526 .60163 L .191 .512 .913 r F P p .70804 .64344 m .63001 .6099 L .61888 .62743 L .623 .34 .467 r F P p .61888 .62743 m .63526 .60163 L .63962 .61403 L .846 .943 .885 r F P p .62149 .60624 m .61419 .6031 L .61888 .62743 L .623 .34 .467 r F P p .61888 .62743 m .62294 .59455 L .63526 .60163 L .584 .556 .789 r F P p .62294 .59455 m .62804 .55324 L .63526 .60163 L .584 .556 .789 r F P p .62608 .52304 m .61464 .52516 L .80956 .50427 L .112 .665 .737 r F P p .65015 .57817 m .62105 .44546 L .80956 .50427 L .801 .576 .597 r F P p .63026 .5874 m .62804 .55324 L .65015 .57817 L .801 .576 .597 r F P p .62804 .55324 m .62105 .44546 L .65015 .57817 L .801 .576 .597 r F P p .58621 .59107 m .55868 .57924 L .58434 .59978 L .623 .34 .467 r F P p .59083 .57611 m .58621 .59107 L .56406 .56844 L .191 .512 .913 r F P p .58621 .59107 m .57072 .57807 L .56406 .56844 L .191 .512 .913 r F P p .53255 .61192 m .4979 .57287 L .54133 .60095 L .796 .577 .604 r F P p .55152 .5882 m .53002 .55869 L .55868 .57924 L .796 .577 .604 r F P p .53255 .61192 m .58621 .59107 L .55678 .56636 L .759 .677 .771 r F P p .61888 .62743 m .53255 .61192 L .59083 .57611 L .584 .556 .789 r F P p .61419 .6031 m .59083 .57611 L .61299 .58884 L .191 .512 .913 r F P p .61568 .61084 m .6078 .59572 L .61419 .6031 L .94 .572 .216 r F P p .61568 .61084 m .59842 .60093 L .59083 .57611 L .94 .572 .216 r F P p .61888 .62743 m .59842 .60093 L .61568 .61084 L .94 .572 .216 r F P p .61888 .62743 m .59083 .57611 L .62294 .59455 L .584 .556 .789 r F P p .63976 .57593 m .59083 .57611 L .5947 .55938 L .465 .321 .6 r F P p .63526 .60163 m .61299 .58884 L .61244 .5823 L .191 .512 .913 r F P p .63526 .60163 m .61244 .5823 L .63026 .5874 L .191 .512 .913 r F P p .60397 .61911 m .59842 .60093 L .60836 .61381 L .94 .572 .216 r F P p .60397 .61911 m .6099 .6158 L .61888 .62743 L .94 .572 .216 r F P p .60397 .61911 m .63026 .5874 L .80956 .50427 L .846 .943 .885 r F P p .56431 .68686 m .57195 .65773 L .5886 .6751 L .846 .943 .885 r F P p .73528 .84043 m .5602 .70852 L .55626 .72051 L .104 .474 .894 r F P p .002 w .73528 .84043 m .54106 .79126 L p .558 .71522 L .796 .577 .604 r F P s P p .62534 .51158 m .57022 .50869 L .62105 .44546 L .465 .321 .6 r F P p .63026 .5874 m .59083 .57611 L .63976 .57593 L .465 .321 .6 r F P p .69028 .51499 m .60242 .526 L .60599 .51057 L .465 .321 .6 r F P p .60331 .52536 m .60242 .526 L .62608 .52304 L .112 .665 .737 r F P p .70804 .64344 m .61888 .62743 L .63526 .60163 L .584 .556 .789 r F P p .63135 .65025 m .61888 .62743 L .63561 .6491 L .94 .572 .216 r F P p .57099 .65465 m .57815 .62475 L .57128 .65558 L 0 0 0 r F P p .57128 .65558 m .53255 .61192 L .57815 .62475 L .796 .577 .604 r F P p .73528 .84043 m .53255 .61192 L .61888 .62743 L .584 .556 .789 r F P p .58234 .65607 m .60277 .65278 L .60218 .65371 L .846 .943 .885 r F P p .58234 .65607 m .60218 .65371 L .5886 .6751 L .846 .943 .885 r F P p .57195 .65773 m .58234 .65607 L .5886 .6751 L .846 .943 .885 r F P p .62367 .6523 m .58234 .65607 L .63135 .65025 L .014 0 0 r F P p .59777 .65502 m .58234 .65607 L .62367 .6523 L .014 0 0 r F P p .61146 .68158 m .62367 .6523 L .59777 .65502 L .623 .34 .467 r F P p .73528 .84043 m .58164 .71612 L .59728 .68718 L .762 .683 .775 r F P p .002 w .65054 .64511 m .70804 .64344 L p .63135 .65025 L .014 0 0 r F P s P p .002 w .70804 .64344 m .73528 .84043 L p .61888 .62743 L .584 .556 .789 r F P s P p .62805 .67503 m .62367 .6523 L .61146 .68158 L .623 .34 .467 r F P p .73528 .84043 m .61484 .65466 L .63135 .65025 L .94 .572 .216 r F P p .73528 .84043 m .59728 .68718 L .65285 .66523 L .762 .683 .775 r F P p .63994 .73679 m .62805 .67503 L .61146 .68158 L .623 .34 .467 r F P p .59728 .68718 m .59777 .65502 L .57195 .65773 L .623 .34 .467 r F P p .61146 .68158 m .59777 .65502 L .59728 .68718 L .623 .34 .467 r F P p .5664 .67891 m .56431 .68686 L .57128 .65558 L 0 0 0 r F P p .58234 .65607 m .57179 .65724 L .57166 .65679 L .014 0 0 r F P p .59777 .65502 m .57871 .65665 L .58234 .65607 L .014 0 0 r F P p .57871 .65665 m .57179 .65724 L .58234 .65607 L .014 0 0 r F P p .73528 .84043 m .58164 .71612 L .5602 .70852 L .104 .474 .894 r F P p .58164 .71612 m .54106 .79126 L .5602 .70852 L .465 .321 .6 r F P p .59728 .68718 m .5602 .70852 L .57195 .65773 L .465 .321 .6 r F P p .63994 .73679 m .58164 .71612 L .59728 .68718 L .465 .321 .6 r F P p .58164 .71612 m .5602 .70852 L .59728 .68718 L .465 .321 .6 r F P p .58164 .71612 m .56273 .70083 L .59728 .68718 L .762 .683 .775 r F P p .5602 .70852 m .63994 .73679 L .56273 .70083 L .104 .474 .894 r F P p .5602 .70852 m .57128 .65558 L .56273 .70083 L 0 0 0 r F P p .56273 .70083 m .57128 .65558 L .57195 .65773 L 0 0 0 r F P p .58164 .71612 m .55923 .71546 L .56273 .70083 L .762 .683 .775 r F P p .002 w .73528 .84043 m .54106 .79126 L p .58164 .71612 L .762 .683 .775 r F P s P p .73528 .84043 m .63994 .73679 L .58164 .71612 L .104 .474 .894 r F P p .002 w .63994 .73679 m .54106 .79126 L p .58164 .71612 L .465 .321 .6 r F P s P p .56273 .70083 m .59728 .68718 L .57195 .65773 L .623 .34 .467 r F P p .56273 .70083 m .57195 .65773 L .57258 .65975 L 0 0 0 r F P p .57166 .65679 m .53485 .66039 L .55213 .65811 L .014 0 0 r F P p .57179 .65724 m .53485 .66039 L .57166 .65679 L .014 0 0 r F P p .58312 .65656 m .53485 .66039 L .59777 .65502 L .014 0 0 r F P p .58234 .65607 m .60277 .65278 L .63135 .65025 L .014 0 0 r F P p .62367 .6523 m .61888 .62743 L .63135 .65025 L .94 .572 .216 r F P p .57195 .65773 m .53485 .66039 L .58312 .65656 L .014 0 0 r F P p .58234 .65607 m .55213 .65811 L .60277 .65278 L .014 0 0 r F P p .55213 .65811 m .57128 .65558 L .60277 .65278 L .014 0 0 r F P p .57195 .65773 m .61888 .62743 L .60277 .65278 L .846 .943 .885 r F P p .59777 .65502 m .59237 .64455 L .57195 .65773 L .623 .34 .467 r F P p .59237 .64455 m .57993 .62043 L .57195 .65773 L .623 .34 .467 r F P p .59777 .65502 m .61888 .62743 L .57993 .62043 L .623 .34 .467 r F P p .60397 .61911 m .57195 .65773 L .59083 .57611 L .465 .321 .6 r F P p .58487 .60844 m .57565 .64041 L .59083 .57611 L 0 0 0 r F P p .57565 .64041 m .57128 .65558 L .57993 .62043 L 0 0 0 r F P p .57565 .64041 m .57993 .62043 L .59083 .57611 L 0 0 0 r F P p .57195 .65773 m .57128 .65558 L .58487 .60844 L 0 0 0 r F P p .57195 .65773 m .57993 .62043 L .53255 .61192 L .623 .34 .467 r F P p .57195 .65773 m .55427 .67906 L .53002 .55869 L .465 .321 .6 r F P p .53674 .70021 m .57195 .65773 L .56431 .68686 L .846 .943 .885 r F P p .55427 .67906 m .53674 .70021 L .53002 .55869 L .465 .321 .6 r F P p .5602 .70852 m .55867 .71317 L .55975 .70837 L 0 0 0 r F P p .5602 .70852 m .55997 .7074 L .5664 .67891 L 0 0 0 r F P p .55867 .71317 m .56431 .68686 L .5664 .67891 L 0 0 0 r F P p .54106 .79126 m .558 .71522 L .55867 .71317 L 0 0 0 r F P p .558 .71522 m .56431 .68686 L .55867 .71317 L 0 0 0 r F P p .5602 .70852 m .53674 .70021 L .55427 .67906 L .465 .321 .6 r F P p .57195 .65773 m .48895 .66645 L .53485 .66039 L .014 0 0 r F P p .62805 .67503 m .70804 .64344 L .62367 .6523 L .623 .34 .467 r F P p .002 w .70804 .64344 m .73528 .84043 L p .65285 .66523 L .762 .683 .775 r F P s P p .52933 .68526 m .57195 .65773 L .53034 .66211 L .623 .34 .467 r F P p .002 w .3942 .87216 m .55249 .73195 L p .49372 .68496 L .759 .677 .771 r F P s P p .55626 .72051 m .51381 .69208 L .55249 .73195 L .104 .474 .894 r F P p .51381 .69208 m .49372 .68496 L .55249 .73195 L .104 .474 .894 r F P p .54211 .71104 m .53674 .70021 L .51381 .69208 L .104 .474 .894 r F P p .002 w .55249 .73195 m .3942 .87216 L p .52119 .71896 L .846 .943 .885 r F P s P p .54106 .79126 m .49372 .68496 L .51381 .69208 L .465 .321 .6 r F P p .47981 .66656 m .48895 .66645 L .44496 .64596 L .104 .474 .894 r F P p .44352 .51298 m .47773 .49997 L .40718 .47061 L .614 .32 .447 r F P p .52763 .50821 m .50008 .52398 L .48246 .48241 L .584 .556 .789 r F P p .46987 .54128 m .47647 .51042 L .47538 .51951 L .763 .754 .239 r F P p .50008 .52398 m .46987 .54128 L .47647 .51042 L .584 .556 .789 r F P p .50008 .52398 m .47647 .51042 L .48246 .48241 L .584 .556 .789 r F P p .57651 .52925 m .62105 .44546 L .51982 .53532 L .759 .677 .771 r F P p .56556 .52987 m .48246 .48241 L .54498 .49222 L .584 .556 .789 r F P p .47773 .49997 m .5118 .48701 L .48246 .48241 L .614 .32 .447 r F P p .51982 .53532 m .46987 .54128 L .51639 .51464 L .584 .556 .789 r F P p .54498 .49222 m .54215 .47547 L .5118 .48701 L .614 .32 .447 r F P p .5118 .48701 m .48246 .48241 L .49855 .40724 L .584 .556 .789 r F P p .47773 .49997 m .51982 .53532 L .49855 .40724 L .759 .677 .771 r F P p .54498 .49222 m .5118 .48701 L .47773 .49997 L .614 .32 .447 r F P p .5118 .48701 m .54215 .47547 L .49855 .40724 L .759 .677 .771 r F P p .54498 .49222 m .5118 .48701 L .49855 .40724 L .584 .556 .789 r F P p .51031 .51353 m .54498 .49222 L .47773 .49997 L .614 .32 .447 r F P p .55847 .50102 m .62105 .44546 L .49855 .40724 L .759 .677 .771 r F P p .55847 .50102 m .54498 .49222 L .54215 .47547 L .94 .572 .216 r F P p .54498 .49222 m .62105 .44546 L .54215 .47547 L .614 .32 .447 r F P p .54498 .49222 m .49855 .40724 L .54215 .47547 L .94 .572 .216 r F P p .52823 .52092 m .51982 .53532 L .52763 .50821 L .584 .556 .789 r F P p .52886 .53424 m .51982 .53532 L .52823 .52092 L .584 .556 .789 r F P p .51982 .53532 m .51639 .51464 L .52763 .50821 L .584 .556 .789 r F P p .56556 .52987 m .52886 .53424 L .52763 .50821 L .584 .556 .789 r F P p .51031 .51353 m .51982 .53532 L .54498 .49222 L .846 .922 .882 r F P p .51729 .52007 m .51982 .53532 L .51031 .51353 L .191 .512 .913 r F P p .59083 .57611 m .57195 .65773 L .54369 .59097 L .465 .321 .6 r F P p .55678 .56636 m .54369 .59097 L .53002 .55869 L .465 .321 .6 r F P p .55678 .56636 m .57651 .52925 L .51982 .53532 L .759 .677 .771 r F P p .57072 .57807 m .51982 .53532 L .55519 .55564 L .191 .512 .913 r F P p .59083 .57611 m .54369 .59097 L .55678 .56636 L .465 .321 .6 r F P p .5499 .56439 m .51982 .53532 L .5506 .56459 L .191 .512 .913 r F P p .5499 .56439 m .53002 .55869 L .51982 .53532 L .191 .512 .913 r F P p .51982 .53532 m .53002 .55869 L .52259 .552 L .191 .512 .913 r F P p .46337 .57167 m .45735 .59078 L .46987 .54128 L .763 .754 .239 r F P p .51982 .53532 m .47647 .51042 L .47773 .49997 L .191 .512 .913 r F P p .46857 .54081 m .51982 .53532 L .47773 .49997 L .759 .677 .771 r F P p .49628 .53784 m .50367 .53725 L .51982 .53532 L .112 .665 .737 r F P p .50367 .53725 m .51044 .5367 L .51982 .53532 L .112 .665 .737 r F P p .51982 .53532 m .5119 .54235 L .5063 .53731 L .191 .512 .913 r F P p .48446 .53911 m .46987 .54128 L .50124 .53805 L .112 .665 .737 r F P p .47773 .49997 m .45387 .49004 L .44244 .47974 L .191 .512 .913 r F P p .47773 .49997 m .44244 .47974 L .45864 .48393 L .191 .512 .913 r F P p .46857 .54081 m .49855 .40724 L .4267 .5453 L .759 .677 .771 r F P p .45735 .59078 m .43805 .54455 L .46987 .54128 L .796 .577 .604 r F P p .45735 .59078 m .46857 .54081 L .4267 .5453 L .759 .677 .771 r F P p .4267 .5453 m .46857 .54081 L .46689 .54022 L .112 .665 .737 r F P p .45864 .48393 m .40718 .47061 L .49855 .40724 L .444 .299 .589 r F P p .002 w .27112 .56498 m .35641 .68038 L p .41576 .63236 L .623 .34 .467 r F P s P p .35641 .68038 m .45735 .59078 L .4267 .5453 L .759 .677 .771 r F P p .002 w .35641 .68038 m .3942 .87216 L p .49372 .68496 L .759 .677 .771 r F P s P p .002 w .54106 .79126 m .3942 .87216 L p .47901 .71263 L .465 .321 .6 r F P s P p .35641 .68038 m .44298 .66697 L .41878 .62502 L .846 .922 .882 r F P p .43948 .67042 m .44496 .64596 L .44298 .66697 L .763 .754 .239 r F P p .47084 .66666 m .44496 .64596 L .35641 .68038 L .759 .677 .771 r F P p .43807 .6718 m .35641 .68038 L .43948 .67042 L .014 0 0 r F P p .002 w .35641 .68038 m .3942 .87216 L p .42608 .72221 L .575 .554 .793 r F P s P p .42608 .72221 m .43178 .69537 L .35641 .68038 L .575 .554 .793 r F P p .002 w .35641 .68038 m .41473 .75928 L p .43807 .6718 L .623 .34 .467 r F P s P p .3942 .87216 m .43178 .69537 L .43948 .67042 L .763 .754 .239 r F P p .43178 .69537 m .43646 .67339 L .43807 .6718 L .763 .754 .239 r F P p .43178 .69537 m .43807 .6718 L .43948 .67042 L .763 .754 .239 r F P p .46347 .66913 m .43807 .6718 L .47084 .66666 L .014 0 0 r F P p .43807 .6718 m .43948 .67042 L .47084 .66666 L .014 0 0 r F P p .47577 .6666 m .44496 .64596 L .47084 .66666 L .104 .474 .894 r F P p .48425 .63069 m .46573 .63789 L .44082 .69717 L .623 .34 .467 r F P p .48425 .63069 m .44082 .69717 L .44758 .69852 L .623 .34 .467 r F P p .50147 .67936 m .48895 .66645 L .47981 .66656 L .104 .474 .894 r F P p .48895 .66645 m .46347 .66913 L .44758 .69852 L .623 .34 .467 r F P p .48895 .66645 m .44758 .69852 L .46115 .70122 L .623 .34 .467 r F P p .46637 .66944 m .46347 .66913 L .48895 .66645 L .014 0 0 r F P p .43178 .69537 m .43646 .67339 L .35641 .68038 L .575 .554 .793 r F P p .53674 .70021 m .48895 .66645 L .50147 .67936 L .104 .474 .894 r F P p .50871 .71378 m .55249 .73195 L .48895 .66645 L .949 .596 .288 r F P p .52119 .71896 m .53674 .70021 L .55249 .73195 L .846 .943 .885 r F P p .55626 .72051 m .54223 .70215 L .54211 .71104 L .104 .474 .894 r F P p .54223 .70215 m .53674 .70021 L .54211 .71104 L .104 .474 .894 r F P p .558 .71522 m .54543 .70635 L .55626 .72051 L .104 .474 .894 r F P p .51381 .69208 m .53674 .70021 L .50147 .67936 L .104 .474 .894 r F P p .52119 .71896 m .51381 .69208 L .53674 .70021 L .465 .321 .6 r F P p .53674 .70021 m .50871 .71378 L .48895 .66645 L .796 .577 .604 r F P p .558 .71522 m .53742 .71462 L .53674 .70021 L .796 .577 .604 r F P p .54106 .79126 m .47901 .71263 L .49372 .68496 L .465 .321 .6 r F P p .3942 .87216 m .48324 .72611 L .50871 .71378 L .846 .943 .885 r F P p .52119 .71896 m .50871 .71378 L .53674 .70021 L .846 .943 .885 r F P p .3942 .87216 m .50871 .71378 L .52119 .71896 L .846 .943 .885 r F P p .50871 .71378 m .47133 .71268 L .48895 .66645 L .796 .577 .604 r F P p .50871 .71378 m .48895 .66645 L .49439 .70783 L .949 .596 .288 r F P p .53674 .70021 m .52933 .68526 L .48895 .66645 L .104 .474 .894 r F P p .47751 .7355 m .46115 .70122 L .43178 .69537 L .575 .554 .793 r F P p .54106 .79126 m .48324 .72611 L .47751 .7355 L .575 .554 .793 r F P p .48324 .72611 m .46115 .70122 L .47751 .7355 L .575 .554 .793 r F P p .54106 .79126 m .43178 .69537 L .42608 .72221 L .575 .554 .793 r F P p .3942 .87216 m .46966 .74838 L .42608 .72221 L .575 .554 .793 r F P p .002 w .3942 .87216 m .41473 .75928 L p .43646 .67339 L .763 .754 .239 r F P s P p .44082 .69717 m .43178 .69537 L .41473 .75928 L .623 .34 .467 r F P p .002 w .3942 .87216 m .41473 .75928 L p .48324 .72611 L .846 .943 .885 r F P s P p .46115 .70122 m .44758 .69852 L .41473 .75928 L .623 .34 .467 r F P p .44758 .69852 m .44082 .69717 L .41473 .75928 L .623 .34 .467 r F P p .002 w .54106 .79126 m .55249 .73195 L p .50871 .71378 L .949 .596 .288 r F P s P p .002 w .3942 .87216 m .54106 .79126 L p .46966 .74838 L .575 .554 .793 r F P s P p .43807 .6718 m .44496 .64596 L .35641 .68038 L .623 .34 .467 r F P p .41473 .75928 m .35641 .68038 L .40419 .67711 L .444 .299 .589 r F P p .43646 .67339 m .35641 .68038 L .43807 .6718 L .014 0 0 r F P p .48056 .60259 m .46987 .54128 L .4979 .57287 L .584 .556 .789 r F P p .46337 .57167 m .46987 .54128 L .48056 .60259 L .584 .556 .789 r F P p .45735 .59078 m .48056 .60259 L .48321 .59805 L .846 .922 .882 r F P p .45735 .59078 m .48321 .59805 L .4979 .57287 L .846 .922 .882 r F P p .48425 .63069 m .53255 .61192 L .48056 .60259 L .623 .34 .467 r F P p .48895 .66645 m .53255 .61192 L .48425 .63069 L .623 .34 .467 r F P p .53255 .61192 m .45735 .59078 L .41878 .62502 L .759 .677 .771 r F P p .44496 .64596 m .42568 .63698 L .35641 .68038 L .623 .34 .467 r F P p .44496 .64596 m .41878 .62502 L .35641 .68038 L .759 .677 .771 r F P p .53255 .61192 m .41878 .62502 L .44496 .64596 L .759 .677 .771 r F P p .41257 .67654 m .35641 .68038 L .43646 .67339 L .014 0 0 r F P p .41086 .6113 m .39508 .60607 L .41878 .62502 L .104 .474 .894 r F P p .35641 .68038 m .41878 .62502 L .41086 .6113 L .846 .922 .882 r F P p .40101 .65231 m .35641 .68038 L .39508 .60607 L .444 .299 .589 r F P p .41878 .62502 m .45735 .59078 L .41086 .6113 L .846 .922 .882 r F P p .4459 .63605 m .41086 .6113 L .44496 .64596 L .104 .474 .894 r F P p .41086 .6113 m .41878 .62502 L .44496 .64596 L .104 .474 .894 r F P p .44496 .64596 m .43646 .67339 L .4459 .63605 L .763 .754 .239 r F P p .44496 .64596 m .4459 .63605 L .45735 .59078 L .763 .754 .239 r F P p .43948 .67042 m .43807 .6718 L .44496 .64596 L .763 .754 .239 r F P p .43807 .6718 m .43646 .67339 L .44496 .64596 L .763 .754 .239 r F P p .45949 .65273 m .44496 .64596 L .43178 .69537 L .623 .34 .467 r F P p .45949 .65273 m .43178 .69537 L .44082 .69717 L .623 .34 .467 r F P p .46115 .70122 m .43646 .67339 L .48895 .66645 L .796 .577 .604 r F P p .45583 .6717 m .46347 .66913 L .47332 .67017 L .014 0 0 r F P p .46347 .66913 m .47084 .66666 L .48895 .66645 L .014 0 0 r F P p .46115 .70122 m .43646 .67339 L .43178 .69537 L .575 .554 .793 r F P p .45583 .6717 m .43807 .6718 L .46347 .66913 L .014 0 0 r F P p .43646 .67339 m .43807 .6718 L .45583 .6717 L .014 0 0 r F P p .41176 .64556 m .39508 .60607 L .41086 .6113 L .444 .299 .589 r F P p .40101 .65231 m .39508 .60607 L .41176 .64556 L .444 .299 .589 r F P p .38966 .62066 m .35641 .68038 L .41086 .6113 L .846 .922 .882 r F P p .40919 .54751 m .40718 .47061 L .4267 .5453 L .444 .299 .589 r F P p .39508 .60607 m .27112 .56498 L .40997 .57745 L .444 .299 .589 r F P p .002 w .35641 .68038 m .27112 .56498 L p .39508 .60607 L .444 .299 .589 r F P s P p .39508 .60607 m .33181 .55547 L .27112 .56498 L .104 .474 .894 r F P p .002 w .33181 .55547 m .35641 .68038 L p .39508 .60607 L .759 .677 .771 r F P s P p .39508 .60607 m .40997 .57745 L .33181 .55547 L .759 .677 .771 r F P p .41086 .6113 m .40997 .57745 L .45735 .59078 L .796 .577 .604 r F P p .42394 .5947 m .40919 .54751 L .4267 .5453 L .444 .299 .589 r F P p .41973 .60004 m .40919 .54751 L .42394 .5947 L .444 .299 .589 r F P p .41086 .6113 m .45735 .59078 L .43572 .57976 L .846 .922 .882 r F P p .46573 .63789 m .44496 .64596 L .45949 .65273 L .623 .34 .467 r F P p .48895 .66645 m .41086 .6113 L .46604 .61158 L .796 .577 .604 r F P p .41086 .6113 m .42201 .61136 L .42279 .61526 L .444 .299 .589 r F P p .48895 .66645 m .48425 .63069 L .45735 .59078 L .949 .596 .288 r F P p .41086 .6113 m .45735 .59078 L .53255 .61192 L .796 .577 .604 r F P p .41086 .6113 m .40919 .54751 L .42201 .61136 L .444 .299 .589 r F P p .40919 .54751 m .33181 .55547 L .40718 .47061 L .796 .577 .604 r F P p .33181 .55547 m .4267 .5453 L .4128 .52467 L .759 .677 .771 r F P p .39907 .54787 m .33181 .55547 L .40919 .54751 L .112 .665 .737 r F P p .42013 .54574 m .4267 .5453 L .4128 .52467 L .949 .596 .288 r F P p .4267 .5453 m .40718 .47061 L .46689 .54022 L .444 .299 .589 r F P p .4267 .5453 m .40718 .47061 L .4128 .52467 L .949 .596 .288 r F P p .4267 .5453 m .43329 .53265 L .42318 .54008 L .759 .677 .771 r F P p .41503 .54607 m .40919 .54751 L .4267 .5453 L .112 .665 .737 r F P p .42267 .55305 m .4267 .5453 L .42022 .54599 L .759 .677 .771 r F P p .39907 .54787 m .40919 .54751 L .41503 .54607 L .112 .665 .737 r F P p .42267 .55305 m .42022 .54599 L .33181 .55547 L .759 .677 .771 r F P p .40997 .57745 m .42267 .55305 L .33181 .55547 L .759 .677 .771 r F P p .41503 .54607 m .4128 .52467 L .33181 .55547 L .614 .32 .447 r F P p .41086 .6113 m .39508 .60607 L .39733 .60175 L .444 .299 .589 r F P p .41086 .6113 m .33181 .55547 L .40997 .57745 L .796 .577 .604 r F P p .40272 .5972 m .33181 .55547 L .41086 .6113 L .104 .474 .894 r F P p .41086 .6113 m .33181 .55547 L .39508 .60607 L .104 .474 .894 r F P p .41086 .6113 m .38966 .62066 L .33181 .55547 L .796 .577 .604 r F P p .38966 .62066 m .41757 .57053 L .33181 .55547 L .575 .554 .793 r F P p .4471 .62332 m .41086 .6113 L .4459 .63605 L .104 .474 .894 r F P p .4459 .63605 m .4471 .62332 L .45735 .59078 L .763 .754 .239 r F P p .4471 .62332 m .4459 .63605 L .48895 .66645 L .104 .474 .894 r F P p .48895 .66645 m .46975 .65751 L .46347 .66913 L .623 .34 .467 r F P p .48895 .66645 m .43646 .67339 L .38966 .62066 L .796 .577 .604 r F P p .48895 .66645 m .4459 .63605 L .44496 .64596 L .104 .474 .894 r F P p .48895 .66645 m .38966 .62066 L .41086 .6113 L .796 .577 .604 r F P p .43646 .67339 m .4471 .62332 L .4459 .63605 L .763 .754 .239 r F P p .47332 .67017 m .46637 .66944 L .48895 .66645 L .014 0 0 r F P p .47332 .67017 m .48895 .66645 L .4471 .62332 L .949 .596 .288 r F P p .53255 .61192 m .45735 .59078 L .46987 .54128 L .796 .577 .604 r F P p .4471 .62332 m .45735 .59078 L .4267 .5453 L .949 .596 .288 r F P p .43572 .57976 m .45735 .59078 L .46689 .54022 L .846 .922 .882 r F P p .45735 .59078 m .45702 .58168 L .46689 .54022 L .763 .754 .239 r F P p .42577 .56197 m .4267 .5453 L .4471 .62332 L .444 .299 .589 r F P p .4979 .57287 m .53002 .55869 L .51982 .53532 L .846 .922 .882 r F P p .53255 .61192 m .55678 .56636 L .51982 .53532 L .759 .677 .771 r F P p .48895 .66645 m .45735 .59078 L .4471 .62332 L .949 .596 .288 r F P p .52933 .68526 m .57195 .65773 L .53674 .70021 L .846 .943 .885 r F P p .65285 .66523 m .59728 .68718 L .61484 .65466 L .762 .683 .775 r F P p .002 w .73528 .84043 m .63994 .73679 L p .61484 .65466 L .94 .572 .216 r F P s P p .58341 .72554 m .63994 .73679 L .59728 .68718 L .623 .34 .467 r F P p .002 w .54106 .79126 m .55249 .73195 L p .558 .71522 L 0 0 0 r F P s P p .54106 .79126 m .52119 .71896 L .53674 .70021 L .465 .321 .6 r F P p .54106 .79126 m .47133 .71268 L .558 .71522 L .796 .577 .604 r F P p .55546 .73118 m .5602 .70852 L .56273 .70083 L 0 0 0 r F P p .5602 .70852 m .52933 .68526 L .54543 .70635 L .104 .474 .894 r F P p .5602 .70852 m .54543 .70635 L .558 .71522 L .104 .474 .894 r F P p .55184 .74628 m .54106 .79126 L .55867 .71317 L 0 0 0 r F P p .54106 .79126 m .55758 .72235 L .58164 .71612 L .762 .683 .775 r F P p .55546 .73118 m .55867 .71317 L .5602 .70852 L 0 0 0 r F P p .5544 .73559 m .55867 .71317 L .55546 .73118 L 0 0 0 r F P p .55019 .75428 m .55867 .71317 L .55305 .74271 L 0 0 0 r F P p .5602 .70852 m .54106 .79126 L .53674 .70021 L .465 .321 .6 r F P p .35641 .68038 m .43646 .67339 L .41176 .64556 L .575 .554 .793 r F P p .41473 .75928 m .40101 .65231 L .41176 .64556 L .444 .299 .589 r F P p .002 w .54106 .79126 m .41473 .75928 L p .47133 .71268 L .796 .577 .604 r F P s P p .002 w .41473 .75928 m .19924 .70472 L p .41347 .71099 L .796 .577 .604 r F P s P p .41473 .75928 m .41347 .71099 L .47133 .71268 L .796 .577 .604 r F P p .50871 .71378 m .52933 .68526 L .53674 .70021 L .846 .943 .885 r F P p .48324 .72611 m .50084 .71051 L .50871 .71378 L .846 .943 .885 r F P p .50084 .71051 m .52933 .68526 L .50871 .71378 L .846 .943 .885 r F P p .49439 .70783 m .52933 .68526 L .48324 .72611 L .846 .943 .885 r F P p .54106 .79126 m .49439 .70783 L .48324 .72611 L .575 .554 .793 r F P p .49688 .72683 m .54106 .79126 L .49439 .70783 L .949 .596 .288 r F P p .54106 .79126 m .51501 .72887 L .50744 .73116 L .949 .596 .288 r F P p .51501 .72887 m .50871 .71378 L .50744 .73116 L .949 .596 .288 r F P p .50744 .73116 m .50871 .71378 L .49439 .70783 L .949 .596 .288 r F P p .47133 .71268 m .46115 .70122 L .48895 .66645 L .796 .577 .604 r F P p .41473 .75928 m .49688 .72683 L .50116 .73307 L .762 .683 .775 r F P p .53742 .71462 m .50871 .71378 L .53674 .70021 L .796 .577 .604 r F P p .54106 .79126 m .52804 .71453 L .49439 .70783 L .575 .554 .793 r F P p .50341 .73635 m .55923 .71546 L .55758 .72235 L .762 .683 .775 r F P p .41473 .75928 m .50116 .73307 L .50341 .73635 L .762 .683 .775 r F P p .50116 .73307 m .55923 .71546 L .50341 .73635 L .762 .683 .775 r F P p .47133 .71268 m .45243 .71213 L .46115 .70122 L .796 .577 .604 r F P p .48324 .72611 m .49439 .70783 L .46115 .70122 L .575 .554 .793 r F P p .41473 .75928 m .49439 .70783 L .48324 .72611 L .846 .943 .885 r F P p .002 w .46047 .70207 m .49688 .72683 L p .48895 .66645 L .623 .34 .467 r F P s P p .002 w .54106 .79126 m .41473 .75928 L p .53055 .72933 L .762 .683 .775 r F P s P p .51982 .90146 m .44551 .72078 L .41473 .75928 L .623 .34 .467 r F P p .49439 .70783 m .48895 .66645 L .47332 .67017 L .949 .596 .288 r F P p .49439 .70783 m .43646 .67339 L .46115 .70122 L .575 .554 .793 r F P p .50116 .73307 m .52804 .71453 L .52972 .72441 L .762 .683 .775 r F P p .49688 .72683 m .52804 .71453 L .50116 .73307 L .762 .683 .775 r F P p .002 w .51982 .90146 m .54106 .79126 L p .49688 .72683 L .949 .596 .288 r F P s P p .49688 .72683 m .53255 .61192 L .48895 .66645 L .623 .34 .467 r F P p .51982 .90146 m .52804 .71453 L .49688 .72683 L .623 .34 .467 r F P p .52804 .71453 m .53255 .61192 L .49688 .72683 L .623 .34 .467 r F P p .57195 .65773 m .5602 .70852 L .55427 .67906 L .465 .321 .6 r F P p .5602 .70852 m .56273 .70083 L .52933 .68526 L .104 .474 .894 r F P p .55923 .71546 m .52804 .71453 L .56273 .70083 L .762 .683 .775 r F P p .52933 .68526 m .51982 .66611 L .57195 .65773 L .846 .943 .885 r F P p .5715 .65984 m .57195 .65773 L .56829 .6601 L .623 .34 .467 r F P p .5715 .65984 m .56829 .6601 L .52933 .68526 L .623 .34 .467 r F P p .52972 .72441 m .52804 .71453 L .55923 .71546 L .762 .683 .775 r F P p .55758 .72235 m .55923 .71546 L .58164 .71612 L .762 .683 .775 r F P p .55305 .74271 m .5544 .73559 L .55546 .73118 L 0 0 0 r F P p .002 w .54106 .79126 m .63994 .73679 L p .55851 .72059 L .575 .554 .793 r F P s P p .54106 .79126 m .53055 .72933 L .55758 .72235 L .762 .683 .775 r F P p .002 w .51982 .90146 m .54106 .79126 L p .55184 .74628 L 0 0 0 r F P s P p .55851 .72059 m .59728 .68718 L .56273 .70083 L .623 .34 .467 r F P p .51982 .90146 m .58341 .72554 L .55851 .72059 L .623 .34 .467 r F P p .58341 .72554 m .59728 .68718 L .55851 .72059 L .623 .34 .467 r F P p .63994 .73679 m .56061 .71207 L .55851 .72059 L .575 .554 .793 r F P p .54223 .70215 m .52933 .68526 L .53674 .70021 L .104 .474 .894 r F P p .52804 .71453 m .5715 .65984 L .52933 .68526 L .623 .34 .467 r F P p .57082 .67072 m .57006 .67025 L .57134 .6686 L .762 .683 .775 r F P p .61484 .65466 m .57195 .65773 L .62991 .65285 L .014 0 0 r F P p .57195 .65773 m .58312 .65656 L .62991 .65285 L .014 0 0 r F P p .63994 .73679 m .61146 .68158 L .59728 .68718 L .623 .34 .467 r F P p .62991 .65285 m .58312 .65656 L .59777 .65502 L .014 0 0 r F P p .62367 .6523 m .61888 .62743 L .59777 .65502 L .623 .34 .467 r F P p .61882 .6536 m .59777 .65502 L .62367 .6523 L .014 0 0 r F P p .57195 .65773 m .58487 .60844 L .60397 .61911 L .846 .943 .885 r F P p .57195 .65773 m .60397 .61911 L .61888 .62743 L .846 .943 .885 r F P p .63994 .73679 m .70804 .64344 L .62805 .67503 L .623 .34 .467 r F P p .61882 .6536 m .63135 .65025 L .70804 .64344 L .014 0 0 r F P p .62367 .6523 m .70804 .64344 L .61888 .62743 L .623 .34 .467 r F P p .65285 .66523 m .64611 .6509 L .70804 .64344 L .762 .683 .775 r F P p .62991 .65285 m .61882 .6536 L .70804 .64344 L .014 0 0 r F P p .64611 .6509 m .6325 .62197 L .70804 .64344 L .762 .683 .775 r F P p .65285 .66523 m .61484 .65466 L .64611 .6509 L .762 .683 .775 r F P p .64541 .6518 m .62991 .65285 L .70804 .64344 L .014 0 0 r F P p .002 w .70804 .64344 m .63994 .73679 L p .64541 .6518 L .801 .576 .597 r F P s P p .002 w .70804 .64344 m .80956 .50427 L p .65032 .60712 L .623 .34 .467 r F P s P p .70804 .64344 m .63526 .60163 L .65015 .57817 L .584 .556 .789 r F P p .70804 .64344 m .63526 .60163 L .63026 .5874 L .191 .512 .913 r F P p .6487 .60069 m .63026 .5874 L .65015 .57817 L .801 .576 .597 r F P p .64707 .62611 m .65015 .57817 L .70804 .64344 L .801 .576 .597 r F P p .5926 .56653 m .59083 .57611 L .58124 .54473 L .94 .572 .216 r F P p .62926 .57207 m .58458 .55566 L .62714 .53929 L .465 .321 .6 r F P p .002 w .80956 .50427 m .69028 .51499 L p .62608 .52304 L .112 .665 .737 r F P s P p .58458 .55566 m .57651 .52925 L .60242 .526 L .465 .321 .6 r F P p .59663 .55102 m .60242 .526 L .69028 .51499 L .465 .321 .6 r F P p .58458 .55566 m .60242 .526 L .59663 .55102 L .465 .321 .6 r F P p .60331 .52536 m .62105 .44546 L .62608 .52304 L .801 .576 .597 r F P p .002 w .62105 .44546 m .69028 .51499 L p .62534 .51158 L .465 .321 .6 r F P s P p .60331 .52536 m .62105 .44546 L .609 .50225 L 0 0 0 r F P p .59083 .57611 m .60242 .526 L .60331 .52536 L 0 0 0 r F P p .60242 .526 m .62105 .44546 L .60331 .52536 L 0 0 0 r F P p .54445 .53268 m .57651 .52925 L .56556 .52987 L .112 .665 .737 r F P p .58124 .54473 m .55847 .50102 L .57651 .52925 L .94 .572 .216 r F P p .60242 .526 m .57651 .52925 L .60599 .51057 L .465 .321 .6 r F P p .53551 .53345 m .54445 .53268 L .56556 .52987 L .112 .665 .737 r F P p .51982 .53532 m .54445 .53268 L .52838 .53406 L .112 .665 .737 r F P p .59083 .57611 m .56406 .56844 L .55519 .55564 L .191 .512 .913 r F P p .55519 .55564 m .51982 .53532 L .56556 .52987 L .584 .556 .789 r F P p .53255 .61192 m .56556 .52987 L .59083 .57611 L .584 .556 .789 r F P p .48809 .69658 m .43646 .67339 L .49439 .70783 L .575 .554 .793 r F P p .52933 .68526 m .50414 .66628 L .48895 .66645 L .104 .474 .894 r F P p .61888 .62743 m .60397 .61911 L .63526 .60163 L .846 .943 .885 r F P p .63994 .73679 m .57195 .65773 L .60397 .61911 L .465 .321 .6 r F P p .61484 .65466 m .58487 .60844 L .60397 .61911 L .94 .572 .216 r F P p .61484 .65466 m .60397 .61911 L .61888 .62743 L .94 .572 .216 r F P p .61484 .65466 m .61888 .62743 L .62367 .6523 L .94 .572 .216 r F P p .6325 .62197 m .61484 .65466 L .60397 .61911 L .465 .321 .6 r F P p .65015 .57817 m .62804 .55324 L .69028 .51499 L .584 .556 .789 r F P p .63026 .5874 m .69028 .51499 L .65015 .57817 L .846 .943 .885 r F P p .57327 .52943 m .56111 .52173 L .55847 .50102 L .94 .572 .216 r F P p .58124 .54473 m .56556 .52987 L .57327 .52943 L .94 .572 .216 r F P p .56556 .52987 m .54865 .51384 L .57327 .52943 L .94 .572 .216 r F P p .57651 .52925 m .60165 .52655 L .60331 .52536 L .112 .665 .737 r F P p .60331 .52536 m .62608 .52304 L .62804 .55324 L .801 .576 .597 r F P p .59083 .57611 m .60331 .52536 L .62804 .55324 L .584 .556 .789 r F P p .60331 .52536 m .62804 .55324 L .63026 .5874 L .801 .576 .597 r F P p .5947 .55938 m .59083 .57611 L .58458 .55566 L .465 .321 .6 r F P p .54071 .53225 m .53551 .53345 L .56556 .52987 L .112 .665 .737 r F P p .50278 .69406 m .43646 .67339 L .49842 .70122 L .575 .554 .793 r F P p .56273 .70083 m .5715 .65984 L .52804 .71453 L .623 .34 .467 r F P p .54625 .66186 m .51982 .66611 L .48895 .66645 L .014 0 0 r F P p .57258 .65975 m .51982 .66611 L .54625 .66186 L .014 0 0 r F P p .61484 .65466 m .48895 .66645 L .57195 .65773 L .014 0 0 r F P p .59728 .68718 m .57082 .67072 L .57991 .65887 L .762 .683 .775 r F P p .57258 .65975 m .48895 .66645 L .61484 .65466 L .014 0 0 r F P p .70804 .64344 m .63026 .5874 L .64837 .59259 L .191 .512 .913 r F P p .65015 .57817 m .69028 .51499 L .80956 .50427 L .846 .943 .885 r F P p .64707 .62611 m .63026 .5874 L .6487 .60069 L .801 .576 .597 r F P p .6325 .62197 m .63026 .5874 L .64707 .62611 L .801 .576 .597 r F P p .002 w .80956 .50427 m .70804 .64344 L p .65015 .57817 L .801 .576 .597 r F P s P p .002 w .69028 .51499 m .70804 .64344 L p .65015 .57817 L .584 .556 .789 r F P s P p .002 w .69028 .51499 m .70804 .64344 L p .6325 .62197 L .762 .683 .775 r F P s P p .64837 .59259 m .60397 .61911 L .63026 .5874 L .465 .321 .6 r F P p .69028 .51499 m .60331 .52536 L .62608 .52304 L .112 .665 .737 r F P p .62804 .55324 m .60331 .52536 L .69028 .51499 L .584 .556 .789 r F P p .59516 .56211 m .60331 .52536 L .63026 .5874 L .801 .576 .597 r F P p .6325 .62197 m .60397 .61911 L .64837 .59259 L .465 .321 .6 r F P p .002 w .69028 .51499 m .81507 .64033 L p .62926 .57207 L .465 .321 .6 r F P s P p .62926 .57207 m .62714 .53929 L .69028 .51499 L .465 .321 .6 r F P p .62511 .57277 m .69028 .51499 L .63026 .5874 L .846 .943 .885 r F P p .54498 .49222 m .55847 .50102 L .62105 .44546 L .846 .922 .882 r F P p .50233 .49524 m .49855 .40724 L .53112 .48317 L .801 .576 .597 r F P p .48895 .66645 m .46604 .61158 L .53255 .61192 L .796 .577 .604 r F P p .52425 .67503 m .4471 .62332 L .52933 .68526 L .104 .474 .894 r F P p .50414 .66628 m .4471 .62332 L .48895 .66645 L .104 .474 .894 r F P p .54419 .66317 m .55633 .66171 L .59728 .68718 L .762 .683 .775 r F P p .56273 .70083 m .51982 .66611 L .59728 .68718 L .762 .683 .775 r F P p .51982 .66611 m .54419 .66317 L .59728 .68718 L .762 .683 .775 r F P p .63994 .73679 m .56534 .69289 L .56273 .70083 L .104 .474 .894 r F P p .61299 .58884 m .59083 .57611 L .59516 .56211 L .191 .512 .913 r F P p .61299 .58884 m .59516 .56211 L .61175 .57407 L .191 .512 .913 r F P p .63026 .5874 m .60397 .61911 L .59083 .57611 L .465 .321 .6 r F P p .63026 .5874 m .61244 .5823 L .61175 .57407 L .191 .512 .913 r F P p .58487 .60844 m .59842 .60093 L .60397 .61911 L .94 .572 .216 r F P p .60397 .61911 m .58487 .60844 L .63026 .5874 L .846 .943 .885 r F P p .59516 .56211 m .63026 .5874 L .6325 .62197 L .801 .576 .597 r F P p .59516 .56211 m .6325 .62197 L .61941 .61825 L .801 .576 .597 r F P p .64541 .6518 m .61484 .65466 L .62991 .65285 L .014 0 0 r F P p .63994 .73679 m .63453 .65325 L .64541 .6518 L .801 .576 .597 r F P p .81507 .64033 m .63453 .65325 L .64541 .6518 L .014 0 0 r F P p .63453 .65325 m .61484 .65466 L .64541 .6518 L .014 0 0 r F P p .64611 .6509 m .61484 .65466 L .6325 .62197 L .762 .683 .775 r F P p .64541 .6518 m .6325 .62197 L .64707 .62611 L .801 .576 .597 r F P p .63453 .65325 m .6325 .62197 L .64541 .6518 L .801 .576 .597 r F P p .63453 .65325 m .61484 .65466 L .6325 .62197 L .465 .321 .6 r F P p .57876 .65901 m .58487 .60844 L .61196 .61614 L .762 .683 .775 r F P p .57006 .67025 m .57258 .65975 L .57876 .65901 L .762 .683 .775 r F P p .57258 .65975 m .58487 .60844 L .57876 .65901 L .762 .683 .775 r F P p .5645 .69546 m .5712 .66583 L .57202 .66574 L 0 0 0 r F P p .5712 .66583 m .57258 .65975 L .57202 .66574 L 0 0 0 r F P p .57202 .66574 m .57258 .65975 L .5731 .66146 L 0 0 0 r F P p .56348 .69857 m .57258 .65975 L .5645 .69546 L 0 0 0 r F P p .56273 .70083 m .57258 .65975 L .56051 .71122 L 0 0 0 r F P p .55546 .73118 m .5645 .69546 L .55851 .72059 L 0 0 0 r F P p .5645 .69546 m .5731 .66146 L .56534 .69289 L 0 0 0 r F P p .5645 .69546 m .56534 .69289 L .55851 .72059 L 0 0 0 r F P p .57082 .67072 m .57134 .6686 L .57876 .65901 L .762 .683 .775 r F P p .57082 .67072 m .57876 .65901 L .57991 .65887 L .762 .683 .775 r F P p .63994 .73679 m .5731 .66146 L .56534 .69289 L .575 .554 .793 r F P p .56774 .68559 m .5731 .66146 L .63994 .73679 L .801 .576 .597 r F P p .60401 .65597 m .57991 .65887 L .61256 .61631 L .762 .683 .775 r F P p .59728 .68718 m .57991 .65887 L .60401 .65597 L .762 .683 .775 r F P p .59728 .68718 m .61256 .61631 L .6325 .62197 L .762 .683 .775 r F P p .60575 .6571 m .57258 .65975 L .61484 .65466 L .014 0 0 r F P p .57991 .65887 m .57876 .65901 L .61196 .61614 L .762 .683 .775 r F P p .57991 .65887 m .61196 .61614 L .61256 .61631 L .762 .683 .775 r F P p .002 w .81507 .64033 m .63994 .73679 L p .61484 .65466 L .465 .321 .6 r F P s P p .63994 .73679 m .59738 .65934 L .61484 .65466 L .94 .572 .216 r F P p .63453 .65325 m .60575 .6571 L .61484 .65466 L .014 0 0 r F P p .60878 .61523 m .63453 .65325 L .61905 .65532 L .801 .576 .597 r F P p .59516 .56211 m .61941 .61825 L .60878 .61523 L .801 .576 .597 r F P p .61941 .61825 m .63453 .65325 L .60878 .61523 L .801 .576 .597 r F P p .42144 .63946 m .42279 .61526 L .44511 .62457 L .444 .299 .589 r F P p .42279 .61526 m .42577 .56197 L .44445 .62244 L .444 .299 .589 r F P p .42279 .61526 m .44445 .62244 L .44511 .62457 L .444 .299 .589 r F P p .56534 .69289 m .4471 .62332 L .56273 .70083 L .104 .474 .894 r F P p .41176 .64556 m .44246 .64516 L .4471 .62332 L .575 .554 .793 r F P p .44246 .64516 m .48332 .64463 L .4471 .62332 L .575 .554 .793 r F P p .55546 .73118 m .56273 .70083 L .56051 .71122 L 0 0 0 r F P p .55851 .72059 m .56273 .70083 L .52804 .71453 L .623 .34 .467 r F P p .49439 .70783 m .51982 .66611 L .52933 .68526 L .846 .943 .885 r F P p .52578 .70122 m .51982 .66611 L .43646 .67339 L .575 .554 .793 r F P p .51982 .66611 m .47332 .67017 L .48895 .66645 L .014 0 0 r F P p .43646 .67339 m .51982 .66611 L .41176 .64556 L .575 .554 .793 r F P p .51982 .66611 m .51611 .6442 L .41176 .64556 L .575 .554 .793 r F P p .46115 .70122 m .19924 .70472 L .43646 .67339 L .796 .577 .604 r F P p .45243 .71213 m .19924 .70472 L .46115 .70122 L .796 .577 .604 r F P p .41473 .75928 m .41939 .67608 L .43479 .67503 L .444 .299 .589 r F P p .41473 .75928 m .43326 .67654 L .43479 .67503 L .763 .754 .239 r F P p .41473 .75928 m .43479 .67503 L .43646 .67339 L .763 .754 .239 r F P p .41473 .75928 m .43479 .67503 L .46017 .67329 L .444 .299 .589 r F P p .46017 .67329 m .49439 .70783 L .47332 .67017 L .949 .596 .288 r F P p .47966 .70172 m .49439 .70783 L .46017 .67329 L .949 .596 .288 r F P p .43479 .67503 m .41257 .67654 L .43646 .67339 L .014 0 0 r F P p .002 w .33181 .55547 m .35641 .68038 L p .38966 .62066 L .575 .554 .793 r F P s P p .34825 .63894 m .35641 .68038 L .38966 .62066 L .846 .922 .882 r F P p .42577 .56197 m .4471 .62332 L .44607 .62766 L .444 .299 .589 r F P p .4471 .62332 m .4267 .5453 L .46689 .54022 L .444 .299 .589 r F P p .4471 .62332 m .45686 .57743 L .45702 .58168 L .763 .754 .239 r F P p .4471 .62332 m .45702 .58168 L .45735 .59078 L .763 .754 .239 r F P p .41086 .6113 m .43572 .57976 L .41757 .57053 L .846 .922 .882 r F P p .41086 .6113 m .41757 .57053 L .40272 .5972 L .846 .922 .882 r F P p .42279 .61526 m .41973 .60004 L .42394 .5947 L .444 .299 .589 r F P p .4471 .62332 m .40272 .5972 L .41086 .6113 L .104 .474 .894 r F P p .38966 .62066 m .19924 .70472 L .33181 .55547 L .796 .577 .604 r F P p .38966 .62066 m .41086 .6113 L .40272 .5972 L .846 .922 .882 r F P p .35641 .68038 m .41176 .64556 L .38966 .62066 L .575 .554 .793 r F P p .40419 .67711 m .35641 .68038 L .40101 .65231 L .444 .299 .589 r F P p .19924 .70472 m .35641 .68038 L .34825 .63894 L .846 .922 .882 r F P p .41176 .64556 m .19924 .70472 L .38966 .62066 L .796 .577 .604 r F P p .43646 .67339 m .41257 .67654 L .41176 .64556 L .796 .577 .604 r F P p .41473 .75928 m .41257 .67654 L .41939 .67608 L .444 .299 .589 r F P p .41939 .67608 m .41086 .6113 L .42279 .61526 L .444 .299 .589 r F P p .41257 .67654 m .41086 .6113 L .41939 .67608 L .444 .299 .589 r F P p .38966 .62066 m .43483 .62275 L .40735 .58889 L .575 .554 .793 r F P p .43483 .62275 m .4471 .62332 L .40735 .58889 L .575 .554 .793 r F P p .40735 .58889 m .4471 .62332 L .41757 .57053 L .575 .554 .793 r F P p .4471 .62332 m .42017 .59556 L .40272 .5972 L .104 .474 .894 r F P p .4471 .62332 m .4128 .52467 L .41757 .57053 L .949 .596 .288 r F P p .41503 .54607 m .41596 .54539 L .41497 .5455 L .614 .32 .447 r F P p .41596 .54539 m .47773 .49997 L .41497 .5455 L .614 .32 .447 r F P p .41497 .5455 m .47773 .49997 L .4128 .52467 L .614 .32 .447 r F P p .002 w .40718 .47061 m .33181 .55547 L p .4128 .52467 L .614 .32 .447 r F P s P p .002 w .28977 .34211 m .33181 .55547 L p .4128 .52467 L .759 .677 .771 r F P s P p .40428 .54678 m .3878 .51731 L .33181 .55547 L .575 .554 .793 r F P p .37476 .54874 m .39907 .54787 L .41503 .54607 L .112 .665 .737 r F P p .38867 .56545 m .41503 .54607 L .33181 .55547 L .614 .32 .447 r F P p .39354 .54807 m .33181 .55547 L .39907 .54787 L .112 .665 .737 r F P p .38867 .56545 m .41612 .5566 L .41503 .54607 L .614 .32 .447 r F P p .37537 .57523 m .41757 .57053 L .38867 .56545 L .614 .32 .447 r F P p .39525 .58425 m .41757 .57053 L .37537 .57523 L .614 .32 .447 r F P p .4471 .62332 m .4267 .5453 L .42013 .54574 L .949 .596 .288 r F P p .41757 .57053 m .46689 .54022 L .38867 .56545 L .614 .32 .447 r F P p .41757 .57053 m .40428 .54678 L .33181 .55547 L .575 .554 .793 r F P p .41176 .64556 m .4471 .62332 L .38966 .62066 L .575 .554 .793 r F P p .43646 .67339 m .43479 .67503 L .4471 .62332 L .763 .754 .239 r F P p .42749 .70228 m .19924 .70472 L .43326 .67654 L .762 .683 .775 r F P p .42903 .6807 m .35641 .68038 L .43479 .67503 L .014 0 0 r F P p .41939 .67608 m .42144 .63946 L .4395 .65524 L .444 .299 .589 r F P p .41939 .67608 m .4395 .65524 L .43479 .67503 L .444 .299 .589 r F P p .42749 .70228 m .43326 .67654 L .46017 .67329 L .762 .683 .775 r F P p .42544 .71147 m .19924 .70472 L .42749 .70228 L .762 .683 .775 r F P p .52804 .71453 m .48809 .69658 L .49439 .70783 L .575 .554 .793 r F P p .41473 .75928 m .51982 .66611 L .49439 .70783 L .846 .943 .885 r F P p .49688 .72683 m .49439 .70783 L .47966 .70172 L .949 .596 .288 r F P p .002 w .41473 .75928 m .19924 .70472 L p .52804 .71453 L .762 .683 .775 r F P s P p .41473 .75928 m .42903 .6807 L .43326 .67654 L .763 .754 .239 r F P p .46017 .67329 m .45583 .6717 L .47332 .67017 L .014 0 0 r F P p .42903 .6807 m .44875 .67407 L .46017 .67329 L .014 0 0 r F P p .44875 .67407 m .45583 .6717 L .46017 .67329 L .014 0 0 r F P p .47966 .70172 m .42749 .70228 L .46017 .67329 L .762 .683 .775 r F P p .48762 .71332 m .42544 .71147 L .48236 .70565 L .762 .683 .775 r F P p .52578 .70122 m .50278 .69406 L .52804 .71453 L .575 .554 .793 r F P p .50278 .69406 m .49842 .70122 L .52804 .71453 L .575 .554 .793 r F P p .42544 .71147 m .42749 .70228 L .52578 .70122 L .762 .683 .775 r F P p .46613 .6961 m .41473 .75928 L .46017 .67329 L .444 .299 .589 r F P p .47966 .70172 m .46017 .67329 L .51982 .66611 L .762 .683 .775 r F P p .46613 .6961 m .47966 .70172 L .46017 .67329 L .949 .596 .288 r F P p .41473 .75928 m .48613 .67152 L .51982 .66611 L .846 .943 .885 r F P p .52578 .70122 m .47966 .70172 L .51982 .66611 L .762 .683 .775 r F P p .56273 .70083 m .52425 .67503 L .52933 .68526 L .104 .474 .894 r F P p .56273 .70083 m .52578 .70122 L .51982 .66611 L .762 .683 .775 r F P p .52804 .71453 m .48762 .71332 L .52578 .70122 L .762 .683 .775 r F P p .48762 .71332 m .48236 .70565 L .52578 .70122 L .762 .683 .775 r F P p .53034 .66211 m .57195 .65773 L .53255 .61192 L .623 .34 .467 r F P p .51982 .66611 m .58487 .60844 L .57195 .65773 L .846 .943 .885 r F P p .57006 .67025 m .55633 .66171 L .57258 .65975 L .762 .683 .775 r F P p .56534 .69289 m .5731 .66146 L .51982 .66611 L .575 .554 .793 r F P p .60575 .6571 m .5731 .66146 L .51982 .66611 L .014 0 0 r F P p .5731 .66146 m .53995 .66588 L .51982 .66611 L .014 0 0 r F P p .60575 .6571 m .51982 .66611 L .57258 .65975 L .014 0 0 r F P p .5731 .66146 m .58487 .60844 L .60575 .6571 L .801 .576 .597 r F P p .58099 .62951 m .57195 .65773 L .58487 .60844 L 0 0 0 r F P p .5731 .66146 m .57195 .65773 L .58099 .62951 L 0 0 0 r F P p .57258 .65975 m .51468 .63579 L .58487 .60844 L .762 .683 .775 r F P p .55633 .66171 m .51468 .63579 L .57258 .65975 L .762 .683 .775 r F P p .5731 .66146 m .60575 .6571 L .63994 .73679 L .801 .576 .597 r F P p .70804 .64344 m .64837 .59259 L .67119 .59912 L .191 .512 .913 r F P p .64541 .6518 m .64707 .62611 L .70804 .64344 L .801 .576 .597 r F P p .002 w .70804 .64344 m .81507 .64033 L p .64541 .6518 L .014 0 0 r F P s P p .81507 .64033 m .63026 .5874 L .63976 .57593 L .465 .321 .6 r F P p .63772 .58351 m .63742 .58326 L .69028 .51499 L .762 .683 .775 r F P p .64837 .59259 m .63026 .5874 L .62955 .57655 L .191 .512 .913 r F P p .6325 .62197 m .61256 .61631 L .69028 .51499 L .762 .683 .775 r F P p .81507 .64033 m .70804 .64344 L .64746 .57059 L .191 .512 .913 r F P p .64746 .57059 m .81507 .64033 L .69028 .51499 L .614 .32 .447 r F P p .54498 .49222 m .62105 .44546 L .55647 .47254 L .846 .922 .882 r F P p .56111 .52173 m .54865 .51384 L .55341 .50763 L .94 .572 .216 r F P p .56111 .52173 m .55341 .50763 L .55847 .50102 L .94 .572 .216 r F P p .52838 .53406 m .53551 .53345 L .54071 .53225 L .112 .665 .737 r F P p .46857 .54081 m .46689 .54022 L .47773 .49997 L .763 .754 .239 r F P p .46689 .54022 m .50124 .53805 L .51044 .5367 L .112 .665 .737 r F P p .4979 .57287 m .46987 .54128 L .51982 .53532 L .584 .556 .789 r F P p .46689 .54022 m .46857 .54081 L .48446 .53911 L .112 .665 .737 r F P p .46857 .54081 m .46987 .54128 L .48446 .53911 L .112 .665 .737 r F P p .45735 .59078 m .46857 .54081 L .46987 .54128 L .763 .754 .239 r F P p .45735 .59078 m .51982 .53532 L .46857 .54081 L .759 .677 .771 r F P p .46689 .54022 m .49628 .53784 L .51982 .53532 L .112 .665 .737 r F P p .002 w .40718 .47061 m .28977 .34211 L p .4128 .52467 L .949 .596 .288 r F P s P p .45387 .49004 m .40718 .47061 L .28977 .34211 L .191 .512 .913 r F P p .45396 .49292 m .40718 .47061 L .45864 .48393 L .444 .299 .589 r F P p .45864 .48393 m .44244 .47974 L .28977 .34211 L .191 .512 .913 r F P p .47903 .48921 m .47773 .49997 L .45864 .48393 L .191 .512 .913 r F P p .44991 .52043 m .46689 .54022 L .47773 .49997 L .614 .32 .447 r F P p .47773 .49997 m .46689 .54022 L .47903 .48921 L .763 .754 .239 r F P p .47773 .49997 m .47903 .48921 L .49855 .40724 L .763 .754 .239 r F P p .50233 .49524 m .47903 .48921 L .50017 .44501 L .444 .299 .589 r F P p .47903 .48921 m .45864 .48393 L .4865 .45782 L .444 .299 .589 r F P p .47903 .48921 m .4865 .45782 L .50017 .44501 L .444 .299 .589 r F P p .47903 .48921 m .51982 .53532 L .47773 .49997 L .191 .512 .913 r F P p .50233 .49524 m .51982 .53532 L .47903 .48921 L .191 .512 .913 r F P p .46689 .54022 m .51031 .51353 L .47773 .49997 L .614 .32 .447 r F P p .48697 .52787 m .51031 .51353 L .50233 .49524 L .846 .922 .882 r F P p .45735 .59078 m .46689 .54022 L .46857 .54081 L .763 .754 .239 r F P p .46689 .54022 m .45735 .59078 L .50233 .49524 L .846 .922 .882 r F P p .46689 .54022 m .44352 .51298 L .50325 .51643 L .444 .299 .589 r F P p .44352 .51298 m .45396 .49292 L .50325 .51643 L .444 .299 .589 r F P p .44352 .51298 m .40718 .47061 L .45396 .49292 L .444 .299 .589 r F P p .4128 .52467 m .44352 .51298 L .40718 .47061 L .614 .32 .447 r F P p .4128 .52467 m .49855 .40724 L .28977 .34211 L .759 .677 .771 r F P p .44352 .51298 m .49855 .40724 L .4128 .52467 L .759 .677 .771 r F P p .54498 .49222 m .5184 .47487 L .49855 .40724 L .94 .572 .216 r F P p .45864 .48393 m .49855 .40724 L .50759 .43806 L .444 .299 .589 r F P p .48022 .47931 m .28977 .34211 L .49855 .40724 L .801 .576 .597 r F P p .41503 .54607 m .46689 .54022 L .44991 .52043 L .614 .32 .447 r F P p .41612 .5566 m .46689 .54022 L .41503 .54607 L .614 .32 .447 r F P p .40272 .5972 m .39525 .58425 L .33181 .55547 L .104 .474 .894 r F P p .002 w .33181 .55547 m .19924 .70472 L p .38867 .56545 L .614 .32 .447 r F P s P p .002 w .37476 .54874 m .33181 .55547 L p .39354 .54807 L .112 .665 .737 r F P s P p .39525 .58425 m .41757 .57053 L .37476 .54874 L .846 .922 .882 r F P p .40272 .5972 m .41757 .57053 L .39525 .58425 L .846 .922 .882 r F P p .39525 .58425 m .41873 .58165 L .41757 .57053 L .614 .32 .447 r F P p .37476 .54874 m .40998 .56667 L .40428 .54678 L .949 .596 .288 r F P p .42017 .59556 m .39525 .58425 L .40272 .5972 L .104 .474 .894 r F P p .39525 .58425 m .37476 .54874 L .33181 .55547 L .104 .474 .894 r F P p .19924 .70472 m .39525 .58425 L .37537 .57523 L .614 .32 .447 r F P p .002 w .37476 .54874 m .19924 .70472 L p .38966 .62066 L .846 .922 .882 r F P s P p .38966 .62066 m .40272 .5972 L .37476 .54874 L .846 .922 .882 r F P p .19924 .70472 m .42017 .59556 L .39525 .58425 L .614 .32 .447 r F P p .42144 .63946 m .44511 .62457 L .46017 .67329 L .444 .299 .589 r F P p .43479 .67503 m .43326 .67654 L .4471 .62332 L .763 .754 .239 r F P p .43326 .67654 m .44043 .6445 L .4471 .62332 L .763 .754 .239 r F P p .44607 .62766 m .45966 .67136 L .45957 .67137 L .444 .299 .589 r F P p .44607 .62766 m .4471 .62332 L .45966 .67136 L .444 .299 .589 r F P p .42126 .60604 m .45272 .64479 L .41757 .57053 L .949 .596 .288 r F P p .45272 .64479 m .47332 .67017 L .4471 .62332 L .949 .596 .288 r F P p .45272 .64479 m .4471 .62332 L .41757 .57053 L .949 .596 .288 r F P p .43268 .54338 m .4267 .5453 L .46689 .54022 L .112 .665 .737 r F P p .002 w .28977 .34211 m .48351 .45209 L p .48022 .47931 L .191 .512 .913 r F P s P p .48022 .47931 m .47903 .48921 L .28977 .34211 L .191 .512 .913 r F P p .47903 .48921 m .45864 .48393 L .28977 .34211 L .191 .512 .913 r F P p .49045 .51032 m .45396 .49292 L .50233 .49524 L .444 .299 .589 r F P p .45396 .49292 m .45864 .48393 L .50233 .49524 L .444 .299 .589 r F P p .47305 .50752 m .28977 .34211 L .48022 .47931 L .801 .576 .597 r F P p .44643 .51868 m .28977 .34211 L .47305 .50752 L .801 .576 .597 r F P p .41757 .57053 m .4128 .52467 L .28977 .34211 L .949 .596 .288 r F P p .002 w .48351 .45209 m .28977 .34211 L .33181 .55547 L p .575 .554 .793 r F P s P p .002 w .28977 .34211 m .37476 .54874 L p .40428 .54678 L .949 .596 .288 r F P s P p .43268 .54338 m .3878 .51731 L .40428 .54678 L .575 .554 .793 r F P p .37476 .54874 m .40428 .54678 L .43268 .54338 L .112 .665 .737 r F P p .40428 .54678 m .4267 .5453 L .43268 .54338 L .112 .665 .737 r F P p .44643 .51868 m .43572 .57976 L .46084 .51264 L .846 .922 .882 r F P p .41757 .57053 m .43572 .57976 L .44643 .51868 L .846 .922 .882 r F P p .47903 .48921 m .48022 .47931 L .49855 .40724 L .763 .754 .239 r F P p .46689 .54022 m .48351 .45209 L .47903 .48921 L .763 .754 .239 r F P p .46084 .51264 m .47305 .50752 L .48351 .45209 L .846 .922 .882 r F P p .43572 .57976 m .50233 .49524 L .46084 .51264 L .846 .922 .882 r F P p .46445 .54171 m .45686 .57743 L .46689 .54022 L .614 .32 .447 r F P p .46492 .53952 m .44643 .51868 L .47305 .50752 L .801 .576 .597 r F P p .44643 .51868 m .46492 .53952 L .48351 .45209 L .575 .554 .793 r F P p .43268 .54338 m .46492 .53952 L .44643 .51868 L .575 .554 .793 r F P p .40998 .56667 m .41757 .57053 L .40428 .54678 L .949 .596 .288 r F P p .42017 .59556 m .41873 .58165 L .39525 .58425 L .614 .32 .447 r F P p .42017 .59556 m .37476 .54874 L .39525 .58425 L .104 .474 .894 r F P p .43268 .54338 m .48351 .45209 L .3878 .51731 L .575 .554 .793 r F P p .41757 .57053 m .43268 .54338 L .40428 .54678 L .575 .554 .793 r F P p .37476 .54874 m .41757 .57053 L .44643 .51868 L .846 .922 .882 r F P p .37476 .54874 m .43268 .54338 L .46492 .53952 L .112 .665 .737 r F P p .43268 .54338 m .46689 .54022 L .46492 .53952 L .112 .665 .737 r F P p .45702 .58168 m .46559 .53976 L .46689 .54022 L .763 .754 .239 r F P p .46559 .53976 m .46857 .52515 L .46689 .54022 L .763 .754 .239 r F P p .42505 .5436 m .28977 .34211 L .46492 .53952 L .801 .576 .597 r F P p .45702 .58168 m .45686 .57743 L .46857 .52515 L .763 .754 .239 r F P p .45735 .59078 m .51982 .53532 L .51031 .51353 L .846 .922 .882 r F P p .45735 .59078 m .51031 .51353 L .48697 .52787 L .846 .922 .882 r F P p .45735 .59078 m .4979 .57287 L .51982 .53532 L .846 .922 .882 r F P p .4979 .57287 m .51982 .53532 L .50861 .58494 L .584 .556 .789 r F P p .50861 .58494 m .51982 .53532 L .53255 .61192 L .584 .556 .789 r F P p .53255 .61192 m .51982 .53532 L .45735 .59078 L .759 .677 .771 r F P p .49206 .59503 m .4471 .62332 L .49517 .57319 L .444 .299 .589 r F P p .49206 .59503 m .49517 .57319 L .49909 .57776 L .444 .299 .589 r F P p .45957 .67137 m .45966 .67136 L .46017 .67329 L .444 .299 .589 r F P p .46017 .67329 m .47332 .67017 L .42126 .60604 L .949 .596 .288 r F P p .19924 .70472 m .42255 .61844 L .42017 .59556 L .614 .32 .447 r F P p .42255 .61844 m .42126 .60604 L .37476 .54874 L .949 .596 .288 r F P p .46017 .67329 m .42126 .60604 L .42255 .61844 L .949 .596 .288 r F P p .4471 .62332 m .45686 .57743 L .41757 .57053 L .575 .554 .793 r F P p .4471 .62332 m .44851 .60841 L .42017 .59556 L .104 .474 .894 r F P p .42255 .61844 m .44049 .61151 L .42017 .59556 L .614 .32 .447 r F P p .4471 .62332 m .51611 .6442 L .50625 .5861 L .575 .554 .793 r F P p .48332 .64463 m .51611 .6442 L .4471 .62332 L .575 .554 .793 r F P p .4807 .63445 m .48857 .61955 L .55633 .66171 L .762 .683 .775 r F P p .4807 .63445 m .55633 .66171 L .54419 .66317 L .762 .683 .775 r F P p .51982 .66611 m .4807 .63445 L .51726 .65099 L .762 .683 .775 r F P p .51982 .66611 m .50873 .64374 L .4471 .62332 L .104 .474 .894 r F P p .47656 .63308 m .4471 .62332 L .49206 .59503 L .444 .299 .589 r F P p .46017 .67329 m .4471 .62332 L .47656 .63308 L .444 .299 .589 r F P p .53168 .53358 m .51982 .53532 L .51729 .52007 L .191 .512 .913 r F P p .55519 .55564 m .51982 .53532 L .53168 .53358 L .191 .512 .913 r F P p .53916 .53248 m .51031 .51353 L .5324 .52272 L .191 .512 .913 r F P p .55519 .55564 m .53168 .53358 L .53916 .53248 L .191 .512 .913 r F P p .53168 .53358 m .51031 .51353 L .53916 .53248 L .191 .512 .913 r F P p .48022 .47931 m .48351 .45209 L .49855 .40724 L .763 .754 .239 r F P p .48663 .45413 m .48351 .45209 L .49855 .40724 L .94 .572 .216 r F P p .50233 .49524 m .48022 .47931 L .49855 .40724 L .801 .576 .597 r F P p .51758 .4287 m .49855 .40724 L .53 .41706 L .801 .576 .597 r F P p .54865 .51384 m .54498 .49222 L .55847 .50102 L .94 .572 .216 r F P p .56556 .52987 m .54498 .49222 L .57859 .49748 L .584 .556 .789 r F P p .57859 .49748 m .62105 .44546 L .54498 .49222 L .614 .32 .447 r F P p .54498 .49222 m .49855 .40724 L .57859 .49748 L .584 .556 .789 r F P p .54254 .53198 m .56556 .52987 L .5515 .53066 L .112 .665 .737 r F P p .54071 .53225 m .56556 .52987 L .54254 .53198 L .112 .665 .737 r F P p .5515 .53066 m .54865 .51384 L .58124 .54473 L .94 .572 .216 r F P p .5515 .53066 m .57859 .49748 L .54498 .49222 L .614 .32 .447 r F P p .53112 .48317 m .51057 .43527 L .62105 .44546 L .801 .576 .597 r F P p .54696 .43863 m .55726 .42556 L .62105 .44546 L .801 .576 .597 r F P p .51057 .43527 m .55726 .42556 L .54696 .43863 L .801 .576 .597 r F P p .51057 .43527 m .53 .41706 L .55726 .42556 L .801 .576 .597 r F P p .57859 .49748 m .55647 .47254 L .62105 .44546 L .801 .576 .597 r F P p .60331 .52536 m .57859 .49748 L .62105 .44546 L .801 .576 .597 r F P p .002 w .62105 .44546 m .65991 .29533 L p .55647 .47254 L .846 .922 .882 r F P s P p .002 w .49855 .40724 m .65991 .29533 L p .57859 .49748 L .584 .556 .789 r F P s P p .50233 .49524 m .50017 .44501 L .50759 .43806 L .444 .299 .589 r F P p .50233 .49524 m .50759 .43806 L .5184 .47487 L .444 .299 .589 r F P p .5184 .47487 m .50759 .43806 L .65991 .29533 L .444 .299 .589 r F P p .5184 .47487 m .48663 .45413 L .49855 .40724 L .94 .572 .216 r F P p .5515 .53066 m .54498 .49222 L .51031 .51353 L .614 .32 .447 r F P p .69028 .51499 m .60331 .52536 L .57859 .49748 L .584 .556 .789 r F P p .60423 .52471 m .60331 .52536 L .69028 .51499 L .112 .665 .737 r F P p .60423 .52471 m .69028 .51499 L .62105 .44546 L .614 .32 .447 r F P p .59879 .55034 m .69028 .51499 L .60423 .52471 L .614 .32 .447 r F P p .5515 .53066 m .59083 .57611 L .53916 .53248 L .191 .512 .913 r F P p .56257 .54345 m .5515 .53066 L .58124 .54473 L .94 .572 .216 r F P p .50233 .49524 m .51031 .51353 L .55647 .47254 L .846 .922 .882 r F P p .51031 .51353 m .54498 .49222 L .55647 .47254 L .846 .922 .882 r F P p .5515 .53066 m .50233 .49524 L .53112 .48317 L .801 .576 .597 r F P p .51057 .43527 m .49855 .40724 L .51758 .4287 L .801 .576 .597 r F P p .50759 .43806 m .49855 .40724 L .65991 .29533 L .444 .299 .589 r F P p .002 w .65991 .29533 m .48351 .45209 L p .50233 .49524 L .846 .922 .882 r F P s P p .50233 .49524 m .55647 .47254 L .65991 .29533 L .846 .922 .882 r F P p .5515 .53066 m .53916 .53248 L .51579 .49873 L .191 .512 .913 r F P p .56087 .48274 m .55458 .49464 L .55647 .47254 L .801 .576 .597 r F P p .59083 .57611 m .55868 .54741 L .58124 .54473 L .94 .572 .216 r F P p .55868 .54741 m .55682 .54306 L .58124 .54473 L .94 .572 .216 r F P p .56556 .52987 m .57651 .52925 L .60331 .52536 L .112 .665 .737 r F P p .59083 .57611 m .56556 .52987 L .60331 .52536 L .584 .556 .789 r F P p .60331 .52536 m .56583 .5292 L .57859 .49748 L .584 .556 .789 r F P p .5515 .53066 m .56556 .52987 L .60331 .52536 L .112 .665 .737 r F P p .59516 .56211 m .59083 .57611 L .59453 .56107 L 0 0 0 r F P p .59516 .56211 m .59459 .56081 L .60331 .52536 L 0 0 0 r F P p .59516 .56211 m .55458 .49464 L .56087 .48274 L .801 .576 .597 r F P p .59516 .56211 m .5515 .53066 L .55458 .49464 L .801 .576 .597 r F P p .5515 .53066 m .51579 .49873 L .52619 .50142 L .191 .512 .913 r F P p .47541 .53498 m .5515 .53066 L .51031 .51353 L .614 .32 .447 r F P p .53255 .61192 m .51982 .53532 L .55519 .55564 L .584 .556 .789 r F P p .51468 .63579 m .50625 .5861 L .58487 .60844 L .762 .683 .775 r F P p .51982 .66611 m .51726 .65099 L .54419 .66317 L .762 .683 .775 r F P p .51982 .66611 m .54321 .62776 L .58487 .60844 L .846 .943 .885 r F P p .51982 .66611 m .5731 .66146 L .53052 .64857 L .575 .554 .793 r F P p .51982 .66611 m .53052 .64857 L .51611 .6442 L .575 .554 .793 r F P p .5731 .66146 m .55619 .62174 L .56581 .61728 L .801 .576 .597 r F P p .59083 .57611 m .55519 .55564 L .53916 .53248 L .191 .512 .913 r F P p .5731 .66146 m .5515 .53066 L .58487 .60844 L .801 .576 .597 r F P p .46689 .54022 m .5515 .53066 L .46864 .53914 L .614 .32 .447 r F P p .49591 .53655 m .54071 .53225 L .50407 .53551 L .112 .665 .737 r F P p .54071 .53225 m .54254 .53198 L .50407 .53551 L .112 .665 .737 r F P p .50407 .53551 m .54254 .53198 L .5515 .53066 L .112 .665 .737 r F P p .46857 .52515 m .47305 .50752 L .46689 .54022 L .763 .754 .239 r F P p .45686 .57743 m .46492 .53952 L .46857 .52515 L .763 .754 .239 r F P p .46689 .54022 m .50325 .51643 L .50407 .53551 L .444 .299 .589 r F P p .46492 .53952 m .52838 .53406 L .54071 .53225 L .112 .665 .737 r F P p .46689 .54022 m .51982 .53532 L .49019 .53759 L .112 .665 .737 r F P p .51982 .53532 m .52838 .53406 L .46492 .53952 L .112 .665 .737 r F P p .50625 .5861 m .5515 .53066 L .46689 .54022 L .614 .32 .447 r F P p .50625 .5861 m .50233 .49524 L .5291 .55811 L .801 .576 .597 r F P p .50625 .5861 m .5291 .55811 L .5731 .66146 L .801 .576 .597 r F P p .5731 .66146 m .57756 .64341 L .51611 .6442 L .575 .554 .793 r F P p .51611 .6442 m .53332 .64398 L .50625 .5861 L .575 .554 .793 r F P p .53332 .64398 m .55732 .64367 L .54321 .62776 L .575 .554 .793 r F P p .53332 .64398 m .54321 .62776 L .50625 .5861 L .575 .554 .793 r F P p .56581 .61728 m .5291 .55811 L .5515 .53066 L .801 .576 .597 r F P p .55619 .62174 m .5291 .55811 L .56581 .61728 L .801 .576 .597 r F P p .52619 .50142 m .50233 .49524 L .5184 .47487 L .444 .299 .589 r F P p .5324 .52272 m .51031 .51353 L .48351 .45209 L .191 .512 .913 r F P p .5291 .55811 m .50233 .49524 L .5515 .53066 L .801 .576 .597 r F P p .53505 .5316 m .49045 .51032 L .50233 .49524 L .444 .299 .589 r F P p .46017 .67329 m .49902 .57795 L .50625 .5861 L .444 .299 .589 r F P p .53505 .5316 m .50407 .53551 L .5515 .53066 L .112 .665 .737 r F P p .46689 .54022 m .49019 .53759 L .46492 .53952 L .112 .665 .737 r F P p .4471 .62332 m .46689 .54022 L .53505 .5316 L .444 .299 .589 r F P p .45686 .57743 m .50625 .5861 L .46689 .54022 L .614 .32 .447 r F P p .49909 .57776 m .49517 .57319 L .50524 .56269 L .444 .299 .589 r F P p .46492 .53952 m .49591 .53655 L .50407 .53551 L .112 .665 .737 r F P p .50625 .5861 m .46492 .53952 L .50233 .49524 L .801 .576 .597 r F P p .50407 .53551 m .50325 .51643 L .53505 .5316 L .444 .299 .589 r F P p .53505 .5316 m .46492 .53952 L .50407 .53551 L .112 .665 .737 r F P p .4471 .62332 m .50625 .5861 L .45686 .57743 L .575 .554 .793 r F P p .44043 .6445 m .45686 .57743 L .4471 .62332 L .763 .754 .239 r F P p .002 w .42903 .6807 m .19924 .70472 L p .35641 .68038 L .014 0 0 r F P s P p .41257 .67654 m .19924 .70472 L .41176 .64556 L .796 .577 .604 r F P p .43326 .67654 m .19924 .70472 L .44851 .60841 L .762 .683 .775 r F P p .44851 .60841 m .45686 .57743 L .44043 .6445 L .763 .754 .239 r F P p .43479 .67503 m .43646 .67339 L .43773 .67483 L .014 0 0 r F P p .43975 .6771 m .43646 .67339 L .45583 .6717 L .014 0 0 r F P p .43479 .67503 m .4395 .65524 L .46017 .67329 L .444 .299 .589 r F P p .42903 .6807 m .43479 .67503 L .43975 .6771 L .014 0 0 r F P p .43479 .67503 m .43773 .67483 L .43975 .6771 L .014 0 0 r F P p .51982 .66611 m .46017 .67329 L .47332 .67017 L .014 0 0 r F P p .44851 .60841 m .50625 .5861 L .45686 .57743 L .614 .32 .447 r F P p .51982 .66611 m .46017 .67329 L .4807 .63445 L .762 .683 .775 r F P p .51468 .63579 m .46218 .60313 L .50625 .5861 L .762 .683 .775 r F P p .46857 .52515 m .48351 .45209 L .47305 .50752 L .763 .754 .239 r F P p .47305 .50752 m .48022 .47931 L .50233 .49524 L .801 .576 .597 r F P p .48351 .45209 m .50233 .49524 L .47903 .48921 L .191 .512 .913 r F P p .47305 .50752 m .50233 .49524 L .48351 .45209 L .846 .922 .882 r F P p .46492 .53952 m .47305 .50752 L .50233 .49524 L .801 .576 .597 r F P p .46857 .52515 m .46683 .52659 L .48351 .45209 L .763 .754 .239 r F P p .45686 .57743 m .50625 .5861 L .46095 .57323 L .575 .554 .793 r F P p .49768 .53559 m .46492 .53952 L .53505 .5316 L .112 .665 .737 r F P p .41757 .57053 m .45686 .57743 L .46492 .53952 L .575 .554 .793 r F P p .41757 .57053 m .46492 .53952 L .43268 .54338 L .575 .554 .793 r F P p .002 w .37476 .54874 m .28977 .34211 L p .44118 .56761 L .801 .576 .597 r F P s P p .45686 .57743 m .49768 .53559 L .46492 .53952 L .575 .554 .793 r F P p .42126 .60604 m .41757 .57053 L .40998 .56667 L .949 .596 .288 r F P p .42017 .59556 m .45686 .57743 L .41873 .58165 L .614 .32 .447 r F P p .41873 .58165 m .45686 .57743 L .41757 .57053 L .614 .32 .447 r F P p .37476 .54874 m .42126 .60604 L .40998 .56667 L .949 .596 .288 r F P p .45686 .57743 m .45666 .57201 L .46492 .53952 L .763 .754 .239 r F P p .42017 .59556 m .44851 .60841 L .45686 .57743 L .614 .32 .447 r F P p .44851 .60841 m .45666 .57201 L .45686 .57743 L .763 .754 .239 r F P p .46218 .60313 m .45122 .59631 L .50625 .5861 L .762 .683 .775 r F P p .45122 .59631 m .37476 .54874 L .45666 .57201 L .762 .683 .775 r F P p .45122 .59631 m .45666 .57201 L .50625 .5861 L .762 .683 .775 r F P p .44049 .61151 m .44851 .60841 L .43545 .60248 L .614 .32 .447 r F P p .44049 .61151 m .43545 .60248 L .42017 .59556 L .614 .32 .447 r F P p .4807 .63445 m .37476 .54874 L .48857 .61955 L .762 .683 .775 r F P p .42017 .59556 m .42626 .58526 L .37476 .54874 L .104 .474 .894 r F P p .37476 .54874 m .44118 .56761 L .45322 .58555 L .801 .576 .597 r F P p .37476 .54874 m .45322 .58555 L .44916 .6015 L .801 .576 .597 r F P p .37476 .54874 m .46084 .51264 L .48351 .45209 L .846 .922 .882 r F P p .464 .53919 m .37476 .54874 L .48351 .45209 L .762 .683 .775 r F P p .002 w .45533 .53612 m .37476 .54874 L p .46492 .53952 L .112 .665 .737 r F P s P p .45322 .58555 m .42505 .5436 L .46492 .53952 L .801 .576 .597 r F P p .46492 .53952 m .464 .53919 L .46857 .52515 L .763 .754 .239 r F P p .45666 .57201 m .37476 .54874 L .464 .53919 L .762 .683 .775 r F P p .45666 .57201 m .45533 .53612 L .464 .53919 L .763 .754 .239 r F P p .45666 .57201 m .464 .53919 L .46492 .53952 L .763 .754 .239 r F P p .46095 .57323 m .50625 .5861 L .49768 .53559 L .575 .554 .793 r F P p .55682 .54306 m .5515 .53066 L .56257 .54345 L .94 .572 .216 r F P p .58487 .60844 m .55754 .56628 L .5886 .58821 L .94 .572 .216 r F P p .55754 .56628 m .55356 .54284 L .5886 .58821 L .94 .572 .216 r F P p .58487 .60844 m .5886 .58821 L .59842 .60093 L .94 .572 .216 r F P p .59842 .60093 m .5886 .58821 L .59083 .57611 L .94 .572 .216 r F P p .5886 .58821 m .55356 .54284 L .59083 .57611 L .94 .572 .216 r F P p .58487 .60844 m .5515 .53066 L .59516 .56211 L .801 .576 .597 r F P p .59516 .56211 m .55647 .47254 L .60331 .52536 L .801 .576 .597 r F P p .57859 .49748 m .609 .50225 L .62105 .44546 L .614 .32 .447 r F P p .002 w .62105 .44546 m .65991 .29533 L p .609 .50225 L 0 0 0 r F P s P p .002 w .65991 .29533 m .69028 .51499 L p .57859 .49748 L .584 .556 .789 r F P s P p .59516 .56211 m .60331 .52536 L .65991 .29533 L 0 0 0 r F P p .58288 .54372 m .60423 .52471 L .58057 .54276 L .614 .32 .447 r F P p .002 w .65991 .29533 m .69028 .51499 L p .60508 .52411 L .762 .683 .775 r F P s P p .61535 .54394 m .60482 .52518 L .69028 .51499 L .762 .683 .775 r F P p .60737 .55765 m .60482 .52518 L .63742 .58326 L .762 .683 .775 r F P p .58487 .60844 m .59516 .56211 L .60468 .59926 L .801 .576 .597 r F P p .63026 .5874 m .61175 .57407 L .61016 .55507 L .191 .512 .913 r F P p .59879 .55034 m .60482 .52518 L .60656 .54734 L .762 .683 .775 r F P p .61175 .57407 m .59516 .56211 L .59879 .55034 L .191 .512 .913 r F P p .59879 .55034 m .60656 .54734 L .60737 .55765 L .762 .683 .775 r F P p .63742 .58326 m .61535 .54394 L .69028 .51499 L .762 .683 .775 r F P p .61175 .57407 m .59879 .55034 L .61061 .56041 L .191 .512 .913 r F P p .59879 .55034 m .60737 .55765 L .60963 .58649 L .762 .683 .775 r F P p .58487 .60844 m .59879 .55034 L .60963 .58649 L .762 .683 .775 r F P p .63026 .5874 m .61016 .55507 L .62039 .55933 L .191 .512 .913 r F P p .58487 .60844 m .62511 .57277 L .63026 .5874 L .846 .943 .885 r F P p .62955 .57655 m .63026 .5874 L .62511 .57277 L .191 .512 .913 r F P p .61196 .61614 m .60737 .55765 L .63742 .58326 L .762 .683 .775 r F P p .58487 .60844 m .59323 .57655 L .69028 .51499 L .846 .943 .885 r F P p .62039 .55933 m .69028 .51499 L .59879 .55034 L .614 .32 .447 r F P p .002 w .69028 .51499 m .60742 .52244 L p .60423 .52471 L .112 .665 .737 r F P s P p .60482 .52518 m .60508 .52411 L .69028 .51499 L .762 .683 .775 r F P p .61016 .55507 m .59879 .55034 L .60742 .52244 L .191 .512 .913 r F P p .61061 .56041 m .59879 .55034 L .61016 .55507 L .191 .512 .913 r F P p .62039 .55933 m .61016 .55507 L .60742 .52244 L .191 .512 .913 r F P p .58487 .60844 m .60468 .59926 L .60878 .61523 L .801 .576 .597 r F P p .58487 .60844 m .60963 .58649 L .61196 .61614 L .762 .683 .775 r F P p .81507 .64033 m .63453 .65325 L .6325 .62197 L .465 .321 .6 r F P p .61941 .61825 m .6325 .62197 L .63453 .65325 L .801 .576 .597 r F P p .61484 .65466 m .59996 .6436 L .58487 .60844 L .94 .572 .216 r F P p .59996 .6436 m .58099 .62951 L .58487 .60844 L .94 .572 .216 r F P p .59879 .55034 m .59516 .56211 L .65991 .29533 L 0 0 0 r F P p .59879 .55034 m .59083 .57611 L .5515 .53066 L .191 .512 .913 r F P p .58288 .54372 m .59879 .55034 L .60423 .52471 L .614 .32 .447 r F P p .55754 .56628 m .59879 .55034 L .58288 .54372 L .614 .32 .447 r F P p .55356 .54284 m .5515 .53066 L .55682 .54306 L .94 .572 .216 r F P p .5515 .53066 m .60423 .52471 L .609 .50225 L .614 .32 .447 r F P p .57214 .52763 m .5515 .53066 L .60331 .52536 L .112 .665 .737 r F P p .55868 .54741 m .55356 .54284 L .55682 .54306 L .94 .572 .216 r F P p .002 w .65991 .29533 m .60742 .52244 L p .59879 .55034 L 0 0 0 r F P s P p .5515 .53066 m .609 .50225 L .57859 .49748 L .614 .32 .447 r F P p .60508 .52411 m .57214 .52763 L .65991 .29533 L .762 .683 .775 r F P p .464 .53919 m .45533 .53612 L .46683 .52659 L .763 .754 .239 r F P p .464 .53919 m .46683 .52659 L .46857 .52515 L .763 .754 .239 r F P p .46492 .53952 m .49768 .53559 L .48351 .45209 L .575 .554 .793 r F P p .53505 .5316 m .50233 .49524 L .51332 .49809 L .444 .299 .589 r F P p .58963 .52636 m .60331 .52536 L .60423 .52471 L .112 .665 .737 r F P p .50625 .5861 m .55565 .55515 L .5515 .53066 L .614 .32 .447 r F P p .55565 .55515 m .60423 .52471 L .5515 .53066 L .614 .32 .447 r F P p .55356 .54284 m .52902 .51104 L .54865 .51384 L .94 .572 .216 r F P p .58487 .60844 m .50625 .5861 L .58037 .55746 L .762 .683 .775 r F P p .51982 .66611 m .50873 .64374 L .54321 .62776 L .846 .943 .885 r F P p .63994 .73679 m .57436 .6655 L .56534 .69289 L .104 .474 .894 r F P p .63994 .73679 m .56534 .69289 L .56061 .71207 L .575 .554 .793 r F P p .002 w .51982 .90146 m .63994 .73679 L p .58341 .72554 L .623 .34 .467 r F P s P p .002 w .63994 .73679 m .51982 .90146 L p .56774 .68559 L .801 .576 .597 r F P s P p .57436 .6655 m .57435 .66551 L .56774 .68559 L .104 .474 .894 r F P p .57436 .6655 m .56774 .68559 L .56775 .68559 L .104 .474 .894 r F P p .56494 .69823 m .56774 .68559 L .57436 .6655 L 0 0 0 r F P p .56774 .68559 m .5731 .66146 L .57436 .6655 L 0 0 0 r F P p .56775 .68559 m .56774 .68559 L .56534 .69289 L .104 .474 .894 r F P p .55851 .72059 m .5731 .66146 L .56494 .69823 L 0 0 0 r F P p .52804 .71453 m .52578 .70122 L .56273 .70083 L .762 .683 .775 r F P p .56061 .71207 m .51982 .66611 L .52578 .70122 L .575 .554 .793 r F P p .56774 .68559 m .55437 .66396 L .5731 .66146 L .801 .576 .597 r F P p .50873 .64374 m .50625 .5861 L .56774 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StyleBox["Mathematica", FontSlant->"Italic"], " ... 1 " }], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["The Front End Versus the Kernel"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " consists of two separate applications, the ", StyleBox["Kernel", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "and the ", StyleBox["Front End", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ". The Kernel is responsible for computing results and is essentially the \ same on all supported platforms. The Front End is the user interface to the \ Kernel and varies from platform to platform. \n\nThere are two major types \ of Front Ends: Notebook Front Ends, which are designed to take advantage of \ graphical user interface features, and command-line oriented Front Ends. \ Both types of Front Ends enable you to enter commands and data. Notebook \ Front Ends provide the additional capability of creating documents, called \ Notebooks, which may contain text, graphics, and ", StyleBox["Mathematica", FontSlant->"Italic"], " input and output. In addition, the editing capabilities of Notebook Front \ Ends are superior to those of command-line Front Ends. \n\nOne benefit that \ results from the way ", StyleBox["Mathematica", FontSlant->"Italic"], " is structured is that the Kernel can be run remotely from a workstation, \ mainframe, or supercomputer (in order to take advantage of the remote \ system's additional memory and speed) and the Front End can be run locally \ (to capitilize on the Notebook interface that may be available on the local \ machine). " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Kernel", "Front End", "Notebooks", "Command-line interfaces"}] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[ "Introduction to Notebooks ... 1 "], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "Notebook Front Ends provide the ability to create documents, called \ Notebooks, which may contain text, graphics, and ", StyleBox["Mathematica", FontSlant->"Italic"], " input and output. Notebooks are similar to documents created with word \ processors and other applications in that they may be saved to disk, opened \ and edited, and printed. Notebooks, however, provide two major advantages \ over normal text files. First, a Notebook can be structured hierarchically \ into sections which can be expanded into subsections and sub-subsections or \ collapsed into section headings as one works through the Notebook. Second, \ Notebooks can be interactive documents in which illustrative computations and \ graphics are embedded in explanatory text. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Types of Cells"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The basic unit of structure in a ", StyleBox["Mathematica", FontSlant->"Italic"], " Notebook is called a ", StyleBox["cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ". Each cell can contain either text, ", StyleBox["Mathematica", FontSlant->"Italic"], " input, ", StyleBox["Mathematica", FontSlant->"Italic"], " output, or graphics, but not combinations of these materials. The \ material a cell contains determines its", StyleBox[" cell type", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " or ", StyleBox["style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " which in turn determines its role in the Notebook. For example, a cell \ which contains ", StyleBox["Mathematica", FontSlant->"Italic"], " input is defined as an ", StyleBox["Input", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "cell. Input cells are ", StyleBox["active", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "cells (cells that can be evaluated by the ", StyleBox["Mathematica", FontSlant->"Italic"], " Kernel). \n\n", StyleBox["Mathematica", FontSlant->"Italic"], " is equipped with several predefined cell styles which can be applied to \ individual cells. When a style is applied to a cell, the cell takes on the \ text and cell attributes that are specified in the style's definition. For \ example, styles can be used to apply text attriubutes such as font, face, \ size, color and alignment to a cell. Styles can also be used to apply cell \ attributes such as margin settings, and whether a cell is active or inactive. \ Predefined styles have names which indicate their roles in the Notebook: \ Title, Subtitle, Subsubtitle, Section, Subsection, Subsubsection, Text, Small \ Text, Input, Output, Graphics, etc. \n\nEvery notebook has an associated ", StyleBox["style sheet", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "which is the collection of currently available styles. Predefined styles \ can be modified and entirely new styles can be created. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "cell", "cell type", "input cell", "text attributes", "cell attributes", "style sheet"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Cell Brackets"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "A ", StyleBox["cell bracket", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "is the bracket located on the far right side of the window which surrounds \ the material in a cell. Cell brackets have four major functions in ", StyleBox["Mathematica.", FontSlant->"Italic"], " First, they are used to indicate the extent of material contained in a \ cell. As material is added to a cell, its cell bracket grows \ correspondingly. Second, cell brackets are used to select entire cells. \ This is accomplished by clicking on the bracket. When a cell is selected, \ its bracket will become highlighted. Many operations, including Cut, Copy, \ Evaluate, and Paste, can be performed on a cell once it has been selected. \ Third, cell brackets are used to differentiate between cell types. For \ example, the bracket to the right of this paragraph features two horizontal \ tick marks at the top of the bracket. This indicates that the bracket \ surrounds a text cell. Finally, ", StyleBox["Mathematica", FontSlant->"Italic"], " automatically creates hierarchical cell groups, or sequences of related \ cells, based on styles assigned to the cells by enclosing related cells in \ group brackets. Group brackets are used by ", StyleBox["Mathematica", FontSlant->"Italic"], " to force a hierarchical, or tree, structure on the Notebook being \ created." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"cell bracket", "Group brackets"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Creating New Cells"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[ "There are three methods that can be used to create new cells. To create a \ new cell in an empty Notebook, simply start typing. The information you type \ will immediately be enclosed within a cell. To create a new cell above or \ below an existing cell, position the pointer accordingly and click the mouse \ when the pointer changes from a veritical I-beam to a horizontal I-beam. The \ location of the new cell will be indicated by a horizotal line spanning the \ width of the window. As soon as you begin to type, the information will be \ enclosed in a cell. Cells created using either of these two methods will \ automatically inherit the Input cell style, unless you indicate otherwise. \ The third method provides a mechanism for copying the cell style from the \ cell above to a new cell. To create a new cell which has the same style as \ the cell above, click within the cell whose style you wish to copy (a \ blinking vertical bar should appear), and press Option-Return."], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Arithmetic in ", StyleBox["Mathematica", FontSlant->"Italic"], " ... 3 " }], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Arithmetic Operators"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " can be used like an electronic calculator to perform arithmetic \ operations such as addition, subtraction, multiplication, division, and \ exponentiation. The following table lists the operators supported by ", StyleBox["Mathematica", FontSlant->"Italic"], ":\n\n", StyleBox["Operation", FontVariations->{"Underline"->True}], "\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\ ", StyleBox["Operator", FontVariations->{"Underline"->True}], " ", StyleBox["\n", FontVariations->{"Underline"->True}], "\nAddition +\t\t\t\t\t\t\t\t\t\t\t\t\ \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\nSubtraction \ - \nDivision \ / \nMultiplication \ * (or a space) \n\ Exponentiation ^ \n\ \nNote that in addition to the asterisk character, a space can also be used \ to denote multiplication. Note also, that spaces are not required around an \ operator, but can be used to make the input easier to read. The following \ Input cell provides example computations which use each of these operators.\n \ " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "addition", "subtraction", "multiplication", "division", "exponentiation"}], Cell[CellGroupData[{ Cell[TextData[ "2 + 3\n20 - 5\n26 * 4319\n26 4319\n237 / 3\n2 ^ 48"], "Input", PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 5\ \>", "\<\ 5\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 15\ \>", "\<\ 15\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 112294\ \>", "\<\ 112294\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 112294\ \>", "\<\ 112294\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 79\ \>", "\<\ 79\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 281474976710656\ \>", "\<\ 281474976710656\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Numerical and Symbolic Computations"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " can do numerical, as well as symbolic, computations. Thus, it can \ compute algebraic formulas as well as numerical expressions. In ", StyleBox["Mathematica", FontSlant->"Italic"], ", a variable name must begin with a letter (or $) and can not include \ spaces. ", StyleBox["Mathematica", FontSlant->"Italic"], " will treat a character string composed of a single letter, or sequence of \ letters, as a symbol. The following provides an example of each type of \ computation. The first expression is a numerical expression. The second is \ a symbolic expression whose terms include the variables (symbols) x and y." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"numerical expression", "symbolic expression"}], Cell[CellGroupData[{ Cell[TextData[ "3 * 4 + 2 \nx y + 2 x^2 y + y^2 x^2 - 2 y x"], "Input", PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 14\ \>", "\<\ 14\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ -(x*y) + 2*x^2*y + x^2*y^2\ \>", "\<\ 2 2 2 -(x y) + 2 x y + x y\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Numerical Approximations"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " computes exact results unless the input includes an approximate number \ (for example, a number with a decimal point) or unless a numerical \ approximation is requested. In ", StyleBox["Mathematica", FontSlant->"Italic"], ", the built-in function ", StyleBox["N[expr, n]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " is used to perform computations to n-digit precision. If the second \ argument is not specified, ", StyleBox["Mathematica", FontSlant->"Italic"], " will display the result in 6-digit precision even though it actually \ computes the result to a higher degree of precision. The default degree of \ precision that ", StyleBox["Mathematica", FontSlant->"Italic"], " computes the result to is dependent upon the computer being used. You \ can use ", StyleBox["N", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", however, to calculate results to a higher degree of precision than the \ floating point precision of the machine being used. \n\nIn the examples that \ follow, note how 1) ", StyleBox["Mathematica", FontSlant->"Italic"], " displays exact results when working with integers, rational numbers, or \ symbols, 2) ", StyleBox["Mathematica", FontSlant->"Italic"], " displays approximate results when working with expressions involving \ floating point numbers, and 3) ", StyleBox["Mathematica", FontSlant->"Italic"], " can display results to any precision by using the function ", StyleBox["N", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"N expr", "n", "floating point precision"}], Cell[CellGroupData[{ Cell[TextData[ "1/5 + 7x + 5/2\n1.5/300 + 1/3\nN[Pi,30]"], "Input", PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 27/10 + 7*x\ \>", "\<\ 27 -- + 7 x 10\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 0.3383333333333333333\ \>", "\<\ 0.338333\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 3.141592653589793238462643383280\ \>", "\<\ 3.14159265358979323846264338328\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Complex Numbers"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " can compute results for input involving complex numbers. You can enter \ complex numbers in ", StyleBox["Mathematica", FontSlant->"Italic"], " by including the constant ", StyleBox["I", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "(which equals the square root of negative one). ", StyleBox["Mathematica", FontSlant->"Italic"], " features several built-in functions for working with complex numbers:\n\n\ ", StyleBox["Re[z]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " displays the real part of the complex number z\n", StyleBox["Im[z]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " displays the imaginary part of the complex number z\n", StyleBox["Conjugate[z]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " returns the complex conjugate of the complex number z\n\nThe following \ uses ", StyleBox["Re", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Im", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", and ", StyleBox["Conjugate", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to respectively give the real part, imaginary part and conjugate of the \ complex number 4+3I. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"I", "Re z", "Im z", "Conjugate z"}], Cell[CellGroupData[{ Cell[TextData["Re[4 + 3I]\nIm[4 + 3I]\nConjugate[4 + 3I]"], "Input", PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 4\ \>", "\<\ 4\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 3\ \>", "\<\ 3\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 4 - 3*I\ \>", "\<\ 4 - 3 I\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Symbols and Storage ... 5 "], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Brackets, Parantheses, and Braces"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "Square brackets", "Parantheses", "Curly braces", "lists", "Double square brackets"}], Cell[TextData[{ "In ", StyleBox["Mathematica", FontSlant->"Italic"], ", brackets, parantheses, and braces are used for different purposes. ", StyleBox["Square brackets", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " are used to enclose agruments of functions. For example, in the function \ ", StyleBox["N[expr,n]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", square brackets are used to enclose the two arguments, ", StyleBox["expr", FontSlant->"Italic"], " and", StyleBox[" n", FontSlant->"Italic"], ". All built-in functions follow this syntax convention. \n\n", StyleBox["Parantheses", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " are used for grouping and serve to control the order in which \ calculations are performed. For example, notice how the use of parentheses \ in the Input cell below affects the output." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "Square brackets", "Parantheses", "Curly braces", "lists", "Double square brackets"}], Cell[CellGroupData[{ Cell[TextData["3/4^20\n(3/4)^20"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "Square brackets", "Parantheses", "Curly braces", "lists", "Double square brackets"}], Cell[OutputFormData["\<\ 3/1099511627776\ \>", "\<\ 3 ------------- 1099511627776\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 3486784401/1099511627776\ \>", "\<\ 3486784401 ------------- 1099511627776\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ StyleBox["Curly braces", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " are used for indicating ", StyleBox["lists", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ". In ", StyleBox["Mathematica", FontSlant->"Italic"], ", a list is defined to be a collection of objects, separated by commas and \ enclosed in curly braces. ", StyleBox["Mathematica", FontSlant->"Italic"], " uses lists, for example, to specify vectors and matrices (where a matrix \ is a list of lists). In the following Input cell, we use a list to ask ", StyleBox["Mathematica", FontSlant->"Italic"], " to compute the cube of each element in the list." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "Square brackets", "Parantheses", "Curly braces", "lists", "Double square brackets"}], Cell[CellGroupData[{ Cell[TextData["{1,2,3,4}^3"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "Square brackets", "Parantheses", "Curly braces", "lists", "Double square brackets"}], Cell[OutputFormData["\<\ {1, 8, 27, 64}\ \>", "\<\ {1, 8, 27, 64}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ StyleBox["Double square brackets", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " are used for indexing. In the Input cell below, we define a list, ", StyleBox["x", FontSlant->"Italic"], ", and then redefine the third element of ", StyleBox["x", FontSlant->"Italic"], " by using double square brackets. Finally, we ask ", StyleBox["Mathematica", FontSlant->"Italic"], " to redisplay ", StyleBox["x", FontSlant->"Italic"], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "Square brackets", "Parantheses", "Curly braces", "lists", "Double square brackets"}], Cell[CellGroupData[{ Cell[TextData["x = {35, 38, 67, 63}\nx[[3]] = 40\nx"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "Square brackets", "Parantheses", "Curly braces", "lists", "Double square brackets"}], Cell[OutputFormData["\<\ {35, 38, 67, 63}\ \>", "\<\ {35, 38, 67, 63}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 40\ \>", "\<\ 40\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ {35, 38, 40, 63}\ \>", "\<\ {35, 38, 40, 63}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["User-defined and Reserved Symbols"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"built-in symbols", "Clear"}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " features many built-in (reserved) symbols, or named objects, such as \ functions and constants. All built-in symbols begin with a capital letter or \ a dollar sign. When defining your own objects, you must be careful to avoid \ using a reserved name. A common technique is to follow the convention of \ always using names that begin with lowercase letters. For example, in the \ following Input cell, we assign the value 7 to the variable ", StyleBox["y", FontSlant->"Italic"], ". Note how we first use the ", StyleBox["Clear", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " function to remove any value previously assigned to ", StyleBox["y", FontSlant->"Italic"], ". " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"built-in symbols", "Clear"}], Cell[CellGroupData[{ Cell[TextData["Clear[y]\ny = 7"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"built-in symbols", "Clear"}], Cell[OutputFormData["\<\ 7\ \>", "\<\ 7\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "It is crucial to realize that function definitions and variable \ assignments are ", StyleBox["permanent", FontSlant->"Italic"], ". Once a function has been defined or a value has been assigned to a \ variable, the definition or value will be kept until you remove it or until \ you begin a new ", StyleBox["Mathematica", FontSlant->"Italic"], " session. Many mistakes in ", StyleBox["Mathematica", FontSlant->"Italic"], " are caused by not clearing old definitions. Therefore, prior to defining \ new functions, constants, or variables, make a practise using ", StyleBox["Clear", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to remove old definitions." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"built-in symbols", "Clear"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Assignments and Equality"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "single equal sign", "immediate assignment operator", "colon equal sign", "delayed assignment operator", "Random", "Table expr", "{imax}", "logical operator", "double equal sign"}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " features two different assignment operators. The ", StyleBox["single equal sign", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "(lhs = rhs) is referred to as the ", StyleBox["immediate assignment operator", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " and the ", StyleBox["colon equal sign", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " (lhs := rhs) is known as the ", StyleBox["delayed assignment operator", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ". The primary difference between these operators is when the expression ", StyleBox["rhs", FontSlant->"Italic"], " is evaluated. If the immediate assignment operator is used, ", StyleBox["rhs", FontSlant->"Italic"], " is evaluated as soon as the assignment is made. With the delayed \ assignment operator, ", StyleBox["rhs", FontSlant->"Italic"], " is only evaluated when the value of ", StyleBox["lhs", FontSlant->"Italic"], " is requested. \n\nThe difference between these two operators is \ clarified by the following example. We use the built-in function, ", StyleBox["Random[ ]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", to generate a uniformly distributed pseudorandom Real in the range 0 to \ 1 and the built-in function, ", StyleBox["Table[expr, {imax}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", to generate a list of ", StyleBox["imax", FontSlant->"Italic"], " copies of ", StyleBox["expr", FontSlant->"Italic"], ". We use the immediate assignment operator to define ", StyleBox["random1", FontSlant->"Italic"], " and the delayed assignment operator to define ", StyleBox["random2", FontSlant->"Italic"], ". Note how ", StyleBox["random1", FontSlant->"Italic"], " always returns the same value whenever it is called, but ", StyleBox["random2", FontSlant->"Italic"], " returns a different value each time it is called." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "single equal sign", "immediate assignment operator", "colon equal sign", "delayed assignment operator", "Random", "Table expr", "{imax}", "logical operator", "double equal sign"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[random1, random2]\nrandom1 = Random[ ]\nTable[random1,{5}]\nrandom2 := \ Random[ ]\nTable[random2, {5}]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "single equal sign", "immediate assignment operator", "colon equal sign", "delayed assignment operator", "Random", "Table expr", "{imax}", "logical operator", "double equal sign"}], Cell[OutputFormData["\<\ 0.02500620225009308736\ \>", "\<\ 0.0250062\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ {0.02500620225009308736, 0.02500620225009308736, 0.02500620225009308736, 0.02500620225009308736, 0.02500620225009308736}\ \>", "\<\ {0.0250062, 0.0250062, 0.0250062, 0.0250062, 0.0250062}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ {0.818175087080554621, 0.9134689103858987654, 0.1229923016852959362, 0.7318670766050867965, 0.5648010415145597162}\ \>", "\<\ {0.818175, 0.913469, 0.122992, 0.731867, 0.564801}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "In addition to the immediate and delayed assignment operators, ", StyleBox["Mathematica", FontSlant->"Italic"], " features a ", StyleBox["logical operator", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ". In ", StyleBox["Mathematica", FontSlant->"Italic"], ", the ", StyleBox["double equal sign", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " (lhs == rhs) tests whether ", StyleBox["lhs", FontSlant->"Italic"], " and ", StyleBox["rhs", FontSlant->"Italic"], " are equal, but causes no explicit action or assignment. When ", StyleBox["lhs == rhs", FontSlant->"Italic"], " is submitted to the Kernel, ", StyleBox["Mathematica", FontSlant->"Italic"], " returns True if ", StyleBox["lhs", FontSlant->"Italic"], " is equal to ", StyleBox["rhs", FontSlant->"Italic"], " and False if otherwise. \n\nIn the following example, note how ", StyleBox["Mathematica", FontSlant->"Italic"], " returns the original expression when it is unable to evaluate whether the \ result should be True or False." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "single equal sign", "immediate assignment operator", "colon equal sign", "delayed assignment operator", "Random", "Table expr", "{imax}", "logical operator", "double equal sign"}], Cell[CellGroupData[{ Cell[TextData["Clear[a]\na==7"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "single equal sign", "immediate assignment operator", "colon equal sign", "delayed assignment operator", "Random", "Table expr", "{imax}", "logical operator", "double equal sign"}], Cell[OutputFormData["\<\ a == 7\ \>", "\<\ a == 7\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Algebraic Manipulations in ", StyleBox["Mathematica ", FontSlant->"Italic"], "... 8" }], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " provides many functions for manipulating algebraic expressions including: \ ", StyleBox["Expand", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Together", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ",", StyleBox[" ", FontFamily->"Courier"], StyleBox["Apart", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Factor", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Simplify", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", and ", StyleBox["ComplexExpand", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". We'll use the first five of these functions to convert the following \ rational expression into several different forms. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "Clear[e, x]\ne = (x-1)^2 (2 + x) / ((1 + x) ( x - 3)^2)"], "Input", PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ ((-1 + x)^2*(2 + x))/((-3 + x)^2*(1 + x))\ \>", "\<\ 2 (-1 + x) (2 + x) ----------------- 2 (-3 + x) (1 + x)\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Expanding Numerators"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Expand expr"], Cell[TextData[{ StyleBox["Expand[expr]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " is used to expand out the products and positive integer powers in ", StyleBox["expr", FontSlant->"Italic"], ". The denominator in ", StyleBox["expr", FontSlant->"Italic"], " will be left in factored form. In the following Input cell, we use ", StyleBox["Expand", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to multiply out the products and powers of the expression we named ", StyleBox["e", FontSlant->"Italic"], " above. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Expand expr"], Cell[CellGroupData[{ Cell[TextData["Expand[e]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Expand expr"], Cell[OutputFormData[ "\<\ 2/((-3 + x)^2*(1 + x)) - (3*x)/((-3 + x)^2*(1 + x)) + x^3/((-3 + x)^2*(1 + x))\ \>", "\<\ 3 2 3 x x ----------------- - ----------------- + ----------------- 2 2 2 (-3 + x) (1 + x) (-3 + x) (1 + x) (-3 + x) (1 + x)\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Collecting Terms over a Common Denominator"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Together expr"], Cell[TextData[{ StyleBox["Together[expr]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " transforms a sum of terms into a single rational function. In the Input \ cell below, we use", StyleBox[" ", FontFamily->"Courier"], StyleBox["Together", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold"], "to collect all terms in the previous output over a common denominator." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Together expr"], Cell[CellGroupData[{ Cell[TextData["Together[%]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Together expr"], Cell[OutputFormData["\<\ (2 - 3*x + x^3)/((-3 + x)^2*(1 + x))\ \>", "\<\ 3 2 - 3 x + x ----------------- 2 (-3 + x) (1 + x)\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "Transforming a Rational Expression into its Partial Fractions"], "Subsection",\ Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Apart expr"], Cell[TextData[{ StyleBox["Apart[expr]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "transforms a rational expression into a sum of terms with simple \ denominators. ", StyleBox["Apart[expr]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " can be used as the inverse of ", StyleBox["Together", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". We will use ", StyleBox["Apart", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to give the partial fraction decomposition of the preceding output." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Apart expr"], Cell[CellGroupData[{ Cell[TextData["Apart[%]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Apart expr"], Cell[OutputFormData[ "\<\ 1 + 5/(-3 + x)^2 + 19/(4*(-3 + x)) + 1/(4*(1 + x))\ \>", "\<\ 5 19 1 1 + --------- + ---------- + --------- 2 4 (-3 + x) 4 (1 + x) (-3 + x)\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Factoring a Polynomial"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Factor expr"], Cell[TextData[{ StyleBox["Factor[poly]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " transforms a polynomial into a product of factors. Note that", StyleBox[" ", FontFamily->"Courier"], StyleBox["Factor", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " works only with integer or rational coefficients. In the Input cell \ below we use ", StyleBox["Factor", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to reduce the preceding output to a product of factors." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Factor expr"], Cell[CellGroupData[{ Cell[TextData["Factor[%]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Factor expr"], Cell[OutputFormData["\<\ ((-1 + x)^2*(2 + x))/((-3 + x)^2*(1 + x))\ \>", "\<\ 2 (-1 + x) (2 + x) ----------------- 2 (-3 + x) (1 + x)\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Simplifying Complicated Results"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Simplify expr"], Cell[TextData[{ "You can ask ", StyleBox["Mathematica", FontSlant->"Italic"], " to simplify a complicated result by using the built-in ", StyleBox["Simplify[expr]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " function. ", StyleBox["Simplify", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "will expand and factor parts of ", StyleBox["expr", FontSlant->"Italic"], " and will return the simplest transformation it can find. In the Input \ cell below, we use ", StyleBox["Simplify", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to have ", StyleBox["Mathematica", FontSlant->"Italic"], " return the simplest form of the expression ", StyleBox["e", FontSlant->"Italic"], " that it can find." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Simplify expr"], Cell[CellGroupData[{ Cell[TextData["Simplify[e]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Simplify expr"], Cell[OutputFormData["\<\ ((-1 + x)^2*(2 + x))/(9 + 3*x - 5*x^2 + x^3)\ \>", "\<\ 2 (-1 + x) (2 + x) ------------------- 2 3 9 + 3 x - 5 x + x\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Expanding Expressions involving Complex Numbers"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"ComplexExpand expr"], Cell[TextData[{ StyleBox["ComplexExpand", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontSlant->"Italic"], "can be used to expand expressions involving complex numbers. If the \ syntax ", StyleBox["ComplexExpand[expr]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " is used, ", StyleBox["Mathematica", FontSlant->"Italic"], " performs the expansion assuming all variables are real. Alternatively, ", StyleBox["ComplexExpand[expr, {x", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["1", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[", x", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["2", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[", ...}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold"], "can be used to expand an expression under the assumption that the \ variables ", StyleBox["x", FontSlant->"Italic"], StyleBox["i", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], " are complex. Following is an example computation for each of these forms \ of ", StyleBox["ComplexExpand", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"ComplexExpand expr"], Cell[CellGroupData[{ Cell[TextData[ "Clear[x, y]\nComplexExpand[ Sin[x + I y] ]\nComplexExpand[ Sin[x + I y], {x, \ y}]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"ComplexExpand expr"], Cell[OutputFormData["\<\ Cosh[y]*Sin[x] + I*Cos[x]*Sinh[y]\ \>", "\<\ Cosh[y] Sin[x] + I Cos[x] Sinh[y]\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ -(Cosh[Im[x] + Re[y]]*Sin[Im[y] - Re[x]]) + I*Cos[Im[y] - Re[x]]*Sinh[Im[x] + Re[y]]\ \>", "\<\ -(Cosh[Im[x] + Re[y]] Sin[Im[y] - Re[x]]) + I Cos[Im[y] - Re[x]] Sinh[Im[x] + Re[y]]\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Functions ... 10 "], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Built-in Functions"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"built-in functions", "*", "?", "??", "Options", "Alias"}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " features over 700 built-in functions. All ", StyleBox["Mathematica", FontSlant->"Italic"], " functions have names which begin with a capital letter. If the name \ includes two or more words, the first letter of each word is capitalized. In \ addition, function arguments are always enclosed in square brackets and \ separated by commas. \n\nYou can obtain information (such as the usage \ statement) about a particular ", StyleBox["Mathematica", FontSlant->"Italic"], " function by using the", StyleBox[" Open Function Browser", FontColor->RGBColor[1, 0, 0]], " command in the ", StyleBox["Help", FontColor->RGBColor[1, 0, 0]], " menu or by using the ", StyleBox["?", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " operator. For example, in the following Input cell, we use the", StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["?", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "operator to access ", StyleBox["Mathematica", FontSlant->"Italic"], "'s on-line help for the ", StyleBox["Plot", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " function." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"built-in functions", "*", "?", "??", "Options", "Alias"}], Cell[CellGroupData[{ Cell[TextData["?Plot"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"built-in functions", "*", "?", "??", "Options", "Alias"}], Cell[TextData[ "Plot[f, {x, xmin, xmax}] generates a plot of f as a\n function of x from \ xmin to xmax. Plot[{f1, f2, ...},\n {x, xmin, xmax}] plots several \ functions fi."], "Print", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "Note that the asterisk (", StyleBox["*", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ") wild card character can be used with the ", StyleBox["?", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " operator to match any alphanumeric character or sequence of characters in \ a partially written command name. In the case of duplicate matches, ", StyleBox["Mathematica", FontSlant->"Italic"], " will present a listing of all matching command names. For example, in \ the follwing Input cell, we request a listing of all commands that begin with \ ", StyleBox["Arc", FontSlant->"Italic"], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"built-in functions", "*", "?", "??", "Options", "Alias"}], Cell[CellGroupData[{ Cell[TextData["?Arc*"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"built-in functions", "*", "?", "??", "Options", "Alias"}], Cell[TextData[ "ArcCos ArcCot ArcCsc ArcSec ArcSin ArcTan ArcTanh\nArcCosh ArcCoth \ ArcCsch ArcSech ArcSinh"], "Print", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "Most functions feature options which can be specified in any order after \ the required arguments. Options are simply rules of the form ", StyleBox["OptionName", FontSlant->"Italic"], " -> ", StyleBox["OptionValue", FontSlant->"Italic"], ", where ", StyleBox["OptionName", FontSlant->"Italic"], " is the name of the option and ", StyleBox["OptionValue", FontSlant->"Italic"], " is the option's assigned value. If a value for an option is not \ specified, the default value will be used. To obtain a listing of default \ values for all options of a specific function, use ", StyleBox["??", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Courier"], "or the", StyleBox[" ", FontFamily->"Courier"], StyleBox["Options[ ]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Courier", FontColor->RGBColor[1, 0, 0]], "command. For example, in the following Input cell, we ask ", StyleBox["Mathematica", FontSlant->"Italic"], " to list default values for all options of the ", StyleBox["ContourPlot", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold"], "command. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"built-in functions", "*", "?", "??", "Options", "Alias"}], Cell[CellGroupData[{ Cell[TextData["??ContourPlot"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"built-in functions", "*", "?", "??", "Options", "Alias"}], Cell[TextData[ "ContourPlot[f, {x, xmin, xmax}, {y, ymin, ymax}]\n generates a contour \ plot of f as a function of x and\n y.\n\nAttributes[ContourPlot] = \ {HoldAll, Protected}\n \nOptions[ContourPlot] = \n {AspectRatio -> 1, Axes \ -> False, AxesLabel -> None, \n AxesOrigin -> Automatic, AxesStyle -> \ Automatic, \n Background -> Automatic, ColorFunction -> Automatic, \n \ ColorOutput -> Automatic, Compiled -> True, \n ContourLines -> True, \ Contours -> 10, \n ContourShading -> True, ContourSmoothing -> True, \n \ ContourStyle -> Automatic, DefaultColor -> Automatic, \n Epilog -> {}, \ Frame -> True, FrameLabel -> None, \n FrameStyle -> Automatic, FrameTicks \ -> Automatic, \n PlotLabel -> None, PlotPoints -> 15, \n PlotRange -> \ Automatic, PlotRegion -> Automatic, \n Prolog -> {}, RotateLabel -> True, \n\ Ticks -> Automatic, DefaultFont :> $DefaultFont, \n DisplayFunction :> \ $DisplayFunction}"], "Print", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["User-Defined Functions"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"user-defined function"], Cell[TextData[{ "In addition to featuring hundreds of built-in functions, ", StyleBox["Mathematica", FontSlant->"Italic"], " provides the capability of creating user-defined functions. Once a \ user-defined function has been created, it can be used over and over again \ during the ", StyleBox["Mathematica", FontSlant->"Italic"], " session.\n\nFor example, suppose we needed to create the function f(x) = \ x", StyleBox["2", FontVariations->{"CompatibilityType"->"Superscript"}], " + 3x - 5. The ", StyleBox["Mathematica", FontSlant->"Italic"], " command to create this function is ", StyleBox["f[x_] := x", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["2", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Superscript"}], StyleBox[" + 3x - 5", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". Note the use of the underscore on the left-hand side. The underscore \ is required when designating variables which are arguments for the function. \ In the following Input cell, we define", StyleBox[" ", FontWeight->"Bold"], StyleBox["f", FontSlant->"Italic"], " (being careful to first clear any old definitions) and then compute ", StyleBox["f", FontSlant->"Italic"], " for ", StyleBox["x", FontSlant->"Italic"], StyleBox[" = ", FontWeight->"Bold"], "2 and ", StyleBox["x", FontSlant->"Italic"], StyleBox[" = ", FontWeight->"Bold"], "a + b. Finally, we use ", StyleBox["f", FontSlant->"Italic"], " as an argument to the built-in ", StyleBox["Expand", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " function. 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Note that ", StyleBox["Solve", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " returns exact values (replacement rules involving integers, rationals and \ symbols).\n\nIn the following Input cell, we ask ", StyleBox["Mathematica", FontSlant->"Italic"], " to solve the quadratic equation 4x", StyleBox["2", FontVariations->{"CompatibilityType"->"Superscript"}], " + 2x - 2 = 0. Since it is a quadratic equation, ", StyleBox["Mathematica", FontSlant->"Italic"], " is able to compute explicit formulas for the solutions. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "Solve"}], Cell[CellGroupData[{ Cell[TextData["Clear[x]\nSolve[4 x^2 + 2 x - 2 == 0, x]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "Solve"}], Cell[OutputFormData["\<\ {{x -> -1}, {x -> 1/2}}\ \>", "\<\ 1 {{x -> -1}, {x -> -}} 2\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "Next, we ask ", StyleBox["Mathematica", FontSlant->"Italic"], " to solve an equation involving a power higher than four. Even though ", StyleBox["Mathematica", FontSlant->"Italic"], " can not find explicit formulas for the solutions, we are still able to \ find solutions numerically by using ", StyleBox["N", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "Solve"}], Cell[CellGroupData[{ Cell[TextData["Clear[x]\nSolve[x^5 - 4 x + 2 == 0, x]\nN[%]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "Solve"}], Cell[OutputFormData["\<\ {ToRules[Roots[-4*x + x^5 == -2, x]]}\ \>", "\<\ 5 {ToRules[Roots[-4 x + x == -2, x]]}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ {{x -> -1.518512152784911904}, {x -> -0.1167918612229820402 - 1.438447695329177034*I}, {x -> -0.1167918612229820402 + 1.438447695329177034*I}, {x -> 0.508499484657332797}, {x -> 1.243596390573543187}}\ \>", "\<\ {{x -> -1.51851}, {x -> -0.116792 - 1.43845 I}, {x -> -0.116792 + 1.43845 I}, {x -> 0.508499}, {x -> 1.2436}}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "Finally, we use ", StyleBox["Solve", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to solve a set of simultaneous equations." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "Solve"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[a, x, y]\nSolve[{a x + y == 0, 2 x + (1 - a) y == 1}, {x, y}]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "Solve"}], Cell[OutputFormData[ "\<\ {{x -> -(-2 + (1 - a)*a)^(-1), y -> a/(-2 + (1 - a)*a)}}\ \>", "\<\ 1 a {{x -> -(--------------), y -> --------------}} -2 + (1 - a) a -2 + (1 - a) a\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Roots"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Roots"], Cell[TextData[{ StyleBox["Roots[lhs==rhs, var]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " can be used to generate equations of the form ", StyleBox["var==r", FontSlant->"Italic"], StyleBox["i", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], " which represent the roots of the polynomial equation ", StyleBox["lhs=rhs", FontSlant->"Italic"], " . For example, in the Input cell below, we use ", StyleBox["Roots", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to find the roots of the equation x", StyleBox["2", FontVariations->{"CompatibilityType"->"Superscript"}], " + 3x = 2. Note the form of the resulting output (x == r", StyleBox["1", FontVariations->{"CompatibilityType"->"Subscript"}], " || x == r", StyleBox["2", FontVariations->{"CompatibilityType"->"Subscript"}], "). The symbol", StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["||", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " is ", StyleBox["Mathematica", FontSlant->"Italic"], "'s logical ", StyleBox["Or", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "function. Thus, the result tells us that ", StyleBox["x", FontSlant->"Italic"], " equals (-3 + Sqrt 17)/2 or ", StyleBox["x", FontSlant->"Italic"], " equals (-3 - Sqrt 17)/2." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Roots"], Cell[CellGroupData[{ Cell[TextData["Clear[x]\nRoots[x^2 + 3x ==2, x]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Roots"], Cell[OutputFormData[ "\<\ x == (-3 - 17^(1/2))/2 || x == (-3 + 17^(1/2))/2\ \>", "\<\ -3 - Sqrt[17] -3 + Sqrt[17] x == ------------- || x == ------------- 2 2\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["NRoots"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "NRoots"}], Cell[TextData[{ StyleBox["NRoots[lhs==rhs, var]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "gives a list of numerical approximations to the roots of the polynomial \ equation ", StyleBox["lhs", FontSlant->"Italic"], "=", StyleBox["rhs", FontSlant->"Italic"], ". In the following Input cell, we first use ", StyleBox["Roots", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to compute exact expressions for the roots of the equation x", StyleBox["2", FontVariations->{"CompatibilityType"->"Superscript"}], " + x + 1 = 0 and then use ", StyleBox["NRoots", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to obtain numerical approximations to these roots." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "NRoots"}], Cell[CellGroupData[{ Cell[TextData[ "Roots[x^2 + x + 1 == 0, x]\nNRoots[x^2 + x + 1 == 0, x]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "NRoots"}], Cell[OutputFormData[ "\<\ x == (-1 - I*3^(1/2))/2 || x == (-1 + I*3^(1/2))/2\ \>", "\<\ -1 - I Sqrt[3] -1 + I Sqrt[3] x == -------------- || x == -------------- 2 2\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ x == -0.5 - 0.8660254037844386468*I || x == -0.5 + 0.8660254037844386468*I\ \>", "\<\ x == -0.5 - 0.866025 I || x == -0.5 + 0.866025 I\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["FindRoot"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "FindRoot"}], Cell[TextData[{ StyleBox["FindRoot[lhs==rhs, {x, x", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["0", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox["}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " searches for a numerical solution to the equation ", StyleBox["lhs = rhs", FontSlant->"Italic"], ", starting with ", StyleBox["x = x", FontSlant->"Italic"], StyleBox["0", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], ". Note that since ", StyleBox["FindRoot", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Courier"], "uses Netwon's method, it may not always find the root nearest ", StyleBox["x", FontSlant->"Italic"], StyleBox["0", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], ". In the Input cell below, we use ", StyleBox["FindRoot", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Courier"], "to find the unique root for sin(e", StyleBox["x", FontVariations->{"CompatibilityType"->"Superscript"}], ") between 1 and 1.5." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "FindRoot"}], Cell[CellGroupData[{ Cell[TextData["FindRoot[Sin[Exp[x]], {x, 1, 1.5}]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Roots", "FindRoot"}], Cell[OutputFormData["\<\ {x -> 1.144729885851329273}\ \>", "\<\ {x -> 1.14473}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Calculus ... 17 "], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Limits"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Limits"], Cell[TextData[{ StyleBox["Limit[expr, x -> x", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["0", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox["]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " can be used to compute the limit of ", StyleBox["expr", FontSlant->"Italic"], " as ", StyleBox["x", FontSlant->"Italic"], " goes to", StyleBox[" x", FontSlant->"Italic"], StyleBox["0", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], ". The ", StyleBox["Direction -> 1", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold"], "option can be used to compute the limit as ", StyleBox["x", FontSlant->"Italic"], " approaches ", StyleBox["x", FontSlant->"Italic"], StyleBox["0", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], " from the left. Likewise, ", StyleBox["Direction -> -1", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " can be used to compute the limit as ", StyleBox["x", FontSlant->"Italic"], " approaches ", StyleBox["x", FontSlant->"Italic"], StyleBox["0", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], " from the right. For example, we use", StyleBox[" Limit ", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "below to compute the limit of sin(x) / x as ", StyleBox["x", FontSlant->"Italic"], " approaches 0." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Limits"], Cell[CellGroupData[{ Cell[TextData["Clear[x]\nLimit[Sin[x] / x, x -> 0]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Limits"], Cell[OutputFormData["\<\ 1\ \>", "\<\ 1\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "Note that on occasion, the output from the", StyleBox[" ", FontFamily->"Courier"], StyleBox["Limit", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Courier"], "command may be incorrect. Therefore it is prudent to check the result by \ making some plots and computing some numerical values around the limit." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Limits"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Differentiation"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Differentiation"], Cell[TextData[{ StyleBox["D[f, x]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " computes the derivative of ", StyleBox["f", FontSlant->"Italic"], " with respect to ", StyleBox["x", FontSlant->"Italic"], ". For example, we use ", StyleBox["D", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " below to calculate the derivative of x", StyleBox["2", FontVariations->{"CompatibilityType"->"Superscript"}], "y", StyleBox["3 ", FontVariations->{"CompatibilityType"->"Superscript"}], "with respect to ", StyleBox["x", FontSlant->"Italic"], ". " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Differentiation"], Cell[CellGroupData[{ Cell[TextData["Clear[x, y]\nD[x^2 y^3, x]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Differentiation"], Cell[OutputFormData["\<\ 2*x*y^3\ \>", "\<\ 3 2 x y\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "As another example, we use ", StyleBox["D", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " below to compute the derivative of x", StyleBox["2", FontVariations->{"CompatibilityType"->"Superscript"}], " y", StyleBox["3", FontVariations->{"CompatibilityType"->"Superscript"}], " with respect to ", StyleBox["y", FontSlant->"Italic"], ", then with respect to ", StyleBox["x", FontSlant->"Italic"], ". Note that the first variable listed is done last." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Differentiation"], Cell[CellGroupData[{ Cell[TextData["Clear[x, y]\nD[x^2 y^3, x, y]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Differentiation"], Cell[OutputFormData["\<\ 6*x*y^2\ \>", "\<\ 2 6 x y\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Integration"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Integration"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " can compute indefinite, definite, and multiple integrals of functions by \ using the built in ", StyleBox["Integrate", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " command. For example, ", StyleBox["Integrate[f, x]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " gives the indefinite integral of", StyleBox[" f", FontSlant->"Italic"], " with respect to", StyleBox[" x", FontSlant->"Italic"], ". Use", StyleBox[" ", FontWeight->"Bold"], StyleBox["Integrate[f, {x, xmin, xmax}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to compute the definite integral of ", StyleBox["f ", FontSlant->"Italic"], "with respect to ", StyleBox["x", FontSlant->"Italic"], " from ", StyleBox["x ", FontSlant->"Italic"], "equal ", StyleBox["xmin", FontSlant->"Italic"], " to", StyleBox[" x", FontSlant->"Italic"], " equal ", StyleBox["xmax", FontSlant->"Italic"], ". Finally, ", StyleBox["Integrate[f, {x, xmin, xmax}, {y, ymin, ymax}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " can be used to calculate multiple integrals. Following is an example of \ each type of computation." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Integration"], Cell[CellGroupData[{ Cell[TextData[ "Clear[a, x, y]\nIntegrate[a x^2, x]\nIntegrate[x^2, {x, 0, 1}]\n\ Integrate[x^2 y^3, x, y]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Integration"], Cell[OutputFormData["\<\ (a*x^3)/3\ \>", "\<\ 3 a x ---- 3\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ 1/3\ \>", "\<\ 1 - 3\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ (x^3*y^4)/12\ \>", "\<\ 3 4 x y ----- 12\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Sums"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Sums"], Cell[TextData[{ "Mathematica can be used to compute sums by using the command ", StyleBox["Sum[f, {i, imin, imax}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". Multiple sums can be calculated using ", StyleBox["Sum[f, {i, imin, imax}, {j, jmin, jmax}, ...]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". Note that for multiple sums, the outermost sum is given first. \ Examples appear below. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Sums"], Cell[CellGroupData[{ Cell[TextData[ "Clear[i]\nSum[1 / i^3, {i, 1, 20}]\nSum[x^i y^j, {i, 1, 3}, {j, 1, i}]\n"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Sums"], Cell[OutputFormData[ "\<\ 336658814638864376538323/280346265322438720204800\ \>", "\<\ 336658814638864376538323 ------------------------ 280346265322438720204800\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData[ "\<\ x*y + x^2*y + x^3*y + x^2*y^2 + x^3*y^2 + x^3*y^3\ \>", "\<\ 2 3 2 2 3 2 3 3 x y + x y + x y + x y + x y + x y\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "A third variant of the ", StyleBox["Sum", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " command,", StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["Sum[f, {i, imin, imax, di}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " can be used to compute a sum with ", StyleBox["i", FontSlant->"Italic"], " increasing in steps of ", StyleBox["di", FontSlant->"Italic"], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Sums"], Cell[CellGroupData[{ Cell[TextData["Clear[x, i]\nSum[x^i/i, {i, 1, 5, 2}]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Sums"], Cell[OutputFormData["\<\ x + x^3/3 + x^5/5\ \>", "\<\ 3 5 x x x + -- + -- 3 5\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Series"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Series"], Cell[TextData[{ StyleBox["Series[f, {x, x0, n}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold"], "computes a power series expansion for ", StyleBox["f", FontSlant->"Italic"], " about the point ", StyleBox["x", FontSlant->"Italic"], " = ", StyleBox["x", FontSlant->"Italic"], StyleBox["0", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], ", to order", StyleBox[" ", FontSlant->"Italic"], "(", StyleBox["x - x", FontSlant->"Italic"], StyleBox["0", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], ")", StyleBox["n", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Superscript"}], ". For example, in the following Input cell, we compute the power series \ expansion for exp(x) about the point ", StyleBox["x", FontSlant->"Italic"], " = 0 to order ", StyleBox["x", FontSlant->"Italic"], StyleBox["4", FontVariations->{"CompatibilityType"->"Superscript"}], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Series"], Cell[CellGroupData[{ Cell[TextData["Clear[x]\nSeries[Exp[x], {x, 1, 4}]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Series"], Cell[OutputFormData[ "\<\ SeriesData[x, 1, {E, E, E/2, E/6, E/24}, 0, 5, 1]\ \>", "\<\ 2 3 E (-1 + x) E (-1 + x) E + E (-1 + x) + ----------- + ----------- + 2 6 4 E (-1 + x) 5 ----------- + O[-1 + x] 24\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Products"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Product"], Cell[TextData[{ "Mathematica can be used to compute products by using the command ", StyleBox["Product[f, {i, imin, imax}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". Multiple products can be calculated using ", StyleBox["Product[f, {i, imin, imax}, {j, jmin, jmax}, ...]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". Note that for multiple products, the outermost product is given first. \ A third variant of the Product command, ", StyleBox["Product[f, {i, imin, imax, di}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " can be used to compute a product with ", StyleBox["i", FontSlant->"Italic"], " increasing in steps of ", StyleBox["di", FontSlant->"Italic"], ". An example of a computation involving the first variant of the ", StyleBox["Product", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " command is given below." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Product"], Cell[CellGroupData[{ Cell[TextData["Product[x + i, {i, 1, 4}]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Product"], Cell[OutputFormData["\<\ (1 + x)*(2 + x)*(3 + x)*(4 + x)\ \>", "\<\ (1 + x) (2 + x) (3 + x) (4 + x)\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Graphics ... 20 "], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " can be used to create plots of functions and data in two and three \ dimensions." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Plot"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "Plot", "PlotRange", "AxesLabel", "PlotStyle", "Frame", "PlotLabel", "PlotPoints"}], Cell[TextData[{ StyleBox["Plot[{f", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["1", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[", f", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["2", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[", ...}, {x, xmin, xmax}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Courier", FontWeight->"Bold"], "can be used to create a graph which includes the plots of the functions ", StyleBox["f", FontSlant->"Italic"], StyleBox["i", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox["(x)", FontSlant->"Italic"], " with ", StyleBox["x", FontSlant->"Italic"], " ranging from ", StyleBox["xmin ", FontSlant->"Italic"], "to ", StyleBox["xmax", FontSlant->"Italic"], ". In the Input cell below, we use ", StyleBox["Plot", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "to create a graph of the function f(x) = x", StyleBox["2", FontVariations->{"CompatibilityType"->"Superscript"}], " + 2x - 3, with ", StyleBox["x", FontSlant->"Italic"], " ranging from -5 to 5. 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We \ use the", StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["Options", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " command to list default values for the options of the ", StyleBox["Plot", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " command. 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FontColor->RGBColor[1, 0, 0]], " uses a finite number of sample points to produce a plot, the resulting \ plot may not be an accurate representation of the specified function. 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PageBreakAbove->True, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["ParametricPlot3D"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"ParametricPlot3D"], Cell[TextData[{ StyleBox["ParametricPlot3D[{f", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["x", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[", f", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["y", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[", f", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["z", FontFamily->"Courier", FontWeight->"Bold", 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Command arguments \ include a domain for ", StyleBox["t", FontSlant->"Italic"], ", and equations for", StyleBox[" x", FontSlant->"Italic"], ", ", StyleBox["y", FontSlant->"Italic"], ", and ", StyleBox["z", FontSlant->"Italic"], ", specified in terms of ", StyleBox["t", FontSlant->"Italic"], ". In the following Input cell, we use another form of ", StyleBox["ParametricPlot3D", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to create the surface shown below. In this case, the resulting \ three-dimensional surface has been parametrized by two variables,", StyleBox[" t ", FontSlant->"Italic"], "and ", StyleBox["p", FontSlant->"Italic"], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"ParametricPlot3D"], Cell[CellGroupData[{ Cell[TextData[ "Clear[t, p]\nParametricPlot3D[(3 Cos[t]^2 -1)^2 {Sin[t] Cos[p],\nSin[t] \ Sin[p], Cos[t]}, {t, 0, Pi}, {p, 0, 2Pi},\nPlotPoints -> 30];"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->"ParametricPlot3D"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 2.54181 MathPictureStart %% Graphics3D /Courier findfont 10 scalefont setfont % Scaling calculations -0.759707 2.53069 -0.0521518 2.53069 [ [(-1)] .38755 2.50856 .00953 -1 Msboxa [(-0.5)] .52012 2.47499 -0.00117 -1 Msboxa [(0)] .65461 2.44093 -0.01209 -1 Msboxa [(0.5)] .79105 2.40638 -0.02322 -1 Msboxa [(1)] .92949 2.37132 -0.03458 -1 Msboxa [(-1)] .03742 2.22337 1 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.58114 .44626 m .50497 .36125 L .5623 .45593 L closepath p .643 .632 .824 r F P s P p .002 w .5623 .45593 m .6074 .5946 L .64122 .57765 L p .591 .498 .718 r F P s P p .002 w .64122 .57765 m .58114 .44626 L .5623 .45593 L p .591 .498 .718 r F P s P p .002 w .43024 .44716 m .3713 .57923 L .40556 .59578 L p .804 .671 .717 r F P s P p .002 w .38156 .75542 m .40556 .59578 L .3713 .57923 L p .832 .628 .626 r F P s P p .002 w .40556 .59578 m .38156 .75542 L .42961 .76916 L p .788 .584 .625 r F P s P p .002 w .43024 .44716 m .50497 .36125 L .41456 .43517 L closepath p .754 .732 .832 r F P s P p .002 w .3713 .57923 m .43024 .44716 L .41456 .43517 L p .836 .713 .728 r F P s P p .002 w .6074 .5946 m .63212 .754 L .67421 .73345 L p .542 .391 .626 r F P s P p .002 w .67421 .73345 m .64122 .57765 L .6074 .5946 L p .542 .391 .626 r F P s P p .002 w .59651 .43408 m .50497 .36125 L .58114 .44626 L closepath p .624 .627 .833 r F P s P p .002 w .58114 .44626 m .64122 .57765 L .66893 .55626 L p .541 .473 .729 r F P s P p .002 w .66893 .55626 m .59651 .43408 L .58114 .44626 L p .541 .473 .729 r F P s P p .002 w .41456 .43517 m .50497 .36125 L .40303 .42117 L closepath p .763 .753 .844 r F P s P p .002 w .34303 .55817 m .41456 .43517 L .40303 .42117 L p .869 .762 .742 r F P s P p .002 w .41456 .43517 m .34303 .55817 L .3713 .57923 L p .836 .713 .728 r F P s P p .002 w .60767 .41995 m .50497 .36125 L .59651 .43408 L closepath p .604 .625 .845 r F P s P p .002 w .59651 .43408 m .66893 .55626 L .68923 .53137 L p .48 .447 .743 r F P s P p .002 w .68923 .53137 m .60767 .41995 L .59651 .43408 L p .48 .447 .743 r F P s P p .002 w .33893 .73536 m .3713 .57923 L .34303 .55817 L p .88 .679 .626 r F P s P p .002 w .3713 .57923 m .33893 .73536 L .38156 .75542 L p .832 .628 .626 r F P s P p .002 w .64122 .57765 m .67421 .73345 L .7088 .70748 L p .463 .339 .626 r F P s P p .002 w .7088 .70748 m .66893 .55626 L .64122 .57765 L p .463 .339 .626 r F P s P p .002 w .40303 .42117 m .50497 .36125 L .3962 .40581 L closepath p .769 .776 .859 r F P s P p .002 w .32207 .53353 m .40303 .42117 L .3962 .40581 L p .9 .821 .76 r F P s P p .002 w .40303 .42117 m .32207 .53353 L .34303 .55817 L p .869 .762 .742 r F P s P p .002 w .61408 .4045 m .50497 .36125 L .60767 .41995 L closepath p .584 .627 .86 r F P s P p .002 w .60767 .41995 m .68923 .53137 L .7011 .50406 L p .402 .418 .762 r F P s P p .002 w .7011 .50406 m .61408 .4045 L .60767 .41995 L p .402 .418 .762 r F P s P p .002 w .55096 .3247 m .50497 .36125 L .57169 .33302 L closepath p .516 .732 .972 r F P s P p .002 w .52802 .31959 m .50497 .36125 L .55096 .3247 L closepath p .53 .763 .983 r F P s P p .002 w .50396 .31796 m .50497 .36125 L .52802 .31959 L closepath p .555 .794 .988 r F P s P p .002 w .47996 .31988 m .50497 .36125 L .50396 .31796 L closepath p .59 .821 .988 r F P s P p .002 w .45716 .32527 m .50497 .36125 L .47996 .31988 L closepath p .629 .843 .982 r F P s P p .002 w .43666 .33384 m .50497 .36125 L .45716 .32527 L closepath p .669 .855 .971 r F P s P p .002 w .41944 .34518 m .50497 .36125 L .43666 .33384 L closepath p .705 .859 .955 r F P s P p .002 w .58922 .34415 m .50497 .36125 L .60272 .35754 L closepath p .518 .678 .938 r F P s P p .002 w .57169 .33302 m .50497 .36125 L .58922 .34415 L closepath p .513 .704 .957 r F P s P p .002 w .4063 .35873 m .50497 .36125 L .41944 .34518 L closepath p .734 .852 .936 r F P s P p .002 w .39784 .37384 m .50497 .36125 L .4063 .35873 L closepath p .754 .839 .916 r F P s P p .002 w .39443 .38978 m .50497 .36125 L .39784 .37384 L closepath p .766 .82 .895 r F P s P p .002 w .3962 .40581 m .50497 .36125 L .39443 .38978 L closepath p .77 .799 .876 r F P s P p .002 w .61542 .38845 m .50497 .36125 L .61408 .4045 L closepath p .564 .633 .878 r F P s P p .002 w .61158 .37255 m .50497 .36125 L .61542 .38845 L closepath p .546 .643 .897 r F P s P p .002 w .60272 .35754 m .50497 .36125 L .61158 .37255 L closepath p .53 .658 .918 r F P s P p .002 w .48077 .9318 m .48094 .77602 L .42961 .76916 L p .741 .485 .543 r F P s P p .002 w .48094 .77602 m .48077 .9318 L .53348 .93151 L p .689 .443 .544 r F P s P p .002 w .53348 .93151 m .53331 .77572 L .48094 .77602 L p .689 .443 .544 r F P s P p .002 w .53331 .77572 m .53348 .93151 L .58495 .9242 L p .633 .397 .543 r F P s P p .002 w .58495 .9242 m .58445 .76828 L .53331 .77572 L p .633 .397 .543 r F P s P p .002 w .30365 .70981 m .34303 .55817 L .32207 .53353 L p .931 .741 .623 r F P s P p .002 w .34303 .55817 m .30365 .70981 L .33893 .73536 L p .88 .679 .626 r F P s P p .002 w .66893 .55626 m .7088 .70748 L .73424 .67721 L p .353 .271 .623 r F P s P p .002 w .73424 .67721 m .68923 .53137 L .66893 .55626 L p .353 .271 .623 r F P s P p .002 w .30948 .50638 m .3962 .40581 L .39443 .38978 L p .923 .89 .781 r F P s P p .002 w .3962 .40581 m .30948 .50638 L .32207 .53353 L p .9 .821 .76 r F P s P p .002 w .61408 .4045 m .7011 .50406 L .70388 .47558 L p .294 .382 .782 r F P s P p .002 w .70388 .47558 m .61542 .38845 L .61408 .4045 L p .294 .382 .782 r F P s P p .002 w .42912 .92506 m .42961 .76916 L .38156 .75542 L p .793 .529 .538 r F P s P p .002 w .42961 .76916 m .42912 .92506 L .48077 .9318 L p .741 .485 .543 r F P s P p .002 w .58445 .76828 m .58495 .9242 L .63292 .91017 L p .568 .345 .537 r F P s P p .002 w .63292 .91017 m .63212 .754 L .58445 .76828 L p .568 .345 .537 r F P s P p .002 w .30592 .47795 m .39443 .38978 L .39784 .37384 L p .918 .96 .794 r F P s P p .002 w .39443 .38978 m .30592 .47795 L .30948 .50638 L p .923 .89 .781 r F P s P p .002 w .61542 .38845 m .70388 .47558 L .69733 .44726 L p .14 .332 .795 r F P s P p .002 w .69733 .44726 m .61158 .37255 L .61542 .38845 L p .14 .332 .795 r F P s P p .002 w .38077 .91157 m .38156 .75542 L .33893 .73536 L p .846 .575 .528 r F P s P p .002 w .38156 .75542 m .38077 .91157 L .42912 .92506 L p .793 .529 .538 r F P s P p .002 w .63212 .754 m .63292 .91017 L .67529 .89 L p .486 .281 .527 r F P s P p .002 w .67529 .89 m .67421 .73345 L .63212 .754 L p .486 .281 .527 r F P s P p .002 w .2774 .67984 m .32207 .53353 L .30948 .50638 L p .979 .814 .608 r F P s P p .002 w .32207 .53353 m .2774 .67984 L .30365 .70981 L p .931 .741 .623 r F P s P p .002 w .68923 .53137 m .73424 .67721 L .74925 .64395 L p .184 .169 .606 r F P s P p .002 w .74925 .64395 m .7011 .50406 L .68923 .53137 L p .184 .169 .606 r F P s P p .002 w .31169 .44956 m .39784 .37384 L .4063 .35873 L p .842 .997 .774 r F P s P p .002 w .39784 .37384 m .31169 .44956 L .30592 .47795 L p .918 .96 .794 r F P s P p .002 w .61158 .37255 m .69733 .44726 L .68166 .42043 L p 0 .259 .769 r F P s P p .002 w .68166 .42043 m .60272 .35754 L .61158 .37255 L p 0 .259 .769 r F P s P p .002 w .33786 .89187 m .33893 .73536 L .30365 .70981 L p .903 .627 .508 r F P s P p .002 w .33893 .73536 m .33786 .89187 L .38077 .91157 L p .846 .575 .528 r F P s P p .002 w .67421 .73345 m .67529 .89 L .7101 .8645 L p .372 .193 .505 r F P s P p .002 w .7101 .8645 m .7088 .70748 L .67421 .73345 L p .372 .193 .505 r F P s P p .002 w .32663 .42255 m .4063 .35873 L .41944 .34518 L p .631 .928 .672 r F P s P p .002 w .4063 .35873 m .32663 .42255 L .31169 .44956 L p .842 .997 .774 r F P s P p .002 w .60272 .35754 m .68166 .42043 L .65749 .3964 L p 0 .159 .659 r F P s P p .002 w .65749 .3964 m .58922 .34415 L .60272 .35754 L p 0 .159 .659 r F P s P p .002 w .26148 .64677 m .30948 .50638 L .30592 .47795 L p .99 .882 .553 r F P s P p .002 w .30948 .50638 m .26148 .64677 L .2774 .67984 L p .979 .814 .608 r F P s P p .002 w .7011 .50406 m .74925 .64395 L .75298 .60919 L p 0 .005 .545 r F P s P p .002 w .75298 .60919 m .70388 .47558 L .7011 .50406 L p 0 .005 .545 r F P s P p .002 w .41944 .34518 m .35013 .39825 L .32663 .42255 L p .631 .928 .672 r F P s P p .002 w .35013 .39825 m .41944 .34518 L .43666 .33384 L p 0 0 0 r F P s P p .002 w .58922 .34415 m .65749 .3964 L .62592 .37638 L p .5 0 0 r F P s P p .002 w .62592 .37638 m .57169 .33302 L .58922 .34415 L p .5 0 0 r F P s P p .002 w .30235 .86678 m .30365 .70981 L .2774 .67984 L p .961 .684 .465 r F P s P p .002 w .30365 .70981 m .30235 .86678 L .33786 .89187 L p .903 .627 .508 r F P s P p .002 w .7088 .70748 m .7101 .8645 L .73571 .83478 L p .197 .061 .459 r F P s P p .002 w .73571 .83478 m .73424 .67721 L .7088 .70748 L p .197 .061 .459 r F P s P p .002 w .38114 .37785 m .43666 .33384 L .45716 .32527 L p 0 0 0 r F P s P p .002 w .43666 .33384 m .38114 .37785 L .35013 .39825 L p 0 0 0 r F P s P p .002 w .57169 .33302 m .62592 .37638 L .58842 .36137 L p .565 0 0 r F P s P p .002 w .58842 .36137 m .55096 .3247 L .57169 .33302 L p .565 0 0 r F P s P p .002 w .25679 .61207 m .30592 .47795 L .31169 .44956 L p .842 .848 .387 r F P s P p .002 w .30592 .47795 m .25679 .61207 L .26148 .64677 L p .99 .882 .553 r F P s P p .002 w .41821 .3624 m .45716 .32527 L .47996 .31988 L p .222 0 0 r F P s P p .002 w .45716 .32527 m .41821 .3624 L .38114 .37785 L p 0 0 0 r F P s P p .002 w .70388 .47558 m .75298 .60919 L .74507 .57454 L p 0 0 .366 r F P s P p .002 w .74507 .57454 m .69733 .44726 L .70388 .47558 L p 0 0 .366 r F P s P p .002 w .55096 .3247 m .58842 .36137 L .54681 .35216 L p .547 0 0 r F P s P p .002 w .54681 .35216 m .52802 .31959 L .55096 .3247 L p .547 0 0 r F P s P p .002 w .45955 .35268 m .47996 .31988 L .50396 .31796 L p .376 0 0 r F P s P p .002 w .47996 .31988 m .45955 .35268 L .41821 .3624 L p .222 0 0 r F P s P p .002 w .52802 .31959 m .54681 .35216 L .50314 .34921 L p .481 0 0 r F P s P p .002 w .50314 .34921 m .50396 .31796 L .52802 .31959 L p .481 0 0 r F P s P p .002 w .50396 .31796 m .50314 .34921 L .45955 .35268 L p .376 0 0 r F P s P p .002 w .48473 1.06008 m .48077 .9318 L .42912 .92506 L p .729 .413 .446 r F P s P p .002 w .48077 .9318 m .48473 1.06008 L .52879 1.05984 L p .669 .365 .45 r F P s P p .002 w .52879 1.05984 m .53348 .93151 L .48077 .9318 L p .669 .365 .45 r F P s P p .002 w .53348 .93151 m .52879 1.05984 L .5718 1.05386 L p .602 .31 .445 r F P s P p .002 w .5718 1.05386 m .58495 .9242 L .53348 .93151 L p .602 .31 .445 r F P s P p .002 w .27592 .83736 m .2774 .67984 L .26148 .64677 L p .989 .73 .367 r F P s P p .002 w .2774 .67984 m .27592 .83736 L .30235 .86678 L p .961 .684 .465 r F P s P p .002 w .73424 .67721 m .73571 .83478 L .75083 .80211 L p 0 0 .354 r F P s P p .002 w .75083 .80211 m .74925 .64395 L .73424 .67721 L p 0 0 .354 r F P s P p .002 w .44155 1.05457 m .42912 .92506 L .38077 .91157 L p .787 .458 .432 r F P s P p .002 w .42912 .92506 m .44155 1.05457 L .48473 1.06008 L p .729 .413 .446 r F P s P p .002 w .58495 .9242 m .5718 1.05386 L .61186 1.04238 L p .521 .241 .43 r F P s P p .002 w .61186 1.04238 m .63292 .91017 L .58495 .9242 L p .521 .241 .43 r F P s P p .002 w .31169 .44956 m .26374 .57735 L .25679 .61207 L p .842 .848 .387 r F P s P p .002 w .26374 .57735 m .31169 .44956 L .32663 .42255 L p 0 0 0 r F P s P p .002 w .69733 .44726 m .74507 .57454 L .72572 .54165 L p .826 .443 0 r F P s P p .002 w .72572 .54165 m .68166 .42043 L .69733 .44726 L p .826 .443 0 r F P s P p .002 w .40118 1.04353 m .38077 .91157 L .33786 .89187 L p .845 .502 .403 r F P s P p .002 w .38077 .91157 m .40118 1.04353 L .44155 1.05457 L p .787 .458 .432 r F P s P p .002 w .63292 .91017 m .61186 1.04238 L .64718 1.02589 L p .412 .148 .4 r F P s P p .002 w .64718 1.02589 m .67529 .89 L .63292 .91017 L p .412 .148 .4 r F P s P p .002 w .25989 .80488 m .26148 .64677 L .25679 .61207 L p .86 .677 .145 r F P s P p .002 w .26148 .64677 m .25989 .80488 L .27592 .83736 L p .989 .73 .367 r F P s P p .002 w .28216 .54426 m .32663 .42255 L .35013 .39825 L p 0 0 .15 r F P s P p .002 w .32663 .42255 m .28216 .54426 L .26374 .57735 L p 0 0 0 r F P s P p .002 w .74925 .64395 m .75083 .80211 L .75459 .76797 L p 0 0 .12 r F P s P p .002 w .75459 .76797 m .75298 .60919 L .74925 .64395 L p 0 0 .12 r F P s P p .002 w .68166 .42043 m .72572 .54165 L .69569 .51214 L p .908 .5 .165 r F P s P p .002 w .69569 .51214 m .65749 .3964 L .68166 .42043 L p .908 .5 .165 r F P s P p .002 w .3654 1.02742 m .33786 .89187 L .30235 .86678 L p .903 .543 .347 r F P s P p .002 w .33786 .89187 m .3654 1.02742 L .40118 1.04353 L p .845 .502 .403 r F P s P p .002 w .67529 .89 m .64718 1.02589 L .67614 1.00508 L p .251 .01 .34 r F P s P p .002 w .67614 1.00508 m .7101 .8645 L .67529 .89 L p .251 .01 .34 r F P s P p .002 w .31134 .51441 m .35013 .39825 L .38114 .37785 L p .254 0 .282 r F P s P p .002 w .35013 .39825 m .31134 .51441 L .28216 .54426 L p 0 0 .15 r F P s P p .002 w .65749 .3964 m .69569 .51214 L .65632 .48751 L p .875 .483 .289 r F P s P p .002 w .65632 .48751 m .62592 .37638 L .65749 .3964 L p .875 .483 .289 r F P s P p .002 w .33586 1.00694 m .30235 .86678 L .27592 .83736 L p .939 .569 .235 r F P s P p .002 w .30235 .86678 m .33586 1.00694 L .3654 1.02742 L p .903 .543 .347 r F P s P p .002 w .25679 .61207 m .25517 .7708 L .25989 .80488 L p .86 .677 .145 r F P s P p .002 w .25517 .7708 m .25679 .61207 L .26374 .57735 L p 0 0 .169 r F P s P p .002 w .7101 .8645 m .67614 1.00508 L .69736 .98084 L p 0 0 .221 r F P s P p .002 w .69736 .98084 m .73571 .83478 L .7101 .8645 L p 0 0 .221 r F P s P p .002 w .75298 .60919 m .75459 .76797 L .74663 .73394 L p .911 .694 .192 r F P s P p .002 w .74663 .73394 m .74507 .57454 L .75298 .60919 L p .911 .694 .192 r F P s P p .002 w .35 .48933 m .38114 .37785 L .41821 .3624 L p .42 .121 .348 r F P s P p .002 w .38114 .37785 m .35 .48933 L .31134 .51441 L p .254 0 .282 r F P s P p .002 w .62592 .37638 m .65632 .48751 L .60946 .46903 L p .816 .445 .352 r F P s P p .002 w .60946 .46903 m .58842 .36137 L .62592 .37638 L p .816 .445 .352 r F P s P p .002 w .39633 .4703 m .41821 .3624 L .45955 .35268 L p .533 .22 .382 r F P s P p .002 w .41821 .3624 m .39633 .4703 L .35 .48933 L p .42 .121 .348 r F P s P p .002 w .58842 .36137 m .60946 .46903 L .55738 .45767 L p .754 .4 .384 r F P s P p .002 w .55738 .45767 m .54681 .35216 L .58842 .36137 L p .754 .4 .384 r F P s P p .002 w .31394 .98294 m .27592 .83736 L .25989 .80488 L p .864 .522 .012 r F P s P p .002 w .27592 .83736 m .31394 .98294 L .33586 1.00694 L p .939 .569 .235 r F P s P p .002 w .73571 .83478 m .69736 .98084 L .70979 .95425 L p 0 0 0 r F P s P p .002 w .70979 .95425 m .75083 .80211 L .73571 .83478 L p 0 0 0 r F P s P p .002 w .26215 .7367 m .26374 .57735 L .28216 .54426 L p 0 0 .375 r F P s P p .002 w .26374 .57735 m .26215 .7367 L .25517 .7708 L p 0 0 .169 r F P s P p .002 w .44807 .45832 m .45955 .35268 L .50314 .34921 L p .618 .292 .396 r F P s P p .002 w .45955 .35268 m .44807 .45832 L .39633 .4703 L p .533 .22 .382 r F P s P p .002 w .54681 .35216 m .55738 .45767 L .50266 .45403 L p .689 .351 .397 r F P s P p .002 w .50266 .45403 m .50314 .34921 L .54681 .35216 L p .689 .351 .397 r F P s P p .002 w .74507 .57454 m .74663 .73394 L .72716 .70163 L p .987 .713 .386 r F P s P p .002 w .72716 .70163 m .72572 .54165 L .74507 .57454 L p .987 .713 .386 r F P s P p .002 w .50314 .34921 m .50266 .45403 L .44807 .45832 L p .618 .292 .396 r F P s P p .002 w .49135 1.14867 m .48473 1.06008 L .44155 1.05457 L p .7 .314 .315 r F P s P p .002 w .48473 1.06008 m .49135 1.14867 L .52095 1.14851 L p .632 .261 .323 r F P s P p .002 w .52095 1.14851 m .52879 1.05984 L .48473 1.06008 L p .632 .261 .323 r F P s P p .002 w .52879 1.05984 m .52095 1.14851 L .54983 1.14456 L p .552 .193 .313 r F P s P p .002 w .54983 1.14456 m .5718 1.05386 L .52879 1.05984 L p .552 .193 .313 r F P s P p .002 w .46236 1.14502 m .44155 1.05457 L .40118 1.04353 L p .761 .357 .286 r F P s P p .002 w .44155 1.05457 m .46236 1.14502 L .49135 1.14867 L p .7 .314 .315 r F P s P p .002 w .5718 1.05386 m .54983 1.14456 L .57669 1.13697 L p .449 .101 .282 r F P s P p .002 w .57669 1.13697 m .61186 1.04238 L .5718 1.05386 L p .449 .101 .282 r F P s P p .002 w .25989 .80488 m .30075 .95651 L .31394 .98294 L p .864 .522 .012 r F P s P p .002 w .30075 .95651 m .25989 .80488 L .25517 .7708 L p 0 0 .296 r F P s P p .002 w .75083 .80211 m .70979 .95425 L .71274 .92651 L p .85 .807 .319 r F P s P p .002 w .71274 .92651 m .75459 .76797 L .75083 .80211 L p .85 .807 .319 r F P s P p .002 w .28068 .70419 m .28216 .54426 L .31134 .51441 L p .25 .094 .465 r F P s P p .002 w .28216 .54426 m .28068 .70419 L .26215 .7367 L p 0 0 .375 r F P s P p .002 w .72572 .54165 m .72716 .70163 L .69694 .67265 L p .945 .661 .47 r F P s P p .002 w .69694 .67265 m .69569 .51214 L .72572 .54165 L p .945 .661 .47 r F P s P p .002 w .43528 1.13772 m .40118 1.04353 L .3654 1.02742 L p .817 .388 .226 r F P s P p .002 w .40118 1.04353 m .43528 1.13772 L .46236 1.14502 L p .761 .357 .286 r F P s P p .002 w .61186 1.04238 m .57669 1.13697 L .60032 1.12608 L p .303 0 .22 r F P s P p .002 w .60032 1.12608 m .64718 1.02589 L .61186 1.04238 L p .303 0 .22 r F P s P p .002 w .41135 1.12709 m .3654 1.02742 L .33586 1.00694 L p .852 .4 .114 r F P s P p .002 w .3654 1.02742 m .41135 1.12709 L .43528 1.13772 L p .817 .388 .226 r F P s P p .002 w .64718 1.02589 m .60032 1.12608 L .61961 1.11236 L p .077 0 .1 r F P s P p .002 w .61961 1.11236 m .67614 1.00508 L .64718 1.02589 L p .077 0 .1 r F P s P p .002 w .31005 .67488 m .31134 .51441 L .35 .48933 L p .41 .217 .505 r F P s P p .002 w .31134 .51441 m .31005 .67488 L .28068 .70419 L p .25 .094 .465 r F P s P p .002 w .297 .92881 m .25517 .7708 L .26215 .7367 L p 0 0 .497 r F P s P p .002 w .25517 .7708 m .297 .92881 L .30075 .95651 L p 0 0 .296 r F P s P p .002 w .69569 .51214 m .69694 .67265 L .65732 .64845 L p .884 .604 .507 r F P s P p .002 w .65732 .64845 m .65632 .48751 L .69569 .51214 L p .884 .604 .507 r F P s P p .002 w .75459 .76797 m .71274 .92651 L .70594 .89891 L p .996 .848 .506 r F P s P p .002 w .70594 .89891 m .74663 .73394 L .75459 .76797 L p .996 .848 .506 r F P s P p .002 w .39166 1.11359 m .33586 1.00694 L .31394 .98294 L p .812 .356 0 r F P s P p .002 w .33586 1.00694 m .39166 1.11359 L .41135 1.12709 L p .852 .4 .114 r F P s P p .002 w .67614 1.00508 m .61961 1.11236 L .63366 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1.30171 L .34488 1.28402 L p .768 .716 .803 r F P s P p .002 w .36558 1.36512 m .36588 1.34085 L .31777 1.32029 L p .845 .578 .533 r F P s P p .002 w .62751 1.30045 m .64821 1.33939 L .69572 1.31833 L p .619 .595 .804 r F P s P p .002 w .64821 1.33939 m .64852 1.36366 L .69613 1.34266 L p .489 .287 .532 r F P s P p .002 w .69613 1.34266 m .69572 1.31833 L .64821 1.33939 L p .489 .287 .532 r F P s P p .002 w .36621 1.06237 m .297 .92881 L .30299 .90115 L p .113 .183 .658 r F P s P p .002 w .297 .92881 m .36621 1.06237 L .36851 1.08048 L p 0 .017 .584 r F P s P p .002 w .71274 .92651 m .64354 1.06087 L .63881 1.04288 L p .98 .886 .661 r F P s P p .002 w .63881 1.04288 m .70594 .89891 L .71274 .92651 L p .98 .886 .661 r F P s P p .002 w .3431 .85112 m .31005 .67488 L .34896 .65023 L p .476 .331 .605 r F P s P p .002 w .31005 .67488 m .3431 .85112 L .31857 .87482 L p .364 .256 .596 r F P s P p .002 w .69694 .67265 m .66436 .84932 L .63137 .82979 L p .869 .652 .605 r F P s P p .002 w .63137 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1.23058 L .50965 1.23137 L p .632 .541 .734 r F P s P p .002 w .51247 1.23058 m .53967 1.30345 L .55106 1.29832 L p .589 .518 .742 r F P s P p .002 w .53967 1.30345 m .57861 1.43384 L .60287 1.4232 L p .573 .476 .706 r F P s P p .002 w .60287 1.4232 m .55106 1.29832 L .53967 1.30345 L p .573 .476 .706 r F P s P p .002 w .51879 1.20118 m .50561 1.21291 L .50555 1.21283 L p .852 .812 .809 r F P s P p .002 w .50555 1.21283 m .51761 1.19947 L .51879 1.20118 L p .852 .812 .809 r F P s P p .002 w .52949 1.2357 m .50552 1.21406 L .50559 1.21397 L p .557 .592 .845 r F P s P p .002 w .50559 1.21397 m .53244 1.23237 L .52949 1.2357 L p .557 .592 .845 r F P s P p .002 w .50455 1.21419 m .49759 1.23066 L .50043 1.23142 L p .762 .67 .76 r F P s P p .002 w .50043 1.23142 m .50469 1.21423 L .50455 1.21419 L p .762 .67 .76 r F P s P p .002 w .50965 1.23137 m .50515 1.21422 L .505 1.21424 L p .673 .591 .755 r F P s P p .002 w .50515 1.21422 m .50965 1.23137 L .51247 1.23058 L p .639 .57 .761 r F P s P 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1.21406 m .49304 1.22817 L .49508 1.22956 L p .817 .742 .781 r F P s P p .002 w .49508 1.22956 m .50442 1.21413 L .50432 1.21406 L p .817 .742 .781 r F P s P p .002 w .45963 1.2988 m .49508 1.22956 L .49304 1.22817 L p .835 .734 .753 r F P s P p .002 w .59351 1.16875 m .66849 1.14753 L .65507 1.12711 L p .703 .77 .904 r F P s P p .002 w .65507 1.12711 m .58612 1.15775 L .59351 1.16875 L p .703 .77 .904 r F P s P p .002 w .51494 1.22946 m .50542 1.21413 L .50529 1.21418 L p .602 .55 .77 r F P s P p .002 w .50542 1.21413 m .51494 1.22946 L .51694 1.22804 L p .559 .533 .783 r F P s P p .002 w .51494 1.22946 m .55106 1.29832 L .56033 1.29188 L p .539 .494 .754 r F P s P p .002 w .56033 1.29188 m .51694 1.22804 L .51494 1.22946 L p .539 .494 .754 r F P s P p .002 w .51694 1.22804 m .50552 1.21406 L .50542 1.21413 L p .559 .533 .783 r F P s P p .002 w .53088 1.19248 m .50555 1.21283 L .50561 1.21291 L p .8 .801 .852 r F P s P p .002 w .47759 1.23266 m .50425 1.21398 L .50432 1.21406 L p .795 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1.21389 L .50419 1.2138 L p .872 .895 .847 r F P s P p .002 w .5042 1.21389 m .49068 1.22478 L .49155 1.22655 L p .862 .838 .821 r F P s P p .002 w .50563 1.21389 m .53411 1.22873 L .53244 1.23237 L p .52 .59 .865 r F P s P p .002 w .53411 1.22873 m .50563 1.21389 L .50564 1.21379 L p .478 .591 .888 r F P s P p .002 w .50563 1.21389 m .51919 1.22463 L .51934 1.22279 L p .365 .486 .849 r F P s P p .002 w .51934 1.22279 m .50564 1.21379 L .50563 1.21389 L p .365 .486 .849 r F P s P p .002 w .50168 1.19521 m .50475 1.21262 L .50461 1.21265 L p .656 .58 .757 r F P s P p .002 w .50461 1.21265 m .49873 1.19581 L .50168 1.19521 L p .656 .58 .757 r F P s P p .002 w .49607 1.19678 m .46422 1.12577 L .47645 1.12125 L p .611 .529 .737 r F P s P p .002 w .47645 1.12125 m .49873 1.19581 L .49607 1.19678 L p .611 .529 .737 r F P s P p .002 w .49226 1.18498 m .50461 1.21265 L .50475 1.21262 L p .662 .627 .804 r F P s P p .002 w .50461 1.21265 m .49226 1.18498 L .48682 1.18697 L p .635 .614 .811 r F P 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Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "graphics primitives", "Graphics", "Graphics3D", "Circle", "Disk", "Line", "Point", "Polygon", "Rectangle", "Text", "Cuboid", "Show"}], Cell[TextData[{ "In addition to plotting functions, ", StyleBox["Mathematica", FontSlant->"Italic"], " can be used to plot graphic objects such as rectangles, lines, and \ circles. These objects are referred to as ", StyleBox["graphics primitives", FontSlant->"Italic"], " and represent the basic building blocks, or elements, of graphic images \ in ", StyleBox["Mathematica", FontSlant->"Italic"], ". \n\nTwo functions,", StyleBox[" ", FontFamily->"Courier"], StyleBox["Graphics[primitives, options]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " and ", StyleBox["Graphics3D[primitives, options]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " can be used to create two- and three-dimensional graphic images through \ the specification of graphics primitives. Graphics primitives that can be \ specified in the ", StyleBox["Graphics", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " command include ", StyleBox["Circle", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Disk", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Line", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Point", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Polygon", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ",", StyleBox[" ", FontFamily->"Courier"], StyleBox["Rectangle", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", and ", StyleBox["Text", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". Primitives that can be specified in ", StyleBox["Graphics3D", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " include ", StyleBox["Cuboid", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Line", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Point", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ",", StyleBox[" ", FontFamily->"Courier"], StyleBox["Polygon", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", and", StyleBox[" ", FontFamily->"Courier"], StyleBox["Text", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". Both commands feature a myriad of options that can be used to control \ various aspects of the graphic, such as the ratio of height to width.\n\nIn \ the following Input cell, we use ", StyleBox["Graphics", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Courier"], "to create a circle and ", StyleBox["Graphics3D", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to generate a cuboid. Note that the ", StyleBox["Show", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " command must be used to display each image." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "graphics primitives", "Graphics", "Graphics3D", "Circle", "Disk", "Line", "Point", "Polygon", "Rectangle", "Text", "Cuboid", "Show"}], Cell[CellGroupData[{ Cell[TextData[ "Show[Graphics[Circle[{0,0}, .1]]];\nShow[Graphics3D[Cuboid[{0, 0, 0}]]];"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "graphics primitives", "Graphics", "Graphics3D", "Circle", "Disk", "Line", "Point", "Polygon", "Rectangle", "Text", "Cuboid", "Show"}], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 4.7619 0.309017 2.94302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .004 w newpath matrix currentmatrix .47619 .2943 scale 1.05 1.05001 1 0 365.73 arc setmatrix s % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.08079 MathPictureStart %% Graphics3D /Courier findfont 10 scalefont setfont % Scaling calculations -0.0260524 1.10184 0.0275459 1.10184 [ [ 0 0 0 0 ] [ 1 1.08079 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g 0 0 m 1 0 L 1 1.08079 L 0 1.08079 L closepath clip newpath p .002 w .11113 .25957 m .02755 .78701 L s .02755 .78701 m .40586 1.05324 L s .40586 1.05324 m .42251 .57709 L s .42251 .57709 m .11113 .25957 L s .66295 .02755 m .90359 .41965 L s .90359 .41965 m .97245 .92345 L s .97245 .92345 m .69507 .58075 L s .69507 .58075 m .66295 .02755 L s .11113 .25957 m .02755 .78701 L s .02755 .78701 m .69507 .58075 L s .69507 .58075 m .66295 .02755 L s .66295 .02755 m .11113 .25957 L s .42251 .57709 m .90359 .41965 L s .90359 .41965 m .97245 .92345 L s .97245 .92345 m .40586 1.05324 L s .40586 1.05324 m .42251 .57709 L s P p .002 w .88762 .42635 m .42645 .57714 L .13012 .27421 L p .672 .728 .891 r F P s P p .002 w .95031 .90638 m .88762 .42635 L .42645 .57714 L p .573 .367 .563 r F P s P p .002 w .42645 .57714 m .41116 1.03212 L .95031 .90638 L p .573 .367 .563 r F P s P p .002 w .13012 .27421 m .42645 .57714 L .41116 1.03212 L p .938 .685 .528 r F P s P p .002 w .13012 .27421 m .65588 .05578 L .88762 .42635 L p .672 .728 .891 r F P s P p .002 w .65588 .05578 m .88762 .42635 L .95031 .90638 L p .973 .663 .31 r F P s P p .002 w .41116 1.03212 m .05473 .7756 L .13012 .27421 L p .938 .685 .528 r F P s P p .002 w .95031 .90638 m .41116 1.03212 L .05473 .7756 L p .625 .78 .956 r F P s P p .002 w .68444 .58061 m .65588 .05578 L .13012 .27421 L p .5 .261 .485 r F P s P p .002 w .13012 .27421 m .05473 .7756 L .68444 .58061 L p .5 .261 .485 r F P s P p .002 w .05473 .7756 m .68444 .58061 L .95031 .90638 L p .625 .78 .956 r F P s P p .002 w .95031 .90638 m .68444 .58061 L .65588 .05578 L p .973 .663 .31 r F P s P p .002 w .66295 .02755 m .90359 .41965 L s .90359 .41965 m .97245 .92345 L s .97245 .92345 m .69507 .58075 L s .69507 .58075 m .66295 .02755 L s .11113 .25957 m .02755 .78701 L s .02755 .78701 m .69507 .58075 L s .69507 .58075 m .66295 .02755 L s .66295 .02755 m .11113 .25957 L s P p P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, ImageSize->{213, 230}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["GraphicsArray"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"GraphicsArray"], Cell[TextData[{ StyleBox["GraphicsArray[{g", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["1", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[", g", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["2", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[", ...}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold"], "can be used to create an array of plots or graphic objects. 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To create an animation using the Notebook front end to ", StyleBox["Mathematica", FontSlant->"Italic"], ", 1) generate a sequence of graphics, 2) select the cells containing the \ graphics, 3) specify animation settings using the ", StyleBox["Animation", FontSlant->"Italic"], StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "command in the ", StyleBox["Graph", FontSlant->"Italic"], " menu, and 4) select ", StyleBox["Animate Selected Graphics", FontSlant->"Italic"], " from the ", StyleBox["Graph", FontSlant->"Italic"], " menu. \n\nTo create an animation using front end versions of ", StyleBox["Mathematica", FontSlant->"Italic"], " that do not support the Notebook interface, first load the animation \ package called ", StyleBox["Graphics`Animation`", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[".", FontWeight->"Bold"], " Use the ", StyleBox["Animate[plot, {t, tmin, tmax}] ", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "command from the package to generate a sequence of plots for values of ", StyleBox["t ", FontSlant->"Italic"], "ranging from ", StyleBox["tmin", FontSlant->"Italic"], " to", StyleBox[" tmax", FontSlant->"Italic"], " and to animate the resulting sequence. To produce an animation from a \ series of graphics objects, use the ", StyleBox["ShowAnimation[{g1, g2, ...}]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " command in the package.\n\nIn the Input cell below we create a series of \ three-dimensional plots using ", StyleBox["Table", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " and ", StyleBox["Plot3D", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". To create an animation of the resulting output, first select the cell \ group that includes all of the plots. Specify the speed of animation by \ executing the ", StyleBox["Animation", FontSlant->"Italic"], " command from the ", StyleBox["Graph", FontSlant->"Italic"], " menu and specifying the number of frames per second. Start the animation \ by selecting the ", StyleBox["Animate Selected Graphics", FontSlant->"Italic"], " command from the ", StyleBox["Graph", FontSlant->"Italic"], " menu. 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Many built in commands are set up to accept lists as function \ arguments and to act seperately on each element included in a list. Thus, \ lists provide a mechanism for doing repetitive processing. In addition, many \ commands use lists to represent the solutions they return. Finally, ", StyleBox["Mathematica", FontSlant->"Italic"], " uses lists to represent vectors and matrices. 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" }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"list", "repetitive processing", "Table"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[tsquare, n]\ntsquare = Table[n^2, {n, 1, 15, 1}]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"list", "repetitive processing", "Table"}], Cell[OutputFormData[ "\<\ {1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225}\ \>", "\<\ {1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ "We can also use", StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["Table", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to create a list of lists." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"list", "repetitive processing", "Table"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[i,j]\nb = Table[i^2 - 4j, {i, 1, 4}, {j, 1, 4}]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"list", "repetitive processing", "Table"}], Cell[OutputFormData[ "\<\ {{-3, -7, -11, -15}, {0, -4, -8, -12}, {5, 1, -3, -7}, {12, 8, 4, 0}}\ \>", "\<\ {{-3, -7, -11, -15}, {0, -4, -8, -12}, {5, 1, -3, -7}, {12, 8, 4, 0}}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["ColumnForm"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"list", "repetitive processing", "ColumnForm"}], Cell[TextData[{ StyleBox["ColumnForm[{e", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["1", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[", e", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["2", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[", ... }]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " prints the specified list as a column with ", StyleBox["e", FontSlant->"Italic"], StyleBox["1", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[" ", FontVariations->{"CompatibilityType"->"Subscript"}], "above ", StyleBox["e", FontSlant->"Italic"], StyleBox["2", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], ", etc. For example, ", StyleBox["ColumnForm", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " is used below to display the list named tsquare above as a column." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"list", "repetitive processing", "ColumnForm"}], Cell[CellGroupData[{ Cell[TextData["ColumnForm[tsquare]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"list", "repetitive processing", "ColumnForm"}], Cell[OutputFormData["\<\ 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225\ \>", "\<\ 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, LineSpacing->{1, 0}, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["MatrixForm"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"list", "repetitive processing", "MatrixForm"}], Cell[TextData[{ StyleBox["MatrixForm[list]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " displays the elements of ", StyleBox["list", FontSlant->"Italic"], " as a rectangular array. 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.68377 .4643 .71343 .4447 .6988 .41685 Metetra .73 .675 .797 r .6988 .41685 .71343 .4447 .74324 .42501 .72878 .39695 Metetra .901 .534 .074 r .72878 .39695 .74324 .42501 .77318 .40522 .77212 .54738 Metetra .529 .276 .476 r .77212 .54738 .77318 .40522 .81992 .56664 .80511 .53783 Metetra .647 .647 .836 r .80511 .53783 .81992 .56664 .85314 .55722 .8385 .52817 Metetra .647 .647 .836 r .8385 .52817 .85314 .55722 .88677 .54768 .8723 .51838 Metetra .647 .647 .836 r .8723 .51838 .88677 .54768 .92081 .53803 .90651 .50848 Metetra .664 .741 .908 r .31326 .5086 .33014 .52432 .35615 .52568 .33996 .49996 Metetra .32 .478 .861 r .33996 .49996 .35615 .52568 .38347 .50728 .36595 .5111 Metetra .303 .795 .771 r .36595 .5111 .38347 .50728 .40949 .52846 .39339 .50232 Metetra .328 .481 .86 r .39339 .50232 .40949 .52846 .43794 .48988 .42046 .51368 Metetra .42046 .51368 .43794 .48988 .46506 .51103 .44916 .48448 Metetra .779 .688 .764 r .44916 .48448 .46506 .51103 .49349 .48206 .47781 .45534 Metetra .672 .264 0 r .47781 .45534 .49349 .48206 .52183 .53432 .50594 .5073 Metetra .73 .675 .797 r .50594 .5073 .52183 .53432 .55098 .51497 .53527 .48775 Metetra .73 .675 .797 r .53527 .48775 .55098 .51497 .58027 .49553 .56473 .4681 Metetra .73 .675 .797 r .56473 .4681 .58027 .49553 .6097 .476 .59433 .44837 Metetra .73 .675 .797 r .59433 .44837 .6097 .476 .63926 .45637 .62407 .42854 Metetra .73 .675 .797 r .62407 .42854 .63926 .45637 .66896 .43666 .65395 .40862 Metetra .73 .675 .797 r .65395 .40862 .66896 .43666 .6988 .41685 .68397 .3886 Metetra .903 .534 .079 r .68397 .3886 .6988 .41685 .72878 .39695 .72417 .52807 Metetra .521 .262 .463 r .72417 .52807 .72878 .39695 .77212 .54738 .75692 .51839 Metetra .647 .647 .836 r .75692 .51839 .77212 .54738 .80511 .53783 .79008 .50859 Metetra .647 .647 .836 r .79008 .50859 .80511 .53783 .8385 .52817 .82363 .49867 Metetra .647 .647 .836 r .82363 .49867 .8385 .52817 .8723 .51838 .8576 .48863 Metetra .647 .647 .836 r .8576 .48863 .8723 .51838 .90651 .50848 .89199 .47846 Metetra .462 .671 .954 r .29605 .49258 .31326 .5086 .33996 .49996 .32228 .49369 Metetra .621 .874 .989 r .32228 .49369 .33996 .49996 .36595 .5111 .34952 .48481 Metetra .653 .643 .828 r .34952 .48481 .36595 .5111 .39339 .50232 .37706 .47583 Metetra .328 .481 .86 r .37706 .47583 .39339 .50232 .42046 .51368 .40413 .48695 Metetra .779 .688 .764 r .40413 .48695 .42046 .51368 .44916 .48448 .43305 .45757 Metetra 0 0 .436 r .43305 .45757 .44916 .48448 .47781 .45534 .46048 .49955 Metetra .31 0 .227 r .46048 .49955 .47781 .45534 .50594 .5073 .48984 .47989 Metetra .73 .675 .797 r .48984 .47989 .50594 .5073 .53527 .48775 .51933 .46013 Metetra .73 .675 .797 r .51933 .46013 .53527 .48775 .56473 .4681 .54897 .44029 Metetra .73 .675 .797 r .54897 .44029 .56473 .4681 .59433 .44837 .57874 .42034 Metetra .73 .675 .797 r .57874 .42034 .59433 .44837 .62407 .42854 .60866 .40031 Metetra .73 .675 .797 r .60866 .40031 .62407 .42854 .65395 .40862 .63871 .38018 Metetra .903 .531 .079 r .63871 .38018 .65395 .40862 .68397 .3886 .67608 .5087 Metetra .513 .247 .449 r .67608 .5087 .68397 .3886 .72417 .52807 .70859 .49888 Metetra .647 .647 .836 r .70859 .49888 .72417 .52807 .75692 .51839 .7415 .48895 Metetra .647 .647 .836 r .7415 .48895 .75692 .51839 .79008 .50859 .77481 .4789 Metetra .647 .647 .836 r .77481 .4789 .79008 .50859 .82363 .49867 .80853 .46872 Metetra .647 .647 .836 r .80853 .46872 .82363 .49867 .8576 .48863 .84267 .45841 Metetra .647 .647 .836 r .84267 .45841 .8576 .48863 .89199 .47846 .87723 .44798 Metetra .664 .741 .908 r .2785 .47623 .29605 .49258 .32228 .49369 .30554 .46724 Metetra .653 .643 .828 r .30554 .46724 .32228 .49369 .34952 .48481 .33287 .45816 Metetra .653 .643 .828 r .33287 .45816 .34952 .48481 .37706 .47583 .36051 .44897 Metetra .328 .481 .86 r .36051 .44897 .37706 .47583 .40413 .48695 .38757 .45984 Metetra .779 .688 .764 r .38757 .45984 .40413 .48695 .43305 .45757 .4167 .43029 Metetra 0 0 .436 r .4167 .43029 .43305 .45757 .46048 .49955 .44397 .47196 Metetra .73 .675 .797 r .44397 .47196 .46048 .49955 .48984 .47989 .4735 .45209 Metetra .73 .675 .797 r .4735 .45209 .48984 .47989 .51933 .46013 .50317 .43213 Metetra .73 .675 .797 r .50317 .43213 .51933 .46013 .54897 .44029 .53298 .41207 Metetra .73 .675 .797 r .53298 .41207 .54897 .44029 .57874 .42034 .56293 .39191 Metetra .73 .675 .797 r .56293 .39191 .57874 .42034 .60866 .40031 .59302 .37167 Metetra .901 .526 .075 r .59302 .37167 .60866 .40031 .63871 .38018 .62783 .48927 Metetra .502 .229 .432 r .62783 .48927 .63871 .38018 .67608 .5087 .6601 .47932 Metetra .647 .647 .836 r .6601 .47932 .67608 .5087 .70859 .49888 .69276 .46925 Metetra .647 .647 .836 r .69276 .46925 .70859 .49888 .7415 .48895 .72583 .45906 Metetra .647 .647 .836 r .72583 .45906 .7415 .48895 .77481 .4789 .7593 .44874 Metetra .647 .647 .836 r .7593 .44874 .77481 .4789 .80853 .46872 .79319 .43829 Metetra .647 .647 .836 r .79319 .43829 .80853 .46872 .84267 .45841 .82751 .42772 Metetra .647 .647 .836 r .82751 .42772 .84267 .45841 .87723 .44798 .86225 .41701 Metetra .462 .671 .954 r .26059 .45956 .2785 .47623 .30554 .46724 .28705 .46041 Metetra .239 .703 .947 r .28705 .46041 .30554 .46724 .33287 .45816 .31397 .46127 Metetra .165 0 0 r .31397 .46127 .33287 .45816 .36051 .44897 .34137 .46215 Metetra .715 .963 .704 r .34137 .46215 .36051 .44897 .38757 .45984 .37078 .43235 Metetra 0 .056 .617 r .37078 .43235 .38757 .45984 .4167 .43029 .39765 .46395 Metetra .174 0 .063 r .39765 .46395 .4167 .43029 .44397 .47196 .42722 .44397 Metetra .73 .675 .797 r .42722 .44397 .44397 .47196 .4735 .45209 .45692 .42389 Metetra .73 .675 .797 r .45692 .42389 .4735 .45209 .50317 .43213 .48677 .40371 Metetra .73 .675 .797 r .48677 .40371 .50317 .43213 .53298 .41207 .51675 .38344 Metetra .73 .675 .797 r .51675 .38344 .53298 .41207 .56293 .39191 .54688 .36307 Metetra .896 .517 .064 r .54688 .36307 .56293 .39191 .59302 .37167 .57943 .46977 Metetra .49 .208 .412 r .57943 .46977 .59302 .37167 .62783 .48927 .61146 .45969 Metetra .647 .647 .836 r .61146 .45969 .62783 .48927 .6601 .47932 .64388 .44949 Metetra .647 .647 .836 r .64388 .44949 .6601 .47932 .69276 .46925 .6767 .43916 Metetra .647 .647 .836 r .6767 .43916 .69276 .46925 .72583 .45906 .70992 .4287 Metetra .647 .647 .836 r .70992 .4287 .72583 .45906 .7593 .44874 .74356 .41811 Metetra .647 .647 .836 r .74356 .41811 .7593 .44874 .79319 .43829 .77761 .40739 Metetra .647 .647 .836 r .77761 .40739 .79319 .43829 .82751 .42772 .8121 .39654 Metetra .647 .647 .836 r .8121 .39654 .82751 .42772 .86225 .41701 .84702 .38555 Metetra .664 .741 .908 r .24232 .44255 .26059 .45956 .28705 .46041 .26971 .43319 Metetra .523 .587 .86 r .26971 .43319 .28705 .46041 .31397 .46127 .29667 .43381 Metetra .523 .587 .86 r .29667 .43381 .31397 .46127 .34137 .46215 .32411 .43445 Metetra .779 .688 .764 r .32411 .43445 .34137 .46215 .37078 .43235 .35374 .40447 Metetra 0 .056 .617 r .35374 .40447 .37078 .43235 .39765 .46395 .38049 .43576 Metetra .73 .675 .797 r .38049 .43576 .39765 .46395 .42722 .44397 .41023 .41557 Metetra .73 .675 .797 r .41023 .41557 .42722 .44397 .45692 .42389 .4401 .39527 Metetra .73 .675 .797 r .4401 .39527 .45692 .42389 .48677 .40371 .47013 .37488 Metetra .73 .675 .797 r .47013 .37488 .48677 .40371 .51675 .38344 .50029 .35439 Metetra .887 .503 .045 r .50029 .35439 .51675 .38344 .54688 .36307 .53088 .45021 Metetra .475 .182 .387 r .53088 .45021 .54688 .36307 .57943 .46977 .56266 .44 Metetra .647 .647 .836 r .56266 .44 .57943 .46977 .61146 .45969 .59483 .42966 Metetra .647 .647 .836 r .59483 .42966 .61146 .45969 .64388 .44949 .6274 .41919 Metetra .647 .647 .836 r .6274 .41919 .64388 .44949 .6767 .43916 .66038 .40859 Metetra .647 .647 .836 r .66038 .40859 .6767 .43916 .70992 .4287 .69376 .39786 Metetra .647 .647 .836 r .69376 .39786 .70992 .4287 .74356 .41811 .72756 .387 Metetra .647 .647 .836 r .72756 .387 .74356 .41811 .77761 .40739 .76179 .376 Metetra .647 .647 .836 r .76179 .376 .77761 .40739 .8121 .39654 .79645 .36486 Metetra .647 .647 .836 r .79645 .36486 .8121 .39654 .84702 .38555 .83155 .35358 Metetra .462 .671 .954 r .22367 .42519 .24232 .44255 .26971 .43319 .25035 .42574 Metetra .79 .879 .912 r .25035 .42574 .26971 .43319 .29667 .43381 .27913 .40597 Metetra .523 .587 .86 r .27913 .40597 .29667 .43381 .32411 .43445 .3066 .40636 Metetra 0 .278 .779 r .3066 .40636 .32411 .43445 .35374 .40447 .3333 .42748 Metetra .3333 .42748 .35374 .40447 .38049 .43576 .36307 .40717 Metetra .73 .675 .797 r .36307 .40717 .38049 .43576 .41023 .41557 .39299 .38675 Metetra .73 .675 .797 r .39299 .38675 .41023 .41557 .4401 .39527 .42304 .36624 Metetra .73 .675 .797 r .42304 .36624 .4401 .39527 .47013 .37488 .45324 .34563 Metetra .873 .482 .014 r .45324 .34563 .47013 .37488 .50029 .35439 .48217 .4306 Metetra .456 .149 .355 r .48217 .4306 .50029 .35439 .53088 .45021 .51371 .42025 Metetra .647 .647 .836 r .51371 .42025 .53088 .45021 .56266 .44 .54564 .40977 Metetra .647 .647 .836 r .54564 .40977 .56266 .44 .59483 .42966 .57795 .39916 Metetra .647 .647 .836 r .57795 .39916 .59483 .42966 .6274 .41919 .61067 .38842 Metetra .647 .647 .836 r .61067 .38842 .6274 .41919 .66038 .40859 .6438 .37755 Metetra .647 .647 .836 r .6438 .37755 .66038 .40859 .69376 .39786 .67734 .36654 Metetra .647 .647 .836 r .67734 .36654 .69376 .39786 .72756 .387 .71131 .35539 Metetra .647 .647 .836 r .71131 .35539 .72756 .387 .76179 .376 .74571 .3441 Metetra .647 .647 .836 r .74571 .3441 .76179 .376 .79645 .36486 .78055 .33267 Metetra .647 .647 .836 r .78055 .33267 .79645 .36486 .83155 .35358 .81583 .32109 Metetra .664 .741 .908 r .20464 .40746 .22367 .42519 .25035 .42574 .23239 .39771 Metetra .295 .468 .861 r .23239 .39771 .25035 .42574 .27913 .40597 .25869 .40828 Metetra .87 .966 .856 r .25869 .40828 .27913 .40597 .3066 .40636 .28885 .37786 Metetra 0 .278 .779 r .28885 .37786 .3066 .40636 .3333 .42748 .31546 .39868 Metetra .73 .675 .797 r .31546 .39868 .3333 .42748 .36307 .40717 .3454 .37815 Metetra .73 .675 .797 r .3454 .37815 .36307 .40717 .39299 .38675 .37549 .35751 Metetra .73 .675 .797 r .37549 .35751 .39299 .38675 .42304 .36624 .40573 .33678 Metetra .849 .45 0 r .40573 .33678 .42304 .36624 .45324 .34563 .43331 .41092 Metetra .431 .107 .313 r .43331 .41092 .45324 .34563 .48217 .4306 .46461 .40043 Metetra .647 .647 .836 r .46461 .40043 .48217 .4306 .51371 .42025 .49628 .38981 Metetra .647 .647 .836 r .49628 .38981 .51371 .42025 .54564 .40977 .52835 .37907 Metetra .647 .647 .836 r .52835 .37907 .54564 .40977 .57795 .39916 .56081 .36819 Metetra .647 .647 .836 r .56081 .36819 .57795 .39916 .61067 .38842 .59368 .35717 Metetra .647 .647 .836 r .59368 .35717 .61067 .38842 .6438 .37755 .62696 .34601 Metetra .647 .647 .836 r .62696 .34601 .6438 .37755 .67734 .36654 .66067 .33472 Metetra .647 .647 .836 r .66067 .33472 .67734 .36654 .71131 .35539 .6948 .32328 Metetra .647 .647 .836 r .6948 .32328 .71131 .35539 .74571 .3441 .72937 .31169 Metetra .647 .647 .836 r .72937 .31169 .74571 .3441 .78055 .33267 .76439 .29996 Metetra .647 .647 .836 r .76439 .29996 .78055 .33267 .81583 .32109 .79986 .28807 Metetra .462 .671 .954 r .1852 .38937 .20464 .40746 .23239 .39771 .21209 .38961 Metetra .637 .867 .985 r .21209 .38961 .23239 .39771 .25869 .40828 .24044 .37956 Metetra .295 .468 .861 r .24044 .37956 .25869 .40828 .28885 .37786 .26737 .39011 Metetra .494 .876 .679 r .26737 .39011 .28885 .37786 .31546 .39868 .29735 .36946 Metetra .73 .675 .797 r .29735 .36946 .31546 .39868 .3454 .37815 .32747 .3487 Metetra .73 .675 .797 r .32747 .3487 .3454 .37815 .37549 .35751 .35774 .32784 Metetra .809 .4 0 r .35774 .32784 .37549 .35751 .40573 .33678 .3843 .39118 Metetra .397 .05 .255 r .3843 .39118 .40573 .33678 .43331 .41092 .41534 .38055 Metetra .647 .647 .836 r .41534 .38055 .43331 .41092 .46461 .40043 .44677 .3698 Metetra .647 .647 .836 r .44677 .3698 .46461 .40043 .49628 .38981 .47858 .35891 Metetra .647 .647 .836 r .47858 .35891 .49628 .38981 .52835 .37907 .51079 .34789 Metetra .647 .647 .836 r .51079 .34789 .52835 .37907 .56081 .36819 .5434 .33672 Metetra .647 .647 .836 r .5434 .33672 .56081 .36819 .59368 .35717 .57642 .32542 Metetra .647 .647 .836 r .57642 .32542 .59368 .35717 .62696 .34601 .60986 .31398 Metetra .647 .647 .836 r .60986 .31398 .62696 .34601 .66067 .33472 .64372 .30238 Metetra .647 .647 .836 r .64372 .30238 .66067 .33472 .6948 .32328 .67802 .29064 Metetra .647 .647 .836 r .67802 .29064 .6948 .32328 .72937 .31169 .71276 .27875 Metetra .647 .647 .836 r .71276 .27875 .72937 .31169 .76439 .29996 .74796 .26671 Metetra .647 .647 .836 r .74796 .26671 .76439 .29996 .79986 .28807 .78361 .2545 Metetra .664 .741 .908 r .16536 .37089 .1852 .38937 .21209 .38961 .19347 .36071 Metetra .65 .645 .832 r .19347 .36071 .21209 .38961 .24044 .37956 .22192 .35042 Metetra .295 .468 .861 r .22192 .35042 .24044 .37956 .26737 .39011 .24881 .36068 Metetra .73 .675 .797 r .24881 .36068 .26737 .39011 .29735 .36946 .27897 .3398 Metetra .73 .675 .797 r .27897 .3398 .29735 .36946 .32747 .3487 .30927 .31881 Metetra .739 .323 0 r .30927 .31881 .32747 .3487 .35774 .32784 .33514 .37137 Metetra .345 0 .17 r .33514 .37137 .35774 .32784 .3843 .39118 .36593 .36061 Metetra .647 .647 .836 r .36593 .36061 .3843 .39118 .41534 .38055 .3971 .34972 Metetra .647 .647 .836 r .3971 .34972 .41534 .38055 .44677 .3698 .42865 .33869 Metetra .647 .647 .836 r .42865 .33869 .44677 .3698 .47858 .35891 .4606 .32752 Metetra .647 .647 .836 r .4606 .32752 .47858 .35891 .51079 .34789 .49295 .31621 Metetra .647 .647 .836 r .49295 .31621 .51079 .34789 .5434 .33672 .52571 .30476 Metetra .647 .647 .836 r .52571 .30476 .5434 .33672 .57642 .32542 .55888 .29317 Metetra .647 .647 .836 r .55888 .29317 .57642 .32542 .60986 .31398 .59247 .28142 Metetra .647 .647 .836 r .59247 .28142 .60986 .31398 .64372 .30238 .6265 .26953 Metetra .647 .647 .836 r .6265 .26953 .64372 .30238 .67802 .29064 .66097 .25748 Metetra .647 .647 .836 r .66097 .25748 .67802 .29064 .71276 .27875 .69589 .24527 Metetra .647 .647 .836 r .69589 .24527 .71276 .27875 .74796 .26671 .73126 .23291 Metetra .647 .647 .836 r .73126 .23291 .74796 .26671 .78361 .2545 .7671 .22038 Metetra .462 .671 .954 r .14509 .35201 .16536 .37089 .19347 .36071 .17219 .35192 Metetra .292 .724 .969 r .17219 .35192 .19347 .36071 .22192 .35042 .19979 .35182 Metetra .758 .978 .917 r .19979 .35182 .22192 .35042 .24881 .36068 .22998 .33081 Metetra .73 .675 .797 r .22998 .33081 .24881 .36068 .27897 .3398 .26031 .3097 Metetra .613 .197 0 r .26031 .3097 .27897 .3398 .30927 .31881 .28581 .35151 Metetra .259 0 .034 r .28581 .35151 .30927 .31881 .33514 .37137 .31635 .34061 Metetra .647 .647 .836 r .31635 .34061 .33514 .37137 .36593 .36061 .34727 .32957 Metetra .647 .647 .836 r .34727 .32957 .36593 .36061 .3971 .34972 .37856 .3184 Metetra .647 .647 .836 r .37856 .3184 .3971 .34972 .42865 .33869 .41025 .30709 Metetra .647 .647 .836 r .41025 .30709 .42865 .33869 .4606 .32752 .44234 .29563 Metetra .647 .647 .836 r .44234 .29563 .4606 .32752 .49295 .31621 .47483 .28403 Metetra .647 .647 .836 r .47483 .28403 .49295 .31621 .52571 .30476 .50773 .27229 Metetra .647 .647 .836 r .50773 .27229 .52571 .30476 .55888 .29317 .54106 .26039 Metetra .647 .647 .836 r .54106 .26039 .55888 .29317 .59247 .28142 .57481 .24834 Metetra .647 .647 .836 r .57481 .24834 .59247 .28142 .6265 .26953 .609 .23613 Metetra .647 .647 .836 r .609 .23613 .6265 .26953 .66097 .25748 .64364 .22377 Metetra .647 .647 .836 r .64364 .22377 .66097 .25748 .69589 .24527 .67873 .21124 Metetra .647 .647 .836 r .67873 .21124 .69589 .24527 .73126 .23291 .71429 .19855 Metetra .647 .647 .836 r .71429 .19855 .73126 .23291 .7671 .22038 .75031 .18569 Metetra .664 .741 .908 r .12438 .33273 .14509 .35201 .17219 .35192 .15286 .32211 Metetra .513 .586 .865 r .15286 .32211 .17219 .35192 .19979 .35182 .1805 .32173 Metetra .73 .675 .797 r .1805 .32173 .19979 .35182 .22998 .33081 .21086 .30049 Metetra 0 0 .562 r .21086 .30049 .22998 .33081 .26031 .3097 .23633 .33158 Metetra .104 0 0 r .23633 .33158 .26031 .3097 .28581 .35151 .26662 .32054 Metetra .647 .647 .836 r .26662 .32054 .28581 .35151 .31635 .34061 .29727 .30936 Metetra .647 .647 .836 r .29727 .30936 .31635 .34061 .34727 .32957 .32831 .29804 Metetra .647 .647 .836 r .32831 .29804 .34727 .32957 .37856 .3184 .35974 .28659 Metetra .647 .647 .836 r .35974 .28659 .37856 .3184 .41025 .30709 .39156 .27498 Metetra .647 .647 .836 r .39156 .27498 .41025 .30709 .44234 .29563 .42378 .26324 Metetra .647 .647 .836 r .42378 .26324 .44234 .29563 .47483 .28403 .45641 .25134 Metetra .647 .647 .836 r .45641 .25134 .47483 .28403 .50773 .27229 .48947 .23929 Metetra .647 .647 .836 r .48947 .23929 .50773 .27229 .54106 .26039 .52294 .22708 Metetra .647 .647 .836 r .52294 .22708 .54106 .26039 .57481 .24834 .55686 .21472 Metetra .647 .647 .836 r .55686 .21472 .57481 .24834 .609 .23613 .59121 .20219 Metetra .647 .647 .836 r .59121 .20219 .609 .23613 .64364 .22377 .62602 .1895 Metetra .647 .647 .836 r .62602 .1895 .64364 .22377 .67873 .21124 .66129 .17664 Metetra .647 .647 .836 r .66129 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For example, in the Input \ cell below, we create a three by three matrix and use", StyleBox[" ", FontFamily->"Courier"], StyleBox["MatrixForm", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to display it in traditional notation. 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In the following Input cell, we define two four by four \ matrices, ", StyleBox["a", FontSlant->"Italic"], " and", StyleBox[" b", FontSlant->"Italic"], ", and then compute ", StyleBox["a+b", FontSlant->"Italic"], ", ", StyleBox["a-b", FontSlant->"Italic"], ", and ", StyleBox["2a", FontSlant->"Italic"], ". 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Below we compute the product between a two by two matrix and a two by \ one column vector." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "matrix arithmetic"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[a, b, c, d, x, y]\n{{a, b}, {c, d}} . {x, y}"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "matrix arithmetic"}], Cell[OutputFormData["\<\ {a*x + b*y, c*x + d*y}\ \>", "\<\ {a x + b y, c x + d y}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[ "Note how changing the order of the two lists causes the vector to be treated \ as a row vector instead of as a column vector."], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "matrix arithmetic"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[a, b, c, d, x, y]\n{x, y} . {{a, b}, {c, d}} "], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "matrix arithmetic"}], Cell[OutputFormData["\<\ {a*x + c*y, b*x + d*y}\ \>", "\<\ {a x + c y, b x + d y}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["IdentityMatrix"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "IdentityMatrix"}], Cell[TextData[{ "The", StyleBox[" ", FontFamily->"Courier"], StyleBox["IdentityMatrix[n]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " command can be used to create an Identity matrix of order ", StyleBox["n", FontSlant->"Italic"], ". Below, we use this command to create a five by five Identity matrix." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "IdentityMatrix"}], Cell[CellGroupData[{ Cell[TextData["IdentityMatrix[5]//MatrixForm"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "IdentityMatrix"}], Cell[OutputFormData["\<\ MatrixForm[{{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}]\ \>", "\<\ 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["DiagonalMatrix"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "DiagonalMatrix"}], Cell[TextData[{ "The ", StyleBox["DiagonalMatrix[list]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Courier"], "command can be used to create a diagonal matrix with the elements of ", StyleBox["list", FontSlant->"Italic"], " on the leading diagonal and zero elsewhere. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "DiagonalMatrix"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[a, b, c]\nDiagonalMatrix[{a, b, c}]//MatrixForm"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "DiagonalMatrix"}], Cell[OutputFormData["\<\ MatrixForm[{{a, 0, 0}, {0, b, 0}, {0, 0, c}}]\ \>", "\<\ a 0 0 0 b 0 0 0 c\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Transpose"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"matrices", "MatrixForm", "PostFix operator", "//", "Transpose"}], Cell[TextData[{ StyleBox["Transpose[list]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " will interchange the rows and columns of ", StyleBox["list", FontSlant->"Italic"], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"matrices", "MatrixForm", "PostFix operator", "//", "Transpose"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[a, b, c, d]\nTranspose[{{a, b}, {c, d}}]//MatrixForm"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"matrices", "MatrixForm", "PostFix operator", "//", "Transpose"}], Cell[OutputFormData["\<\ MatrixForm[{{a, c}, {b, d}}]\ \>", "\<\ a c b d\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Inverse"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"matrices", "MatrixForm", "PostFix operator", "//", "Inverse"}], Cell[TextData[{ StyleBox["Inverse[m]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontFamily->"Courier"], "computes the inverse of the square matrix ", StyleBox["m", FontSlant->"Italic"], ". Below, we compute the inverse of a two by two matrix." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"matrices", "MatrixForm", "PostFix operator", "//", "Inverse"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[a, b, c, d]\nInverse[{{a,b}, {c,d}}]//MatrixForm\n"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"matrices", "MatrixForm", "PostFix operator", "//", "Inverse"}], Cell[OutputFormData[ "\<\ MatrixForm[{{d/(-(b*c) + a*d), -(b/(-(b*c) + a*d))}, {-(c/(-(b*c) + a*d)), a/(-(b*c) + a*d)}}]\ \>", "\<\ d b ------------ -(------------) -(b c) + a d -(b c) + a d c a -(------------) ------------ -(b c) + a d -(b c) + a d\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Det"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "determinant", "Det"}], Cell[TextData[{ StyleBox["Det[m]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " computes the determinant of the square matrix ", StyleBox["m", FontSlant->"Italic"], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "determinant", "Det"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[a, b, c, d]\nDet[{{a, b}, {c, d}}]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "determinant", "Det"}], Cell[OutputFormData["\<\ -(b*c) + a*d\ \>", "\<\ -(b c) + a d\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Minors"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"matrices", "MatrixForm", "PostFix operator", "//", "Minors"}], Cell[TextData[{ StyleBox["Minors[m, k]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " generates a matrix composed of the determinants of all ", StyleBox["k", FontSlant->"Italic"], " x ", StyleBox["k", FontSlant->"Italic"], " submatrices of ", StyleBox["m", FontSlant->"Italic"], ". 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Finally we use ", StyleBox["LinearSolve", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to compute the vector of solutions to the set of linear equations." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "LinearSolve"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[m, x, y, a, b]\nm = {{1, 5}, {2, 1}}\nm . {x, y} == {a, b}\n\ LinearSolve[m, {a, b}]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "LinearSolve"}], Cell[OutputFormData["\<\ {{1, 5}, {2, 1}}\ \>", "\<\ {{1, 5}, {2, 1}}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ {x + 5*y, 2*x + y} == {a, b}\ \>", "\<\ {x + 5 y, 2 x + y} == {a, b}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData["\<\ {a - (5*(2*a - b))/9, (2*a - b)/9}\ \>", "\<\ 5 (2 a - b) 2 a - b {a - -----------, -------} 9 9\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["RowReduce"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "row-reduced form"}], Cell[TextData[{ StyleBox["RowReduce[m]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " computes the row-reduced form of the matrix ", StyleBox["m", FontSlant->"Italic"], ". " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "row-reduced form"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Eigensystem"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "eigenvalues", "eigenvectors", "eigensystem"}], Cell[TextData[{ StyleBox["Eigensystem[m]", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "returns a list whose first element is a list of eigenvalues and whose \ second element is a list eigenvectors for the square matrix ", StyleBox["m", FontSlant->"Italic"], ". For example, in the Input cell below we define a matrix", StyleBox[" m", FontSlant->"Italic"], " and then use ", StyleBox["Eigensystem", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to compute the eigenvalues and eigenvectors for ", StyleBox["m", FontSlant->"Italic"], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "eigenvalues", "eigenvectors", "eigensystem"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[m]\nm = {{1, 1, 2}, {1, 2, 1}, {2, 1, 1}}\nEigensystem[m]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "matrices", "MatrixForm", "PostFix operator", "//", "eigenvalues", "eigenvectors", "eigensystem"}], Cell[OutputFormData["\<\ {{1, 1, 2}, {1, 2, 1}, {2, 1, 1}}\ \>", "\<\ {{1, 1, 2}, {1, 2, 1}, {2, 1, 1}}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[OutputFormData[ "\<\ {{-1, 1, 4}, {{-1, 0, 1}, {1, -2, 1}, {1, 1, 1}}}\ \>", "\<\ {{-1, 1, 4}, {{-1, 0, 1}, {1, -2, 1}, {1, 1, 1}}}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Special Operators ... 40"], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " features many special operators, some of which are listed in the table \ below. 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For example, in the following Input cell we apply the \ transformation rules 10y -> 3 and y -> 7 to the expression 10y - y. Note \ that the transformation rules are not applied until after the expression has \ been evaluted." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[CellGroupData[{ Cell[TextData["Clear[y]\n10y - y /. {10y -> 3, y -> 7}"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[OutputFormData["\<\ 63\ \>", "\<\ 63\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[ "As another example, we use the \"slash-dot\" operator to apply a list of \ rules to the same expression."], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[CellGroupData[{ Cell[TextData["Clear[x, y]\nx - y /. {x -> 1, y -> 3}"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[OutputFormData["\<\ -2\ \>", "\<\ -2\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[TextData[ "Finally, by specifying a list of lists of rules, we obtain a list of \ results."], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[CellGroupData[{ Cell[TextData[ "Clear[x, y]\nx - y /. {{x -> 3, y -> 4}, {x -> 7, y -> 6}}"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[OutputFormData["\<\ {-1, 1}\ \>", "\<\ {-1, 1}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Condition Operator"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[TextData[{ "The", StyleBox[" ", FontColor->RGBColor[1, 0, 0]], StyleBox["Condition", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " operator (", StyleBox["/;", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "), pronounced \"slash-semi\", \"whenever\", or \"provided that\", is used \ to 1) place constraints on classes of expressions, 2) conditionally apply \ rules, and 3) conditionally apply definitions. For example, to define a \ function", StyleBox[" f(x)", FontSlant->"Italic"], " such that ", StyleBox["f(x)", FontSlant->"Italic"], " equals 1 + x", StyleBox["2", FontVariations->{"CompatibilityType"->"Superscript"}], " if ", StyleBox["x", FontSlant->"Italic"], " is greater than or equal to 0, but less than or equal to 2, or ", StyleBox["f(x)", FontSlant->"Italic"], " equals 1 - x if", StyleBox[" x", FontSlant->"Italic"], " is greater than 2 but less than or equal to 5, we use the following Input \ statement." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[TextData[ "Clear[f, x]\nf[x_] := 1 + x^2 /; 0 <= x <= 2\nf[x_] := 1 - x /; 2 < x <= 5"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["ReplaceRepeated"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[TextData[{ "The ", StyleBox["ReplaceRepeated", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " Operator (", StyleBox["//.", FontFamily->"Courier", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ") is used to repeatedly apply the specified rule or rules to the \ expression until the expression no longer changes. For example, note how it \ requires two iterations of applying the transformation rules x -> 2 + a and a \ -> 3 to the expression x", StyleBox["2", FontVariations->{"CompatibilityType"->"Superscript"}], " + y", StyleBox["6", FontVariations->{"CompatibilityType"->"Superscript"}], " before the expression no longer changes." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[CellGroupData[{ Cell[TextData["Clear[x, y, a]\nx^2 + y^6 //. {x -> 2 + a, a -> 3}"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[OutputFormData["\<\ 25 + y^6\ \>", "\<\ 6 25 + y\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Rules"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[TextData[{ "In ", StyleBox["Mathematica", FontSlant->"Italic"], " the ", StyleBox["Rule", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " operator (", StyleBox["->", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ") provides a mechanism for ", StyleBox["defining", FontSlant->"Italic"], " transformation rules for variables in expressions. In addition, many \ functions such as ", StyleBox["Solve", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " return lists whose elements are lists of transformation rules \ representing solutions. ", StyleBox["ReplaceAll ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "and ", StyleBox["ReplaceRepeated", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " can be used in conjuntion with ", StyleBox["Rule", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to apply the transformation rule or rules to the specified expression.\n\n\ In the Input cell below, we use ", StyleBox["Rule", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to define the transformation rule log[x_ y_] -> log[x] + log[y]. ", StyleBox["ReplaceRepeated", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " is used to repeatedly apply the transformation rule to the expression \ Log[a b c d e]. 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A delayed rule is a rule such that rhs is evaluated only when the rule \ is applied. For example in the expression below, the rule x -> Random[ ] is \ applied three times and hence, ", StyleBox["Random[ ]", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " is evaluated three times. Note that if the ", StyleBox["Rule", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " operator (", StyleBox["->", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ") had been used instead, the right-hand side of the rule x -> Random[ ] \ would only be evaluated once." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[CellGroupData[{ Cell[TextData["Clear[x]\nTable[x, {3}] /. x :> Random[ ]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[OutputFormData["\<\ {0.5965385453556260729, 0.2346508696809635601, 0.3477185584257036171}\ \>", "\<\ {0.596539, 0.234651, 0.347719}\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Logical Not"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[TextData[{ "The logical ", StyleBox["Not ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "function is represented as ", StyleBox["!", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["expr", FontSlant->"Italic"], ". It returns False if ", StyleBox["expr", FontSlant->"Italic"], " is True, and True if it is False. In the example below, 2 is not equal \ to 3, so 2 != 3 is True." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[CellGroupData[{ Cell[TextData["2 != 3"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[OutputFormData["\<\ True\ \>", "\<\ True\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Logical And"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[TextData[{ "The logical ", StyleBox["And", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " function is represented as ", StyleBox["e", FontSlant->"Italic"], StyleBox["1", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[" ", FontWeight->"Bold"], StyleBox["&&", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" e", FontSlant->"Italic"], StyleBox["2", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], ". Arguments are evaluated from left to right and a False is returned if \ any are not True. For example, in the following Input cell, since the first \ argument is False, ", StyleBox["Mathematica", FontSlant->"Italic"], " returns a False." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[CellGroupData[{ Cell[TextData["5 < 3 && 2 != 3"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[OutputFormData["\<\ False\ \>", "\<\ False\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Logical Or"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[TextData[{ "The logical ", StyleBox["Or", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " function, represented as ", StyleBox["e", FontSlant->"Italic"], StyleBox["1", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[" ||", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold"], StyleBox["e", FontSlant->"Italic"], StyleBox["2", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[" ", FontWeight->"Bold"], StyleBox["||", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ...", FontWeight->"Bold"], ", evaluates arguments from left to right and returns a True if any of the \ arguments are True, and a False if all arguments are False. In the Input \ cell below, ", StyleBox["Mathematica", FontSlant->"Italic"], " returns a True since the second argument is True." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[CellGroupData[{ Cell[TextData["5 < 3 || 2 != 3"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[OutputFormData["\<\ True\ \>", "\<\ True\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Exclusive Or"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[TextData[{ "The ", StyleBox["exclusive", FontSlant->"Italic"], StyleBox[" ", FontWeight->"Bold"], StyleBox["Or", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontWeight->"Bold"], "function, represented as", StyleBox[" ", FontWeight->"Bold"], StyleBox["Xor[e", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["1", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[",e", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["2", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[", ...]", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", evaluates to True if an odd number of the", StyleBox[" e", FontSlant->"Italic"], StyleBox["i", FontSlant->"Italic", FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[" ", FontSlant->"Italic"], "are True, and the rest are False. 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" }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[CellGroupData[{ Cell[TextData["Xor[5 < 6, 6 < 7, 7 < 8, 1 > 2]"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[OutputFormData["\<\ True\ \>", "\<\ True\ \>"], "Output", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Get"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[TextData[{ "A file or package can be loaded with the ", StyleBox["Get", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "operator (", StyleBox["<<", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ") by specifying the appropriate directory and name for the file or \ package. For example, on a Macintosh system ", StyleBox["<<", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " is used below to load the package named ", StyleBox["VectorAnalysis.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " found in the ", StyleBox["Calculus", FontWeight->"Bold"], " folder inside the ", StyleBox["Packages", FontWeight->"Bold"], " folder." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[OutputFormData["\<\ <", "\<\ << Calculus`VectorAnalysis`\ \>"], "Input", PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Put"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "/.", "/", "//.", "->", ">", "!", "&&", "||", "Xor", "<<", ">>", "ReplaceAll", "Condition", "ReplaceRepeated", "Rule", "RuleDelayed", "Not", "And", "Or", "Get", "Put"}], Cell[TextData[{ "Information can be written to a file by using the ", StyleBox["Put", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " command or operator (", StyleBox[">>", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "). In the example below, we use ", StyleBox["Table", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to generate a list of squares of the first twenty natural numbers, \ indexed by values of n and then use the ", StyleBox["Put", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " operator to write the list of data points to a file named ", StyleBox["data.m", FontSlant->"Italic"], ". 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", StyleBox["Mathematica", FontSlant->"Italic"], " provides users the ability to add functionality to the program through \ development of files called ", StyleBox["packages", FontSlant->"Italic"], ". Packages are files intended to be used as ", StyleBox["Mathematica", FontSlant->"Italic"], " input. They consist of function definitions and are written in the ", StyleBox["Mathematica", FontSlant->"Italic"], " programming language. The standard packages (those distributed with the \ software) span such areas as algebra, calculus, discrete mathematics, \ geometry, graphics, linear algebra, number theory, numerical mathematics, and \ statistics.\n\nPrior to using a function defined in a package, the package \ must be read into ", StyleBox["Mathematica", FontSlant->"Italic"], ". Packages can be loaded on all platforms using the following command:\n\n\ ", StyleBox["Needs[\"Context`\"]", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], "\n\nwhere the argument of Needs is a ", StyleBox["context name ", FontSlant->"Italic"], "or ", StyleBox["list of contexts", FontSlant->"Italic"], ". A context name is a string ending in a back quote and consisting of the \ names of the directories or folders where the package resides, concatenated \ with the root name of the package (that is the package name excluding the \ suffix ", StyleBox[".m", FontSlant->"Italic"], "). For example, the package named ", StyleBox["Graphics.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ", located in the ", StyleBox["Graphics", FontWeight->"Bold"], " folder in the ", StyleBox["Packages", FontWeight->"Bold"], " folder, includes functions for creating graphics such as bar and pie \ charts. 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L .97826 .01472 L .8913 .01472 L s P P P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False] }, Open ]], Cell[TextData[{ "Note that if you mistakenly refer to a function that is defined in a \ package prior to loading the package, you will need to execute the command", StyleBox[" ", FontColor->RGBColor[1, 0, 0]], StyleBox["Remove[\"name\"]", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " to delete the function before loading the package which defines it. \n\n\ Appearing below are descriptions of some of the packages supplied with ", StyleBox["Mathematica", FontSlant->"Italic"], " that deal with Algebra, Calculus, Graphics, and Linear Algebra." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"packages"], Cell[CellGroupData[{ Cell[TextData[{ "Extending ", StyleBox["Mathematica", FontSlant->"Italic"], "'s Algebraic Functionality " }], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"packages"], Cell[CellGroupData[{ Cell[TextData["CountRoots.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["CountRoots.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " can be used to compute the number of roots of a real polynomial in a \ given interval." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["PolynomialMod.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["PolynomialMod.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " extends to primes larger than 2", StyleBox["16", FontVariations->{"CompatibilityType"->"Superscript"}], " the built-in polynomial functions Factor, FactorList, and \ PolynomialTGCD." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["ReIm.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"packages", "ReIm.m"}], Cell[TextData[{ "The package named ", StyleBox["ReIm.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " defines simplification rules for built-in functions such as ", StyleBox["Re[ ]", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " and ", StyleBox["Im[ ]", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". Routines in this package provide a mechanism for declaring variables \ real." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"packages", "ReIm.m"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["SymbolicSum.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"packages", "SymbolicSum.m"}], Cell[TextData[{ StyleBox["SymbolicSum.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " provides a mechanism for evaluating symbolic sums of the type\n\n Sum[ \ a[k], {k, min, max}], \n \n where a[k+1]/a[k] is a rational function." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"packages", "SymbolicSum.m"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Trigonometry.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"packages", "Trigonometry.m"}], Cell[TextData[{ "The package named ", StyleBox["Trigonometry.m", 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PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["DSolve.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["DSolve.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " extends the capabilities of ", StyleBox["Mathematica", FontSlant->"Italic"], "'s built-in DSolve function." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["EllipticIntegrate.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["EllipticIntegrate.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " extends the capabilities of the built-in Integrate function to handle \ elliptic integrals and their analogs written in algebraic, trigonometric or \ hyperbolic form." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ 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find limits of expressions that contain a wide class of \ elementary and special functions." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Pade.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Pade.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " computes Pade approximations and economized rational approximations." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["PDSolve1.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["PDSolve1.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " enables the DSolve function to handle first-order PDEs." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["VariationalMethods"], 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" }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"packages", "Graphics3D.m"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["ImplicitPlot.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"packages", "ImplicitPlot.m"}], Cell[TextData[{ StyleBox["ImplicitPlot.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " provides a mechanism for creating sketches of figures defined by \ equations (such as circles and ellipses)." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"packages", "ImplicitPlot.m"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Legend.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"packages", "Legend.m"}], Cell[TextData[{ "The package named ", StyleBox["Legend.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " can be used to draw a legend box on a graphic. 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" }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"packages", "PlotField.m"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["PlotField3D.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"packages"], Cell[TextData[{ "The package named ", StyleBox["PlotField3D.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " includes routines for plotting vector fields in three dimensional space." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"packages"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Polyhedra.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Polyhedra.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " contains the graphics primitives necessary for rendering Platonic solids \ and nonconvex polyhedra that have faces and vertices all of the same type." }], "Text", 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products and dot products." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["GaussianElimination.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["GaussianElimination.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " provides functions for solving a linear system using Gaussian elimination \ and back substitution." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["MatrixManipulation.m"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"packages", "MatrixManipulation.m"}], Cell[TextData[{ StyleBox["MatrixManipulation.m", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " features matrix manipulation routines for creating matrices from block \ elements and extracting subblocks from a matrix." }], "Text", 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PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Menu Items (Macintosh Version) ... 50"], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["File Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontSlant->"Italic"], "menu in the Macintosh Front End provides commands for creating, saving, \ retrieving, and printing Notebooks. Following are brief descriptions of \ each of these commands." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Creating New Notebooks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File New", "creating notebooks"}], Cell[TextData[{ "To create a new Notebook, choose ", StyleBox["New", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. An empty, untitled Notebook will appear on the screen. If you \ begin to type, without specifying a cell style, ", StyleBox["Mathematica", FontSlant->"Italic"], " will automatically create an Input cell to hold the information you \ enter." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File New", "creating notebooks"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "Opening Existing Notebooks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File Open", "retrieving notebooks"}], Cell[TextData[{ "To retrieve an existing Notebook, choose ", StyleBox["Open", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. From the dialog box that is presented, select the drive, folder, \ and filename of the Notebook you wish to open. You can have multiple \ Notebook windows open concurrently and you can copy or move information from \ one Notebook to another.\n\nThe ", StyleBox["File Open", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command can also be used to retrieve files saved in ASCII, PICT, PICS and \ EPSF formats. The information contained in the file being retrieved will be \ translated into a ", StyleBox["Mathematica", FontSlant->"Italic"], " Notebook comprised of one or more cells, with the style of each cell \ being determined by the format of the incoming file. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File Open", "retrieving notebooks"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Closing Notebooks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File Close", "closing notebooks"}], Cell[TextData[{ "To close the current Notebook, choose ", StyleBox["Close", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. ", StyleBox["Mathematica", FontSlant->"Italic"], " will give you an opportunity to save the current Notebook if it has not \ yet been saved." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File Close", "closing notebooks"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Saving Notebooks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File Save", "File Save As", "saving notebooks"}], Cell[TextData[{ "To save a new Notebook, choose", StyleBox["Save", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontSlant->"Italic"], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. A dialog box will prompt you to specify a name for the Notebook as \ well as the destination drive and folder where the Notebook should be saved. \ The ", StyleBox["File Save", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command can also be used to replace an existing Notebook with the revised \ edition that is currently in memory. To save the revised edition without \ replacing the original version, choose ", StyleBox["Save As", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. The ", StyleBox["Save As", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command can be used to save the current Notebook under a new name or in a \ new location. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File Save", "File Save As", "saving notebooks"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Printing Notebooks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File Print", "printing notebooks"}], Cell[TextData[{ "To print one or more copies of all or part of the current Notebook, select \ ", StyleBox["Print", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. The Notebook will print on the printer you have specified in the \ Chooser desk accessory found in the Apple menu. To define headers and \ footers and to specify margin settings, orientation mode, and other page \ setup and printing options, select ", StyleBox["Printing Settings", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File Print", "printing notebooks"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ending a ", StyleBox["Mathematica", FontSlant->"Italic"], " Session" }], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File Quit", "leaving Mathematica"}], Cell[TextData[{ "To end a ", StyleBox["Mathematica", FontSlant->"Italic"], " session, select ", StyleBox["Quit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. ", StyleBox["Mathematica", FontSlant->"Italic"], " will give you an opportunity to save the current Notebook if it has not \ yet been saved." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"File Quit", "leaving Mathematica"}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Edit Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu contains commands for 1) moving, copying, and deleting material in \ the Notebook, 2) identifying incorrectly nested formulas, and 3) adjusting \ global defaults and preferences settings. The following sub-subsections \ describe how to use each of these commands. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Moving Information "], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Edit Cut", "moving information"}], Cell[TextData[{ "To delete material from a Notebook and transfer it to the Clipboard so \ that it can later be inserted elsewhere in the Notebook, select the material \ (text, graphics, cells, etc.) to be deleted and choose ", StyleBox["Cut", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. Once the material has been transferred to the Clipboard it can be \ inserted elsewhere in the Notebook by using the ", StyleBox["Paste", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command from the ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Edit Cut", "moving information"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Duplicating Information"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Edit Copy", "Edit Paste", "duplicating information"}], Cell[TextData[{ "To transfer material from the Notebook to the Clipboard without deleting \ it from the Notebook, select the material and choose ", StyleBox["Copy", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Edit ", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], "menu. Once the material has been copied to the Clipboard it can be \ inserted elsewhere in the Notebook by using the ", StyleBox["Paste", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command from the ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. Note that to copy the structure of a cell as well as its content to \ the Clipboard, the cell's bracket must be selected prior to issuing the ", StyleBox["Copy", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Edit Copy", "Edit Paste", "duplicating information"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Inserting Information"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "vertical I-bar", "horizontal I-bar", "text insertion point", "cell insertion point", "Edit Paste", "inserting information"}], Cell[TextData[{ "To place a copy of the material that has been cut or copied to the \ Clipboard into the Notebook, position the insertion point at the location \ where the material should be inserted and select ", StyleBox["Paste", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. Note that material can either be inserted into an existing \ unformatted cell (by positioning the ", StyleBox["text", FontSlant->"Italic"], " (vertical I-bar) ", StyleBox["insertion point", FontSlant->"Italic"], ") or into a new cell (by positioning the ", StyleBox["cell", FontSlant->"Italic"], " (horizontal I-bar)", StyleBox[" insertion point", FontSlant->"Italic"], "). Also note that graphics can only be inserted at cell insertion points \ (and not text insertion points)." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "vertical I-bar", "horizontal I-bar", "text insertion point", "cell insertion point", "Edit Paste", "inserting information"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Deleting Information"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"deleting information", "Edit Clear"}], Cell[TextData[{ "To erase material from the Notebook without placing it on the Clipboard, \ select the material and choose ", StyleBox["Clear", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"deleting information", "Edit Clear"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Entering Nested ", StyleBox["Mathematica", FontSlant->"Italic"], " Formulas" }], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "nested formulas", "Edit Nesting", "unbalanced parantheses", "parantheses", "brackets", "braces", "Paranthesize", "Bracketize", "List Bracketize", "Unparanthesize", "Indent Left", "Indent Right"}], Cell[TextData[{ "The ", StyleBox["Nesting", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " commands available in the ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu can be used to enter correctly nested ", StyleBox["Mathematica", FontSlant->"Italic"], " formulas and to identify those that are incorrectly nested.\n\nTo check \ the structure of ", StyleBox["Mathematica", FontSlant->"Italic"], " input, position the insertion point within the expression and choose ", StyleBox["Balance", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Nesting", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu. If the expression has unbalanced parantheses, or parantheses, \ brackets, or braces that are incorrectly mixed, ", StyleBox["Mathematica", FontSlant->"Italic"], " will beep and position the text insertion point at the location of the \ error.\n\nTo enclose selected text within parentheses, brackets, or braces, \ choose ", StyleBox["Parenthesize", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Bracketize", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ", or ", StyleBox["List Bracketize", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " respectively from the ", StyleBox["Nesting", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu.\n\nTo remove parentheses, brackets, or braces from selected \ text, choose ", StyleBox["Unparenthesize", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Nesting", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu.\n\nTo aid in documenting the nesting structure of an \ expression, use the ", StyleBox["Indent Left", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "and ", StyleBox["Indent Right", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "commands in the ", StyleBox["Nesting", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu. These commands shift selected text one tab width to the left or \ right respectively." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "nested formulas", "Edit Nesting", "unbalanced parantheses", "parantheses", "brackets", "braces", "Paranthesize", "Bracketize", "List Bracketize", "Unparanthesize", "Indent Left", "Indent Right"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "Setting Defaults and Preferences"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Preferences"], Cell[TextData[{ "The ", StyleBox["Preferences", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu lists commands for adjusting global defaults and preferences \ settings.\n\nTo modify the settings used for on-screen display of Notebooks \ (for example to toggle between displaying and not displaying a dialog box for \ all errors), select ", StyleBox["Display", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Preferences", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu.\n\nTo control how graphs are displayed and printed, select ", StyleBox["Graphics", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Preferences", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu. \n\nTo control what occurs while ", StyleBox["Mathematica", FontSlant->"Italic"], " is computing a result, choose ", StyleBox["Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Preferences", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu. For example, use this menu to have ", StyleBox["Mathematica", FontSlant->"Italic"], " display a clock timing after each evaluation or to request that ", StyleBox["Mathematica", FontSlant->"Italic"], " beep when a kernel message is generated.\n\nTo specify the location of \ the ", StyleBox["Defaults Notebook", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " file and", StyleBox[" Help", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " file, select ", StyleBox["File Locations", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Preferences", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu. These files contain styles that are copied to each new Notebook \ and Help messages for the Front End. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Preferences"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Cell Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu includes commands that enable you to divide, merge, group, and \ ungroup cells. The ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu also includes commands that let you concurrently open or close all \ subgroups in a Notebook." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Dividing Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"dividing cells"], Cell[TextData[{ "The ", StyleBox["Divide Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command can be used to divide a cell into two or three cells. To divide a \ cell so that everything before the text insertion point is included in the \ first cell and everything after the insertion point is in the second cell, \ position the insertion point where you want the split to occur and choose ", StyleBox["Divide Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu.\n\nAlternatively, to split one cell into three cells (where the \ first cell contains all material preceding the selected text, the second cell \ contains only the selected text and the third cell contains all material \ appearing after the selected text), highlight the text that should be placed \ in the second cell and choose ", StyleBox["Divide Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"dividing cells"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Merging Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"merging cells"], Cell[TextData[{ "To combine two or more cells into one cell, highlight the brackets of the \ cells to be combined and choose ", StyleBox["Merge Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"merging cells"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Grouping and Ungrouping Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"grouping cells", "ungrouping cells"}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " automatically groups cells depending upon their styles. The ", StyleBox["Automatic Grouping", FontSlant->"Italic"], " feature can be turned off by choosing ", StyleBox["Automatic Grouping", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. Once this feature has been turned off, you can change cell grouping \ manually by using commands in the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. To group a range of cells manually, highlight the brackets of the \ contiguous cells you wish to group and select ", StyleBox["Group Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. The selected cells will be enclosed in a grouping bracket. Note \ that there is no limit to the number grouping levels possible in a Notebook. \ To undo a cell group, highlight the grouping bracket for the group to be \ undone and choose ", StyleBox["Ungroup Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"grouping cells", "ungrouping cells"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "Opening and Closing Multilevel Cell Groups"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"opening cell groups", "closing cell groups"}], Cell[TextData[{ "To open all cells in multiple closed cell groups (identified by solid \ triangles at the bottom of the grouping brackets), select the closed group \ brackets and choose ", StyleBox["Open All Subgroups", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. All levels of the selected groups will open. Similarly, to close \ all levels of selected groups, choose ", StyleBox["Close All Subgroups", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. Since a closed group will display the first cell in the group, \ closing groups is useful for collapsing notebooks into outline form. Note \ that a single group can be opened or closed by alternately double-clicking on \ its grouping bracket." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"opening cell groups", "closing cell groups"}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Graph Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Graph", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu includes commands for converting graphics in a Notebook from one \ format to another including PICT, Bitmap PICT, and PostScript. Note that the \ converted form of the graphic will replace the original form in the \ Notebook." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "Converting to PICT, Bitmap PICT and PostScript"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"PICT", "Bitmap PICT", "PostScript"}], Cell[TextData[{ "Graphics can be converted into different formats depending upon the level \ of visual quality desired and on the amount of disk space available. PICT \ and Bitmap PICT formats are more compact than PostScript, but do not provide \ the same level of resolution when printed or resized. Graphics saved in \ PostScript format can also be edited. If you will never need to print or \ resize a graphic, converting the graphic to Bitmap PICT can result in \ appreciable disk storage savings. To convert a graphic to PICT, Bitmap PICT, \ or PostScript format, highlight the cell bracket surrounding the graphic and \ select either ", StyleBox["Convert to PICT", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ", ", StyleBox["Convert to Bitmap PICT", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ", or ", StyleBox["Convert to PostScript", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Graph", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu.\n" }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"PICT", "Bitmap PICT", "PostScript"}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Find Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Find", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu includes commands that can be used to locate and optionally replace \ text according to criteria you specify. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Searching for Text"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"locating text", "Find", "Find Again"}], Cell[TextData[{ "Use the ", StyleBox["Find", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command in the ", StyleBox["Find", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu to locate text strings or cell characteristics (including attributes, \ keywords, and style). The search will begin at the position where the text \ insertion point is located. You can ask ", StyleBox["Mathematica", FontSlant->"Italic"], " to stop the search after the first match or to search the entire document \ for all matches. If you request that all matches be found, the result of the \ search will include only entire cells rather than individual text ranges. You \ can also find the next occurence of the search string by choosing ", StyleBox["Find Again", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Find", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"locating text", "Find", "Find Again"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Replacing Text"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "replacing text", "Replace", "Replace and Find Again", "Replace All"}], Cell[TextData[{ "Three commands in the ", StyleBox["Find", FontSlant->"Italic"], " menu provide a mechanism for replacing text with text you specify in the \ ", StyleBox["Replace with", FontSlant->"Italic"], " field of the dialog box for the ", StyleBox["Find", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command. Select the ", StyleBox["Replace", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command to overwrite the selected text range that is the result of the \ last ", StyleBox["Find", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "request. Choose ", StyleBox["Replace and Find Again", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "to not only replace the selected text, but to also find the next \ occurrence of the string. Finally, use ", StyleBox["Replace All", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "to replace all occurences of the search text from the current selection to \ the end of the file. Note that if the ", StyleBox["Wrap around", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "option is ", StyleBox["on", FontSlant->"Italic"], " in the ", StyleBox["Find", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " dialog box, ", StyleBox["Mathematica", FontSlant->"Italic"], " will \"wrap around\" from the end of the document to the beginning of the \ Notebook and replace matches that occur above, as well as below, the current \ selection." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "replacing text", "Replace", "Replace and Find Again", "Replace All"}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Action Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Simplifying the Creation of Input"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "Copy Input from Above", "Complete Selection", "Copy Output from Above", "Make Template"}], Cell[TextData[{ "The ", StyleBox["Prepare Input", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu of the ", StyleBox["Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu includes commands which help to minimize the time required to create \ input and minimize the possibility of making typographical errors. There are \ also commands for rotating graphs and recording sounds.\n\nUse the ", StyleBox["Copy Input from Above", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command to copy the immediately preceding input to the location \ currently marked by the text or cell insertion point. Once the input has \ been copied, it can be edited and submitted to the Kernel. The ", StyleBox["Copy Output from Above", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command works similarly except that it copies the immediately preceding \ output. These commands serve as an aid in creating new input that varies \ only slightly from existing input or output. \n\nUse the", StyleBox[" ", FontSlant->"Italic"], StyleBox["Complete Selection", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command to have ", StyleBox["Mathematica", FontSlant->"Italic"], " complete the name of a partially entered built-in or user-defined \ command, function, or variable. If there is only one match that completes \ the currently selected text range, then ", StyleBox["Mathematica", FontSlant->"Italic"], " will replace the selection with the match. If there are several names \ that begin with the selected text, ", StyleBox["Mathematica", FontSlant->"Italic"], " will display a menu of possible matches, and you can choose the \ appropriate match by highlighting it and pressing Shift-Return. Note that \ the keyboard equivalent for the ", StyleBox["Complete Selection", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command is ", StyleBox["Command-k", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[".", FontColor->RGBColor[1, 0, 0]], "\n\nIf you would like ", StyleBox["Mathematica", FontSlant->"Italic"], " to create a template which includes the syntax and commonly used \ arguments of the currently highlighted function name, choose ", StyleBox["Make Template", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Prepare Input", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu. Once ", StyleBox["Mathematica", FontSlant->"Italic"], " has created the template, you can individually select arguments and \ replace them with their appropriate values.\n\nThe ", StyleBox["3D ViewPoint Selector", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command provides a dialog box that can be used to select the Cartesian \ viewpoint coordinates for 3-dimensional graphs. Once the coordinates have \ been specified in the dialog box, they can be pasted (by clicking on the ", StyleBox["Paste", FontSlant->"Italic"], " button) at the location marked by the text insertion point in the current \ input line.\n\nThe ", StyleBox["Color Selector", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command provides a mechanism for choosing colors of graphical objects \ without having to figure out the RGBColor settings. The ", StyleBox["Color Selector", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command features a dialog box that can be used to select a color and then \ paste the RGBColor command into the input line currently marked by the text \ insertion point. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{ "Copy Input from Above", "Complete Selection", "Copy Output from Above", "Make Template"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Creating and Controlling Kernel Connections"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To create, configure, launch, abort, interrupt, or quit a kernel \ connection, choose ", StyleBox["Kernels and Tasks", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the", StyleBox[" Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Evaluating a Notebook"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Evaluate Notebook", "initialization cells"}], Cell[TextData[{ "To select and evaluate all active cells in the current Notebook, choose ", StyleBox["Evaluate Notebook", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. This command is especially useful for recalculating a final result \ that depends on output generating by computing all preceding input cells. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Evaluate Notebook", "initialization cells"}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "Evaluating Initialization Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "In ", StyleBox["Mathematica", FontSlant->"Italic"], ", cells can be created that contain definitions of ", StyleBox["Mathematica", FontSlant->"Italic"], " functions. Subsequent cells may contain expressions that use these \ definitions to produce output. Often it is desirable to declare the cells \ that contain the definitions as ", StyleBox["initialization cells ", FontSlant->"Italic"], "and to configure ", StyleBox["Mathematica", FontSlant->"Italic"], " so that the initialization cells are automatically evaluated whenever a \ Notebook is opened. If, however, automatic evaluation has been suppressed, \ you can still have ", StyleBox["Mathematica", FontSlant->"Italic"], " evaluate initialization cells by choosing ", StyleBox["Evaluate Initialization", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Interrupting Calculations"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Interrupt Calculation", "Abort Calculation"}], Cell[TextData[{ "To completely abort a calculation, select ", StyleBox["Interrupt Calculation", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu and click the ", StyleBox["Abort", FontSlant->"Italic"], " button. Alternatively, choose ", StyleBox["Abort Calculation", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. Note that the ", StyleBox["Interrupt Calculation", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command can also be used to momentarily stop the current computation so \ that you can check the state of the Kernel or send other evaluations to the \ Kernel before resuming the original computation." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->{"Interrupt Calculation", "Abort Calculation"}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Style Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Applying Cell Styles"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell styles"], Cell[TextData[{ "The ", StyleBox["Cell Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu of the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu provides a complete list of available cell styles. To apply a style, \ either select the style prior to typing information into a new cell, or after \ selecting the cell bracket of an existing cell. Alternatively, keyboard \ equivalent commands can be used to apply the most frequently used styles" }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell styles"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Assigning Attributes to Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell attributes"], Cell[TextData[{ "The ", StyleBox["Attributes", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu of the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu lists cell attributes that can be applied to cells. Each of these \ attribute commands acts as a toggle switch (if a check appears beside the \ command, then the attribute has been applied to the currently selected cell). \ Note that cell attributes can be applied to entire cells only. \n\nTo apply \ an attribute to a cell, highlight the bracket of the cell that you want to \ apply the attribute to (or place a text insertion point within the cell) and \ select the attribute from the ", StyleBox["Attribute", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu.\n\nFollowing is a list of available cell attributes and a brief \ description of their use:\n\n1) ", StyleBox["Formatted", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "versus ", StyleBox["Unformatted Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ": The formatted attribute is usually applied to cells containing ", StyleBox["Mathematica", FontSlant->"Italic"], " output. Formatted cells can not be edited. Cells containing text and ", StyleBox["Mathematica", FontSlant->"Italic"], " input are typically unformatted. \n\n2) ", StyleBox["Active", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " versus ", StyleBox["Inactive Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ": Active cells are cells that can be evaluated by the Kernel. Cells that \ are inactive are ignored by the Kernel.\n\n3) ", StyleBox["Initialization Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ": Initialization cells are cells that can be evaluated automatically as \ soon as a Notebook is opened.\n\n4) ", StyleBox["Locked Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ": Locked cells are cells that can not be deleted or modified.\n\n5) ", StyleBox["Closed Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ": A closed cell is a cell that has been collapsed so that the content of \ the cell is no longer visible. Note that a closed cell can only be opened by \ selecting the ", StyleBox["Closed", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command from the ", StyleBox["Attributes", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu.\n\n6) ", StyleBox["Fixed Height Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ": Fixed height cells are cells whose heighth can be manually adjusted. \ Assigning this attribute to a cell is useful if you wish to decrease the size \ of a large cell.\n\n7) ", StyleBox["Scroll Horizontally", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ": This attribute is useful if a cell contains information that is too \ wide to fit on the screen (for example a wide graphic cell or a long formula \ that has been entered on one line).\n\n8) ", StyleBox["Box around Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ": The Box around Cell attribute can be used to add emphasis to a \ particular cell in the Notebook (such as a Title cell or a cell containing a \ major result)." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell attributes"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Assigning Fonts"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"assigning fonts"], Cell[TextData[{ "The ", StyleBox["Font", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu of the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu lists all fonts installed in the System file stored in your System \ folder. Fonts may be applied to text ranges or to entire cells. Note that \ text included in Kernel output must be formatted with a monospaced font, such \ as Courier, to be displayed correctly." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"assigning fonts"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Assigning Typefaces"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"assigning typefaces"], Cell[TextData[{ "The ", StyleBox["Face", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu of the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu lists nine typefaces (Plain, Bold, Italic, Underline, Outline, \ Shadow, Superscript, Subscript, and Overstrike) that can be applied to some \ or all of the text in a cell depending upon whether a text range or cell \ bracket is highlighted. Note that selecting the Plain typeface turns all \ other typefaces off. Also note that multiple typefaces can be applied to the \ same piece of text." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"assigning typefaces"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Assigning Type Sizes"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"assigning type sizes"], Cell[TextData[{ "The ", StyleBox["Size", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu of the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu lists type sizes that can be applied to selected text. The sizes \ appearing in the outline typeface are those that will look best on your \ screen. The ", StyleBox["Size", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu also includes commands (", StyleBox["Larger", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "and ", StyleBox["Smaller", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ") for changing the size of selected text one point at a time and for \ specifying a size not listed in the menu (", StyleBox["Custom Size", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], "). " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"assigning type sizes"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Applying Color to Text "], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"text color"], Cell[TextData[{ "The ", StyleBox["Text Color", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu of the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu lists colors that can be applied to selected text ranges or to all \ text in cells whose brackets are currently highlighted. In addition, the ", StyleBox["Text Color", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu lists a series of ", StyleBox["Special", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "commands that can be used to assign colors from the Macintosh color wheel \ to selected text. There is also a ", StyleBox["Cell Bracket", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command that can be used to assign a color from the Macintosh color wheel \ to all cell brackets in the current Notebook." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"text color"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Applying Color to the Background of Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell background color"], Cell[TextData[{ "The ", StyleBox["Background Color", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu of the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu lists the same commands that are found in the ", StyleBox["Text Color", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu. A color chosen from this submenu is applied to the background of \ the cell whose bracket is currently selected. If the ", StyleBox["Cell Bracket", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command is used to select a color from the Macintosh color wheel, the \ color chosen is applied to the bracket and background of the selected cell. \ \n\nThe ", StyleBox["Background Color", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu also features a ", StyleBox["Gray Box", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command that can be used to draw a box around a cell and to color the \ background of the cell to various shades of gray. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell background color"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Controlling Page Breaks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"page breaks"], Cell[TextData[{ "The ", StyleBox["Page Breaks", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu of the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu provides commands for forcing or suppressing a page break above or \ below the selected cell. Use the ", StyleBox["Break above Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "and ", StyleBox["Break below Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "commands to force a page break above or below the selected cell. Use the \ ", StyleBox["No Break above Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "and ", StyleBox["No Break below Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "commands to suppress page breaks around the selected cell.\n\nThere are \ also commands in this submenu for preventing page breaks within a cell or \ cell group (to the extent that the cell or cell group can fit on one printed \ page). Note that the ", StyleBox["Show Page Breaks", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command in the ", StyleBox["Printing Settings", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu of the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu is useful for displaying page breaks on the screen. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"page breaks"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Controlling Cell Margins"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell margins"], Cell[TextData[{ "The ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu includes a ", StyleBox["Show Ruler", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command that can be used to display a ruler across the top of the Notebook \ window. The ruler features two triangular markers that can be used to \ control the left and right margins of the selected cell. Margin settings can \ be changed by dragging the markers along the ruler." }], "Text", CellMargins->{{8, 107}, {Inherited, Inherited}}, Evaluatable->False, PageBreakAbove->True, CellLabelMargins->{{0, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, CellTags->"cell margins"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Editing Cell Styles"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell styles"], Cell[TextData[{ "Predefined cell styles can be modified and entirely new styles can be \ created by using the ", StyleBox["Edit Styles", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command in the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. Once a style is changed, the modifications will automatically be \ applied to cells in the Notebook which exhibit that style. Note that \ attributes that have been applied locally (by using the ", StyleBox["Attributes", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command in the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu) are not overridden by cell style settings. \n\nTo modify an \ existing style, 1) access the ", StyleBox["Styles", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "dialog box by selecting the ", StyleBox["Edit Styles", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command from the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu, 2) highlight the cell bracket corresponding to the style you wish \ to edit, 3) use the ", StyleBox["Attributes", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command in the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu to modify the attributes settings, and 4) close the dialog box to \ apply the changes to the cells that have been assigned that style. Note that \ style changes are saved when you save the Notebook and that style sheets \ associated with one Notebook are not tied to (do not affect) other Notebooks. \ " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell styles"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Restoring Styles to their Original Settings"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell styles"], Cell[TextData[{ "To restore cell styles that have been modified via the ", StyleBox["Styles", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "dialog box, select the ", StyleBox["All Default Styles", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command from the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. This command will restore all styles to their original settings and \ will automatically apply the changes to the appropriate cells in the \ Notebook." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell styles"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Window Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Window", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu provides commands for organizing your open ", StyleBox["Mathematica", FontSlant->"Italic"], " windows on the screen. In addition, a listing of titles of open windows \ appears at the bottom of the menu. You can use this listing to select the \ title of the window you wish to make current. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Stacking Windows"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"stacking windows"], Cell[TextData[{ "Use the ", StyleBox["Stack Windows", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command in the", StyleBox["Windows", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu to make all open windows the same size and to overlap them on the \ screen such that the window title bars remain visible. ", StyleBox[" ", FontSlant->"Italic"], "In this arrangement, you can bring a window to the front of the stack by \ clicking on its title bar. Note that the size of the windows will be \ determined by the size of the monitor screen being used." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"stacking windows"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Tiling Windows "], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"tiling windows"], Cell[TextData[{ "Two commands provide a means of arranging all open windows into \ side-by-side rectangles of equal size. Use the ", StyleBox["Tile Windows Tall", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command to choose a tall and narrow shape for the tiled windows and the ", StyleBox["Tile Windows Wide", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command to choose a short and wide shape." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"tiling windows"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Help Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Help", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu includes commands for listing ", StyleBox["Mathematica", FontSlant->"Italic"], " functions and keyboard shortcuts for ", StyleBox["Mathematica", FontSlant->"Italic"], " commands. This menu also provides access to an on-line ", StyleBox["Mathematica", FontSlant->"Italic"], " tutorial. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[{ "Using ", StyleBox["Mathematica", FontSlant->"Italic"], " Functions and Packages" }], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Open Function Browser", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command lists, by category, the names of built-in functions and standard \ packages. You can use this command to view the description, syntax, and \ options of a built-in function, to evaluate a function, or to paste a \ function into a cell. You can also use this command to view a description of \ a standard package, load a package, and access functions in a loaded package.\ \n\nTo obtain information (syntax, options, description) about a function \ name you have selected in your Notebook, choose ", StyleBox["Find in Function Browser", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Help", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Troubleshooting Problems"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To view an explanation of why ", StyleBox["Mathematica", FontSlant->"Italic"], " beeped at you, select ", StyleBox["Why the Beep?", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the Help menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Getting Started with ", StyleBox["Mathematica", FontSlant->"Italic"], "" }], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To view an introduction to some of the basic features of ", StyleBox["Mathematica", FontSlant->"Italic"], ", choose ", StyleBox["Getting Started", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the Help menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Getting Help on Menu Commands"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To view a description of a menu command, select ", StyleBox["Help Pointer", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Help", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu and then select the command of interest. To view a summary of \ keyboard shortcuts for ", StyleBox["Mathematica", FontSlant->"Italic"], " commands, select ", StyleBox["Shortcuts", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Help", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Magnification Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"magnifying notebook contents"], Cell[TextData[{ "The ", StyleBox["Magnification", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu, located at the bottom of the Notebook window, is useful for \ enlarging or reducing the magnification of the Notebook's contents while \ keeping the window the same size. The pop-up menu lists preset magnification \ values and an ", StyleBox["Other", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command that can be used to specify a magnification that is not listed. \ In addition, the pop-up includes a ", StyleBox["Fit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command that is useful for previewing the page layout that will be used \ when the Notebook is printed." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"magnifying notebook contents"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[ "Menu Items (Windows Version) ... 60"], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["File Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[ "The File menu in the Windows Front End provides commands for creating, \ saving, retrieving, and printing Notebooks. Following are brief descriptions \ of each of these commands."], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Creating New Notebooks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To create a new Notebook, choose ", StyleBox["New", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. An empty, untitled Notebook will appear on the screen. If you \ begin to type, without specifying a cell style, ", StyleBox["Mathematica", FontSlant->"Italic"], " will automatically create an Input cell to hold the information you \ enter." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Opening Existing Notebooks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To retrieve an existing Notebook, choose ", StyleBox["Open/Import", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontSlant->"Italic"], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. From the dialog box that is presented, select the drive, \ directory, and filename of the Notebook you wish to open. You can have \ multiple Notebook windows open concurrently and you can copy or move \ information from one Notebook to another.\n\nThe ", StyleBox["File Open/Import", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command can also be used to retrieve files saved in other file formats \ including ASCII, Bitmap, and Metafile formats. The information contained in \ the file being retrieved will be translated into a Mathematica Notebook \ comprised of one cell, with the style of the cell being determined by the \ format of the incoming file. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Closing Notebooks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To close the current Notebook, choose ", StyleBox["Close", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. ", StyleBox["Mathematica", FontSlant->"Italic"], " will give you an opportunity to save the current Notebook if it has not \ yet been saved." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Saving Notebooks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To save a new Notebook, choose ", StyleBox["Save", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontSlant->"Italic"], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. A dialog box will prompt you to specify a name for the Notebook as \ well as the destination drive and directory where the Notebook should be \ saved. The ", StyleBox["File Save", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command can also be used to replace an existing Notebook with the revised \ edition that is currently in memory. To save the revised edition without \ replacing the original version, choose ", StyleBox["Save As/Export", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. The ", StyleBox["Save As/Export", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command can be used to save the current Notebook under a new name or in a \ new location. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Printing Notebooks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To print one or more copies of all or part of the current Notebook, select \ ", StyleBox["Print", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. To specify the printer to which your Notebook is sent, as well as \ the paper size and orientation mode to be used, click ", StyleBox["Setup", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Print", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " dialog box. To define headers and footers and to specify margin settings \ and other printing options, select ", StyleBox["Printing Options", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Options", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ending a ", StyleBox["Mathematica", FontSlant->"Italic"], " Session" }], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To end a ", StyleBox["Mathematica", FontSlant->"Italic"], " session, select ", StyleBox["Exit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["File", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. ", StyleBox["Mathematica", FontSlant->"Italic"], " will give you an opportunity to save the current Notebook if it has not \ yet been saved." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Edit Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu contains commands for moving, copying, searching for, and deleting \ material in the Notebook. The following sub-subsections describe how to use \ each of these commands. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Moving Information "], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To delete material from a Notebook and transfer it to the Clipboard so \ that it can later optionally be inserted elsewhere in the Notebook, select \ the material (text, graphics, or cells) to be deleted and choose ", StyleBox["Cut", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. Once the material has been transferred to the Clipboard it can be \ inserted elsewhere in the Notebook by using the ", StyleBox["Paste", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command from the ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Duplicating Information"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To transfer material from the Notebook to the Clipboard without deleting \ it from the Notebook, select the material and choose ", StyleBox["Copy", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Edit ", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], "menu. Once the material has been copied to the Clipboard it can be \ inserted elsewhere in the Notebook by using the ", StyleBox["Paste", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command from the ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Inserting Information"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To place a copy of the material that has been cut or copied to the \ Clipboard into the Notebook, position the insertion point at the location \ where the material should be inserted and select ", StyleBox["Paste", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. Note that material can either be inserted into an existing cell or \ into a new cell (by positioning the ", StyleBox["cell", FontSlant->"Italic"], " (horizontal I-bar)", StyleBox[" insertion point", FontSlant->"Italic"], "). Also note that graphics can only be pasted between cells and not into \ existing cells. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Searching for Text"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[ "The Find command in the Edit menu enables you to search the current Notebook \ for the text you specify. You can specify the direction of the search and \ whether or not to match the case of the characters being searched for.\n\nThe \ Find and Replace command in the Edit menu lets you search the current \ Notebook for text you specify and then, optionally, replace the found text \ with text you specify."], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Deleting Information"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To erase material from the Notebook without placing it on the Clipboard, \ select the material and choose ", StyleBox["Clear", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Edit", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. You can also delete pieces of text within a cell by selecting the \ text and pressing the Del key." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Cell Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu includes commands that enable you to divide, merge, group and ungroup \ cells, and concurrently open or close all subgroups in a Notebook. The ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu also includes commands that let you assign attributes to cells and \ control where page breaks should occur." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Dividing Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"dividing cells"], Cell[TextData[{ "The ", StyleBox["Divide Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command can be used to divide a cell into two or three cells. To divide a \ cell so that everything before the text insertion point is included in the \ first cell and everything after the insertion point is in the second cell, \ position the insertion point where you want the split to occur and choose ", StyleBox["Divide Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu.\n\nAlternatively, to split one cell into three cells (where the \ first cell contains all material preceding the selected text, the second cell \ contains only the selected text and the third cell contains all material \ appearing after the selected text), highlight the text that should be placed \ in the second cell and choose ", StyleBox["Divide Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"dividing cells"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Merging Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"merging cells"], Cell[TextData[{ "To combine two or more cells into one cell, highlight the brackets of the \ cells to be combined and choose ", StyleBox["Merge Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"merging cells"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Grouping and Ungrouping Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To group a range of cells, highlight the brackets of the contiguous cells \ you wish to group and select ", StyleBox["Group Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. The selected cells will be enclosed in a grouping bracket. Note \ that there is no limit to the number grouping levels possible in a Notebook. \ To undo a cell group, highlight the grouping bracket for the group to be \ undone and choose ", StyleBox["Ungroup Cells", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Opening and Closing Multilevel Cell Groups"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To open all cells in multiple closed cell groups (identified by solid \ triangles at the bottom of the grouping brackets), select the closed group \ brackets and choose ", StyleBox["Open All Subgroups", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. All levels of the selected groups will open. Similarly, to close \ all levels of selected groups, choose ", StyleBox["Close All Subgroups", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. Since a closed group will display the first cell in the group, \ closing groups is useful for collapsing notebooks into outline form. Note \ that a single group can be opened or closed by alternately double-clicking on \ its grouping bracket, or by choosing ", StyleBox["Open/Close Group", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Assigning Attributes to Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The Cell menu contains four commands for assigning attributes to cells. \ Each of these attribute commands acts as a toggle switch (if a check appears \ beside the command, then the attribute has been applied to the currently \ selected cell). Note that cell attributes can be applied to entire cells \ only. \n\nTo apply an attribute to a cell, highlight the bracket of the cell \ that you want to apply the attribute to (or place a text insertion point \ within the cell) and select the appropriate command from the ", StyleBox["Cell ", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], "menu. Following is a brief description of the available attributes:\n\n1) \ The formatted attribute is usually applied to cells containing ", StyleBox["Mathematica", FontSlant->"Italic"], " output. Formatted cells can not be edited. Cells containing text and ", StyleBox["Mathematica", FontSlant->"Italic"], " input are typically unformatted. To toggle between formatted and \ unformatted form, choose the ", StyleBox["Formatted", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu.\n\n2) Active cells are cells that can be evaluated by the Kernel. \ Cells that are inactive are ignored by the Kernel. To toggle between active \ and inactive status, choose ", StyleBox["Inactive", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu.\n\n3) Initialization cells are cells that can be evaluated \ automatically as soon as a Notebook is opened. To mark a selected cell as an \ initialization cell, select ", StyleBox["Initialization", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu.\n\n4) Locked cells are cells that can not be deleted or modified. \ To toggle between locked and unlocked status, select ", StyleBox["Locked", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Controlling Page Breaks"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Page Breaks", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command of the ", StyleBox["Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu provides a mechanism for forcing or suppressing a page break above \ the selected cell. Use the ", StyleBox["Force Page Break Above Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "and ", StyleBox["Prevent Page Break Above Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "commands of the ", StyleBox["Page Breaks", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " sub-menu to respectively force or suppress a page break above the \ selected cell. Use the ", StyleBox["Show Page Breaks", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command to display page breaks on the screen." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Graph Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Graph", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu includes commands for converting a ", StyleBox["Mathematica", FontSlant->"Italic"], " PostScript graphic to a Bitmap or to a ", StyleBox["Mathematica", FontSlant->"Italic"], " Input form. Note that the converted form of the graphic will replace the \ original form in the Notebook." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[{ "Converting to Bitmap or ", StyleBox["Mathematica", FontSlant->"Italic"], " Input Form" }], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "Graphics can be converted into different formats depending upon the level \ of visual quality desired and on the amount of disk space available. Bitmap \ formats are more compact than PostScript, but do not provide the same level \ of resolution when printed or resized. Graphics saved in PostScript format \ can also be edited. If you will never need to print or resize a graphic, \ converting the graphic to Bitmap can result in appreciable disk storage \ savings. To convert a graphic to Bitmap format, highlight the cell bracket \ surrounding the graphic and select ", StyleBox["Image Conversions", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Graph", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. Choose the ", StyleBox["Convert to Bitmap", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " image conversion. Note that a Bitmap graphic can not be subsequently \ converted to PostScript.\n\n", StyleBox["Mathematica", FontSlant->"Italic"], " graphics can also be converted into a form that can be treated as ", StyleBox["Mathematica", FontSlant->"Italic"], " input. To transform a graphic into ", StyleBox["Mathematica", FontSlant->"Italic"], " input, highlight the cell bracket surrounding the graphic and select ", StyleBox["Image Conversions", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Graph", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. Choose the ", StyleBox["Convert to Input Form", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command. Note that representing the graphic in this form requires much \ more memory than the graphic itself." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Action Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The Action menu includes commands for preparing input for the Kernel, for \ evaluating ", StyleBox["Mathematica", FontSlant->"Italic"], " input, and for stopping the current calculation." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Simplifying the Creation of Input"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Prepare Input", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu of the ", StyleBox["Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu includes commands which help to minimize the time required to create \ input and minimize the possibility of making typographical errors. There is \ also a command for rotating graphs.\n\nUse the ", StyleBox["Copy Input from Above", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command to copy the immediately preceding input to the location \ currently marked by the text or cell insertion point. Once the input has \ been copied, it can be edited and submitted to the Kernel. The ", StyleBox["Copy Output from Above", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command works similarly except that it copies the immediately preceding \ output. These commands serve as an aid in creating new input that varies \ only slightly from existing input or output. \n\nUse the", StyleBox[" ", FontSlant->"Italic"], StyleBox["Complete Selection", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command to have ", StyleBox["Mathematica", FontSlant->"Italic"], " complete the name of a partially entered built-in or user-defined \ command, function, or variable. If there is only one match that completes \ the currently selected text range, then ", StyleBox["Mathematica", FontSlant->"Italic"], " will replace the selection with the match. If there are several names \ that begin with the selected text, ", StyleBox["Mathematica", FontSlant->"Italic"], " will display a menu of possible matches, and you can choose the \ appropriate match by clicking it. Note that the keyboard equivalent for the \ ", StyleBox["Complete Selection", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command is ", StyleBox["Ctrl+K", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[".", FontColor->RGBColor[1, 0, 0]], "\n\nThe ", StyleBox["3D ViewPoint Selector", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command provides a dialog box that can be used to select the Cartesian \ viewpoint coordinates for 3-dimensional graphs. Once the coordinates have \ been specified in the dialog box, they can be pasted (by clicking on the ", StyleBox["Paste", FontSlant->"Italic"], " button) at the location marked by the text insertion point in the current \ input line.\n\nThe ", StyleBox["Color Selector", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command provides a mechanism for choosing colors of graphical objects \ without having to figure out the RGBColor settings. The ", StyleBox["Color Selector", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command features a dialog box that can be used to select a color and then \ paste the RGBColor command into the input line currently marked by the text \ insertion point. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Evaluating a Notebook"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To select and evaluate all cells in the current Notebook, choose ", StyleBox["Evaluate Notebook", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. This command is especially useful for recalculating a final result \ that depends on output generating by computing all preceding input cells. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Evaluating Initialization Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "In ", StyleBox["Mathematica", FontSlant->"Italic"], ", cells can be created that contain definitions of ", StyleBox["Mathematica", FontSlant->"Italic"], " functions. Subsequent cells may contain expressions that use these \ definitions to produce output. Often it is desirable to declare the cells \ that contain the definitions as ", StyleBox["initialization cells ", FontSlant->"Italic"], "and to configure ", StyleBox["Mathematica", FontSlant->"Italic"], " so that the initialization cells are automatically evaluated whenever a \ Notebook is opened. If, however, automatic evaluation has been suppressed, \ you can still have ", StyleBox["Mathematica", FontSlant->"Italic"], " evaluate initialization cells by choosing ", StyleBox["Evaluate Initialization", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Interrupting Calculations"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To completely abort a calculation, select ", StyleBox["Interrupt", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu and click the ", StyleBox["Abort", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " button. Note that the ", StyleBox["Interrupt", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command can also be used to step through the current computation so that \ you can check the state of the Kernel or send other evaluations to the Kernel \ before resuming the original computation." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Style Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Applying Cell Styles"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Cell Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "submenu of the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu provides a complete list of available cell styles. To apply a style \ to one or more cells, select the cell and choose the appropriate style from \ the ", StyleBox["Cell Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " submenu or enter the keyboard equivalent command. Alternatively, a style \ can be applied to a selected cell by choosing the style from the drop down \ menu featured in the ", StyleBox["Toolbar", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Editing Cell Styles"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell styles"], Cell[TextData[{ "Predefined cell styles can be modified and entirely new styles can be \ created by using the ", StyleBox["Edit Notebook Styles", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command in the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. Once a style is changed, the modifications will automatically be \ applied to cells in the Notebook which exhibit that style.\n\nTo modify an \ existing style, 1) access the ", StyleBox["Styles for Notebook", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "dialog box by selecting the ", StyleBox["Edit Notebook Styles", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command from the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu, 2) click the name of the style you wish to redefine, 3) alter style \ settings using the Font and Format dialog boxes, and 4) close the dialog box \ to apply the changes to the cells that have been assigned that style. Note \ that style changes are saved when you save the Notebook and that style sheets \ associated with one Notebook are not tied to (do not affect) other Notebooks. \ " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"cell styles"] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Assigning Fonts"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "When the ", StyleBox["Font", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command is chosen from the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu, a dialog box will be displayed that lists all fonts installed on \ your computer. To apply a font to selected text, click on the name of the \ font you wish to apply and select", StyleBox[" OK", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ". Note that text included in Kernel output must be formatted with a \ monospaced font, such as Courier, to be displayed correctly." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Assigning Typefaces"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To assign a typeface to selected text, choose the ", StyleBox["Font", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command from the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. A dialog box will be displayed that includes a drop box listing \ four typefaces (Regular, Italic, Bold and Bold Italic). Typefaces can be \ applied to some or all of the text in a cell depending upon whether a text \ range or cell bracket is highlighted. Note that selecting the Regular \ typeface turns all other typefaces off. Also note that multiple typefaces \ can be applied to the same piece of text." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Assigning Type Sizes"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The change the type size used in displaying and printing the selected \ text, choose the ", StyleBox["Font", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command from the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. A dialog box will be displayed that includes a drop box listing \ available type sizes." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Applying Color to Text "], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To change the color of the selected text, choose the ", StyleBox["Font", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command from the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu and select the desired color from the included drop box." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Applying Color to the Background of Cells"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To apply color to the background of one or more selected cells, choose the \ ", StyleBox["Format", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command from the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. A dialog box will be displayed that includes a ", StyleBox["Cell Background", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " option. This option can be used to apply a predefined color, or to \ define and apply a custom color to a cell's background. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Assigning Display Attributes"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To enclose a cell within a box, choose the ", StyleBox["Fomat ", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], "command from the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu and select the ", StyleBox["Box Around Cell", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " option. Similarly, to enable the horizontal movement of a selected \ cell's contents when the horizontal scroll box is dragged along the bottom of \ a window, select ", StyleBox["Format", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Style", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu and turn on the ", StyleBox["Scroll Horizontally", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " option." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Options Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Controlling Cell Margins"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To change cell margin definitions, use the ", StyleBox["Ruler Bars", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " command in the ", StyleBox["Options", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu to toggle the display of the ruler and margin markers across the top \ of the Notebook window. The margin markers that can be used to control the \ left and right margins of the selected cell. Margin settings can be changed \ by dragging the markers along the ruler." }], "Text", CellMargins->{{8, 107}, {Inherited, Inherited}}, Evaluatable->False, PageBreakAbove->True, CellLabelMargins->{{0, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Setting Defaults and Preferences"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Preferences"], Cell[TextData[{ "To control how and when graphs are rendered, select ", StyleBox["Graphics", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Options", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu. \n\nTo control when and how input cells are evaluated, choose ", StyleBox["Action", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Options", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. For example, use this command to have ", StyleBox["Mathematica", FontSlant->"Italic"], " display a clock timing after each evaluation.\n\nTo specify the Kernel \ that will be launched automatically with the first computation, and to \ allocate additional memory to the Kernel, select ", StyleBox["Kernel", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "from the ", StyleBox["Options", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, CellTags->"Preferences"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Windows Menu"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Window", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu provides commands for organizing your open ", StyleBox["Mathematica", FontSlant->"Italic"], " windows on the screen. In addition, a listing of titles of open windows \ appears at the bottom of the menu. You can use this listing to activate a \ particular window. " }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Stacking Windows"], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "Use the ", StyleBox["Cascade Windows", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "command in the", StyleBox["Windows", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], "menu to make all open windows the same size and to overlap them on the \ screen such that the window title bars remain visible. ", StyleBox[" ", FontSlant->"Italic"], "In this arrangement, you can bring a window to the front of the stack by \ clicking on its title bar." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Tiling Windows "], "Subsubsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "To place two or more open windows one above the other in horizontal \ rectangles of equal size, choose ", StyleBox["Tile Windows Wide", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " from the ", StyleBox["Window", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " menu. To place position the windows side-by-side in vertical rectangles \ of equal size, choose ", StyleBox["Tile Windows Tall", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], "." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Transferring Notebooks Between the Macintosh and Windows Versions of ", StyleBox["Mathematica", FontSlant->"Italic"], " ... 69 " }], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[{ "Converting Macintosh ", StyleBox["Mathematica", FontSlant->"Italic"], " Notebooks into Windows ", StyleBox["Mathematica", FontSlant->"Italic"], " Notebooks" }], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "The following procedure can be used to convert a Macintosh ", StyleBox["Mathematica", FontSlant->"Italic"], " Notebook into a Windows ", StyleBox["Mathematica", FontSlant->"Italic"], " Notebook:\n\n1) Launch ", StyleBox["Apple File Exchange", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], ", an application supplied with the Macintosh system software for use on \ Macintosh computers equipped with a ", StyleBox["SuperDrive", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " (a high-density 3.5-inch floppy diskette drive that can read disks from \ computers that use the DOS operating system.) 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This command restores all of a cell's default style attributes and \ will eliminate font variation within cells.\n\n2) Provide a name for the \ Notebook that conforms to the filenaming conventions used by the destination \ computer system. Windows Notebooks should be given a filename that is less \ than or equal to eight characters in length and ends in the ", StyleBox[".ma", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], " file extension.\n\n3) Cells in a Notebook may be assigned different fonts \ on different computer systems. To minimize this possibility, use fonts that \ that are common across Notebook front ends such as Times, Helvetica, or \ Courier.\n\n4) Do not convert graphics to Bitmap form since Bitmap graphics \ are not compatible across platforms. Instead, keep graphics in PostScript \ form.\n\n5) Special characters, such as Greek symbols, typically have to be \ translated by hand." }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["References ... 71"], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ "Material appearing in this book has been adapted from the references \ listed below.\n\nBlachman, Nancy. ", StyleBox["Mathematica: A Practical Approach", FontSlant->"Italic"], ". New Jersey: Prentice-Hall, Inc., 1992.\n\nCrooke, Philip, & \ Ratcliffe, John. ", StyleBox["A Guidebook to Calculus with Mathematica. ", FontSlant->"Italic"], "California: Wadsworth Publishing Company, 1991.\n \nWolfram, Stephen.", StyleBox[" Mathematica A System for Doing Mathematics by Computer, ", FontSlant->"Italic"], "Second Edition, Addison-Wesley \n \n Wolfram Research. ", StyleBox["User's Guide for the Macintosh", FontSlant->"Italic"], " (Rev. ed.), 1991.\n \n Wolfram Research. ", StyleBox[" User's Guide for Microsoft Windows", FontSlant->"Italic"], ", 1992.\n \n \"Q&A-How can I transfer Notebooks from the Macintosh to \ Windows and vice versa?\" ", StyleBox["MathUser", FontSlant->"Italic"], " pp 6-7, Fall/Winter 1992.\n \t" }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Acknowledgement ... 71 "], "Section", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[ "I wish to thank Dr. Philip Crooke, Professor of Mathematics at Vanderbilt \ University, who developed the outline used in this Notebook and provided \ guidance during its development. 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