਀㰀洀攀琀愀 渀愀洀攀㴀倀爀漀最䤀搀 挀漀渀琀攀渀琀㴀圀漀爀搀⸀䐀漀挀甀洀攀渀琀㸀 ਀㰀洀攀琀愀 渀愀洀攀㴀伀爀椀最椀渀愀琀漀爀 挀漀渀琀攀渀琀㴀∀䴀椀挀爀漀猀漀昀琀 圀漀爀搀 ㄀㈀∀㸀 Symbmath਀㰀漀㨀匀洀愀爀琀吀愀最吀礀瀀攀 渀愀洀攀猀瀀愀挀攀甀爀椀㴀∀甀爀渀㨀猀挀栀攀洀愀猀ⴀ洀椀挀爀漀猀漀昀琀ⴀ挀漀洀㨀漀昀昀椀挀攀㨀猀洀愀爀琀琀愀最猀∀ name="State"/>਀㰀漀㨀匀洀愀爀琀吀愀最吀礀瀀攀 渀愀洀攀猀瀀愀挀攀甀爀椀㴀∀甀爀渀㨀猀挀栀攀洀愀猀ⴀ洀椀挀爀漀猀漀昀琀ⴀ挀漀洀㨀漀昀昀椀挀攀㨀猀洀愀爀琀琀愀最猀∀ name="place"/>਀㰀℀ⴀⴀ嬀椀昀 最琀攀 洀猀漀 㤀崀㸀㰀砀洀氀㸀 ਀  㰀漀㨀䄀甀琀栀漀爀㸀圀 䠀甀愀渀最㰀⼀漀㨀䄀甀琀栀漀爀㸀 w huang਀  㰀漀㨀刀攀瘀椀猀椀漀渀㸀㈀㰀⼀漀㨀刀攀瘀椀猀椀漀渀㸀 210਀  㰀漀㨀䰀愀猀琀倀爀椀渀琀攀搀㸀㄀㤀㤀㔀ⴀ ㄀ⴀ 㘀吀 㔀㨀㈀㄀㨀  娀㰀⼀漀㨀䰀愀猀琀倀爀椀渀琀攀搀㸀 2014-03-24T22:57:00Z਀  㰀漀㨀䰀愀猀琀匀愀瘀攀搀㸀㈀ ㄀㐀ⴀ ㌀ⴀ㈀㐀吀㈀㈀㨀㔀㜀㨀  娀㰀⼀漀㨀䰀愀猀琀匀愀瘀攀搀㸀 62਀  㰀漀㨀圀漀爀搀猀㸀㄀㠀 ㈀㠀㰀⼀漀㨀圀漀爀搀猀㸀 102762਀  㰀漀㨀䌀漀洀瀀愀渀礀㸀䠀一䰀 䰀䤀䴀䤀吀䔀䐀㰀⼀漀㨀䌀漀洀瀀愀渀礀㸀 856਀  㰀漀㨀倀愀爀愀最爀愀瀀栀猀㸀㈀㐀㄀㰀⼀漀㨀倀愀爀愀最爀愀瀀栀猀㸀 120549਀  㰀漀㨀嘀攀爀猀椀漀渀㸀㄀㈀⸀  㰀⼀漀㨀嘀攀爀猀椀漀渀㸀 ਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀 ਀ 㰀眀㨀圀漀爀搀䐀漀挀甀洀攀渀琀㸀 ਀  㰀眀㨀䠀椀搀攀匀瀀攀氀氀椀渀最䔀爀爀漀爀猀⼀㸀 false਀  㰀眀㨀吀爀愀挀欀䘀漀爀洀愀琀琀椀渀最⼀㸀 ਀  㰀眀㨀倀甀渀挀琀甀愀琀椀漀渀䬀攀爀渀椀渀最⼀㸀 6 pt਀  㰀眀㨀䐀爀愀眀椀渀最䜀爀椀搀嘀攀爀琀椀挀愀氀匀瀀愀挀椀渀最㸀㘀 瀀琀㰀⼀眀㨀䐀爀愀眀椀渀最䜀爀椀搀嘀攀爀琀椀挀愀氀匀瀀愀挀椀渀最㸀 0਀  㰀眀㨀䐀椀猀瀀氀愀礀嘀攀爀琀椀挀愀氀䐀爀愀眀椀渀最䜀爀椀搀䔀瘀攀爀礀㸀㌀㰀⼀眀㨀䐀椀猀瀀氀愀礀嘀攀爀琀椀挀愀氀䐀爀愀眀椀渀最䜀爀椀搀䔀瘀攀爀礀㸀 ਀  㰀眀㨀嘀愀氀椀搀愀琀攀䄀最愀椀渀猀琀匀挀栀攀洀愀猀⼀㸀 false਀  㰀眀㨀䤀最渀漀爀攀䴀椀砀攀搀䌀漀渀琀攀渀琀㸀昀愀氀猀攀㰀⼀眀㨀䤀最渀漀爀攀䴀椀砀攀搀䌀漀渀琀攀渀琀㸀 false਀  㰀眀㨀䐀漀一漀琀倀爀漀洀漀琀攀儀䘀⼀㸀 EN-US਀  㰀眀㨀䰀椀搀吀栀攀洀攀䄀猀椀愀渀㸀娀䠀ⴀ䌀一㰀⼀眀㨀䰀椀搀吀栀攀洀攀䄀猀椀愀渀㸀 X-NONE਀  㰀眀㨀䐀漀一漀琀匀栀愀搀攀䘀漀爀洀䐀愀琀愀⼀㸀 ਀   㰀眀㨀䈀爀攀愀欀圀爀愀瀀瀀攀搀吀愀戀氀攀猀⼀㸀 ਀   㰀眀㨀圀爀愀瀀吀攀砀琀圀椀琀栀倀甀渀挀琀⼀㸀 ਀   㰀眀㨀䐀漀渀琀䜀爀漀眀䄀甀琀漀昀椀琀⼀㸀 ਀   㰀眀㨀䐀漀渀琀嘀攀爀琀䄀氀椀最渀䌀攀氀氀圀椀琀栀匀瀀⼀㸀 ਀   㰀眀㨀䐀漀渀琀嘀攀爀琀䄀氀椀最渀䤀渀吀砀戀砀⼀㸀 ਀   㰀眀㨀䌀愀挀栀攀搀䌀漀氀䈀愀氀愀渀挀攀⼀㸀 ਀  㰀⼀眀㨀䌀漀洀瀀愀琀椀戀椀氀椀琀礀㸀 ਀   㰀洀㨀洀愀琀栀䘀漀渀琀 洀㨀瘀愀氀㴀∀䌀愀洀戀爀椀愀 䴀愀琀栀∀⼀㸀 ਀   㰀洀㨀戀爀欀䈀椀渀匀甀戀 洀㨀瘀愀氀㴀∀☀⌀㐀㔀㬀ⴀ∀⼀㸀 ਀   㰀洀㨀搀椀猀瀀䐀攀昀⼀㸀 ਀   㰀洀㨀爀䴀愀爀最椀渀 洀㨀瘀愀氀㴀∀ ∀⼀㸀 ਀   㰀洀㨀眀爀愀瀀䤀渀搀攀渀琀 洀㨀瘀愀氀㴀∀㄀㐀㐀 ∀⼀㸀 ਀   㰀洀㨀渀愀爀礀䰀椀洀 洀㨀瘀愀氀㴀∀甀渀搀伀瘀爀∀⼀㸀 ਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀℀ⴀⴀ嬀椀昀 最琀攀 洀猀漀 㤀崀㸀㰀砀洀氀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 儀䘀漀爀洀愀琀㴀∀琀爀甀攀∀ 一愀洀攀㴀∀栀攀愀搀椀渀最 ㄀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 儀䘀漀爀洀愀琀㴀∀琀爀甀攀∀ 一愀洀攀㴀∀栀攀愀搀椀渀最 ㌀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 儀䘀漀爀洀愀琀㴀∀琀爀甀攀∀ 一愀洀攀㴀∀栀攀愀搀椀渀最 㔀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㌀㤀∀ 一愀洀攀㴀∀琀漀挀 ㈀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㤀㤀∀ 一愀洀攀㴀∀昀漀漀琀攀爀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 儀䘀漀爀洀愀琀㴀∀琀爀甀攀∀ 一愀洀攀㴀∀吀椀琀氀攀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 儀䘀漀爀洀愀琀㴀∀琀爀甀攀∀ 一愀洀攀㴀∀匀甀戀琀椀琀氀攀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 儀䘀漀爀洀愀琀㴀∀琀爀甀攀∀ 一愀洀攀㴀∀䔀洀瀀栀愀猀椀猀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㤀㤀∀ 匀攀洀椀䠀椀搀搀攀渀㴀∀琀爀甀攀∀ Name="Placeholder Text"/>਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㄀∀ 儀䘀漀爀洀愀琀㴀∀琀爀甀攀∀ 一愀洀攀㴀∀一漀 匀瀀愀挀椀渀最∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㄀∀ 一愀洀攀㴀∀䰀椀最栀琀 䰀椀猀琀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㌀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 匀栀愀搀椀渀最 ㄀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㔀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䰀椀猀琀 ㄀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㜀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㄀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㤀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㌀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㄀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 匀栀愀搀椀渀最∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㌀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 䜀爀椀搀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㄀∀ 一愀洀攀㴀∀䰀椀最栀琀 䰀椀猀琀 䄀挀挀攀渀琀 ㄀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㌀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 匀栀愀搀椀渀最 ㄀ 䄀挀挀攀渀琀 ㄀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㔀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䰀椀猀琀 ㄀ 䄀挀挀攀渀琀 ㄀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㌀㐀∀ 儀䘀漀爀洀愀琀㴀∀琀爀甀攀∀ Name="List Paragraph"/>਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㈀㤀∀ 儀䘀漀爀洀愀琀㴀∀琀爀甀攀∀ 一愀洀攀㴀∀儀甀漀琀攀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㜀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㄀ 䄀挀挀攀渀琀 ㄀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㤀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㌀ 䄀挀挀攀渀琀 ㄀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㄀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 匀栀愀搀椀渀最 䄀挀挀攀渀琀 ㄀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㌀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 䜀爀椀搀 䄀挀挀攀渀琀 ㄀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㄀∀ 一愀洀攀㴀∀䰀椀最栀琀 䰀椀猀琀 䄀挀挀攀渀琀 ㈀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㌀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 匀栀愀搀椀渀最 ㄀ 䄀挀挀攀渀琀 ㈀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㔀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䰀椀猀琀 ㄀ 䄀挀挀攀渀琀 ㈀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㜀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㄀ 䄀挀挀攀渀琀 ㈀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㤀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㌀ 䄀挀挀攀渀琀 ㈀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㄀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 匀栀愀搀椀渀最 䄀挀挀攀渀琀 ㈀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㌀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 䜀爀椀搀 䄀挀挀攀渀琀 ㈀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㄀∀ 一愀洀攀㴀∀䰀椀最栀琀 䰀椀猀琀 䄀挀挀攀渀琀 ㌀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㌀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 匀栀愀搀椀渀最 ㄀ 䄀挀挀攀渀琀 ㌀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㔀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䰀椀猀琀 ㄀ 䄀挀挀攀渀琀 ㌀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㜀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㄀ 䄀挀挀攀渀琀 ㌀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㤀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㌀ 䄀挀挀攀渀琀 ㌀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㄀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 匀栀愀搀椀渀最 䄀挀挀攀渀琀 ㌀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㌀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 䜀爀椀搀 䄀挀挀攀渀琀 ㌀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㄀∀ 一愀洀攀㴀∀䰀椀最栀琀 䰀椀猀琀 䄀挀挀攀渀琀 㐀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㌀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 匀栀愀搀椀渀最 ㄀ 䄀挀挀攀渀琀 㐀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㔀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䰀椀猀琀 ㄀ 䄀挀挀攀渀琀 㐀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㜀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㄀ 䄀挀挀攀渀琀 㐀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㤀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㌀ 䄀挀挀攀渀琀 㐀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㄀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 匀栀愀搀椀渀最 䄀挀挀攀渀琀 㐀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㌀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 䜀爀椀搀 䄀挀挀攀渀琀 㐀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㄀∀ 一愀洀攀㴀∀䰀椀最栀琀 䰀椀猀琀 䄀挀挀攀渀琀 㔀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㌀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 匀栀愀搀椀渀最 ㄀ 䄀挀挀攀渀琀 㔀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㔀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䰀椀猀琀 ㄀ 䄀挀挀攀渀琀 㔀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㜀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㄀ 䄀挀挀攀渀琀 㔀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㤀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㌀ 䄀挀挀攀渀琀 㔀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㄀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 匀栀愀搀椀渀最 䄀挀挀攀渀琀 㔀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㌀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 䜀爀椀搀 䄀挀挀攀渀琀 㔀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㄀∀ 一愀洀攀㴀∀䰀椀最栀琀 䰀椀猀琀 䄀挀挀攀渀琀 㘀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㌀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 匀栀愀搀椀渀最 ㄀ 䄀挀挀攀渀琀 㘀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㔀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䰀椀猀琀 ㄀ 䄀挀挀攀渀琀 㘀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㜀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㄀ 䄀挀挀攀渀琀 㘀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㘀㤀∀ 一愀洀攀㴀∀䴀攀搀椀甀洀 䜀爀椀搀 ㌀ 䄀挀挀攀渀琀 㘀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㄀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 匀栀愀搀椀渀最 䄀挀挀攀渀琀 㘀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㜀㌀∀ 一愀洀攀㴀∀䌀漀氀漀爀昀甀氀 䜀爀椀搀 䄀挀挀攀渀琀 㘀∀⼀㸀 ਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㌀㜀∀ 匀攀洀椀䠀椀搀搀攀渀㴀∀琀爀甀攀∀ UnhideWhenUsed="true" Name="Bibliography"/>਀  㰀眀㨀䰀猀搀䔀砀挀攀瀀琀椀漀渀 䰀漀挀欀攀搀㴀∀昀愀氀猀攀∀ 倀爀椀漀爀椀琀礀㴀∀㌀㤀∀ 匀攀洀椀䠀椀搀搀攀渀㴀∀琀爀甀攀∀ UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>਀ 㰀⼀眀㨀䰀愀琀攀渀琀匀琀礀氀攀猀㸀 ਀㰀⼀猀琀礀氀攀㸀 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000330033000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>1.2       能力਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 ㌀㐀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>608D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000330035000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

.......................................................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000330036000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>2.2     葾豶䝔扲蒗㱎㱐⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ渀漀ⴀ瀀爀漀漀昀㨀礀攀猀✀㸀㰀猀瀀愀渀 style='mso-tab-count:1 dotted'>.................................. 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000330037000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>2.3    未定义和驎ཛ㱟⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ渀漀ⴀ瀀爀漀漀昀㨀礀攀猀✀㸀㰀猀瀀愀渀 style='mso-tab-count:1 dotted'>............................................. 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000330038000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>3  简化਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 ㌀㤀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>908D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000340030000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>3.2  比较和测试数字਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㐀㄀ 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>1008D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000340032000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

.................................................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000340033000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>4.1.1    定义条件函数਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㐀㐀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>1208D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000340035000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>4.1.3    定义分段函数਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㐀㘀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>1208D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000340037000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>4.1.5    定义多值函数਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㐀㠀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>1308D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000340039000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>4.3    定义规则਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㔀  尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>1408D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000350031000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

...................................................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000350032000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>5.2    数值范围:(..................................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000350033000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>6 ................................................................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000350034000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

.................................................. 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000350035000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>6.2   微分的定义਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㔀㘀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>1508D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000350037000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㔀㠀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>1608D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000350039000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>7.3    数值积分:)਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㘀  尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>1808D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000360031000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

................................................. 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000360032000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>8.2   解方程:਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㘀㌀ 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>1908D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000360035000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>8.5    解微分方程਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㘀㘀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>2108D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000360037000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>9   总和及相乘਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㘀㠀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>2108D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000370030000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>10  系列与多项式਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㜀㄀ 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>2208D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000370033000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>11        列表和数组,向量和矩阵਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㜀㐀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>2308D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000370037000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

.......................................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000370038000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>14.2    让运营商਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㜀㤀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>2308D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000380030000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>15     图像਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㠀㄀ 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>2408D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000380034000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>15.4      在极坐标绘制函数图 (........................ 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000380035000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>15.5    绘制数据਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㠀㘀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>2508D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000380037000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

............................................. 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000380038000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>16.2    从简单的积分学习䉙葧ٹ㱒⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ渀漀ⴀ瀀爀漀漀昀㨀礀攀猀✀㸀㰀猀瀀愀渀 style='mso-tab-count:1 dotted'>..................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000380039000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>16.3    从驎ٹ晒恛驎ٹ㱒⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ渀漀ⴀ瀀爀漀漀昀㨀礀攀猀✀㸀㰀猀瀀愀渀 style='mso-tab-count:1 dotted'>................................ 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000390030000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>16.4  从简单的微分学习䉙깧ٟ㱒⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ渀漀ⴀ瀀爀漀漀昀㨀礀攀猀✀㸀㰀猀瀀愀渀 style='mso-tab-count:1 dotted'>........................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000390031000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>16.5    从代数学习积分਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㤀㈀ 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>2708D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000390034000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>      .......................................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000390035000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

............................................................. 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000390036000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

.................................................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000390037000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.1.1    数字਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀 㤀㠀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>2808D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003000390039000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.1.3    变量਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀   尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3008D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100300031000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.1.5    函数,过程和规则਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀ ㈀ 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3108D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100300033000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.1.5.2    微积分函数਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀ 㐀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3208D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100300035000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.1.5.4    杂项函数਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀ 㘀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3408D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100300037000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.1.5.6    程序਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀ 㠀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3508D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100300039000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.1.6    方程਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㄀  尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3508D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100310032000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.2.1     运营商਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㄀㌀ 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3608D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100310034000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.2.1.2.  ਀㰀⼀猀瀀愀渀㸀刀攀氀愀琀椀漀渀愀氀 伀瀀攀爀愀琀漀爀猀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀ 搀漀琀琀攀搀✀㸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㄀㔀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3708D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100310036000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.2.2   Function਀䌀愀氀氀猀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀ 搀漀琀琀攀搀✀㸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㄀㜀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3708D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100310038000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.3.1   Comment਀匀琀愀琀攀洀攀渀琀猀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀ 搀漀琀琀攀搀✀㸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㄀㤀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3808D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100320030000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.3.3   Assignment਀匀琀愀琀攀洀攀渀琀猀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀ 搀漀琀琀攀搀✀㸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㈀㄀ 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3808D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100320032000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.3.5.   Loop਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㈀㌀ 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>3908D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100320034000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>17.4    ਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㈀㔀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>4008D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100320036000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>Part 3 Reference Guide........................................ 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100320037000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

................................................................................. 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100320038000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

...................................................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100320039000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>19.1.1.    ਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㌀  尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>4208D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100330031000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>19.1.3.   Save਀䤀渀瀀甀琀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀ 搀漀琀琀攀搀✀㸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㌀㈀ 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>4208D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100330033000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>19.1.5.    打印਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㌀㐀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>4208D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100330035000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>19.2   Input Window਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㌀㘀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>4308D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100330037000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>19.4   Graph Menu਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㌀㠀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>4308D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100330039000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>20    Inside਀䐀爀䴀愀琀栀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀ 搀漀琀琀攀搀✀㸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㐀  尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>4408D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100340032000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>21 System Extension........................................ 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100340033000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

...................................................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100340034000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

.......................... 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100340035000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>22.2     Keywords in਀䄀氀瀀栀愀戀攀琀椀挀愀氀 伀爀搀攀爀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀ 搀漀琀琀攀搀✀㸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㐀㘀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>4908D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100340037000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>22.4       词汇表਀倀䄀䜀䔀刀䔀䘀 开吀漀挀㌀㜀㘀㈀ 㔀㄀㐀㠀 尀栀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ攀氀攀洀攀渀琀㨀昀椀攀氀搀ⴀ猀攀瀀愀爀愀琀漀爀✀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀猀瀀愀渀 lang=EN-AU style='mso-no-proof:yes'>4908D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003300370036003200300035003100340039000000਀㰀⼀砀洀氀㸀㰀℀嬀攀渀搀椀昀崀ⴀⴀ㸀㰀⼀猀瀀愀渀㸀㰀℀ⴀⴀ嬀椀昀 猀甀瀀瀀漀爀琀䘀椀攀氀搀猀崀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-no-proof:yes'>

਀㰀⼀猀瀀愀渀㸀 ਀㰀栀㄀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀最漀漀最氀攀ⴀ猀爀挀ⴀ琀攀砀琀㄀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ昀愀爀攀愀猀琀ⴀ昀漀渀琀ⴀ昀愀洀椀氀礀㨀 "Times New Roman"'>PART 1 用户指南 1. Introduction 1.1. What is DrMath 

            DrMath (former Visual Math)DrMath(原可视化数学)是一个在线符号数学和计算机代数系统。  is a਀挀漀洀瀀甀琀攀爀 愀氀最攀戀爀愀 猀礀猀琀攀洀 琀栀愀琀 挀愀渀 瀀攀爀昀漀爀洀 攀砀愀挀琀Ⰰ 渀甀洀攀爀椀挀Ⰰ 猀礀洀戀漀氀椀挀 愀渀搀 最爀愀瀀栀椀挀 computation.

            DrMathDrMath是一个专家系统,其能够从用户输入学习。If the user only input one formula without਀眀爀椀琀椀渀最 愀渀礀 挀漀搀攀Ⰰ 椀琀 眀椀氀氀 愀甀琀漀洀愀琀椀挀愀氀氀礀 氀攀愀爀渀 洀愀渀礀 瀀爀漀戀氀攀洀猀 爀攀氀愀琀攀搀 琀漀 琀栀椀猀 formula (eg. it learns many derivatives involving an unknown function f(x) from਀漀渀攀 搀攀爀椀瘀愀琀椀瘀攀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>x

  is a਀猀礀洀戀漀氀椀挀Ⰰ 渀甀洀攀爀椀挀 愀渀搀 最爀愀瀀栀椀挀猀 挀漀洀瀀甀琀椀渀最 攀渀瘀椀爀漀渀洀攀渀琀 眀栀攀爀攀 礀漀甀 挀愀渀 猀攀琀 甀瀀Ⰰ 爀甀渀 and document your calculation, draw your graph.DrMath是一个符号,数字和图形计算环境,你可以设置,运行并记录你的计算,绘制你的图形。 uses਀攀砀琀攀爀渀愀氀 昀甀渀挀琀椀漀渀猀 愀猀 椀昀 猀琀愀渀搀愀爀搀 昀甀渀挀琀椀漀渀猀 猀椀渀挀攀 琀栀攀 攀砀琀攀爀渀愀氀 昀甀渀挀琀椀漀渀猀 椀渀 library are auto-loaded.਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀戀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>DrMath

         DrMath             It runs on any machine that਀猀甀瀀瀀漀爀琀猀 䨀愀瘀愀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 

1.2.能力  

            It can provide analytical and਀渀甀洀攀爀椀挀 愀渀猀眀攀爀猀 昀漀爀㨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>            * Differentiation: regular or higher order, partial or਀琀漀琀愀氀Ⰰ 洀椀砀攀搀 愀渀搀 椀洀瀀氀椀挀椀琀 搀椀昀昀攀爀攀渀琀椀愀琀椀漀渀Ⰰ 漀渀攀ⴀ猀椀搀攀搀 搀攀爀椀瘀愀琀椀瘀攀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 微分:定期或更高阶,部分或全部,混合和隐函数的微分,片面的微分。

            * Integration: indefinite or definite integration,਀洀甀氀琀椀瀀氀攀 椀渀琀攀最爀愀琀椀漀渀Ⰰ 椀渀昀椀渀椀琀礀 愀猀 愀 戀漀甀渀搀Ⰰ 瀀愀爀愀洀攀琀爀椀挀 漀爀 椀琀攀爀愀琀攀搀 椀洀瀀氀椀挀椀琀 integration. 积分:驎ᙛ驢ٹ౒᫿쵙ٹ౒睥艺텙驾౛싿灓ᙥ遢ྖٹɒ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN>

            * Solution of equations: roots of a polynomial, systems of਀愀氀最攀戀爀愀椀挀 漀爀 搀椀昀昀攀爀攀渀琀椀愀氀 攀焀甀愀琀椀漀渀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>

            * Manipulation of expressions: simplification, factoring਀漀爀 攀砀瀀愀渀猀椀漀渀Ⰰ 猀甀戀猀琀椀琀甀琀椀漀渀Ⰰ 攀瘀愀氀甀愀琀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>

 *              * Limits: real, complex or one-sided limits, indeterminate਀昀漀爀洀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>            * Complex: calculation, functions, derivatives, and਀椀渀琀攀最爀愀琀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> *   和与积:局部的,有限的还是无限的。

            * Series.系列。     还包括:

            **   External਀昀甀渀挀琀椀漀渀猀 椀渀 氀椀戀爀愀爀礀 愀猀 椀昀 猀琀愀渀搀愀爀搀 昀甀渀挀琀椀漀渀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 在库外部函数,如果标准函数。

            *  剧情:函数,极坐标,参数和数据。 * *  程序,条件,迭代,递归,函数性,以规则为基础,逻辑,模式匹配和图形编程。 

2

,

            In the following examples, a line਀漀昀 ☀焀甀漀琀㬀䤀渀㨀 ☀焀甀漀琀㬀 洀攀愀渀猀 椀渀瀀甀琀Ⰰ 眀栀椀挀栀 礀漀甀 琀礀瀀攀 椀渀 琀栀攀 䤀渀瀀甀琀 眀椀渀搀漀眀Ⰰ 琀栀攀渀 爀甀渀 the program by clicking the "Run" menu; while a line of "Out:਀☀焀甀漀琀㬀 洀攀愀渀猀 漀甀琀瀀甀琀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>输入:=输出: 键入输出 你鑎⺋斕啑쵓㲋⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>键入 一些输出可以在实例被删去。

# and // are for comment਀猀琀愀琀攀洀攀渀琀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>You਀挀愀渀 猀瀀氀椀琀 愀 氀椀渀攀 漀昀 挀漀洀洀愀渀搀 椀渀琀漀 洀甀氀琀椀ⴀ氀椀渀攀猀 漀昀 挀漀洀洀愀渀搀 戀礀 琀栀攀 猀攀洀椀ⴀ挀漀氀甀洀渀 㬀Ⰰ similar to Java 您可以通过半列分割线命令进入多行命令 ;,类似于a  请注意,如果在下面的例子有些函数没有工作时,他们的图书馆是⽎⡦꒞蒋啶ⵟ㩎ᅿ㱜⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>

 

2.1 精确计算

 ਀最椀瘀攀猀 琀栀攀 攀砀愀挀琀 瘀愀氀甀攀 漀昀 挀愀氀挀甀氀愀琀椀漀渀 戀礀 搀攀昀愀甀氀琀Ⰰ 漀爀 琀栀攀 愀瀀瀀爀漀砀椀洀愀琀攀 瘀愀氀甀攀 漀昀 numeric calculation when by N().DrMath给出了计算时用n()的精确值默认情况下,或数值计算的近似值。   can਀洀愀渀椀瀀甀氀愀琀攀 甀渀椀琀猀 愀猀 眀攀氀氀 愀猀 渀甀洀戀攀爀猀Ⰰ 戀攀 甀猀攀搀 愀猀 愀 猀礀洀戀漀氀椀挀 挀愀氀挀甀氀愀琀漀爀Ⰰ 愀渀搀 搀漀 exact computation. 实数的范围是从负无穷到正无穷,如。Ln(Infinity), Exp(Infinity), etc. DrMath਀挀漀渀琀愀椀渀猀 洀愀渀礀 愀氀最漀爀椀琀栀洀猀 昀漀爀 瀀攀爀昀漀爀洀椀渀最 渀甀洀攀爀椀挀 挀愀氀挀甀氀愀琀椀漀渀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> DrMath包含了许多算法进行数值计算。eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀最漀漀最氀攀ⴀ猀爀挀ⴀ琀攀砀琀㄀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>Ln(I), I^I, (2.3)^(-3.2), 2^3^4^5^6^7^8^9, etc.Ln(II਀帀 䤀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,(2.3-3.2),等。

            Note that DrMath usually਀最椀瘀攀猀 愀 瀀爀椀渀挀椀瀀氀攀 瘀愀氀甀攀 椀昀 琀栀攀爀攀 愀爀攀 洀甀氀琀椀ⴀ瘀愀氀甀攀猀Ⰰ 戀甀琀 琀栀攀 匀漀氀瘀攀⠀⤀ 愀渀搀 刀漀漀琀⠀⤀ can give all values. 需要注意的是  例如:

            Exact and numeric calculations of਀㄀⼀㈀ ⬀ ㄀⼀㌀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>   

1/2+1/31/2 +1/3

# exact calculation;;

Out: 5/6:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>6 

In:输入: N(1/2+1/3)(਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>1/2 +1/3  

# numeric calculation;;

Out: 0.8333333333:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>3 

            Evaluate਀琀栀攀 瘀愀氀甀攀 漀昀 琀栀攀 昀甀渀挀琀椀漀渀 昀⠀砀⤀ 愀琀 砀㴀砀  戀礀 昀⠀砀 ⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> ff 

            Example:  评估的x),当x਀㴀 ㄀㠀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>度,X = I

In:输入  Pi),180 *degree

Out: 0, 0:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>0 

In:输入: Sin(I), N(Sin(I))N( Sin(I))

Out: Sin(I), 1.175201 I:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>),1.175201I

  例如:

            Set the units converter from the਀洀椀渀甀琀攀 琀漀 琀栀攀 猀攀挀漀渀搀Ⰰ 琀栀攀渀 挀愀氀挀甀氀愀琀攀 渀甀洀戀攀爀猀 眀椀琀栀 搀椀昀昀攀爀攀渀琀 甀渀椀琀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 从分钟将单位转换到第二个,然后计算౎啔䵓葏灶坥ɛ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>   

t := 60 s ; v*t

In:D0:=;

In:V * T + D0;

Out: 250 meter;:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>;

  通过计算表达式的值

                        Replace(y, x,Y  

            Example:  评估x਀㴀 ㌀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>和y = 4

In:输入: z:=x^2;:= X ^ 2                               #为;

In:输入: Replace(z, x,X ;  

# evaluate z when x = 3;Z  

In:输入:                                  x

In:输入: z;                                #评估; 6 

  注意x赋值后:=x应该从分配清除清除x)的分化之前。Otherwise the x values still is 4 until new਀瘀愀氀甀攀猀 愀猀猀椀最渀攀搀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 style='mso-bidi-font-size:10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>否则,x,直到指定新值。If evaluating z by the Replace(), the਀瘀愀爀椀愀戀氀攀 砀 椀猀 愀甀琀漀洀愀琀椀挀愀氀氀礀 挀氀攀愀爀攀搀 愀昀琀攀爀 攀瘀愀氀甀愀琀椀漀渀Ⰰ 椀攀 琀栀攀 瘀愀爀椀愀戀氀攀 砀 椀渀 Replace() is local variable.如果评估Z被评估后自动清零,即变量x 这条规则也适用于其他业务。

            The complex numbers, complex਀椀渀昀椀渀椀琀礀Ⰰ 愀渀搀 洀漀猀琀 洀愀琀栀 昀甀渀挀琀椀漀渀猀 眀椀琀栀 琀栀攀 挀漀洀瀀氀攀砀 愀爀最甀洀攀渀琀 挀愀渀 戀攀 挀愀氀挀甀氀愀琀攀搀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 灙౥姿数无穷大,并且最数学函数的䉙쉧灓ꭎꆈ鞋嗢救ɧ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

            Example .   

Sign(1+I), Sign(-1-I), I^2;1 + I),Ln(I਀帀 ㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>;

Out: 1, -1, -1

1-

  例如:

In:输入: ;

Out: -Infinity

-无穷远

  

Ln(Infinity);Ln(Infinite 输出

无限 

            The built-in constants (eg.਀䤀渀昀椀渀椀琀礀⤀ 挀愀渀 戀攀 甀猀攀搀 愀猀 渀甀洀戀攀爀猀 椀渀 挀愀氀挀甀氀愀琀椀漀渀 漀昀 攀砀瀀爀攀猀猀椀漀渀猀 漀爀 昀甀渀挀琀椀漀渀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 内置的常量(例如, 

2.2    葾豶䝔扲蒗㱎㱐⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 ㌀㜀✀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN style='mso-fareast-font-family:"Times New Roman"'>  

            Some math functions are਀搀椀猀挀漀渀琀椀渀甀漀甀猀 愀琀 砀㴀砀 Ⰰ 愀渀搀 漀渀氀礀 栀愀瘀攀 漀渀攀ⴀ猀椀搀攀搀 昀甀渀挀琀椀漀渀 瘀愀氀甀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 有些数学函数是葾౶⣿㱗⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-bidi-font-size:10.0pt;font-family:"Arial","sans-serif"'>x = X0,而且只有片面的函数值。਀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

2.3   未定义和驎ཛ㱟⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 ㌀㠀✀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN style='mso-fareast-font-family:"Times New Roman"'>  

            If the function value is਀甀渀搀攀昀椀渀攀搀Ⰰ 椀琀 洀愀礀 戀攀 椀渀搀攀琀攀爀洀椀渀愀琀攀 昀漀爀洀 ⠀攀最⸀  ⼀ Ⰰ 䤀渀昀椀渀椀琀礀⼀䤀渀昀椀渀椀琀礀⤀Ⰰ 礀漀甀 挀愀渀 evaluate it by Lim(). 如果函数值是湎驸葛౶菿ﵓ⾀书确定的形式(如0/0,无限 

3

 ਀愀甀琀漀洀愀琀椀挀愀氀氀礀 猀椀洀瀀氀椀昀椀攀猀 琀栀攀 漀甀琀瀀甀琀 攀砀瀀爀攀猀猀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> You਀挀愀渀 昀甀爀琀栀攀爀 猀椀洀瀀氀椀昀礀 椀琀 戀礀 甀猀椀渀最 琀栀攀 戀甀椀氀琀ⴀ椀渀 瘀愀爀椀愀戀氀攀 氀愀猀琀 椀渀 愀 猀椀渀最氀攀 氀椀渀攀 again and again until you are happy with the answer.  表达式可以通过扩展

                        Expand(x) 

            Example:    A਀⬀ 䈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)^ 2 输出:2

..............................       Expand(x)਀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> Expand.........................................

(a+b)^2A + B2              to      a^2+2*a*b+b^2^ 2 +2 * A *਀䈀 ⬀ 䈀 帀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-bidi-font-size:10.0pt'>2

(a+b)^nA + BN              to      a^n+਀⸀⸀⸀⸀⸀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>^਀一 ⬀ ⸀⸀⸀⸀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-bidi-font-size:10.0pt'>. B + C    

(b+c)/pB + CP              to      b/p +਀挀⼀瀀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>B / P + C਀⼀ 倀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

-------------------------------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 其中 

 该输出可以,如果你知道的x

            A first way is to evaluate਀砀⨀匀椀最渀⠀砀⤀ 戀礀 猀甀戀猀琀椀琀甀琀椀渀最 匀椀最渀⠀砀⤀ 眀椀琀栀 ㄀ 椀昀 砀 椀猀 瀀漀猀椀琀椀瘀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 第一种方法是用x)如果X਀⨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>符号(x

  

Sqrt(;

Out: x*Sign(x):਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>x

 

                        3.1.Assuming਀䐀漀洀愀椀渀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㐀 ✀㸀㰀猀瀀愀渀 class=notranslate>਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㐀 ✀㸀㰀猀瀀愀渀 class=notranslate>

            A਀猀攀挀漀渀搀 眀愀礀 椀猀 琀漀 愀猀猀甀洀攀 砀☀最琀㬀  戀攀昀漀爀攀 攀瘀愀氀甀愀琀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 第二种方法是,假设If਀礀漀甀 愀猀猀甀洀攀 琀栀攀 瘀愀爀椀愀戀氀攀 砀 椀猀 瀀漀猀椀琀椀瘀攀 漀爀 渀攀最愀琀椀瘀攀Ⰰ 琀栀攀 漀甀琀瀀甀琀 攀砀瀀爀攀猀猀椀漀渀 椀猀 simpler than that if you do not declare it.如果假设变量x 

In:输入: If( Y਀☀氀琀㬀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)            #假设;

Sqrt(x^2), Sqrt(y^2), Sqrt(z^2);f(x_):=If(x_>0, x_, 2x_); f(2),਀昀⠀ⴀ㈀⤀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 输出

2, -4

 以这种方式,所有的x   默认情况下,<无限和所有的变量是灙౥仿同的是在獎䥞葻콓⾑鹦灛౥쿿聐㡟^㝎॓鹧灛푎葢ɶ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN> x)的灙౥䛿㱏⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>是真正的在Y> 1

              1       Assuming 

Assume假设               Assignment              Meaning 

Assume(x>y)X> Y   ਀吀刀唀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>E   # 假设 If(              x>=y਀㨀㴀 吀爀甀攀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>X> = Y:=         X> =

Assume(x<y)X <Y   ਀吀刀唀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>E   # 假设 If( = Y   ਀吀刀唀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>E # assume x <= y#਀舀鱙㱧⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>X <=

Assume(x==y)X = Y   ਀吀刀唀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>E # assume x == y#਀䜀빐㲋⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>X =

Assume(x<>y)x <> y ਀吀刀唀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>E # assume x <> yX <>

IsEven(b) := TrueIsEven(          # assume b is evenb为什

IsOdd:=   #假设 :=   #假设2    #਀愀猀猀甀洀攀 戀 椀猀 爀愀琀椀漀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>b为比

IsReal2਀吀刀唀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>E   #假设2   #਀愀猀猀甀洀攀 戀 椀猀 挀漀洀瀀氀攀砀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>b为䉙㱧⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>2E   #假设Y:=         #਀愀猀猀甀洀攀 礀 椀猀 昀爀攀攀 漀昀 砀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>y是自由的B:=E                    # assume b is positive complexb为正䉙㱧⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

  If(    例如:

  

IsReal( b:=; #假设;

In:Sqrt(; 输出

Abs(b 

  3 Simplification in different਀搀漀洀愀椀渀猀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>------------------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 表达   䉙㱧⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-bidi-font-size:10.0pt'>  real                  x਀☀最琀㬀  㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>x> 0

   x਀匀椀最渀⠀砀⤀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>X登录(x)   x)的   x)的          Abs(x)ABS              xx

Abs(x)*Sign(x)ABS*符号(       Abs(x)਀匀椀最渀⠀砀⤀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>ABSx)的                      xx

Abs(x)/xABS/਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>X   x)的          1/Sign(x)1/Sign(x)  

 

3.2 比较和测试数字

  您可以通过关系运算符比较两个数字: 

                        a < bA <B  a 

                        a <> b<>b

                        a == b==

  例如:

In:输入: 2 > 1, 2 < 12 < 输出

真,假 

 ^ 2> 0万,如果你知道变量的属性。 x是偶数,奇数,整数,实数或列表的函数:  x)的

                        IsOdd(x)IsOddx

                        IsInteger(x)IsIntegerx

                        IsReal(x)x

                        IsNumber(x)IsNumberx

                        IsFree(y,x)IsFreeX

  例如:

In:输入: 2                             输出

                  

  请注意,由是false,而是通过关系运算符比较提供真,假,或左ꅎ鞋登홑Ɏ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN>

 

4    定义函数,过程和规则

    你可以让你定义的函数,就好像内置的函数,通过保存您的定义为磁盘文件作为函数ꁔ੒楎啢呜。虚拟机作为文件㱔⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>eg.save the factorial function as the਀昀愀挀琀漀爀椀愀氀⸀瘀洀 昀椀氀攀 ⠀猀攀攀 匀攀挀琀椀漀渀 䰀椀戀爀愀爀椀攀猀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 保存阶乘函数作为 

4.1.定义函数  

            You਀挀愀渀 搀攀昀椀渀攀 礀漀甀爀 漀眀渀 昀甀渀挀琀椀漀渀猀 戀礀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>

                        X_:2  下面是一些函数的定义:

                        X_:X਀⬀쀀⼃ ㌀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)   g(x_, y_) :=਀砀开帀㈀ ጀ†礀开帀㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>X_ 2) 在该定义中的参数应该是模式X_ 否则,函数f X ^ 2 X_应该在分配的两侧。

            Once defined, functions can be਀甀猀攀搀 椀渀 攀砀瀀爀攀猀猀椀漀渀猀 漀爀 椀渀 漀琀栀攀爀 昀甀渀挀琀椀漀渀 搀攀昀椀渀椀琀椀漀渀猀㨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 一旦定义,函数可以在表达式或其它函数定义中使用:

                        y := f(3.2)Y:=  ਀䜀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>(4.1 

            Example: 定义一个新的函数对于x ^ 2,然后评估它。

              

G: 2),G,g(x);G;

Out: g(2), g(a),:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>2),  x^2;X ^ 2; 只为一个象征性的值;

  

f(x_) := x_^2;F= X ^ 2

In:FF;

Out: 4, a^2

4                         对于任何值工作 

4.1.1.4.1.1   Defining਀䌀漀渀搀椀琀椀漀渀愀氀 䘀甀渀挀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-bookmark:_Toc376205044'>

 您可以通过If( )函数定义一个条件函数:

                        f1(x_) := If(x_>0 ,F1 If( X> 0   1)1,

                        f2(x_) := If(x_>0 , x_^2 , x_)F2 If( X> 0 f1()被调用的第一个定义,它提供了1 由如()的()被调用第二个定义它给出x ^ 2x如果   X_:=),X ^ 2

 f:=关于后者,当fx是。关于前者,当函数fx是一个数字,或左未计算的除外。 

            Example:评估为x ^ 2仅当   

f(x_) := If(IsNumber(x_) , x_^2);F If( IsMunberX਀帀 ㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)

In:FF;

Out: 4, f(a);

4A 

In:输入: X_:=;

In:Fff;

Out: 4, f(-2), f(a);

4-2),A 

In:输入: X_:=X_Fff 输出

4F;

 

定义情况函数  

            You can define the case function਀戀礀 搀椀昀昀攀爀攀渀琀 瀀愀琀琀攀爀渀 渀愀洀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> 此函数类似于BASIC语言的  例如:

  

f(x_) := If( x_ > 0 And x_ < 1 , 1);F If( X_>਀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,X_ <1;

In:U_:=2 V_:=3 0.2),1.2),2.2 输出2; 

4.1.3.4.1.3   Defining਀倀椀攀挀攀ⴀ眀椀猀攀 䘀甀渀挀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-bookmark:_Toc376205046'>

 你可以定义一个分段函数。 

            Example:  确定

  如果 X                if x਀㴀  㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>x਀㴀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>0

      \ x^2\ X ^ 2      if x > 0x> 0

然后评估-2),0),3),A)。

  

f(x_) := If(x_<0, x_, x_^2);F If( X_਀☀氀琀㬀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,X_;

In:FfFf 输出

-2,0f 

 

定义递归函数  

            You can define a recursion਀昀甀渀挀琀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>            Example:   

factorial(1) := 1;1:=;N_:=* fac(;

 

定义多值函数  

            You can define a function with the਀洀甀氀琀椀 昀甀渀挀琀椀漀渀 瘀愀氀甀攀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>            Example:   

squreroot(x_) := (Sqrt(x_), 0-Sqrt(x_));squreroot(=0-Sqrt(X_)) 4 输出:-

 

4.2  

 您可以通过定义一个函数作为一个程序  X_:1,命令...

  默认情况下,封锁所有变量()是本地的。The multi-statement should be grouped by਀䈀氀漀挀欀⠀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>The਀䈀氀漀挀欀⠀⤀ 漀渀氀礀 漀甀琀瀀甀琀猀 琀栀攀 爀攀猀甀氀琀 漀昀 琀栀攀 氀愀猀琀 猀琀愀琀攀洀攀渀琀 愀猀 椀琀猀 瘀愀氀甀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> Block( 多行语句必须由被终止

  例如:

define a numeric integration procedure nint()਀愀渀搀 挀愀氀挀甀氀愀琀攀 椀渀琀攀最爀愀氀 漀昀 砀帀㈀ 昀爀漀洀 砀㴀㄀ 琀漀 砀㴀㈀ 戀礀 挀愀氀氀 渀椀渀琀⠀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 定义一个数值积分程序 x = 1NInt()。

输入 X_B_  Y:=/ 50

            aa:=a_+dd,AA:=            bb:=b_-dd,BB:=            y0:=Replace(y_, x_ , a_),Y0:= Replace( Y_A_

            yn:=Replace(y_, x_ , b_),YN:= Replace( Y_B_

            (Sum(y_,x_,aa,bb,dd)+(y0+yn)/2)*dd);Y_AA+*日) 

In:NInt(χ^ 2, 1;

 

4.3  

            You਀挀愀渀 搀攀昀椀渀攀 琀爀愀渀猀昀漀爀洀 爀甀氀攀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> 定义的规则是类似于定义函数。In defining functions, all arguments must be਀猀椀洀瀀氀攀 瘀愀爀椀愀戀氀攀猀Ⰰ 戀甀琀 椀渀 搀攀昀椀渀椀渀最 爀甀氀攀猀Ⰰ 琀栀攀 昀椀爀猀琀 愀爀最甀洀攀渀琀 挀愀渀 戀攀 愀 complicated expression. 在界定函数,所有参数都必须是简单的变量,但是在定义规则,第一个参数可以是一个䉙葧ﵶ灑ɥ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN>

  例如:

            Define log rules.    登录(日志(X_日志(Y_;    登录( N_ *日志(;

In:输入: log(a*b);登录(A * B 输出:日志(+日志(b; 

            Example:   

Sin(=;

In:

Out: -Sin(a);:਀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ猀瀀愀挀攀爀甀渀㨀礀攀猀✀㸀ꀀ㰀⼀猀瀀愀渀㸀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>;

  例如:

            Define derivatives (see Chapter਀䐀攀昀椀渀椀渀最 ⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>In:输入: D(f(x_), x_) := Sin(x_);F),X_ Sin(X_ FT 输出

Sin(T; 

            Example: ਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>定义积分(见第四章驎ٹ॒˿㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN>

In:输入: Int(f(x_),x_) := Sin(x_);X_:=;

In:Int(਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>FT 输出

Sin;

  例如:

            Define the trig simplification਀爀甀氀攀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>   

simplify(Sin(x_)^2, x_) := 1/2*(1-Cos(x_));sin^਀㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,X_=਀㄀⼀㈀ ⨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>(1-Cos(X_)) sin^਀㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,x 输出

1/2))

  例如:

            Definetransform਀爀甀氀攀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>   

laplaceLaplace(਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀最漀漀最氀攀ⴀ猀爀挀ⴀ琀攀砀琀㄀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>(Sin(t_), t_) := 1/(t_^2+1);Sin),T_਀㄀ ⼀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>(T_ ^ 2 +1 ( SS),;

Out: 1/(s^2 + 1);:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>S਀帀 ㈀ ⬀ ㄀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)

 

5     5.1.片面极限  

5.2.数值范围:NLim(  

            If਀猀礀洀戀漀氀椀挀 氀椀洀椀琀 昀愀氀氀猀Ⰰ 礀漀甀 猀栀漀甀氀搀 琀爀礀 渀甀洀攀爀椀挀 氀椀洀椀琀 戀礀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 如果象征性的极限下跌,你应该尝试数字的极限

                        NLim(y, x,x0)NLim( X 

6.Differentiation微分  

            Differentiate਀愀渀 攀砀瀀爀攀猀猀椀漀渀 礀 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 砀 戀礀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> x :਀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀㰀猀瀀愀渀 style='mso-spacerun:yes'>  

                        D(y, x)D( X

            Differentiate y in the n order ( n਀☀最琀㬀   ⤀ 戀礀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>n:  YN

                                      例如:

            Differentiate Sin(x) and x^(x^x).sinX਀帀堀 帀 砀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>

In: D(Sin(x), x);输入: inx

Out: Cos(x);:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>x

  

Dx 输出:

X ^-1 + X1 + Ln(X))) 

  例如:

 微分表达式਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>f = Sin(X ^ 2 + Y ^ 2CosCOS਀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀最漀漀最氀攀ⴀ猀爀挀ⴀ琀攀砀琀㄀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>(2*(x^2+y^3)) with respect to x, and with respect to both x and y.2 *,并相对于x   

F+ (2*(x^2+y^3));2 *; F;

Out: 2 x

2* X ^ 2 + Y ^਀㌀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>))

  

D(D(f, x), y);D(D(X),;

Out: -6 xy^2 Sin(x^2 + y^3) - 12 xy^2:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>sin2 X ^ 2 + Y ^ 3)) 

6.1    

6.2.微分的定义

            Defining derivatives is similar to਀搀攀昀椀渀椀渀最 爀甀氀攀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>

  例如:

In:输入: D(f(x_),x_) := Sin(x_);(F),X_ Sin(X_ FX 输出: 

In:输入: D(f(x^6), x)(਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>Fx

Out: 6 x^5 Sin(x^6):਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>sin 

7  

         You਀挀愀渀 昀椀渀搀 椀渀琀攀最爀愀氀猀 漀昀 砀帀洀⨀䔀砀瀀⠀砀帀渀⤀Ⰰ 砀帀洀⨀䔀砀瀀⠀ⴀ砀帀渀⤀Ⰰ 䔀砀瀀⠀⠀愀⨀砀⬀戀⤀帀渀⤀Ⰰ Exp(-(a*x+b)^n), x^m*Ln(x)^n, Ln(a*x+b)^n, etc., (where m and n are any real਀渀甀洀戀攀爀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>X਀帀 䴀 ⨀ 䔀砀瀀⠀堀 帀 渀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 style='mso-bidi-font-size:10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)的积分,X ^ M * Exp(-X ^ n)的地契((^਀一㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>),Exp( - ^਀一㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>), 次方,Ln(A * X + Bn

 expand਀琀栀攀 椀渀琀攀最爀愀渀搀 戀礀 䔀砀瀀愀渀搀⠀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>             If਀猀礀洀戀漀氀椀挀 椀渀琀攀最爀愀琀椀漀渀 昀愀椀氀猀Ⰰ 礀漀甀 猀栀漀甀氀搀 愀搀搀 椀渀琀攀最爀愀氀 爀甀氀攀猀 椀渀琀漀 琀栀攀 䤀渀琀⸀瘀洀 library file, then do integration again (see Chapter Learning From User).Int.vm库文件,然后再做整合(见第三章学习从用户)。 

7.1.Indefinite਀䤀渀琀攀最爀愀琀椀漀渀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㔀㠀✀㸀㰀猀瀀愀渀 class=notranslate>਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㔀㠀✀㸀㰀猀瀀愀渀 class=notranslate>

 通过查找expr的驎ٹ㱒⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>  Int(X

            Find the double indefinite਀椀渀琀攀最爀愀氀猀 戀礀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>                        Int(Int(expr, x), y)Int(Int(EXPRY

            Note that the arbitrary constant਀椀猀 渀漀琀 爀攀瀀爀攀猀攀渀琀攀搀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>  例如:

            Find integrals of 1/a, 1/b and਀㄀⼀砀Ⰰ 欀渀漀眀椀渀最 愀 ☀最琀㬀 Ⰰ 戀 椀猀 爀攀愀氀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> 1 / bb是实数。

  

If( a> 0), True

In:Int(A),Int(B),

Out: Ln(a), Ln(Abs(b)), Ln(x*Sign(x));:

Ln(A),b)),X)) 

            Example:  求驎ٹɒ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

In:输入: Int(Sin(a*x+b), x);X 输出 ; 

In:输入: Int( Sin(x)/x^2, x);/ X ^ 2;

Out: ci(x) - Sin(x)/x;:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>X/ x 

In:输入: x),;

Out: -x输出:

- * (x) +਀匀椀渀⠀砀⤀㬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>xx 

In:输入: Int(Sin(x)*Cos(x), x);(xx 输出

1/2x 

In:输入: X ^ 6),;

Out: 1/6 Ei(-5/6, x^6);:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>-5਀⼀ 㘀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,X ^ 6 

In:输入: ,਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>x

Out: Ei(2, x);:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>2 

In:输入: Int( /਀匀焀爀琀⠀砀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>), 输出

EIx

  

Int(x

Out: Ei(1.5, x);:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>1.5 

In:输入: Int(Sin(x)*Exp(x), x);x,਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>x

Out: 1/2 * (Sin(x) - Cos(x)) * e^x;:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>1/2 *਀ⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>Cos*਀䔀 帀 砀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

In:输入: Int( x*Ln(x), x);x * Ln(x, 输出: 

In:输入: Int( 6 输出 

Li(6;

  

Int( Ln(x)/Sqrt(x), x);Ln(xx

Out: -4 Sqrt(x) + 2 Sqrt(x) Ln(x);:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>+਀㈀ 匀焀爀琀⠀砀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 style='mso-bidi-font-size:10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>) * 

In:输入: Int(x, 输出

Ln(x 

  例如:

            Find the line integral. 

In:输入: x:=2*t;X:=;    3 * T

In:输入: z:=5*t;Z:=;    X + Y

In:输入: v:=xy;:=    X + Y + Z

In:输入: Int(u*D(u,t)+v*D(v,t)+w*D(w,t), t);U * DTTWT 输出

64 T ^ 2

  例如:

            Integrate x^2*e^x, then expand it਀戀礀 琀栀攀 洀攀愀渀 漀昀 琀栀攀 瀀愀挀欀愀最攀猀 ☀焀甀漀琀㬀䔀砀瀀愀渀搀䔀椀⸀瘀洀☀焀甀漀琀㬀 ⠀攀砀瀀愀渀搀 䔀椀⠀渀Ⰰ砀⤀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 整合“ExpandEi.vm”ExpandN ExapndGa(N))和“ExpandLi.vm”X

  

Int(x^2*Exp(x), x);Int(X ^ 2 * Exp(x 输出

EIx

In:输入: ExpandEi(Ei(2, x));EIx; 输出

X ^ 2 Exp(X              

  限定积分是类似定义规则。਀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>  例如:

   诠释(X_), Sin(X_    T

Out: Sin(t);:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>仙(T; 

7.2.Definite਀䤀渀琀攀最爀愀琀椀漀渀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㔀㤀✀㸀㰀猀瀀愀渀 class=notranslate>਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㔀㤀✀㸀㰀猀瀀愀渀 class=notranslate>  

            Find਀搀攀昀椀渀椀琀攀 椀渀琀攀最爀愀氀猀 戀礀 攀砀琀攀爀渀愀氀 昀甀渀挀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>

                        Int(expr, x , xmin , xmax)expr, XMIN  Int(xXMAX

  例如:

            Find the definite integral of਀礀㴀䔀砀瀀⠀㄀ⴀ砀⤀ 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 砀 琀愀欀攀渀 昀爀漀洀   琀漀 椀渀昀椀渀椀琀礀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 发现为取到无穷x

  

Int(Exp(1-x0Infinite  

            Example:1 / X ^ 2 

In:输入: Int(1/x^2, x , -1 , 2);x2

                        # singularity at x=0;x = 0

Out: Infinity;:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

In:输入: Int(1/x^3, x , -1 , 1);x1

                        # singularity at x=0;x = 0

Out: 0输出:

0

  

Int(Sqrt((x-1)^2), x , 0 , 2);Int(Sqrt(^਀㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>), 0  #奇点在;  

            DrMathDrMath可以检测奇异性,但有时它﵎⢀춏앹땠୑౎惿앏筟킘魣䝏륙ɰ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN>

  例如:

In:输入: Int(1/(x-1)^2, x , 0 , 1 , 2);x-102  #奇异提供在; 输出

无限 

            Example: 

In:输入: Int(1/x, x , I , 2*I);X2਀⨀ 䤀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)

Out: Ln(2):਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>2

 

7.3   数值积分:NInt()

  数值积分函数

                        NInt(y, x , xmin , xmax)NInt(YXMIN  例如:

Compare numeric and symbolic integrals of਀㐀⼀⠀砀帀㈀⬀㄀⤀ 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 砀 琀愀欀攀渀 昀爀漀洀   琀漀 ㄀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 相对于取从比较的 

In:输入: NInt(4/(x^2+1), x , 0 , 1);4 /0

Out: 3.1415:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>5 

In:输入: N(Int(4/(x^2+1), x , 0 , 1));Int(4 /0))

Out: 3.1416:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>6 

8.解方程 8.1.Solving਀䄀氀最攀戀爀愀椀挀 䔀焀甀愀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㘀㈀✀㸀㰀猀瀀愀渀 class=notranslate>਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㘀㈀✀㸀㰀猀瀀愀渀 class=notranslate>  

 +/Expand(),Int())。 You਀挀愀渀 昀椀渀搀 爀漀漀琀猀 漀昀 瀀漀氀礀渀漀洀椀愀氀Ⰰ 愀氀最攀戀爀愀椀挀 攀焀甀愀琀椀漀渀猀Ⰰ 猀礀猀琀攀洀猀 漀昀 攀焀甀愀琀椀漀渀猀Ⰰ differential and integral equations.你可以找到方程,微分和积分方程的多项式,代数方程,系统的根。  您可以指定方程的变量。

  例如:

  

eq1:= x + y = 3;EQ1:=EQ2:= 输出:       ; 

In:输入: eq1-eq2;EQ2 输出:; 

            Example:         Solve਀愀渀 攀焀甀愀琀椀漀渀 匀焀爀琀⠀砀⬀㈀⨀欀⤀ ⴀ 匀焀爀琀⠀砀欀⤀ 㴀 匀焀爀琀⠀欀⤀Ⰰ 琀栀攀渀 挀栀攀挀欀 琀栀攀 猀漀氀甀琀椀漀渀 戀礀 substituting the root into the equation.求解方程਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>Sqrt(X +2 * K 

In:输入: Sqrt(X਀⬀ ㈀ ⨀ 䬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>) - K

Out: eq1 := Sqrt(x + 2*k) - Sqrt(x - k) =਀匀焀爀琀⠀欀⤀㬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> Sqrt(X਀⬀ ㈀ ⨀ 䬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>) -=਀匀焀爀琀⠀䬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)

  

EQ1 ^ 2;

Out: ((2*k + x)^0.5 - ((-k) + x)^0.5)^2 = k;:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>^ 0.5 - ((+਀堀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)^ 0.5; 

  你可以一步解决代数方程组的步骤,方法同上。This method is useful in teaching, eg.showing਀猀琀甀搀攀渀琀猀 栀漀眀 琀漀 猀漀氀瘀攀 攀焀甀愀琀椀漀渀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>

 

8.2.解方程:Solve(  

            The਀匀漀氀瘀攀⠀⤀ 昀甀渀挀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 

                        Solve(expr1਀㴀 攀砀瀀爀㈀Ⰰ 砀⤀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>1਀㴀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>表达式2 

solve a polynomial and systems of linear਀攀焀甀愀琀椀漀渀猀 漀渀 漀渀攀 猀琀攀瀀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>所有方程的实数和灙㥥٨ᩜ자㲏⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>The਀昀甀渀挀琀椀漀渀 匀漀氀瘀攀⠀⤀ 漀甀琀瀀甀琀猀 愀 氀椀猀琀 漀昀 爀漀漀琀猀 眀栀攀渀 琀栀攀爀攀 愀爀攀 洀甀氀琀椀ⴀ爀漀漀琀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 函数,可以你可以得到一个根从列表中。

  例如:

            Solve a+b*x+x^2 = 0 for x, save਀琀栀攀 爀漀漀琀 琀漀 砀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>A਀⬀ 䈀 ⨀ 堀 ⬀ 堀 帀 ㈀ 㴀  㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 style='mso-bidi-font-size:10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>的x 

In:输入: Solve(a+b*x+x^2 = 0, x);x)

Out: (-b/2 + Sqrt((b/2)^2 - a),:਀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ猀瀀愀挀攀爀甀渀㨀礀攀猀✀㸀ꀀ㰀⼀猀瀀愀渀㸀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

            Example: 

  

NX)) 输出

1-1

 Solve()앎뎉虑N⩎聎啻葓콓㲑⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>,但也解决了一个未知的函数,例如。Ln(x).Ln( 

            Example:  解方程为 

In:输入: Solve( ^਀㈀ ⬀㔀 ⨀ 䰀渀⠀堀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 style='mso-bidi-font-size:10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)= -6;

Out: (-2, -3);:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>-3; 

8.3.解多项式:PSolve(  

            The਀攀砀琀攀爀渀愀氀 昀甀渀挀琀椀漀渀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>  Fx

solves f(x)=0 for x.F=਀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>对于x 它类似于 Solve(),但它只能解决多项式顺序<3

  例如:

In:输入: PSolve(x^2+5*x+6, x);(਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>χ^ 2 +5 * X +6;

Out: (-2, -3):਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>-3

 

8.4    

            数值求解代数方程

                        NSolve(f(x)਀Ⰰ 砀⤀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>NSolve(X),  FXnumerically solves an algebraic਀攀焀甀愀琀椀漀渀 眀椀琀栀 愀渀 椀渀椀琀椀愀氀 瘀愀氀甀攀 砀 ⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> By default x0=1.X0 = 1 NSolve()只给出了一个解决方案附近 

            Example:   

NSolve਀ⴀ 堀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,X; 输出

X = 0.73911289091

  

NSolveX;

Out: x = 0;:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>;  #只给出了近X0 = 0一个解决方案 

In:输入: NSolve( Sin(x) , x,3);(਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>Sin(X, 3 输出

X = 3.14

            # only gives one solution near਀砀 㴀㌀㬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>0 = 3一个解决方案 

8.5.  

            You can solve the differential਀攀焀甀愀琀椀漀渀猀㨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>                        y'(x) = f(x)Y'=਀䘀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>(X

by integrating the equation. 

            Example:  通过积分解决'=਀匀椀渀⠀堀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)。   

Int( D(y(x),x) = Sin(x), x)D(X),=਀匀椀渀⠀堀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>),x 输出:X-Cos 

8.6.微分求解:DSolve()  

9  

            You਀挀愀渀 挀漀洀瀀甀琀攀 瀀愀爀琀椀愀氀Ⰰ 昀椀渀椀琀攀 漀爀 椀渀昀椀渀椀琀攀 猀甀洀猀 愀渀搀 瀀爀漀搀甀挀琀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 你可以计算局部,有限的还是无限的总和, 款项和相乘可以分化和整合。You construct functions likeTaylorpolynomials or finite Fourier series.多项式或有限傅里叶级数。਀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀最漀漀最氀攀ⴀ猀爀挀ⴀ琀攀砀琀㄀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>The procedure is the same for sums as products so all examples will be਀爀攀猀琀爀椀挀琀攀搀 琀漀 猀甀洀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>一般格式为这些函数是:  XMIN  XMINDX

                        Product(expr, x , xmin , xmax)exprXMAX

                        Product(expr, x , xmin , xmax ,਀搀砀⤀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>XMINDX

            The expression expr is evaluated਀愀琀 砀洀椀渀Ⰰ 砀洀椀渀⬀搀砀Ⰰ ⸀⸀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>expr求值在XMIN਀⬀ 䐀堀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,..XMAX大于最后一个条目,将所得值相加或相乘。   The part਀☀焀甀漀琀㬀猀琀攀瀀 搀砀☀焀甀漀琀㬀 椀猀 漀瀀琀椀漀渀愀氀 愀渀搀 搀攀昀愀甀氀琀猀 琀漀 ㄀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 部分DX”是可选的,默认为1 XMINDX的值可以是任意实数。

            Here are some examples: Sum(j, j from 1 to 10)十,J10 .+ 10.+10

            Sum(3^j, j , 0 , 10 , 2)3 ^Ĵ02   

for 1 + 3^2 + ...1 +3 ^ 2 + ...+ 3^10.+ 3 ^ 10

            Here are some sampleTaylorpolynomials:多项式:

            Sum(x^j/j!, j , 0 , n)Sum(X ^ J / J 1O 对于  Sum(^Ĵ*x਀帀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>(2 * j +12਀⨀ 樀 ⬀㄀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)!,Jn 因为罪(2਀⨀ 一 ⬀㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>。 

9.1.部分和  

            部分和(符号总和)

                        PartialSum(f(x),x)PartialSum( ,਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>x

finds the partial sum (symbolic sum). 

            Example: .....        

  

PartialSumN

Out: 1/6 n (1 + n) (1 + 2 n):਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>1਀⬀ 一㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)(1 +2 N

 

9.2  

  该函数

                        InfiniteSum(f(x), x)InfiniteSumX, 找无限的总和,即 X0 

            Example:   

InfiniteSumN!)

Out: E输出:

E

10.Series਀愀渀搀 倀漀氀礀渀漀洀椀愀氀猀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㜀㄀✀㸀㰀猀瀀愀渀 class=notranslate>਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㜀㄀✀㸀㰀猀瀀愀渀 class=notranslate> 10.1.系列  

            The਀昀甀渀挀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>  Taylor( X,   Taylor( F),X  Taylor( X),X0

找到 泰勒 x਀㴀 堀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>。The argument (order) is optional and defaults਀琀漀 㔀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>(阶数)是可选的,缺省值为5

              例如:

            Find the power series expansion਀昀漀爀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>CosCos(x਀㴀  㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>处。   

Taylor 输出:; 

 ff਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>数值计算很有用(X 如果您可以提供)和F),即使F)是未知的,则可以计算出函数值在任意的x 计算的精确度取决于串联扩展的顺序。Higher order, more accuracy, but longer਀挀愀氀挀甀氀愀琀椀漀渀 琀椀洀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 style='mso-bidi-font-size:10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>高阶,更准确,但更长的计算时间。 

 

10.2  

  

            You਀挀愀渀 昀愀挀琀漀爀 瀀漀氀礀渀漀洀椀愀氀猀 椀渀 漀爀搀攀爀 ☀氀琀㬀 㔀 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 砀 戀礀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 您可以通过因式分解,以x

                        Factor(poly, x)x

  例如:

In:输入: Factor(x^2+5*x+6, x) +5 * X 6 输出3਀⬀ 砀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)

11. Lists and Arrays,਀嘀攀挀琀漀爀猀 愀渀搀 䴀愀琀爀椀挀攀猀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-bookmark:_Toc376205074'>

 

 

13   

  

13.1  

                         Re(z), Im(z), Abs(z), Arg(z),਀匀椀最渀⠀稀⤀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>Z),Abs(Z),精氨酸(Z  实数转换为整数

                        Floor(x)x  x

            The rational number is converted਀琀漀 琀栀攀 爀攀愀氀 渀甀洀戀攀爀 戀礀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>  x)的

14. 14.1.获取数据的类型  

            You਀挀愀渀 最攀琀 琀礀瀀攀 漀昀 搀愀琀愀 戀礀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>  Type( 

In:输入:   Type(2);Type( 输出: 

14.2  

 您还可以通过获得运营商  Type( 

In:输入:   Type(a>b);;

Out: >

>

  Type( x)) 输出: 

14.3.获得操作数  

15.图像             包括图形广泛的设施。

15.1.绘制直线和圆弧 15.2.绘函数图 F(X  

            You can plot a function of y =਀昀⠀砀⤀ 漀渀 琀栀攀 砀礀ⴀ瀀氀愀渀攀 戀礀 攀砀琀攀爀渀愀氀 昀甀渀挀琀椀漀渀㨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 绘制 x)在 

                        Plot(f(x),x)FX

                        Plot(f(x),x,xmin,xmax)FXXMAX

                        Plot(f(x),x,xmin,xmax,ymin,ymax)FXXMAXYMAX

                        Plot(f(x),x,xmin,xmax,ymin,ymax,NoPoint)FXXMAXYMAX 

f(x) can be either a functionFx或涉及X ^ 2            The਀砀洀椀渀 愀渀搀 砀洀愀砀 愀爀攀 爀愀渀最攀 漀昀 砀ⴀ愀砀椀猀Ⰰ 琀栀攀 礀洀椀渀 愀渀搀 礀洀愀砀 愀爀攀 爀愀渀最攀 漀昀 礀ⴀ愀砀椀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> XMAX最小和y轴的范围。默认值是y最小The values of xmin, xmax, ymin, ymax are real਀渀甀洀戀攀爀猀Ⰰ 猀甀挀栀 琀栀愀琀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-bidi-font-size:10.0pt;font-family:"Arial","sans-serif"'>XMINYMIN and   ymin < ymax.  值告诉平面的一部分与  xmin <= x਀☀氀琀㬀㴀 砀洀愀砀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>XMIN <=਀堀 ☀氀琀㬀㴀 砀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 style='mso-bidi-font-size:10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>最大  and    1点(F轴的每个像素,并连接的连续点。  

如果你希望你的圆圈和方块看起来正确的也就是说,如果你想要一个垂直单位,真正做到相同的距离为一个水平单元-

   

            plot x^3 and Sin(x).X਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>^ 3x)。

In:输入:   

Plot(x^3,x);X ^ 3       

In:Plot( Sin(x

15.3. 

            You਀挀愀渀 瀀氀漀琀 琀栀攀 瀀愀爀愀洀攀琀爀椀挀 昀甀渀挀琀椀漀渀猀 漀昀 砀㴀砀⠀琀⤀ 愀渀搀 礀㴀礀⠀琀⤀ 戀礀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 您可以绘制出 t)和)的参数函数图 

                        ParametricPlot(x(t),y(t),t)ParametricPlot( t),T),  XYTTMAX

                        ParametricPlot(x(t),y(t),t,tmin,tmax,ymin,ymax)ParametricPlot( t),T),TMINYMIN 

            Example:   ),Sin( 

15.4.

  您可以绘制一个极坐标曲线的部分  r = f(t) that਀氀椀攀猀 椀渀 琀栀攀 眀椀渀搀漀眀 眀椀琀栀 攀砀琀攀爀渀愀氀 昀甀渀挀琀椀漀渀㨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> t)的那在于与外部函数的窗口: 

                       FT

                       RTMINPolarPlot(r, t,tmin,tmax,rmin,rmax)PolarPlot(TTMAXRMAX

函数f)可以用绑定变量t

  例如:

            Plot a circle    PolarPlott 

The variable t covers the domain (0, 2*Pi);਀礀漀甀 挀愀渀 挀栀愀渀最攀 琀栀椀猀 搀攀昀愀甀氀琀 戀礀 猀瀀攀挀椀昀礀椀渀最 愀 爀愀渀最攀 昀漀爀 琀㨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 变量0更改此默认值:PolarPlot(1, t,0,Pi)PolarPlot( T,਀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,Pi

 

15.5  

  

 

16  

 DrMath is its ability to deduce and expand its knowledge.DrMath的最重要的特点是它的演绎和扩大其知识的能力。If you provide it with the necessary facts, DrMath਀挀愀渀 猀漀氀瘀攀 洀愀渀礀 瀀爀漀戀氀攀洀猀 琀栀愀琀 眀攀爀攀 甀渀愀戀氀攀 琀漀 戀攀 猀漀氀瘀攀搀 戀攀昀漀爀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 如果你向它提供必要的事实以下是几种方式 

16.1.  

16.2   从简单的积分学习䉙葧ٹ㱒⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㠀㤀✀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN style='mso-fareast-font-family:"Times New Roman"'>  

            You supply a simple indefinite਀椀渀琀攀最爀愀氀Ⰰ 愀渀搀 椀渀 爀攀琀甀爀渀Ⰰ 㰀戀㸀䐀爀䴀愀琀栀㰀⼀戀㸀 眀椀氀氀 瀀攀爀昀漀爀洀 琀栀攀 爀攀氀愀琀攀搀 挀漀洀瀀氀椀挀愀琀攀搀 integrals. 你提供一个简单的驎ٹ౒೿岀㩏ꕖ㱢戀㸀ఀ㳿⼀戀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>਀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

            Example: DrMath是否已经公知以下的积分或没有。 

In:输入:   

Int(f(x), x);Fx 输出

Int( FX 

In:输入:   Int((2*f(x)+x),਀砀⤀㬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>2 * F+਀堀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)中,x; 输出

Int( + X),;

 Int( X),Y; 输出

Int( Int( F+਀夀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>),X

 fF਀ⴀ 堀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>上;X x)的yChange the first line, and then run the਀瀀爀漀最爀愀洀 愀最愀椀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>  诠释(F),X_X_  Int( 2 * F+਀堀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,X; 输出:X 

In:输入:   

Int(Int(f(x)+y, x), y);;Int( Int( F+਀夀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,X

Out: f(x)*y - x*y + x*y^2:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>X2

 您也可以要求 X)中,Y

Int(Int(f(x)*y, x), y),Int( Int( F*਀夀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,X), X)中, X 

16.3   从驎ٹ晒恛驎ٹ㱒⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀 㤀 ✀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN style='mso-fareast-font-family:"Times New Roman"'>  

            You਀挀漀渀琀椀渀甀攀 琀漀 愀猀欀 椀渀搀攀昀椀渀椀琀攀 椀渀琀攀最爀愀氀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>  

In:输入:   

Int(Int(f(x)+y, x , 0 , 1), y , 0 , 2);Int( Int( F(+਀夀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,X10

Out: 2 f(1)

21

 

16.4 从简单的微分学习䉙㱧⼀猀瀀愀渀㸀글ٟ㱒⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-bookmark:_Toc376205091'>

  can਀氀攀愀爀渀 挀漀洀瀀氀椀挀愀琀攀搀 搀攀爀椀瘀愀琀椀瘀攀猀 昀爀漀洀 愀 猀椀洀瀀氀攀 搀攀爀椀瘀愀琀椀瘀攀Ⰰ 攀瘀攀渀 琀栀漀甀最栀 琀栀攀 function to be differentiated is an unknown function, instead of standard਀昀甀渀挀琀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 style='mso-bidi-font-size:10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>可以从简单的 

             Differentiate f(x^2)^6, where f(x)਀椀猀 愀渀 甀渀欀渀漀眀渀 昀甀渀挀琀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 style='mso-bidi-font-size:10.0pt;font-family:"Arial","sans-serif"'>Ff 

In:输入:   D(f(x^2)^6,਀砀⤀㬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>(਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>FX 输出

12 X*FX ^ 2 

            Output is only the part਀搀攀爀椀瘀愀琀椀瘀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>f'(x^2)਀椀渀 琀栀攀 漀甀琀瀀甀琀 猀甀最最攀猀琀 琀栀愀琀 礀漀甀 猀栀漀甀氀搀 琀攀愀挀栀 㰀戀㸀䐀爀䴀愀琀栀㰀⼀戀㸀 昀✀⠀砀开⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> X਀帀 ㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)的输出建议你应该教 F'eg.the derivative of f(x) is another unknown਀昀甀渀挀琀椀漀渀 搀昀⠀砀⤀Ⰰ 椀攀 昀✀⠀砀开⤀ 㴀 搀昀⠀砀⤀Ⰰ 愀猀猀椀最渀 昀✀⠀砀开⤀ 眀椀琀栀 搀昀⠀砀⤀ 愀渀搀 爀甀渀 椀琀 愀最愀椀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> x)是另一个未知函数DF)的,即F'= DFF'DF 

In:输入:   D(f(x_),x_)਀㨀㴀 搀昀⠀砀开⤀㬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>F),X_X_ FX 输出

12 XFX ^ 2 

            This਀琀椀洀攀 礀漀甀 最攀琀 琀栀攀 挀漀洀瀀氀攀琀攀 搀攀爀椀瘀愀琀椀瘀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>

 

16.5   从代数学习积分  

            If਀礀漀甀 猀栀漀眀 㰀戀㸀䐀爀䴀愀琀栀㰀⼀戀㸀 愀氀最攀戀爀愀Ⰰ 㰀戀㸀䐀爀䴀愀琀栀㰀⼀戀㸀 挀愀渀 氀攀愀爀渀 椀渀琀攀最爀愀氀猀 昀爀漀洀 琀栀愀琀 algebra. 如果你表现出 

            Example : 输入F^ 2 = 1/2-1/2 * COSf的积分(^਀㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>。 

In:输入:   f(x)਀㨀㴀 ㄀⼀㈀ⴀ㄀⼀㈀⨀䌀漀猀⠀㈀⨀砀⤀㬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>X2 * x

In:Int(਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>Fx 输出 个)

  is਀瘀攀爀礀 昀氀攀砀椀戀氀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>DrMath是非常灵活的。 learning integrals from derivatives or਀愀氀最攀戀爀愀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 

16.6.

  has਀琀栀攀 愀戀椀氀椀琀礀 琀漀 氀攀愀爀渀 挀漀洀瀀氀椀挀愀琀攀搀 愀氀最攀戀爀愀 昀爀漀洀 猀椀洀瀀氀攀 愀氀最攀戀爀愀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>  

            Example: 改造日志(X * Y)到日志(+日志( 

 

16.7   学习与编程

            The਀搀椀昀昀攀爀攀渀挀攀 戀攀琀眀攀攀渀 氀攀愀爀渀椀渀最 愀渀搀 瀀爀漀最爀愀洀洀椀渀最 椀猀 愀猀 昀漀氀氀漀眀猀㨀 琀栀攀 氀攀愀爀渀椀渀最 瀀爀漀挀攀猀猀 of DrMath is very similar to the way human beings learn, and that is਀愀挀挀漀洀瀀氀椀猀栀攀搀 戀礀 欀渀漀眀椀渀最 挀攀爀琀愀椀渀 爀甀氀攀 琀栀愀琀 挀愀渀 戀攀 愀瀀瀀氀椀攀搀 琀漀 猀攀瘀攀爀愀氀 瀀爀漀戀氀攀洀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 学习和编程之间的区别如下First, the programmer defines many਀猀甀戀爀漀甀琀椀渀攀猀 昀漀爀 琀栀攀 椀渀搀椀瘀椀搀甀愀氀 椀渀琀攀最爀愀渀搀猀 ⠀攀最⸀ 昀⠀砀⤀Ⰰ 昀⠀砀⤀⬀礀帀㈀Ⰰ ㈀⨀昀⠀砀⤀⬀砀Ⰰ x*f(x), etc.), and for individual integrals (eg. the indefinite integral,਀搀攀昀椀渀椀琀攀 椀渀琀攀最爀愀氀Ⰰ 琀栀攀 椀渀搀攀昀椀渀椀琀攀 搀漀甀戀氀攀 椀渀琀攀最爀愀氀猀Ⰰ 椀渀搀攀昀椀渀椀琀攀 琀爀椀瀀氀攀 integrals, definite double integrals, definite triple integrals, etc.), second,਀眀爀椀琀攀 洀愀渀礀 氀椀渀攀猀 漀昀 瀀爀漀最爀愀洀 昀漀爀 琀栀攀 椀渀搀椀瘀椀搀甀愀氀 猀甀戀爀漀甀琀椀渀攀猀Ⰰ ⠀椀攀 琀漀 琀攀氀氀 琀栀攀 computer how to calculate these integrals), third, load these subroutines,਀昀椀渀愀氀氀礀Ⰰ 挀愀氀氀 琀栀攀猀攀 猀甀戀爀漀甀琀椀渀攀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> Xx2 * F+਀堀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,X*F

第二,写多少行程序对个人子程序,(即告诉计算机如何计算这些积分),

第三,加载这些子程序,

最后,调用这些子程序。That is precisely what DrMath do not਀愀猀欀 礀漀甀 琀漀 搀漀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>DrMath腎䊉恬婏ɐ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>  相比之下,学习意味着你只需要提供必要的事实(通常是一个x)和f)的),DrMath将决定如何去许多问题的解决方案。 DrMath again when you run DrMath਀渀攀砀琀 琀椀洀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>DrMath,你就N膗趉契㱥⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>DrMath

 

2部分    

17.编程  

            DrMathDrMath program in the Input window, which is਀眀爀椀琀琀攀渀 戀礀 愀渀礀 攀搀椀琀漀爀 椀渀 琀栀攀 琀攀砀琀 ⠀䄀匀䌀䤀䤀⤀ 昀椀氀攀 昀漀爀洀愀琀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> DrMath程序在输入窗口,这是写在文本(ASCII)文件格式的编辑器。

            DrMath FORTRANIt਀愀氀猀漀 椀猀 愀渀 攀砀瀀爀攀猀猀椀漀渀ⴀ漀爀椀攀渀琀攀搀 氀愀渀最甀愀最攀 愀渀搀 昀甀渀挀琀椀漀渀愀氀 氀愀渀最甀愀最攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 它也是一种面向表达式的语言和函数式语言。

            The DrMath program consists਀漀昀 愀 渀甀洀戀攀爀 漀昀 猀琀愀琀攀洀攀渀琀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> DrMath程序由若干语句。

            The structure of DrMath਀氀愀渀最甀愀最攀 椀猀㨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>DrMath语言的结构是:

                        data -> expression ->਀猀琀愀琀攀洀攀渀琀 ⴀ☀最琀㬀 瀀爀漀最爀愀洀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>-਀☀最琀㬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>表达- >报表 DrMath language, (eg. abc is different from਀䄀䈀䌀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>需要注意的是大写和小写字母是౎葔㱶⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>DrMath语言,(如ABC౎॔˿㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>  在下面的例子中,行是指输入,您在输入窗口中输入,通过点击菜单中的运行程序;了一声: 输出 你鑎⺋斕啑쵓㲋⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 一些输出可以在实例被删去。

 

17.1  

  没有必要申报数据是何种类型,如 

17.1.1. 17.1.1

   实际上,输入的实数的范围是-∞^-300),10਀帀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>(-3000010਀帀 ㌀  㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>),无限远。  关闭,但是当开关数字:=

            -Infinity, -1.E300 to -1.E-300, 0,਀㄀⸀䔀ⴀ㌀   琀漀 ㄀⸀䔀㌀  Ⰰ 䤀渀昀椀渀椀琀礀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> -1.E3000            It means that the number larger਀琀栀愀渀 ㄀⸀攀㌀   椀猀 挀漀渀瘀攀爀琀攀搀 愀甀琀漀洀愀琀椀挀愀氀氀礀 琀漀 䤀渀昀椀渀椀琀礀Ⰰ 琀栀攀 愀戀猀漀氀甀琀攀 瘀愀氀甀攀猀 漀昀 琀栀攀 number less than 1.e-300 is converted to 0, and the number less than -1e300 is਀挀漀渀瘀攀爀琀攀搀 琀漀 ⴀ䤀渀昀椀渀椀琀礀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>1.E-300数的绝对值被转换为0 

  举例来说:

--------------------------------------------------------------------------------------             类型

                  integer   理数

0.230.23   实数

2+3*I2 +3 *I  complex灙㱥⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>             complex------------------------------------------------------------------------------------------ 

            That "a" and਀☀焀甀漀琀㬀戀☀焀甀漀琀㬀 愀爀攀 琀栀攀 猀愀洀攀 洀攀愀渀猀 愀戀 㴀  Ⰰ 眀栀椀氀攀 琀栀愀琀 琀栀攀礀 愀爀攀 搀椀昀昀攀爀攀渀琀 洀攀愀渀猀 愀戀 <> 0.

 

   常量  

            The constants are the unchangeable਀瘀愀氀甀攀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>The name of these built-in constants should਀戀攀 愀瘀漀椀搀攀搀 椀渀 琀栀攀 甀猀攀爀ⴀ搀攀昀椀渀攀搀 挀漀渀猀琀愀渀琀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=ZH-CN style='mso-bidi-font-size:10.0pt;font-family:SimSun;mso-bidi-font-family:਀匀椀洀匀甀渀✀㸀鐀罞䶐⡑⡗㝵驢䥛葎㡶콞鮏蕎湑㡿콞蒑呶称。

Built-in Constants                    Meanings 

Pi:=3.1415926536Pi    圆周率。

E:=2.7182818285E     自然对数的底。

I:=Sqrt(-1)= SQRT       Infinity                              无穷大。

-Infinitythe undefined value, eg.未定义的值,例如:indeterminate਀昀漀爀洀猀㨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀昀漀渀琀ⴀ昀愀洀椀氀礀㨀 SimSun;mso-bidi-font-family:SimSun'>湎驸葛扶ཟ᩟㳿⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 0/0,无限0਀⨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>无穷大,0 ^ 0等。

True False                          

----------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

            The Infinity਀挀愀渀 戀攀 挀漀洀瀀甀琀攀搀 愀猀 椀昀 渀甀洀戀攀爀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>

  例如:

In:输入:   Infinity+2;;

Out: Infinity:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>            Notice਀琀栀愀琀 琀栀攀 搀椀猀挀漀渀琀 愀渀搀 甀渀搀攀昀椀渀攀搀 挀漀渀猀琀愀渀琀猀 愀爀攀 搀椀昀昀攀爀攀渀琀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 注意,If the value of an expression at x=x0 is discont, the expression only਀栀愀猀 琀栀攀 漀渀攀ⴀ猀椀搀攀搀 瘀愀氀甀攀 愀琀 砀㴀砀  愀渀搀 琀栀椀猀 漀渀攀ⴀ猀椀搀攀搀 瘀愀氀甀攀 椀猀 攀瘀愀氀甀愀琀攀搀 戀礀 x=x0+zero or x=x0-zero. 如果在x = x0和这个片面值由X = X0 +零或If਀琀栀攀 瘀愀氀甀攀 漀昀 愀渀 攀砀瀀爀攀猀猀椀漀渀 愀琀 砀㴀砀  椀猀 甀渀搀攀昀椀渀攀搀Ⰰ 琀栀攀 攀砀瀀爀攀猀猀椀漀渀 洀愀礀 戀攀 evaluated by the function lim().如果在x = X0表达式的值是湎驸葛౶棿뺈ྏㅎﵵ灑㱥⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt;font-family:"Arial","sans-serif"'>LIM进行评估()。

 例如:评估地契(1 / x)和的x 

In:输入:   

f(x_) := Exp(1/x);F=਀䔀堀倀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>(1 / x

Out: f(x_) := Exp(1/x);:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>X_ 

In:输入:   

f(0);F;

Out: Discont;:਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>           # f(0)਀椀猀 搀椀猀挀漀渀琀椀渀甀椀琀礀Ⰰ 漀渀氀礀 栀愀猀 漀渀攀 猀椀搀攀搀 瘀愀氀甀攀㬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 0)是౾엿睎॑g⩎챎打㲗㱐⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>; 

 Replacex0; 输出

未定义

 

 

   变量  

 128个字符长。 他们必须以字母开头,并且只能使用字母和数字。  DrMath਀欀渀漀眀猀 甀瀀瀀攀爀 愀渀搀 氀漀眀攀爀 挀愀猀攀 搀椀猀琀椀渀挀琀椀漀渀猀 椀渀 瘀愀爀椀愀戀氀攀 渀愀洀攀猀Ⰰ 猀漀 䄀䈀Ⰰ 愀戀Ⰰ 䄀戀 愀渀搀 愀䈀 are the different variables.DrMath知道变量❔ཙ饜葑㩶⭓౒䃿㱎⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>ABabThey are case sensitive.            Variables਀挀愀渀 戀攀 甀猀攀搀 琀漀 猀琀漀爀攀 琀栀攀 爀攀猀甀氀琀猀 漀昀 挀愀氀挀甀氀愀琀椀漀渀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 变量可以用来存储计算的结果。 Having਀搀攀昀椀渀攀搀 堀 愀猀 愀戀漀瘀攀Ⰰ 礀漀甀 挀漀甀氀搀 搀攀昀椀渀攀 夀 㨀㴀 䄀匀䤀一⠀堀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 在定义਀㨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:"Arial","sans-serif"'>= X)。   分配的结果给一个变量,只要把  =   expression  例如: =਀㈀ ⬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>3 # assign value to xx

            Variables can be used like਀挀漀渀猀琀愀渀琀猀 椀渀 攀砀瀀爀攀猀猀椀漀渀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>

            For example:       a := 2 + 3A :=        b := a*4B :=    

                        y := 3 + xY :=     #਀昀漀爀洀甀氀愀 爀攀猀甀氀琀猀 猀椀渀挀攀 砀 甀渀搀攀昀椀渀攀搀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> 未定义  4   #现在的                     # y਀爀攀琀甀爀渀猀 㜀Ⰰ 戀甀琀 椀琀猀 瘀愀氀甀攀 椀猀 猀琀椀氀氀 琀栀攀 昀漀爀洀甀氀愀 ㌀ ⬀ 砀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 7,但其价值仍然是公式3 +   7   #升值压力                     # new਀瘀愀氀甀攀 昀漀爀 礀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>Y#新价值

             Symbolic values for variables are਀甀猀攀昀甀氀 洀漀猀琀氀礀 昀漀爀 瘀椀攀眀椀渀最 琀栀攀 搀攀昀椀渀椀琀椀漀渀猀 漀昀 昀甀渀挀琀椀漀渀猀 愀渀搀 猀礀洀戀漀氀椀挀 differentiation and integration.变量符号值大多用于查看的函数和象征性的分化和整合的定义是有用的。  注意无限递归在这里。   Defining  X਀⬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>3

when x has no initial value, it will not਀挀愀甀猀攀 愀渀 椀洀洀攀搀椀愀琀攀 瀀爀漀戀氀攀洀Ⰰ 戀甀琀 愀渀礀 昀甀琀甀爀攀 爀攀昀攀爀攀渀挀攀 琀漀 砀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 将导致无穷递归!

            A value can be assigned to the਀瘀愀爀椀愀戀氀攀Ⰰ 戀礀 漀渀攀 漀昀 琀栀爀攀攀 洀攀琀栀漀搀猀㨀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>

            (1) the assignment :=,1)赋值 :  (),  YX0)。

y:=x^2;Y := ; 2  

# assignment;;

yŸ

f(2)F                                   #如果x)已定义,例如: X_Replace(x^2, x , 2);X ^ 22                   #计算x਀㴀 ㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>。 

            The variable named last is the਀戀甀椀氀琀ⴀ椀渀 愀猀 琀栀攀 瘀愀爀椀愀戀氀攀 氀愀猀琀 椀猀 愀氀眀愀礀猀 愀甀琀漀洀愀琀椀挀愀氀氀礀 愀猀猀椀最渀攀搀 琀栀攀 瘀愀氀甀攀 漀昀 琀栀攀 last output result. 最后命葔콓⾑蕦湑葿S๧㭔⽠ꢁْ䵒蒑v๧鍔摒퍑鱾葧㱎ɐ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN>

            The usual used independent਀瘀愀爀椀愀戀氀攀 椀猀 砀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>            By਀搀攀昀愀甀氀琀Ⰰ 䄀戀猀⠀砀⤀ ☀氀琀㬀 䤀渀昀椀渀椀琀礀 愀渀搀 愀氀氀 瘀愀爀椀愀戀氀攀猀 愀爀攀 挀漀洀瀀氀攀砀Ⰰ 攀砀挀攀瀀琀 琀栀愀琀 variables in inequalities are real, as usual only real numbers can be compared.ABS<无限和所有的变量是䉙葧౶仿同的是在獎䥞葻콓⾑鹦灛౥쿿聐㡟^㝎॓鹧灛푎葢ɶ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN> x)的䉙౧䛿㱏⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>是真正的在Y> 1

            You can restrict the domain of a਀瘀愀爀椀愀戀氀攀 戀礀 愀猀猀甀洀椀渀最 琀栀攀 瘀愀爀椀愀戀氀攀 椀猀 攀瘀攀渀Ⰰ 漀搀搀Ⰰ 椀渀琀攀最攀爀Ⰰ 爀攀愀氀 渀甀洀戀攀爀Ⰰ 瀀漀猀椀琀椀瘀攀 or negative (see Chapter Simplification and Assumption). 

   模式

 模式代表类的表达式。 

x_X_  任何表达式,给出的㱹⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 

 Patterns਀愀爀攀 漀渀氀礀 甀猀攀搀 椀渀 搀攀昀椀渀椀琀椀漀渀 漀昀 昀甀渀挀琀椀漀渀猀Ⰰ 瀀爀漀挀攀搀甀爀攀猀 愀渀搀 爀甀氀攀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 模式只用于函数,程序和规则的定义。

            Patterns are used to define਀昀甀渀挀琀椀漀渀猀 愀渀搀 爀甀氀攀猀 昀漀爀 瀀愀琀琀攀爀渀 洀愀琀挀栀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>

 

函数,过程和规则  

            These are two types of functions:਀椀渀琀攀爀渀愀氀 愀渀搀 攀砀琀攀爀渀愀氀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>The਀椀渀琀攀爀渀愀氀 昀甀渀挀琀椀漀渀 椀猀 挀漀洀瀀椀氀攀搀 椀渀琀漀 琀栀攀 㰀戀㸀䐀爀䴀愀琀栀㰀⼀戀㸀 猀礀猀琀攀洀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>DrMath系统。 DrMath language, which is਀愀甀琀漀洀愀琀椀挀愀氀氀礀 氀漀愀搀攀搀 眀栀攀渀 椀琀 椀猀 渀攀攀搀攀搀 ⠀猀攀攀 䌀栀愀瀀琀攀爀 䰀椀戀爀愀爀礀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 外部函数是写在您可以通过修改它的库文件改变外部函数的性质或౹᛿ꡢ᩠자ᮏ禍荞葛鍶蝞ⵎפֿꁭR⩎끎葥ᙶ﶐灑౥䛿恏乏能改变内部函数。 

17.1.5.1.17.1.5.1   Standard਀䴀愀琀栀攀洀愀琀椀挀愀氀 䘀甀渀挀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-bookmark:_Toc376205103'>

x),FACATAN2Y)),可以分化和整合。


਀㰀⼀猀瀀愀渀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph;mso-outline-level:1'> 
17.1.5. 标准数学函数

Functions               Meanings 

n!n   x square root, the same as x^0.5.平方根,同样为x ^ 0.5

Exp(x)Exp(                       同为Sign(x)Log(x                       当重(xXxx = 0

                                    -1਀漀琀栀攀爀眀椀猀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>-1

Abs(x)Abs(                       的绝对值。 x            (x x

Tan(x)Tan(x

Cot(x)Cot( x xx)。

Acos(x)Acos( x

Acot(x)Acot(x

Asec(x)Asec(x

Acsc(x)Acsc(x

Atan2(x,y)Atan2(X x hyperbolic sine function of x.x的双曲正弦函数。

Cosh(x)Cosh(

Asinh(x)Asinh(  x的双曲正弦函数,双曲正弦(X

Acosh(x)Acosh(x

----------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

17.1.5.2.17.1.5.2   Calculus਀䘀甀渀挀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-bookmark:_Toc376205104'>

  微积分函数是微积分的计算。The first argument of the function is for evaluation,਀愀渀搀 琀栀攀 猀攀挀漀渀搀 愀爀最甀洀攀渀琀 椀猀 愀 瘀愀爀椀愀戀氀攀 琀栀愀琀 椀猀 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 该函数的第一个参数是评价,第二个参数是一个变量,它是相对于x

 

                        Table 17.1.5.217.1.5. 微积分函数

函数                                     含义

Replace(X evaluates਀礀 眀栀攀渀 砀 㴀 砀 ⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>Ÿ Y                   differentiate਀礀 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 砀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>Ÿ关于 Y gives the nth order derivative of਀礀 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 愀渀 甀渀搀攀昀椀渀攀搀 瘀愀爀椀愀戀氀攀 砀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>           给出n阶导数,以一个未定义的变量x

D(y)D(                        implicit਀搀椀昀昀攀爀攀渀琀椀愀琀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀猀瀀愀渀 style='mso-tab-count:1'>          隐函数的微分。

X  yx的驎ٹɒ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀✀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀最漀漀最氀攀ⴀ猀爀挀ⴀ琀攀砀琀㄀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>Int(y,x,a,b)Int( YA      find the definite integral of y਀眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 愀渀 甀渀搀攀昀椀渀攀搀 瘀愀爀椀愀戀氀攀 砀 琀愀欀攀渀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 的定积分 x਀㴀 戀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>的。 XB            find the definite integral of y਀眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 愀渀 甀渀搀攀昀椀渀攀搀 瘀愀爀椀愀戀氀攀 砀 琀愀欀攀渀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 的定积分,,,,x਀㴀 戀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,则与x = c,其中 XB   一样A)。 Y   

Sum(y, x , xmin , xmax)YXMIN                         sum਀漀昀 礀 猀琀攀瀀㴀㄀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>=਀㄀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>。 Sum( XXMAX                 sum਀漀昀 礀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 夀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 

Product(y, x , xmin , xmax)YXMIN                  product਀漀昀 礀 猀琀攀瀀㴀㄀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>=਀㄀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>的相乘。 Product( XXMAX           

            If a਀猀攀挀漀渀搀 愀爀最甀洀攀渀琀 砀 椀猀 漀洀椀琀琀攀搀 椀渀 琀栀攀 昀甀渀挀琀椀漀渀猀 䐀⠀礀⤀ 愀渀搀 䤀渀琀⠀礀⤀Ⰰ 琀栀攀礀 愀爀攀 implicit derivatives and integrals.如果第二个参数YY),它们是隐式的导数和积分。If f(x) is undefined, D(f(x), x) is਀搀椀昀昀攀爀攀渀琀椀愀琀椀漀渀 漀昀 昀⠀砀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 xDX)是f)的。These are useful in the differential and਀椀渀琀攀最爀愀氀 攀焀甀愀琀椀漀渀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>(见后面的章节)。

  举例来说:

            Int(Int(F,x), y) is double਀椀渀琀攀最爀愀氀 漀昀 䘀 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 戀漀琀栀 瘀愀爀椀愀戀氀攀猀 砀 愀渀搀 礀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> X),F的双积分对于两个变量x DYt)是x         The਀欀攀礀眀漀爀搀猀 ☀焀甀漀琀㬀昀爀漀洀☀焀甀漀琀㬀 ☀焀甀漀琀㬀琀漀☀焀甀漀琀㬀 ☀焀甀漀琀㬀猀琀攀瀀☀焀甀漀琀㬀 ☀焀甀漀琀㬀Ⰰ☀焀甀漀琀㬀 愀爀攀 琀栀攀 same as separators in multi-argument functions.”“ Int( X)中,0F(x)0, 

                        Examples:

differentiation               D()D()   X਀帀 ㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,X

integration               Int()Int(   X

-----------------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

17.1.5.3. 17.1.5.3

  1.5.3.1  The is*(x)਀䘀甀渀挀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>

Function               Meaning 

IsOdd(x)IsOdd(x)   测试,如果 x 测试,如果                test਀椀昀 砀 椀猀 愀渀 椀渀琀攀最攀爀 渀甀洀戀攀爀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> 是一个整数。               test਀椀昀 砀 椀猀 愀 爀愀琀椀漀渀愀氀 渀甀洀戀攀爀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> 是有理数。 IsReal(x)   测试,如果              test਀椀昀 砀 椀猀 愀 挀漀洀瀀氀攀砀 渀甀洀戀攀爀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> 是一个灙ɥ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN>

IsNumber(x)IsMunber(x)   测试,如果 Y          是自由的x

------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

            All of the is* functions give਀攀椀琀栀攀爀 吀爀甀攀 漀爀 䘀愀氀猀攀 漀琀栀攀爀眀椀猀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> False,否则。

            The Type(x) gives the type of x.x的类型。Its value is a string. 

              2  The Type(x)਀昀甀渀挀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>x)的函数

----------------------------------------------------------------------------------------------------                     Type(x)x

                    Integer                  Real                  ComplexSin(x)Sign        

a+bA + B                 **

a^b^               ^^

a=bA = B   b                  >>             >=> =                <<              <=<= a              <><> B  

------------------------------------------------------------------ 

17.1.5.4.17.1.5.4   Miscellaneous Functions  

                        Table 17.1.5.4.117.1.5.4. 代数函数

-----------------------------------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

Expand(F)F  扩大(A + B^਀㈀ ⬀ ㈀ ⨀ 䄀 ⨀ 䈀 ⬀ 䈀 帀 ㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 style='mso-bidi-font-size:10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>。 系数(                   factorise਀愀帀㈀ ⬀ ㈀⨀愀⨀戀 ⬀ 戀帀㈀ 琀漀 ⠀愀⬀戀⤀帀㈀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> A਀⬀ 䈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)^ 2

Solve(f(x)=0, x)F=਀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>,x   求解多项式和线性方程组

-----------------------------------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

  例如:

-------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>   解决()   解决()的 扩大   展开()   展开((^਀㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)         

factoring        Factor()                   Factor(a*c+b*c)A * C + B *਀䌀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)         

------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

            Conversion਀昀甀渀挀琀椀漀渀猀 挀漀渀瘀攀爀琀 愀 琀礀瀀攀 漀昀 搀愀琀愀 琀漀 愀渀漀琀栀攀爀 琀礀瀀攀 漀昀 搀愀琀愀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 转换函数转换为数据类型到另一种数据类型。

  2   Conversion਀䘀甀渀挀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>

Re(x)回㱙⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>                                  real਀瀀愀爀琀 漀昀 挀漀洀瀀氀攀砀 渀甀洀戀攀爀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 x)的  ਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>灙葥챶ज़慠鮌葒vڐɒ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN>

N(x)N                                convert਀砀 琀漀 琀栀攀 昀氀漀愀琀椀渀最ⴀ瀀漀椀渀琀 渀甀洀戀攀爀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> 地板(                           convert਀砀 琀漀 琀栀攀 爀漀甀渀搀攀搀 椀渀琀攀最攀爀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> 转换为圆角整数。 x)的  x

------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

  

17.1.5.5.17.1.5.5      User-defined਀䘀甀渀挀琀椀漀渀猀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-bookmark:_Toc376205107'>

             Define a new function f(x) byf  X_ 然后调用X)作为标准函数。 该函数⽎ﭦ啎呏称。  通过清除从赋值的变量或函数  Clear(x)  ਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>#清除x

                        Clear(f(x))F        #਀挀氀攀愀爀 昀⠀砀⤀ 昀爀漀洀 愀猀猀椀最渀洀攀渀琀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> X

                        Clear(a>0)> 0  #从分配清除> 0

         Variables can be used in function਀搀攀昀椀渀椀琀椀漀渀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>它会导致函数和变量之间的重要区别。  When a variable਀椀猀 搀攀昀椀渀攀搀Ⰰ 愀氀氀 琀攀爀洀猀 漀昀 琀栀攀 搀攀昀椀渀椀琀椀漀渀 愀爀攀 攀瘀愀氀甀愀琀攀搀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 当一个变量被定义,该定义的所有方面进行评估。   When a function਀椀猀 搀攀昀椀渀攀搀Ⰰ 椀琀猀 琀攀爀洀猀 愀爀攀 渀漀琀 攀瘀愀氀甀愀琀攀搀㬀 琀栀攀礀 愀爀攀 攀瘀愀氀甀愀琀攀搀 眀栀攀渀 琀栀攀 昀甀渀挀琀椀漀渀 is evaluated. 当一个函数被定义,其条款쑎る౏叿ﶋ灑ꭥ쒈る荏䲏쒈るɏ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN>  

   程序  

  Block(ACB,只有最后一个参数返回它的值。It is used as grouper in definition of a਀瀀爀漀挀攀搀甀爀攀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>在块中的所有变量都是局部的。

            eg.f(x_):=Block(p:=x^6,p);F= Block( f= X_ ^ 6;

            Remember that you can split a line਀漀昀 猀琀愀琀攀洀攀渀琀 椀渀琀漀 洀甀氀琀椀ⴀ氀椀渀攀猀 猀琀愀琀攀洀攀渀琀 戀礀 攀渀搀椀渀最 㬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 记住,你可以通过结束分割线语句为多行语句 

17.1.5.7. 17.1.5.7

  规则是类似于函数。 在函数定义,函数的所有参数都是简单的变量,但是在规则的定义,第一个参数可以是一个䉙葧桶뺈ྏɟ㰰⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=ZH-CN>

  例如:

            f(x_,y_) := x_^2+y_^2FY_ := 2                                   #਀搀攀昀椀渀椀渀最 昀甀渀挀琀椀漀渀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>  X_=਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀㬀 font-family:SimSun;mso-bidi-font-family:SimSun;mso-ansi-language:EN-US'>BlockA := A਀⬀ 堀 帀 ㈀ ⬀ 夀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一 style='mso-bidi-font-size:10.0pt;font-family:SimSun;mso-bidi-font-family:SimSun'>)    # defining procedure  f=XY   #定义规则

 

17.1.6. 17.1.6

            An਀攀焀甀愀琀椀漀渀 椀猀 愀渀 攀焀甀愀氀椀琀礀 漀昀 琀眀漀 猀椀搀攀猀 氀椀渀欀攀搀 戀礀 愀渀 攀焀甀愀琀椀漀渀 猀椀最渀 㴀Ⰰ 攀最⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 一个方程有两个由公式符号x^2+p਀㴀  Ⰰ 眀栀攀爀攀 琀栀攀 猀礀洀戀漀氀 㴀 猀琀愀渀搀猀 昀漀爀 愀渀 攀焀甀愀琀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate> 表示的方程。Note that the symbols "=",਀☀焀甀漀琀㬀㴀㴀☀焀甀漀琀㬀 愀渀搀 ☀焀甀漀琀㬀㨀㴀☀焀甀漀琀㬀 愀爀攀 搀椀昀昀攀爀攀渀琀㨀 ☀焀甀漀琀㬀㨀㴀☀焀甀漀琀㬀 椀猀 琀栀攀 assignment, "==" is the equal sign, but "=" is the equation਀猀椀最渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>“=”:=”是赋值,“=”是方程符号。

  例如:

In:输入:   

2 = 2;2 = 2;

Out: 2 = 2;

2 = 2

            # unevaluated; 

In:输入:   2਀㴀㴀 ㈀㬀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 输出:; 

 

   䥎ཻ㱟⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀漀漀欀洀愀爀欀㨀开吀漀挀㌀㜀㘀㈀ 㔀㄀㄀㄀✀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-bookmark:_Toc466966849'>

  例如:

                        a < bA <B              less than  a   小于或等于

                        a > bA> B              greater than  大于或等于

                        a == b==   等于

                        a <> b<>b 䥎蹻㱎⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀娀䠀ⴀ䌀一㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

17.2   

            The expressions (ie expr) are made਀甀瀀 漀昀 漀瀀攀爀愀琀漀爀猀 愀渀搀 漀瀀攀爀愀渀搀猀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> 二元运算符使用通常的代数形式,如:。a+b.A + B

            There are two kinds of਀攀砀瀀爀攀猀猀椀漀渀猀㨀 渀甀洀攀爀椀挀 愀渀搀 䈀漀漀氀攀愀渀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> x*(x>0)਀椀猀 搀椀昀昀攀爀攀渀琀 昀爀漀洀 砀⨀砀☀最琀㬀 ⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> X> 0)是从x*x>0 is the same as (x*x)>0.X * X> 0时是相同的(X * X  例如:

a+b+3A + B +3   数值表达式,

a>0>               a>0 and਀戀☀最琀㬀  㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀✀㸀ꀀꀀꀀ 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-spacerun:yes'> Boolean expression

                        17.2.1. 17.2.1

 Table 17.2.1-------------------------------------------------------------------------------------------------- 作业  Operators        Examples  Order 

comma逗号                a:=2, b:=3        11

assignment               :=               2਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>2

and                    a>2 and a<8 22

or                   or                           方程                         ==                     larger than਀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㈀✀㸀ꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀ 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>   a>2                 33

           >=> =                  less than    a<2                 33

              a<=2               33

                                                                                        abAB   mutilation                                                                        factorial                    66

positive                               ++  +a                   77

negative                   --                77

function                            Sin(x)              77

parentheses                (a+b)*c                        77

--------------------------------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

           

           

           

           

 

਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀栀㌀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

plus                               ++  a+b                 44

minus                               --                    44

                     **  a*b                  55

division                                   //  a/b                  55

power                                   ^^  a^b                  66

 

਀㰀漀㨀瀀㸀㰀⼀漀㨀瀀㸀㰀⼀猀瀀愀渀㸀㰀⼀栀㌀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

           

           

 a < b               less਀琀栀愀渀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>  a  less than or equal to

                        a > bA> B              greater than a >= b            

                        a == b==਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>b  equal to

                        a <> b<>b  not equals

 DrMath uses the double equals sign ==਀⠀氀椀欀攀 䌀 氀愀渀最甀愀最攀⤀ 昀漀爀 ☀焀甀漀琀㬀椀猀 攀焀甀愀氀 琀漀☀焀甀漀琀㬀 琀漀 搀椀猀琀椀渀最甀椀猀栀 琀栀椀猀 漀瀀攀爀愀琀漀爀 昀爀漀洀 the equation =.

             

17.2.1.3.     Logical਀伀瀀攀爀愀琀漀爀猀㰀⼀猀瀀愀渀㸀㰀⼀愀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ昀愀爀攀愀猀琀ⴀ昀漀渀琀ⴀ昀愀洀椀氀礀㨀∀吀椀洀攀猀 一攀眀 刀漀洀愀渀∀✀㸀

 DrMath uses the logical operators: And,਀愀渀搀 伀爀⸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ猀瀀愀挀攀爀甀渀㨀礀攀猀✀㸀ꀀꀀ 㰀⼀猀瀀愀渀㸀夀漀甀 挀愀渀 挀漀洀戀椀渀攀 挀漀洀瀀愀爀椀猀漀渀 operators with them to any level of complexity. In contrast to Pascal, logical਀漀瀀攀爀愀琀漀爀猀 椀渀 㰀戀㸀䐀爀䴀愀琀栀㰀⼀戀㸀 栀愀瘀攀 愀 氀漀眀攀爀 漀爀搀攀爀 漀爀 瀀爀攀挀攀搀攀渀挀攀 琀栀愀渀 琀栀攀 comparisons, so a < b and c > d works as expected.

           

 

 A function call activates the function਀猀瀀攀挀椀昀椀攀搀 戀礀 琀栀攀 昀甀渀挀琀椀漀渀 渀愀洀攀⸀ 吀栀攀 昀甀渀挀琀椀漀渀 挀愀氀氀 洀甀猀琀 栀愀瘀攀 愀 氀椀猀琀 漀昀 愀挀琀甀愀氀 parameters if the corresponding function declaration contains a list of formal਀瀀愀爀愀洀攀琀攀爀猀⸀ 䔀愀挀栀 瀀愀爀愀洀攀琀攀爀 琀愀欀攀猀 琀栀攀 瀀氀愀挀攀 漀昀 琀栀攀 挀漀爀爀攀猀瀀漀渀搀椀渀最 昀漀爀洀愀氀 parameter. If the function is external, the function call will automatically਀氀漀愀搀 琀栀攀 氀椀戀爀愀爀礀 猀瀀攀挀椀昀椀攀搀 戀礀 椀琀猀 昀甀渀挀琀椀漀渀 渀愀洀攀 瀀氀甀猀 攀砀琀攀渀猀椀漀渀 㰀戀㸀⸀瘀洀㰀⼀戀㸀 眀栀攀渀 needed.

           

             # load the library Sin.vm when needed Int(x^2, x)       

 

17.3    

 #  are਀琀栀攀 挀漀洀洀攀渀琀 猀琀愀琀攀洀攀渀琀 猀椀最渀猀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> You can add comments into a line, or even਀瀀爀漀搀甀挀攀 愀 猀椀渀最氀攀 氀椀渀攀 眀栀椀挀栀 椀猀 攀渀琀椀爀攀氀礀 愀 挀漀洀洀攀渀琀Ⰰ 戀礀 瀀爀攀挀攀搀椀渀最 琀栀攀 挀漀洀洀攀渀琀 sign with #.

  例如:

                          # My first calculation;

 Comments make your calculations more਀甀渀搀攀爀猀琀愀渀搀愀戀氀攀Ⰰ 眀栀攀琀栀攀爀 礀漀甀 愀爀攀 洀愀欀椀渀最 愀 瀀爀椀渀琀攀搀 爀攀挀漀爀搀 漀昀 眀栀愀琀 礀漀甀 愀爀攀 搀漀椀渀最 or if you just want to jot some notes to yourself while you are working. 

17.3.2.17.3.2   Evaluation Statements 

           

 Expression;

 DrMath evaluates any expression which਀椀渀 愀 氀椀渀攀 愀渀搀 最椀瘀攀猀 琀栀攀 瘀愀氀甀攀 漀昀 琀栀攀 攀砀瀀爀攀猀猀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=google-src-text1>eg. 

In:输入:   

7; 

In:输入:   

6 x^5; 

17.3.3.17.3.3   Assignment Statements 

          

                := The assignment statement specifies that a new਀瘀愀氀甀攀 漀昀 攀砀瀀爀㈀ 戀攀 愀猀猀椀最渀攀搀 琀漀 攀砀瀀爀㄀Ⰰ 愀渀搀 猀愀瘀攀搀 椀渀琀漀 洀攀洀漀爀礀⸀ 吀栀攀 昀漀爀洀 漀昀 琀栀攀 assignment statements is

 expr1  

           

             := SIN(4.2).

               You can save yourself a਀氀漀琀 漀昀 爀攀挀愀氀挀甀氀愀琀椀漀渀猀 戀礀 愀氀眀愀礀猀 猀琀漀爀椀渀最 琀栀攀 爀攀猀甀氀琀猀 漀昀 礀漀甀爀 挀愀氀挀甀氀愀琀椀漀渀猀 椀渀 your own variables instead of leaving them in the default variable last.You can destroy the assignment to X with the command Clear(X). If X਀猀琀漀爀攀搀 愀 氀愀爀最攀 氀椀猀琀Ⰰ 礀漀甀 挀漀甀氀搀 爀攀最愀椀渀 愀 挀漀渀猀椀搀攀爀愀戀氀攀 愀洀漀甀渀琀 漀昀 洀攀洀漀爀礀 戀礀 clearing X. Also, since a variable and a function can have the same name, you਀挀愀渀 挀氀攀愀爀 愀 瘀愀爀椀愀戀氀攀 瀀Ⰰ 渀漀琀 愀 昀甀渀挀琀椀漀渀 瀀⠀砀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> The assignment operator is also used in the਀搀攀昀椀渀椀琀椀漀渀 漀昀 愀 昀甀渀挀琀椀漀渀 漀爀 瀀爀漀挀攀搀甀爀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> Variables can be used in function definitions,਀愀渀搀 琀栀愀琀 氀攀愀搀猀 琀漀 愀渀 椀洀瀀漀爀琀愀渀琀 搀椀昀昀攀爀攀渀挀攀 戀攀琀眀攀攀渀 昀甀渀挀琀椀漀渀猀 愀渀搀 瘀愀爀椀愀戀氀攀猀⸀㰀猀瀀愀渀 style='mso-spacerun:yes'>   When a variable is defined, all terms of the਀搀攀昀椀渀椀琀椀漀渀 愀爀攀 攀瘀愀氀甀愀琀攀搀⸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ猀瀀愀挀攀爀甀渀㨀礀攀猀✀㸀ꀀꀀ 㰀⼀猀瀀愀渀㸀圀栀攀渀 愀 function is defined, its terms are not evaluated; they are evaluated when the਀昀甀渀挀琀椀漀渀 椀猀 攀瘀愀氀甀愀琀攀搀⸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ猀瀀愀挀攀爀甀渀㨀礀攀猀✀㸀ꀀꀀ 㰀⼀猀瀀愀渀㸀吀栀愀琀 洀攀愀渀猀 琀栀愀琀 if a component of the function definition is changed, that change will be਀爀攀昀氀攀挀琀攀搀 琀栀攀 渀攀砀琀 琀椀洀攀 琀栀攀 昀甀渀挀琀椀漀渀 椀猀 攀瘀愀氀甀愀琀攀搀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

            eg.   # 2+3 is evaluated at the time of assignment,਀瀀 椀猀 愀猀猀椀最渀攀搀 眀椀琀栀 㔀㬀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>Out:

 p  := 5; 

In:输入:   

           

           

p(x)  

             Clear a variable, function or expression from਀愀猀猀椀最渀洀攀渀琀 戀礀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                         # clear x from assignment. Clear(f(x))      

                         # clear a>0 from Assume(a>0). 

17.3.4.

 There are two conditional functions: If(test , x)

                         

           

             It is useful in definition of the use-defined਀昀甀渀挀琀椀漀渀 琀漀 氀攀昀琀 琀栀攀 昀甀渀挀琀椀漀渀 甀渀攀瘀愀氀甀愀琀攀搀 椀昀 琀栀攀 愀爀最甀洀攀渀琀 漀昀 琀栀攀 昀甀渀挀琀椀漀渀 椀猀 not number. 例如: define਀昀⠀砀开⤀ 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ猀瀀愀挀攀爀甀渀㨀礀攀猀✀㸀ꀀ㰀⼀猀瀀愀渀㸀㨀㴀 䤀昀⠀䤀猀一甀洀戀攀爀⠀砀开⤀Ⰰ ㄀⤀Ⰰ 琀栀攀渀 挀愀氀氀 f(x), f(10) gives 1, and f(a) gives f(a).

 

   Loop

 You can use two kinds of loops in DrMath਀Ⰰ 昀椀砀攀搀 氀攀渀最琀栀 氀漀漀瀀猀 挀漀渀琀爀漀氀氀攀搀 戀礀 䘀漀爀⠀⤀ 愀渀搀 瘀愀爀椀愀戀氀攀ⴀ氀攀渀最琀栀 氀漀漀瀀猀 挀漀渀琀爀漀氀氀攀搀 by While(). The For() loop is similar to the FOR loop in BASIC language. The control variable in the For() loop is not਀氀椀洀椀琀攀搀 琀漀 椀渀琀攀最攀爀 瘀愀氀甀攀猀⸀ 夀漀甀 挀愀渀 猀愀礀㨀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                       

 It is similar to

                         := xmin TO xmax STEP dx 

                        where xmin,਀砀洀愀砀Ⰰ 愀渀搀 搀砀 愀爀攀 爀攀愀氀 瘀愀氀甀攀猀⸀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ猀瀀愀挀攀爀甀渀㨀礀攀猀✀㸀ꀀꀀ 㰀⼀猀瀀愀渀㸀䤀昀 匀吀䔀倀 dx is omitted, it defaults to 1.

  例如:

In:输入:  

 x:=0;

x  For( j , 1਀Ⰰ 㔀 Ⰰ ㄀Ⰰ 砀㨀㴀砀⬀㄀⤀㬀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>Out:

 x := 5;

The conditional loops are probably more useful than the For() loops if a਀渀甀洀戀攀爀 漀昀 椀琀攀爀愀琀椀漀渀 椀猀 甀渀欀渀漀眀渀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=google-src-text1>It is While(test, body);

           

  例如:

In:输入:   

x := 1; 

In:输入:   

 

17.3.9.   Sequence਀匀琀愀琀攀洀攀渀琀猀㰀⼀猀瀀愀渀㸀㰀⼀愀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ昀愀爀攀愀猀琀ⴀ昀漀渀琀ⴀ昀愀洀椀氀礀㨀∀吀椀洀攀猀 一攀眀 刀漀洀愀渀∀✀㸀

 The all above statements are simple਀猀琀愀琀攀洀攀渀琀猀⸀ 吀栀攀 猀攀焀甀攀渀挀攀 猀琀愀琀攀洀攀渀琀 猀瀀攀挀椀昀椀攀猀 琀栀愀琀 椀琀猀 挀漀洀瀀漀渀攀渀琀 猀琀愀琀攀洀攀渀琀猀 愀爀攀 to be executed in the same sequence as they are written. They are separated by਀琀栀攀 猀攀瀀愀爀愀琀漀爀猀 ⠀挀漀洀洀愀 ☀焀甀漀琀㬀Ⰰ☀焀甀漀琀㬀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=google-src-text1>eg. a+b, 2+3;

 

17.4  

 A library is a file of an external function,਀眀栀椀挀栀 昀椀氀攀渀愀洀攀 椀猀 椀琀猀 昀甀渀挀琀椀漀渀 渀愀洀攀 瀀氀甀猀 攀砀琀攀渀猀椀漀渀 ⸀瘀洀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 the library named Sin.vm is a file of the਀匀椀渀⠀砀⤀ 昀甀渀挀琀椀漀渀 搀攀昀椀渀椀琀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> The library (the *.vm file) is similar to the਀䴀匀ⴀ䐀伀匀 ⨀⸀䈀䄀吀 昀椀氀攀⸀ 夀漀甀 搀漀 渀漀琀 渀攀攀搀 琀漀 氀漀愀搀 漀爀 爀攀愀搀 琀栀攀 氀椀戀爀愀爀礀 戀礀 愀渀礀 挀漀洀洀愀渀搀⸀ 㰀戀㸀䐀爀䴀愀琀栀㰀⼀戀㸀 automatically load the library when it is needed. For example, when you use the਀匀椀渀⠀砀⤀ 昀甀渀挀琀椀漀渀 昀椀爀猀琀 琀椀洀攀Ⰰ 琀栀攀 氀椀戀爀愀爀礀 匀椀渀⸀瘀洀 眀椀氀氀 戀攀 愀甀琀漀ⴀ氀漀愀搀攀搀⸀ 吀栀攀 氀椀戀爀愀爀礀 must be in the default directory, otherwise the library is not loaded and the਀昀甀渀挀琀椀漀渀 椀猀 渀漀琀 眀漀爀欀椀渀最⸀ 伀渀氀礀 琀栀攀 愀猀猀椀最渀洀攀渀琀猀 椀渀 琀栀攀 氀椀戀爀愀爀礀 挀愀渀 戀攀 氀漀愀搀攀搀Ⰰ 愀渀搀 others in the library will be omitted, but all of these assignments will be not਀攀瘀愀氀甀愀琀攀搀 眀栀攀渀 琀栀攀礀 愀爀攀 氀漀愀搀攀搀⸀ 夀漀甀 挀愀渀 挀氀攀愀爀 琀栀攀 氀椀戀爀愀爀礀 匀椀渀⸀琀砀琀 昀爀漀洀 洀攀洀漀爀礀 by Clear(Sin(x)).

             There are many libraries. The following are਀猀漀洀攀 漀昀 琀栀攀洀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                               Libraries

File Name  函数

Plot.txt  plotting functions.

                            Int.txt   积分。

                                   NInt.txt  numeric integration.

                  

                  

                  Ei.txt  exponential integral function.

 

17.5   Interface with਀伀琀栀攀爀 匀漀昀琀眀愀爀攀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ昀愀爀攀愀猀琀ⴀ昀漀渀琀ⴀ昀愀洀椀氀礀㨀 "Times New Roman"'>

 You can run DrMath from another software as a਀攀渀最椀渀攀⸀ 䄀渀漀琀栀攀爀 猀漀昀琀眀愀爀攀 猀攀渀搀猀 愀 琀攀砀琀 昀椀氀攀 琀漀 䐀爀䴀愀琀栀Ⰰ 琀栀攀渀 爀甀渀 䐀爀䴀愀琀栀 椀渀 background, get result back from DrMath.

 

19. 

             The screen is divided into four areas: a menu਀氀椀渀攀Ⰰ 愀渀 䤀渀瀀甀琀 眀椀渀搀漀眀Ⰰ 愀渀 伀甀琀瀀甀琀 眀椀渀搀漀眀Ⰰ 愀渀搀 琀栀攀 䜀爀愀瀀栀 眀椀渀搀漀眀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

           

           

           

 

文件菜单  

   Open

 The Open menu opens a file for edit in the਀䤀渀瀀甀琀 眀椀渀搀漀眀⸀ 吀栀椀猀 洀攀渀甀 昀椀爀猀琀 漀瀀攀渀猀 愀 䐀椀爀攀挀琀漀爀礀 眀椀渀搀漀眀 琀漀 挀栀漀漀猀攀 愀 昀椀氀攀 昀漀爀 edit. You select a file from the Directory window to open for edit in the Input਀眀椀渀搀漀眀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

   Import Data

 

   Save Input 

             

19.1.4.

 The "Save Output" menu saves the਀昀椀氀攀 椀渀 琀栀攀 伀甀琀瀀甀琀 眀椀渀搀漀眀 椀渀琀漀 搀椀猀欀 甀渀搀攀爀 愀 搀椀昀昀攀爀攀渀琀 渀愀洀攀 漀爀 椀渀 愀 搀椀昀昀攀爀攀渀琀 directory.

 

   Print

 

   Exit

 

19.2.

 You can copy-and-paste from and to your਀搀漀挀甀洀攀渀琀 戀礀 爀椀最栀琀ⴀ戀甀琀琀漀渀 挀氀椀挀欀椀渀最 漀渀 琀栀攀 琀攀砀琀 昀椀攀氀搀 琀漀 瀀漀瀀ⴀ甀瀀 洀攀渀甀⸀ 䘀漀爀 猀攀挀漀渀搀 way of copy-and-paste, first select the text, then key in Ctrl+C (ie press the਀䌀琀爀氀 欀攀礀 愀渀搀 琀栀攀 䌀 欀攀礀 愀琀 琀栀攀 猀愀洀攀 琀椀洀攀⤀Ⰰ 琀栀攀渀 瀀漀椀渀琀 琀漀 眀栀攀爀攀 礀漀甀 眀愀渀琀 琀漀 paste, and finally key in Ctrl+V (ie press the Ctrl key and the V key at the਀猀愀洀攀 琀椀洀攀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

19.3   Run Menu 

            ਀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

19.4   Graph Menu 

It changes graph of size and colour. 放大缩小 

19.5   Option Menu menu converts output toTeX 格式。

਀㰀⼀猀瀀愀渀㸀 ਀㰀栀㄀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀最漀漀最氀攀ⴀ猀爀挀ⴀ琀攀砀琀㄀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ昀愀爀攀愀猀琀ⴀ昀漀渀琀ⴀ昀愀洀椀氀礀㨀 "Times New Roman"'>20.

20.1   Internal Structure 

             

  用户 Library文库         disk  /|\       ਀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀最漀漀最氀攀ⴀ猀爀挀ⴀ琀攀砀琀㄀㸀簀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU>                ||         ||                    

                        \|/                    \|/ 

                       

                        ----------------------------------------------------------------------------       /|\

                                           \|/

                        ------------------------------------------------------------ ------->|      |<----------

            ||         ------------------------------------------------------------            ||

           \|/

                           | Global਀䐀愀琀愀 䈀愀猀攀 簀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>

                                                                    ||

                                                            ----------------------------------------  数据文件 |਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>|

                                                            ---------------------------------------- 

                   Structure of DrMath 


 Table 20.1

----------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 函数:  Symbolic computation.

Domain:域:                           Mathematics.Search਀搀椀爀攀挀琀椀漀渀㨀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㈀✀㸀ꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀ 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-spacerun:yes'> Forward chaining.

                

                

                        

                    

                            Output਀昀漀爀洀愀琀㨀 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㌀✀㸀ꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀ 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-spacerun:yes'> Math notation, Input from:਀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㌀✀㸀ꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀ 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-spacerun:yes'> Keyboard, disk.

                               

                         Java.Computer:  Any machine that supports Java  16 MBytes.

Operating system:                

 

20.2   Internal Format 

21 System Extension 

22.关键词  

            DrMath keywords is upper-case. There are two types of the keywords: internal਀愀渀搀 攀砀琀攀爀渀愀氀⸀ 吀栀攀 椀渀琀攀爀渀愀氀 欀攀礀眀漀爀搀猀 栀愀瘀攀 戀攀攀渀 挀漀洀瀀椀氀攀搀 椀渀琀漀 琀栀攀 㰀戀㸀䐀爀䴀愀琀栀㰀⼀戀㸀 system, so you cannot change them. The external ones are in files, so you can਀挀栀愀渀最攀 琀栀攀椀爀 渀愀洀攀 漀爀 瀀爀漀瀀攀爀琀礀⸀ 唀猀愀最攀猀 漀昀 戀漀琀栀 琀礀瀀攀猀 愀爀攀 琀栀攀 猀愀洀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

           

 

22.1      Keywords in਀吀漀瀀椀挀 伀爀搀攀爀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ昀愀爀攀愀猀琀ⴀ昀漀渀琀ⴀ昀愀洀椀氀礀㨀∀吀椀洀攀猀 一攀眀 刀漀洀愀渀∀✀㸀

 +, -, *, /      

                       

 ==              equals     >>              greater than     >=> =           大于等于     <<                        <><>                         

   :=  

Equation:     ==

 Solve(x^2=1,x)                                               solve਀昀⠀砀⤀㴀  昀漀爀 砀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>                           

 NSolve(f(x)=0,x,x0)  numerically solve f(x)=0 for x with initial x0 

评论:

 

Built-in constants:    

Logic operators:      

 -x                                 square root of x

                              Expand(x)             expand x

  Factor(x)  factor x

Complex to real:      real part of the complex number x      imaginative part of the complex number x     Abs(x)Abs(x                 ਀愀戀猀漀氀甀琀攀 瘀愀氀甀攀 漀昀 砀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>      argument of complex number x      sign of complex number of x 

 Exp(x)                   

 Ln(x)                     

Trig functions:      sine of x

 Cos(x)                          tangent of x

 Csc(x)                          secant of x

 Cot(x)                      

 Asin(x)                         angle whose cosine is x      angle whose tangent is x      angle whose tangent is x/y 

 Sinh(x)                         hyperbolic cosine of x਀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>      hyperbolic tangent of x 

 Ei(x)                       exponential਀椀渀琀攀最爀愀氀 昀甀渀挀琀椀漀渀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>      incomplete exponential integral function਀䤀渀琀⠀琀帀⠀渀ⴀ㄀⤀⨀䔀砀瀀⠀琀⤀Ⰰ 琀Ⰰⴀ䤀渀昀椀渀椀琀礀Ⰰ砀⤀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>      gamma function Int(t^(n-1)*Exp(-t),਀琀Ⰰ Ⰰ䤀渀昀椀渀椀琀礀⤀㴀⠀渀ⴀ㄀⤀℀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>      incomplete gamma function Int(t^(n-1)*Exp(-t),਀琀Ⰰ Ⰰ砀⤀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>      error function 2/Sqrt(Pi)*Int(Exp(-t^2),t,0,x)    

 Ci(x)                      

 Li(x)                      

 Li(n,x)                    

Defining functions:     f(x_)਀㨀㴀 砀开帀㈀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>F(= X_ ^

 f(x_) := If(x_>0 , x_^2) 

 f(x_) := Block(p:=x_^2,p) 

 log(x_ * y_) := log(x_)+log(y_) 

      clear variable x

 Clear(f(x))                     clear unequal a>0

Calculus functions:Differentiating:      differentiate y with respect to x      differentiate y with respect to x in the n-th਀漀爀搀攀爀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU> 

积分:       integrate y with respect to x      integrate y with respect to x਀昀爀漀洀 砀洀椀渀 琀漀 砀洀愀砀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>                 numerically਀椀渀琀攀最爀愀琀攀 礀 眀爀琀 砀 昀爀漀洀 砀洀椀渀 琀漀 砀洀愀砀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU> 

代:

 Replace(y,x,x0)       Laplace transform

          sum of y wrt x from xmin਀琀漀 砀洀愀砀 猀琀攀瀀 搀砀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>      partial sum of y

 InfSum(y,x)                                      

 Product(y, x,xmin,xmax,dx)  product of y wrt x from xmin to xmax step dx 

 Taylor(y,x)             

 Taylor(y,x,order) Conversion functions:                

 Ceil(x)                   

 Type(x)                   

 N(x)                                                                            

 NSolve(Cos(x)-x,x,x0)  NInt(y,x,xmin,xmax)  numerically integrate y wrt x from xmin to਀砀洀愀砀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU> 

 IsConstant(x)         

                     IsEven(x)IsEven          ਀琀攀猀琀 椀昀 砀 椀猀 攀瘀攀渀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>      test if x is integer

 IsRational(x)          

 IsReal(x)                      test if x is complex

 IsNumber(x)                IsFree(y,x)IsFreeX  test if y is free of x਀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>      test if x is real

Comma:

 

Assume:               assume a > 0           assume x is real 

 If(x>0 , x)  If(x>0 , x , 0-x) Loop:

 While(x<5, body )  For(x,xmin,xmax,dx, body)

Getting parts:      type of x

 Re(x)                            imaginative part

Graph:

 Plot(y,x)                

 Plot(y,x,xmin,xmax)  Plot(y,x,xmin,xmax,ymin,ymax)  

 plot y wrt x from x=xmin to xmax, from y=ymin਀琀漀 礀洀愀砀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU> 

 ParametricPlot(x(t),y(t),t)  parametric plot x(t) and y(t) wrt t from t=0਀琀漀 ㈀⨀倀椀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>               

                         polar plot਀爀⠀琀⤀ 眀爀琀 琀 昀爀漀洀 琀㴀  琀漀 ㈀⨀倀椀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU style='mso-bidi-font-size:10.0pt'>         polar਀瀀氀漀琀 砀⠀琀⤀ 愀渀搀 礀⠀琀⤀ 眀爀琀 琀 昀爀漀洀 琀㴀琀洀椀渀 琀漀 琀洀愀砀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀愀戀ⴀ猀琀漀瀀猀㨀㄀㐀⸀㈀瀀琀✀㸀㰀猀瀀愀渀 lang=EN-AU> 


 

22.2     Keywords in਀䄀氀瀀栀愀戀攀琀椀挀愀氀 伀爀搀攀爀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ昀愀爀攀愀猀琀ⴀ昀漀渀琀ⴀ昀愀洀椀氀礀㨀 "Times New Roman"'>

 

 

                    --                       //   ****   ()                        :==

       <=

                            -------------------------------------------------------------------------------------------------- 

 You can use library as standard functions by਀氀椀戀爀愀爀礀 渀愀洀攀 眀椀琀栀漀甀琀 攀砀琀攀渀猀椀漀渀⸀ 䔀最 䄀戀猀Ⰰ 渀漀琀 䄀戀猀⸀瘀洀⸀ 倀氀攀愀猀攀 猀攀攀 昀椀氀攀 渀愀洀攀 椀渀 琀栀攀 vmath\library directory.

22.4     

 The keywords indicated internal are the਀椀渀琀攀爀渀愀氀 昀甀渀挀琀椀漀渀猀 漀爀 挀漀渀猀琀愀渀琀猀Ⰰ 漀琀栀攀爀眀椀猀攀 琀栀攀礀 愀爀攀 琀栀攀 攀砀琀攀爀渀愀氀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

 

                                     

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>  Abs(-1),਀䄀戀猀⠀ⴀ䤀⤀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>Out:

*Acos()Acos(x) is਀琀栀攀 愀爀挀 挀漀猀椀渀攀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 吀栀攀 椀渀瘀攀爀猀攀 昀甀渀挀琀椀漀渀 漀昀 䌀漀猀⠀砀⤀⸀ 吀栀攀 爀攀猀甀氀琀 椀猀 given in radians.

*Acosh()Acosh(x) is਀琀栀攀 椀渀瘀攀爀猀攀 栀礀瀀攀爀戀漀氀椀挀 挀漀猀椀渀攀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 吀栀攀 椀渀瘀攀爀猀攀 昀甀渀挀琀椀漀渀 漀昀 䌀漀猀栀⠀砀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

* Acot()

Acot(x) is਀琀栀攀 愀爀挀 挀漀琀愀渀最攀渀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀渀漀琀爀愀渀猀氀愀琀攀㸀㰀猀瀀愀渀 lang=EN-AU> ACOTx)是婴儿床的逆函数(= Pi/2-AtanSee also:਀䄀挀漀琀Ⰰ 䌀漀琀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

Acoth(x) is਀琀栀攀 椀渀瘀攀爀猀攀 栀礀瀀攀爀戀漀氀椀挀 挀漀琀愀渀最攀渀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 吀栀攀 椀渀瘀攀爀猀攀 昀甀渀挀琀椀漀渀 漀昀 Coth(x). Acoth(x)=Atanh(1/x).

* Acsc()

See also:਀愀挀猀挀Ⰰ 挀猀挀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

Acsch(x) is਀琀栀攀 椀渀瘀攀爀猀攀 栀礀瀀攀爀戀漀氀椀挀 挀漀猀攀挀愀渀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 吀栀攀 椀渀瘀攀爀猀攀 昀甀渀挀琀椀漀渀 漀昀 䌀猀挀栀⠀砀⤀⸀ Acsch(x)=Asinh(1/x).

* And                                                 

See also:਀伀爀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

Arg(x)਀最椀瘀攀猀 琀栀攀 愀爀最甀洀攀渀琀 ⠀瀀栀愀猀攀 愀渀最氀攀⤀ 漀昀 砀 椀渀 爀愀搀椀愀渀猀⸀ 䤀琀 漀渀氀礀 最椀瘀攀猀 琀栀攀 瀀爀椀渀挀椀瀀氀攀 value (PV): -Pi < arg(x) <= Pi. arg(x) = atan2(re(x),im(x)). x can be਀挀漀洀瀀氀攀砀 渀甀洀戀攀爀⸀ 䘀漀爀 瀀漀猀椀琀椀瘀攀 爀攀愀氀 砀Ⰰ 䄀爀最⠀砀⤀㴀 ⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀䄀戀猀Ⰰ 䄀爀最Ⰰ 匀椀最渀Ⰰ 䄀琀愀渀㈀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> N(Arg(I))਀最椀瘀攀猀 ㄀⸀㔀⸀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

* Asech()

See also:਀䄀猀攀挀栀Ⰰ 匀攀挀栀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

x的反正弦函数。 x)。 The result is given in radians.

* Asinh()

See also:਀䄀猀椀渀栀Ⰰ 匀椀渀栀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

Assume(x਀☀最琀㬀 ㄀⤀ 愀猀猀甀洀攀猀 琀栀攀 瘀愀爀椀愀戀氀攀 砀 ☀最琀㬀 ㄀ 椀渀 爀攀愀氀 搀漀洀愀椀渀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>  默认情况下,x)的eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 挀氀愀猀猀㴀最漀漀最氀攀ⴀ猀爀挀ⴀ琀攀砀琀㄀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀 10.0pt'>x is complex in Sin(x), but y is real in y > 1.x是仙(y The਀䄀猀猀甀洀攀⠀⤀ 挀愀渀 戀攀 挀氀攀愀爀攀搀 戀礀 䌀氀攀愀爀⠀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀匀椀最渀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> Assume(x>0),਀䄀猀猀甀洀攀⠀砀☀最琀㬀 Ⰰ 礀☀氀琀㬀 ⤀Ⰰ 䤀猀䔀瘀攀渀⠀砀⤀㨀㴀吀爀甀攀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                     

Atan(x) is the arc tangent function of x.਀㰀猀瀀愀渀 挀氀愀猀猀㴀最漀漀最氀攀ⴀ猀爀挀ⴀ琀攀砀琀㄀㸀吀栀攀 椀渀瘀攀爀猀攀 昀甀渀挀琀椀漀渀 漀昀 琀愀渀⠀砀⤀⸀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 class=notranslate>x)。 The result is given in radians.

* Atan2()                                                  内部

 Atan2(x,y)          if x=0

                              if x>0

                           if x<0, y>=0

                           if x<0, y<0 .

See also:਀愀琀愀渀Ⰰ 愀爀最⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

atanh(x) is਀琀栀攀 椀渀瘀攀爀猀攀 栀礀瀀攀爀戀漀氀椀挀 琀愀渀最攀渀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 吀栀攀 椀渀瘀攀爀猀攀 昀甀渀挀琀椀漀渀 漀昀 琀愀渀栀⠀砀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

*Block()                                               internalBlock(a,b,c)਀最爀漀甀瀀猀 愀Ⰰ戀Ⰰ挀 愀渀搀 漀渀氀礀 爀攀琀甀爀渀猀 琀栀攀 氀愀猀琀 愀爀最甀洀攀渀琀 愀猀 椀琀猀 瘀愀氀甀攀⸀ 䤀琀 椀猀 甀猀攀搀 愀猀 grouper in definition of a procedure. All variables in block are local.See also:਀氀漀挀愀氀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> f(x_):=Block(p:=x_^6,p) 

                                      internalCeil(x)਀挀漀渀瘀攀爀琀猀 砀 琀漀 琀栀攀 爀漀甀渀搀攀搀 椀渀琀攀最攀爀 挀氀漀猀攀猀琀 琀漀 砀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀䘀氀漀漀爀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

Ci()

*Clear()                                                 内部

See also:਀愀猀猀甀洀攀Ⰰ 㨀㴀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> Clear(p),਀䌀氀攀愀爀⠀昀⠀砀⤀⤀Ⰰ 䌀氀攀愀爀⠀愀☀最琀㬀 ⤀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                     

*Cosh()Cosh(x) is਀琀栀攀 栀礀瀀攀爀戀漀氀椀挀 挀漀猀椀渀攀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 䌀漀猀栀⠀砀⤀㴀⠀䔀砀瀀⠀砀⤀⬀䔀砀瀀⠀ⴀ砀⤀⤀⼀㈀⸀ 砀 挀愀渀 戀攀 complex numbers.

*Cot()Cot(x) is਀琀栀攀 挀漀琀愀渀最攀渀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 吀栀攀 愀渀最氀攀 砀 椀猀 洀攀愀猀甀爀攀搀 椀渀 爀愀搀椀愀渀猀⸀ ⠀洀甀氀琀椀瀀氀礀 戀礀 degree to convert from degrees). cot(x)=1/tan(x).

*Coth()Coth(x) is਀琀栀攀 栀礀瀀攀爀戀漀氀椀挀 挀漀琀愀渀最攀渀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 挀漀琀栀⠀砀⤀㴀㄀⼀琀愀渀栀⠀砀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

*Csc()Csc (x) is਀琀栀攀 挀漀猀攀挀愀渀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 吀栀攀 愀渀最氀攀 砀 椀猀 洀攀愀猀甀爀攀搀 椀渀 爀愀搀椀愀渀猀 ⠀洀甀氀琀椀瀀氀礀 戀礀 degree to convert from degrees). Csc(x)=1/Sin(x) x can be complex numbers.See also:਀䄀挀猀挀Ⰰ 匀椀渀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

See also:਀愀挀猀挀栀Ⰰ 猀椀渀栀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                           

                     ਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                                      internalIt਀搀椀昀昀攀爀攀渀琀椀愀琀攀 礀 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 砀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> D(x^2,x) gives਀㈀⨀砀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> D(Sin(x),x)਀最椀瘀攀猀 䌀漀猀⠀砀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

D(y, x, n)D( XIt gives਀琀栀攀 渀ⴀ琀栀 漀爀搀攀爀 搀攀爀椀瘀愀琀椀瘀攀 漀昀 礀 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 愀渀 甀渀搀攀昀椀渀攀搀 瘀愀爀椀愀戀氀攀 砀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀䐀⠀匀椀渀⠀砀⤀Ⰰ砀Ⰰ㈀⤀ gives -Sin(x).

 

See also:਀倀椀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 45*degree,਀匀椀渀⠀㐀㔀⨀搀攀最爀攀攀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                               internalThe਀搀椀猀挀漀渀琀椀渀甀椀琀礀⸀ 䤀昀 昀⠀砀 ⤀ 最椀瘀攀猀 搀椀猀挀漀渀琀Ⰰ 琀栀攀 昀甀渀挀琀椀漀渀 栀愀猀 愀 搀椀猀挀漀渀琀椀渀甀椀琀礀 愀渀搀 only has the one-sided value at x=x0. You should evaluate its left-sided or਀爀椀最栀琀ⴀ猀椀搀攀搀 瘀愀氀甀攀 戀礀 昀⠀砀 ⴀ稀攀爀漀⤀ 漀爀 昀⠀砀 ⬀稀攀爀漀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀稀攀爀漀Ⰰ 䤀渀昀椀渀椀琀礀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                               internalFor(x,xmin,xmax,dx,਀攀砀瀀爀⤀ 攀瘀愀氀甀愀琀攀猀 攀砀瀀爀 眀椀琀栀 琀栀攀 砀 氀漀漀瀀椀渀最 昀爀漀洀 砀洀椀渀 琀漀 砀洀愀砀 漀渀 猀琀攀瀀 搀砀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>  

*Done                                                internalIt਀椀渀搀椀挀愀琀攀猀 琀栀愀琀 琀栀攀 挀漀洀洀愀渀搀 栀愀猀 戀攀攀渀 搀漀渀攀⸀ 匀攀攀 愀氀猀漀㨀 愀猀猀甀洀攀搀Ⰰ 挀氀攀愀爀攀搀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

*E                                                   (1) e is਀琀栀攀 攀砀瀀漀渀攀渀琀椀愀氀 挀漀渀猀琀愀渀琀 ⠀戀愀猀攀 漀昀 渀愀琀甀爀愀氀 氀漀最愀爀椀琀栀洀猀⤀Ⰰ 䔀㴀㈀⸀㜀㄀㠀⸀⸀⸀Ⰰ 琀栀攀 戀甀椀氀琀ⴀ椀渀 constant, E is converted to 2.718... by N(E). e^x is the same as Exp(x).

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀㄀⸀㄀攀㈀ 椀猀 琀栀攀 same as 1.1E2.

*Ei(x) is਀琀栀攀 攀砀瀀漀渀攀渀琀椀愀氀 椀渀琀攀最爀愀氀 昀甀渀挀琀椀漀渀 䔀椀⠀砀⤀Ⰰ 䔀椀⠀砀⤀ 㴀 䤀渀琀⠀攀帀琀⼀琀Ⰰ 琀Ⰰⴀ䤀渀昀椀渀椀琀礀Ⰰ砀⤀Ⰰ ei'(x) = e^x/x.

Ei(n,x) is਀琀栀攀 椀渀挀漀洀瀀氀攀琀攀 攀砀瀀漀渀攀渀琀椀愀氀 椀渀琀攀最爀愀氀 昀甀渀挀琀椀漀渀Ⰰ 䔀椀⠀渀Ⰰ砀⤀ 㴀 䤀渀琀⠀琀帀渀⨀攀帀琀Ⰰ t,-Infinity,x), D(Ei(n,x),x) = x^n*e^x, Ei(-1, x) = Ei(x), Ei(0,x) = e^x.See also:਀䜀愀洀洀愀Ⰰ 䔀爀昀Ⰰ 䌀椀Ⰰ 匀椀Ⰰ 䰀椀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

Erf()

See also:਀䔀椀Ⰰ 䜀愀洀洀愀Ⰰ 䌀椀Ⰰ 匀椀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                          内部

See also:਀䔀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                  

   expands out products and਀瀀漀猀椀琀椀瘀攀 瀀漀眀攀爀猀 椀渀 礀⸀ 䔀砀瀀愀渀䐀⠀⤀ 眀漀爀欀猀 漀渀氀礀 漀渀 瀀漀猀椀琀椀瘀攀 椀渀琀攀最攀爀 瀀漀眀攀爀猀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀䔀砀瀀愀渀䐀⠀⠀愀⬀戀⤀帀㈀⤀ gives a^2 + 2*a*b + b^2.

(2) the਀猀眀椀琀挀栀 漀昀 攀砀瀀愀渀猀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>expand:=on 例如: c*(a+b)਀琀漀 挀⨀愀⬀挀⨀戀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>expand:=off

*ExpandExp()                                           The਀攀砀瀀漀渀攀渀琀椀愀氀 攀砀瀀愀渀猀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> c^(a+b) to਀挀帀愀⨀挀帀戀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀攀砀瀀愀渀搀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

Gamma()

 

*I                                                     内部

See also:਀刀攀Ⰰ 䤀洀Ⰰ 匀椀最渀Ⰰ 䄀爀最⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 1+2*I. 

                                      internalIf(condition,x)਀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀✀㸀ꀀ 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-spacerun:yes'> gives x if condition evaluates to True, or਀氀攀昀琀 甀渀攀瘀愀氀甀愀琀攀搀 漀琀栀攀爀眀椀猀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

It is਀甀猀攀昀甀氀 椀渀 搀攀昀椀渀椀琀椀漀渀 漀昀 琀栀攀 甀猀攀ⴀ搀攀昀椀渀攀搀 昀甀渀挀琀椀漀渀 琀漀 氀攀昀琀 琀栀攀 昀甀渀挀琀椀漀渀 unevaluated if the argument of the function is not number.See also: .

In:输入:   f(x_) := If(IsNumber(x_), 1);  

*Im()                                       internalIm(x) gives਀琀栀攀 椀洀愀最椀渀愀琀椀瘀攀 瀀愀爀琀 漀昀 琀栀攀 挀漀洀瀀氀攀砀 渀甀洀戀攀爀 砀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀刀攀Ⰰ 䄀戀猀Ⰰ 匀椀最渀Ⰰ 䄀爀最⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> Im(1+2*I)਀最椀瘀攀猀 ㈀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                            internalInfinity is਀愀 瀀漀猀椀琀椀瘀攀 椀渀昀椀渀椀琀礀Ⰰ 愀猀 琀栀攀 戀甀椀氀琀ⴀ椀渀 挀漀渀猀琀愀渀琀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 另请参阅:

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀䤀渀昀椀渀椀琀礀⬀㈀⨀䤀渀昀椀渀椀琀礀 gives Infinity, 1/Infinity gives 0.

*InfSum()InfSum(y,x)਀椀猀 椀渀昀椀渀椀琀攀 猀甀洀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀倀愀爀琀匀甀洀Ⰰ 匀甀洀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                           Int() is਀琀栀攀 椀渀琀攀最爀愀氀 昀甀渀挀琀椀漀渀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

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See also:਀一䤀渀琀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                           internalIsComplex(x)਀琀攀猀琀猀 椀昀 砀 椀猀 挀漀洀瀀氀攀砀⸀ 䤀琀 最椀瘀攀猀 吀爀甀攀 椀昀 砀 椀猀 挀漀洀瀀氀攀砀Ⰰ 漀爀 䘀愀氀猀攀 漀琀栀攀爀眀椀猀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

IsComplex(I)਀最椀瘀攀猀 吀爀甀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

 *IsEven()                                               

See also:਀䤀猀䌀漀洀瀀氀攀砀Ⰰ 䤀猀䔀瘀攀渀Ⰰ 䤀猀䘀爀攀攀Ⰰ 䤀猀䤀渀琀攀最攀爀Ⰰ 䤀猀伀搀搀Ⰰ 䤀猀刀攀愀氀Ⰰ 䤀猀刀愀琀椀漀渀愀氀Ⰰ 䤀猀一甀洀戀攀爀Ⰰ IsConstant.

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀䤀猀䔀瘀攀渀⠀㈀⤀ gives True, IsEven(3) gives False.

*IsFree()                                              internalIsFree(y,x)਀最椀瘀攀猀 吀爀甀攀 椀昀 礀 椀猀 昀爀攀攀 漀昀 砀Ⰰ 漀爀 䘀愀氀猀攀 漀琀栀攀爀眀椀猀攀⸀ 夀漀甀 挀愀渀 愀猀猀甀洀攀 礀 椀猀 昀爀攀攀 漀昀 砀 by IsEven(y,x) := True.

IsFree(a*b,x)਀最椀瘀攀猀 吀爀甀攀Ⰰ 䤀猀䘀爀攀攀⠀砀⨀礀Ⰰ砀⤀ 最椀瘀攀猀 䘀愀氀猀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                                内部

See also:਀䤀猀䌀漀洀瀀氀攀砀Ⰰ 䤀猀䔀瘀攀渀Ⰰ 䤀猀䘀爀攀攀Ⰰ 䤀猀䤀渀琀攀最攀爀Ⰰ 䤀猀伀搀搀Ⰰ 䤀猀刀攀愀氀Ⰰ 䤀猀刀愀琀椀漀渀愀氀Ⰰ 䤀猀一甀洀戀攀爀Ⰰ IsConstant.

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀䤀猀䤀渀琀攀最攀爀⠀㈀⤀ gives True, IsInteger(3.2) gives False.

*IsOdd()                                               internalIsOdd(x)਀最椀瘀攀猀 吀爀甀攀 椀昀 砀 椀猀 愀渀 漀搀搀 椀渀琀攀最攀爀Ⰰ 漀爀 䘀愀氀猀攀 漀琀栀攀爀眀椀猀攀⸀ 夀漀甀 挀愀渀 愀猀猀甀洀攀 砀 椀猀 漀搀搀 by IsOdD(x) := True.

IsOdd(3) gives਀吀爀甀攀Ⰰ 䤀猀伀搀搀⠀㈀⤀ 最椀瘀攀猀 䘀愀氀猀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                            内部

See also:਀䤀猀䌀漀洀瀀氀攀砀Ⰰ 䤀猀䔀瘀攀渀Ⰰ 䤀猀䘀爀攀攀Ⰰ 䤀猀䤀渀琀攀最攀爀Ⰰ 䤀猀伀搀搀Ⰰ 䤀猀刀攀愀氀Ⰰ 䤀猀刀愀琀椀漀渀愀氀Ⰰ 䤀猀一甀洀戀攀爀Ⰰ IsConstant.

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀䤀猀刀愀琀椀漀渀愀氀⠀㈀⼀㌀⤀ gives True, IsRational(2) gives False.

*IsReal()                                                内部

See also:਀䤀猀䌀漀洀瀀氀攀砀Ⰰ 䤀猀䔀瘀攀渀Ⰰ 䤀猀䘀爀攀攀Ⰰ 䤀猀䤀渀琀攀最攀爀Ⰰ 䤀猀伀搀搀Ⰰ 䤀猀刀攀愀氀Ⰰ 䤀猀刀愀琀椀漀渀愀氀Ⰰ 䤀猀一甀洀戀攀爀Ⰰ IsConstant.

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀䤀猀刀攀愀氀⠀㈀⸀㈀⤀ gives True, IsReal(a) gives False.

*IsNumber()                                            internalIsNumber(x)਀最椀瘀攀猀 吀爀甀攀 椀昀 砀 椀猀 愀 渀甀洀戀攀爀Ⰰ 漀爀 䘀愀氀猀攀 漀琀栀攀爀眀椀猀攀⸀ 夀漀甀 挀愀渀 愀猀猀甀洀攀 砀 椀猀 愀 渀甀洀戀攀爀 by IsNumber(x) := True.

IsNumber(2.2)਀最椀瘀攀猀 吀爀甀攀Ⰰ 䤀猀一甀洀戀攀爀⠀愀⤀ 最椀瘀攀猀 䘀愀氀猀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀䰀愀瀀氀愀挀攀⠀匀椀渀⠀琀⤀Ⰰ琀⤀ gives 1/(1+t^2).

*Li(x) is਀琀栀攀 䰀渀 椀渀琀攀最爀愀氀 昀甀渀挀琀椀漀渀Ⰰ 䰀椀⠀砀⤀ 㴀 䤀渀琀⠀㄀⼀䰀渀⠀琀⤀Ⰰ 琀Ⰰ Ⰰ砀⤀ 㴀 䔀椀⠀䰀渀⠀砀⤀⤀Ⰰ D(Li(x),x)=1/Ln(x).

Li(n,x) is਀琀栀攀 椀渀挀漀洀瀀氀攀琀攀 氀渀 椀渀琀攀最爀愀氀 昀甀渀挀琀椀漀渀Ⰰ 䰀椀⠀渀Ⰰ砀⤀ 㴀 䤀渀琀⠀䰀渀⠀琀⤀帀渀Ⰰ 琀Ⰰ Ⰰ砀⤀ 㴀 Ei(n,Ln(x)), D(Li(n,x),x) = Ln(x)^n. Li(n,0) = 0.

*Ln()                                                   

*NInt()NInt(y, x ,਀砀洀椀渀 Ⰰ 砀洀愀砀⤀ 渀甀洀攀爀椀挀愀氀氀礀 椀渀琀攀最爀愀琀攀猀 礀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀䤀渀琀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> NInt(x^2, x ,਀  Ⰰ ㄀⤀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

See also:਀䄀渀搀Ⰰ 伀爀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

           

NSolve(Cos(x)=x,਀砀⤀ 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀✀㸀ꀀꀀꀀ 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-spacerun:yes'> numerically solves equation with default਀椀渀椀琀椀愀氀 砀 㴀㄀ 愀渀搀 渀㴀㔀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>NSolve(Cos(x)=x,਀砀Ⰰ砀 ⤀ 㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀✀㸀ꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀ 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-spacerun:yes'> numerically solves the equation with initial਀砀  愀渀搀 渀㴀㔀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀猀漀氀瘀攀Ⰰ 搀猀漀氀瘀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> NSolve(Sin(x)=0,਀砀Ⰰ㌀⤀ 最椀瘀攀猀 ㌀⸀㄀㐀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

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See also:਀渀甀洀攀爀椀挀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> N(Pi) gives਀㌀⸀㄀㐀㄀㘀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                       internalThe logic਀漀瀀攀爀愀琀漀爀⸀ 吀栀攀 爀攀猀甀氀琀 椀猀 吀爀甀攀 漀爀 䘀愀氀猀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀䄀渀搀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

           

           

           

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀倀愀爀愀洀攀琀爀椀挀倀氀漀琀⠀匀椀渀⠀琀⤀Ⰰ匀椀渀⠀㈀⨀琀⤀Ⰰ琀⤀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

*PiPi=3.1416...,਀愀猀 琀栀攀 戀甀椀氀琀ⴀ椀渀 挀漀渀猀琀愀渀琀Ⰰ 倀椀 椀猀 挀漀渀瘀攀爀琀攀搀 琀漀 ㌀⸀㄀㐀㄀㘀⸀⸀⸀ 眀栀攀渀 琀栀攀 猀眀椀琀挀栀 numeric:=on.

*Plot()Plot(y,x)਀瀀氀漀琀猀 愀 昀甀渀挀琀椀漀渀 礀㴀昀⠀砀⤀ 椀渀 砀礀 瀀氀愀渀攀 眀椀琀栀 琀栀攀 搀攀昀愀甀氀琀 瘀愀氀甀攀猀 砀 昀爀漀洀 ⴀ㔀 琀漀 㔀Ⰰ 愀渀搀 y from -5 to 5.

Plot(y,x,xmin,xmax)

Plot(y,x,xmin,xmax,ymin,ymax)

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀倀氀漀琀⠀砀帀㌀Ⰰ砀⤀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

*PolarPlot()PolarPlot(r,t)਀瀀氀漀琀猀 愀 昀甀渀挀琀椀漀渀 爀㴀昀⠀琀⤀ 椀渀 瀀漀氀愀爀 挀漀漀爀搀椀渀愀琀攀猀 眀椀琀栀 琀栀攀 搀攀昀愀甀氀琀 瘀愀氀甀攀猀 琀 昀爀漀洀   to 2 Pi, and r from 0 to 5.

PolarPlot(r,t,tmin,tmax)

PolarPlot(r,t,tmin,tmax,rmin,rmax)

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀最爀愀瀀栀Ⰰ PolarPlot(1,t)

*Product()Product(f,x,xmin,xmax)਀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㈀✀㸀ꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀꀀ 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-spacerun:yes'> with the default step dx = 1.Product(f,x,xmin,xmax,dx)਀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ琀愀戀ⴀ挀漀甀渀琀㨀㄀✀㸀ꀀꀀꀀꀀꀀꀀ 㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 style='mso-spacerun:yes'> evaluates the product of f when x runs from xmin to xmax with step dx.See also: Sum. 

See also:਀匀漀氀瘀攀Ⰰ 一匀漀氀瘀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> PSolve(x^2+5*x+6,਀砀⤀ 最椀瘀攀猀 嬀ⴀ㈀Ⰰⴀ㌀崀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

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eg.例如:

*Sec()Sec(x) is਀琀栀攀 猀攀挀愀渀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 吀栀攀 愀渀最氀攀 砀 椀猀 洀攀愀猀甀爀攀搀 椀渀 爀愀搀椀愀渀猀 ⠀洀甀氀琀椀瀀氀礀 戀礀 degree to convert from degrees). Sec(x)=1/Cos(x).

*Sech()Sech(x) is਀琀栀攀 栀礀瀀攀爀戀漀氀椀挀 猀攀挀愀渀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 猀攀挀栀⠀砀⤀㴀㄀⼀挀漀猀栀⠀砀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀

*Taylor()Taylor(y,਀砀⤀㰀猀瀀愀渀 猀琀礀氀攀㴀✀洀猀漀ⴀ猀瀀愀挀攀爀甀渀㨀礀攀猀✀㸀ꀀꀀ 㰀⼀猀瀀愀渀㸀最椀瘀攀猀 猀攀爀椀攀猀 攀砀瀀愀渀猀椀漀渀 漀昀 礀 愀琀 砀㴀  to order of 5.

   gives series expansion of y਀愀琀 砀㴀  琀漀 漀爀搀攀爀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀匀甀洀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> Taylor(Sin(x),x) gives x - 1/6*x^3਀⬀ ㄀⼀㄀㈀ ⨀砀帀㔀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

Si()

*Sign()                                                   内部

 

   00      if x=0.

            otherwise. 

 

   00      if x=0.

            otherwise. 

           

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀匀椀最渀⠀㈀⤀ 最椀瘀攀猀 1, Sign(1+I) gives 1.

*Sin()                                                  

 

 

                                              internalSolve(x^2=0,਀砀⤀ 猀漀氀瘀攀猀 愀 瀀漀氀礀渀漀洀椀愀氀 漀爀搀攀爀攀搀 甀瀀 琀漀 㐀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀一匀漀氀瘀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> Solve(x^2+5*x+6=0,਀砀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                               internalSqrt(x) is਀琀栀攀 猀焀甀愀爀攀 爀漀漀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 䤀琀 椀猀 琀栀攀 猀愀洀攀 愀猀 砀帀 ⸀㔀⸀ 䤀琀 漀渀氀礀 最椀瘀攀猀 琀栀攀 principal value (PV) (Sign(Sqrt(x)) >= 0). root(x,2) gives all branch of਀猀焀甀愀爀攀 爀漀漀琀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>See also:਀爀漀漀琀Ⰰ 帀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> Sqrt(4) gives਀㈀Ⰰ 一⠀匀焀爀琀⠀㈀⨀䤀⤀⤀ 最椀瘀攀猀 ㄀⬀䤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                          internalReplace(y,਀砀Ⰰ砀 ⤀ 爀攀瀀氀愀挀攀 砀 椀渀 礀 眀椀琀栀 砀 ⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> Replace(x^6,਀砀Ⰰ砀 ⤀ 最椀瘀攀猀 砀 帀㘀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                  Sum(f,x,xmin,xmax)It਀攀瘀愀氀甀愀琀攀猀 琀栀攀 猀甀洀 漀昀 昀 眀栀攀渀 砀 爀甀渀猀 昀爀漀洀 砀洀椀渀 琀漀 砀洀愀砀 眀椀琀栀 琀栀攀 搀攀昀愀甀氀琀 猀琀攀瀀 dx=1.

Sum(f,x,xmin,xmax,dx)                           It਀攀瘀愀氀甀愀琀攀猀 琀栀攀 猀甀洀 漀昀 昀 眀栀攀渀 砀 爀甀渀猀 昀爀漀洀 砀洀椀渀 琀漀 砀洀愀砀 眀椀琀栀 猀琀攀瀀 搀砀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

See also:਀倀爀漀搀甀挀琀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> Sum(2^n,n,1,5,1.1),਀匀甀洀⠀砀帀渀Ⰰ渀Ⰰ㄀Ⰰ㔀⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                   Tan(x) is਀琀栀攀 琀愀渀最攀渀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀ 吀栀攀 愀渀最氀攀 砀 椀猀 洀攀愀猀甀爀攀搀 椀渀 爀愀搀椀愀渀猀 ⠀洀甀氀琀椀瀀氀礀 戀礀 degree to convert from degrees).

*Tanh()Tanh(x) is਀琀栀攀 栀礀瀀攀爀戀漀氀椀挀 琀愀渀最攀渀琀 昀甀渀挀琀椀漀渀 漀昀 砀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

逻辑值。

*Type()                                                  内部

xx  Type(x)

                    Integer                  Real    Rational理数

                  Complexf(x)F            

                 ++

                  **

                  ^^

                 ==

               a>b  

               >=> =a<b  

               <=<=a<>b  

a,bA              ,--------------------------------- 

You also can test x, eg. if x is type of real number, by Type(x)==Real. 

                                             internalThe਀戀甀椀氀琀ⴀ椀渀 挀漀渀猀琀愀渀琀⸀ 䤀琀 椀渀搀椀挀愀琀攀猀 琀栀愀琀 琀栀攀 瘀愀氀甀攀 漀昀 琀栀攀 攀砀瀀爀攀猀猀椀漀渀 椀猀 甀渀搀攀昀椀渀攀搀Ⰰ and may be the indeterminate form: 0/0, Infinity/Infinity, 0*Infinity, 0^0. You਀猀栀漀甀氀搀 琀爀礀 愀最愀椀渀 戀礀 氀椀洀⠀礀Ⰰ 砀㴀砀 ⤀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

                                                             内部

eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>  x:=1,਀圀栀椀氀攀⠀砀☀氀琀㬀㔀Ⰰ 砀㨀㴀砀⬀㄀⤀㬀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>Out:

+          eg.a+b.

--  subtract or negative sign.eg.例如:਀㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀 猀琀礀氀攀㴀✀洀猀漀ⴀ戀椀搀椀ⴀ昀漀渀琀ⴀ猀椀稀攀㨀㄀ ⸀ 瀀琀✀㸀愀戀Ⰰ ⴀ㄀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 lang=EN-AU>

**  multiply. 例如:          eg.a/b.

^^  power in BASIC, the same as ** in FORTRAN, eg.਀㈀帀㌀ 最椀瘀攀猀 㠀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'>  factorial, eg. 100!

 less than.

      

         >= greater than or equal to. 

<><>      unequal====   等于

a==b gives True if a is equal to b, False if a is not equal to b, or਀氀攀昀琀 甀渀攀瘀愀氀甀愀琀攀搀 漀琀栀攀爀眀椀猀攀⸀ 䤀琀 挀愀渀 琀攀猀琀 琀眀漀 挀漀洀瀀氀攀砀 渀甀洀戀攀爀猀 漀爀 攀砀瀀爀攀猀猀椀漀渀猀⸀ 䤀琀 gives True if a and b are the same expression or left unevaluated otherwise. 2==2 gives਀吀爀甀攀Ⰰ 愀㴀㴀愀 最椀瘀攀猀 吀爀甀攀⸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

==  equation sign

eg.x^6+1 = 0

:=  分配。

  逗号

;;  the end of statement

         ---------------------------------------------------------------------------------------------------------------------------਀ⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀⴀ㰀⼀猀瀀愀渀㸀㰀⼀猀瀀愀渀㸀㰀猀瀀愀渀 氀愀渀最㴀䔀一ⴀ䄀唀㸀 㰀⼀猀瀀愀渀㸀㰀⼀瀀㸀 ਀㰀瀀 挀氀愀猀猀㴀䴀猀漀一漀爀洀愀氀 猀琀礀氀攀㴀✀洀愀爀最椀渀ⴀ爀椀最栀琀㨀ⴀ㈀⸀㘀㔀瀀琀㬀琀攀砀琀ⴀ愀氀椀最渀㨀樀甀猀琀椀昀礀㬀琀攀砀琀ⴀ樀甀猀琀椀昀礀㨀 inter-ideograph'> 

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