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key | value |
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macFileType | [TEXT] |
macFileCreator | [R*ch] |
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|00000000| 5c 73 65 63 74 69 6f 6e | 7b 42 75 69 6c 74 2d 69 |\section|{Built-i|
|00000010| 6e 20 4d 6f 64 75 6c 65 | 20 5c 73 65 63 74 63 6f |n Module| \sectco|
|00000020| 64 65 7b 6d 61 74 68 7d | 7d 0d 0d 5c 62 69 6d 6f |de{math}|}..\bimo|
|00000030| 64 69 6e 64 65 78 7b 6d | 61 74 68 7d 0d 5c 72 65 |dindex{m|ath}.\re|
|00000040| 6e 65 77 63 6f 6d 6d 61 | 6e 64 7b 5c 69 6e 64 65 |newcomma|nd{\inde|
|00000050| 78 73 75 62 69 74 65 6d | 7d 7b 28 69 6e 20 6d 6f |xsubitem|}{(in mo|
|00000060| 64 75 6c 65 20 6d 61 74 | 68 29 7d 0d 54 68 69 73 |dule mat|h)}.This|
|00000070| 20 6d 6f 64 75 6c 65 20 | 69 73 20 61 6c 77 61 79 | module |is alway|
|00000080| 73 20 61 76 61 69 6c 61 | 62 6c 65 2e 0d 49 74 20 |s availa|ble..It |
|00000090| 70 72 6f 76 69 64 65 73 | 20 61 63 63 65 73 73 20 |provides| access |
|000000a0| 74 6f 20 74 68 65 20 6d | 61 74 68 65 6d 61 74 69 |to the m|athemati|
|000000b0| 63 61 6c 20 66 75 6e 63 | 74 69 6f 6e 73 20 64 65 |cal func|tions de|
|000000c0| 66 69 6e 65 64 20 62 79 | 20 74 68 65 20 43 0d 73 |fined by| the C.s|
|000000d0| 74 61 6e 64 61 72 64 2e | 0d 54 68 65 79 20 61 72 |tandard.|.They ar|
|000000e0| 65 3a 0d 5c 69 66 74 65 | 78 69 0d 5c 62 65 67 69 |e:.\ifte|xi.\begi|
|000000f0| 6e 7b 66 75 6e 63 64 65 | 73 63 7d 7b 61 63 6f 73 |n{funcde|sc}{acos|
|00000100| 7d 7b 78 7d 0d 5c 66 75 | 6e 63 6c 69 6e 65 7b 61 |}{x}.\fu|ncline{a|
|00000110| 73 69 6e 7d 7b 78 7d 0d | 5c 66 75 6e 63 6c 69 6e |sin}{x}.|\funclin|
|00000120| 65 7b 61 74 61 6e 7d 7b | 78 7d 0d 5c 66 75 6e 63 |e{atan}{|x}.\func|
|00000130| 6c 69 6e 65 7b 61 74 61 | 6e 32 7d 7b 78 2c 20 79 |line{ata|n2}{x, y|
|00000140| 7d 0d 5c 66 75 6e 63 6c | 69 6e 65 7b 63 65 69 6c |}.\funcl|ine{ceil|
|00000150| 7d 7b 78 7d 0d 5c 66 75 | 6e 63 6c 69 6e 65 7b 63 |}{x}.\fu|ncline{c|
|00000160| 6f 73 7d 7b 78 7d 0d 5c | 66 75 6e 63 6c 69 6e 65 |os}{x}.\|funcline|
|00000170| 7b 63 6f 73 68 7d 7b 78 | 7d 0d 5c 66 75 6e 63 6c |{cosh}{x|}.\funcl|
|00000180| 69 6e 65 7b 65 78 70 7d | 7b 78 7d 0d 5c 66 75 6e |ine{exp}|{x}.\fun|
|00000190| 63 6c 69 6e 65 7b 66 61 | 62 73 7d 7b 78 7d 0d 5c |cline{fa|bs}{x}.\|
|000001a0| 66 75 6e 63 6c 69 6e 65 | 7b 66 6c 6f 6f 72 7d 7b |funcline|{floor}{|
|000001b0| 78 7d 0d 5c 66 75 6e 63 | 6c 69 6e 65 7b 66 6d 6f |x}.\func|line{fmo|
|000001c0| 64 7d 7b 78 2c 20 79 7d | 0d 5c 66 75 6e 63 6c 69 |d}{x, y}|.\funcli|
|000001d0| 6e 65 7b 66 72 65 78 70 | 7d 7b 78 7d 0d 5c 66 75 |ne{frexp|}{x}.\fu|
|000001e0| 6e 63 6c 69 6e 65 7b 6c | 64 65 78 70 7d 7b 78 2c |ncline{l|dexp}{x,|
|000001f0| 20 79 7d 0d 5c 66 75 6e | 63 6c 69 6e 65 7b 6c 6f | y}.\fun|cline{lo|
|00000200| 67 7d 7b 78 7d 0d 5c 66 | 75 6e 63 6c 69 6e 65 7b |g}{x}.\f|uncline{|
|00000210| 6c 6f 67 31 30 7d 7b 78 | 7d 0d 5c 66 75 6e 63 6c |log10}{x|}.\funcl|
|00000220| 69 6e 65 7b 6d 6f 64 66 | 7d 7b 78 7d 0d 5c 66 75 |ine{modf|}{x}.\fu|
|00000230| 6e 63 6c 69 6e 65 7b 70 | 6f 77 7d 7b 78 2c 20 79 |ncline{p|ow}{x, y|
|00000240| 7d 0d 5c 66 75 6e 63 6c | 69 6e 65 7b 73 69 6e 7d |}.\funcl|ine{sin}|
|00000250| 7b 78 7d 0d 5c 66 75 6e | 63 6c 69 6e 65 7b 73 69 |{x}.\fun|cline{si|
|00000260| 6e 68 7d 7b 78 7d 0d 5c | 66 75 6e 63 6c 69 6e 65 |nh}{x}.\|funcline|
|00000270| 7b 73 71 72 74 7d 7b 78 | 7d 0d 5c 66 75 6e 63 6c |{sqrt}{x|}.\funcl|
|00000280| 69 6e 65 7b 74 61 6e 7d | 7b 78 7d 0d 5c 66 75 6e |ine{tan}|{x}.\fun|
|00000290| 63 6c 69 6e 65 7b 74 61 | 6e 68 7d 7b 78 7d 0d 5c |cline{ta|nh}{x}.\|
|000002a0| 65 6e 64 7b 66 75 6e 63 | 64 65 73 63 7d 0d 5c 65 |end{func|desc}.\e|
|000002b0| 6c 73 65 0d 5c 63 6f 64 | 65 7b 61 63 6f 73 28 5c |lse.\cod|e{acos(\|
|000002c0| 76 61 72 76 61 72 73 7b | 78 7d 29 7d 2c 0d 5c 63 |varvars{|x})},.\c|
|000002d0| 6f 64 65 7b 61 73 69 6e | 28 5c 76 61 72 76 61 72 |ode{asin|(\varvar|
|000002e0| 73 7b 78 7d 29 7d 2c 0d | 5c 63 6f 64 65 7b 61 74 |s{x})},.|\code{at|
|000002f0| 61 6e 28 5c 76 61 72 76 | 61 72 73 7b 78 7d 29 7d |an(\varv|ars{x})}|
|00000300| 2c 0d 5c 63 6f 64 65 7b | 61 74 61 6e 32 28 5c 76 |,.\code{|atan2(\v|
|00000310| 61 72 76 61 72 73 7b 78 | 5c 2c 20 79 7d 29 7d 2c |arvars{x|\, y})},|
|00000320| 0d 5c 63 6f 64 65 7b 63 | 65 69 6c 28 5c 76 61 72 |.\code{c|eil(\var|
|00000330| 76 61 72 73 7b 78 7d 29 | 7d 2c 0d 5c 63 6f 64 65 |vars{x})|},.\code|
|00000340| 7b 63 6f 73 28 5c 76 61 | 72 76 61 72 73 7b 78 7d |{cos(\va|rvars{x}|
|00000350| 29 7d 2c 0d 5c 63 6f 64 | 65 7b 63 6f 73 68 28 5c |)},.\cod|e{cosh(\|
|00000360| 76 61 72 76 61 72 73 7b | 78 7d 29 7d 2c 0d 5c 63 |varvars{|x})},.\c|
|00000370| 6f 64 65 7b 65 78 70 28 | 5c 76 61 72 76 61 72 73 |ode{exp(|\varvars|
|00000380| 7b 78 7d 29 7d 2c 0d 5c | 63 6f 64 65 7b 66 61 62 |{x})},.\|code{fab|
|00000390| 73 28 5c 76 61 72 76 61 | 72 73 7b 78 7d 29 7d 2c |s(\varva|rs{x})},|
|000003a0| 0d 5c 63 6f 64 65 7b 66 | 6c 6f 6f 72 28 5c 76 61 |.\code{f|loor(\va|
|000003b0| 72 76 61 72 73 7b 78 7d | 29 7d 2c 0d 5c 63 6f 64 |rvars{x}|)},.\cod|
|000003c0| 65 7b 66 6d 6f 64 28 5c | 76 61 72 76 61 72 73 7b |e{fmod(\|varvars{|
|000003d0| 78 5c 2c 20 79 7d 29 7d | 2c 0d 5c 63 6f 64 65 7b |x\, y})}|,.\code{|
|000003e0| 66 72 65 78 70 28 5c 76 | 61 72 76 61 72 73 7b 78 |frexp(\v|arvars{x|
|000003f0| 7d 29 7d 2c 0d 5c 63 6f | 64 65 7b 6c 64 65 78 70 |})},.\co|de{ldexp|
|00000400| 28 5c 76 61 72 76 61 72 | 73 7b 78 5c 2c 20 79 7d |(\varvar|s{x\, y}|
|00000410| 29 7d 2c 0d 5c 63 6f 64 | 65 7b 6c 6f 67 28 5c 76 |)},.\cod|e{log(\v|
|00000420| 61 72 76 61 72 73 7b 78 | 7d 29 7d 2c 0d 5c 63 6f |arvars{x|})},.\co|
|00000430| 64 65 7b 6c 6f 67 31 30 | 28 5c 76 61 72 76 61 72 |de{log10|(\varvar|
|00000440| 73 7b 78 7d 29 7d 2c 0d | 5c 63 6f 64 65 7b 6d 6f |s{x})},.|\code{mo|
|00000450| 64 66 28 5c 76 61 72 76 | 61 72 73 7b 78 7d 29 7d |df(\varv|ars{x})}|
|00000460| 2c 0d 5c 63 6f 64 65 7b | 70 6f 77 28 5c 76 61 72 |,.\code{|pow(\var|
|00000470| 76 61 72 73 7b 78 5c 2c | 20 79 7d 29 7d 2c 0d 5c |vars{x\,| y})},.\|
|00000480| 63 6f 64 65 7b 73 69 6e | 28 5c 76 61 72 76 61 72 |code{sin|(\varvar|
|00000490| 73 7b 78 7d 29 7d 2c 0d | 5c 63 6f 64 65 7b 73 69 |s{x})},.|\code{si|
|000004a0| 6e 68 28 5c 76 61 72 76 | 61 72 73 7b 78 7d 29 7d |nh(\varv|ars{x})}|
|000004b0| 2c 0d 5c 63 6f 64 65 7b | 73 71 72 74 28 5c 76 61 |,.\code{|sqrt(\va|
|000004c0| 72 76 61 72 73 7b 78 7d | 29 7d 2c 0d 5c 63 6f 64 |rvars{x}|)},.\cod|
|000004d0| 65 7b 74 61 6e 28 5c 76 | 61 72 76 61 72 73 7b 78 |e{tan(\v|arvars{x|
|000004e0| 7d 29 7d 2c 0d 5c 63 6f | 64 65 7b 74 61 6e 68 28 |})},.\co|de{tanh(|
|000004f0| 5c 76 61 72 76 61 72 73 | 7b 78 7d 29 7d 2e 0d 5c |\varvars|{x})}..\|
|00000500| 66 69 0d 0d 4e 6f 74 65 | 20 74 68 61 74 20 5c 63 |fi..Note| that \c|
|00000510| 6f 64 65 7b 66 72 65 78 | 70 7d 20 61 6e 64 20 5c |ode{frex|p} and \|
|00000520| 63 6f 64 65 7b 6d 6f 64 | 66 7d 20 68 61 76 65 20 |code{mod|f} have |
|00000530| 61 20 64 69 66 66 65 72 | 65 6e 74 20 63 61 6c 6c |a differ|ent call|
|00000540| 2f 72 65 74 75 72 6e 0d | 70 61 74 74 65 72 6e 20 |/return.|pattern |
|00000550| 74 68 61 6e 20 74 68 65 | 69 72 20 43 20 65 71 75 |than the|ir C equ|
|00000560| 69 76 61 6c 65 6e 74 73 | 3a 20 74 68 65 79 20 74 |ivalents|: they t|
|00000570| 61 6b 65 20 61 20 73 69 | 6e 67 6c 65 20 61 72 67 |ake a si|ngle arg|
|00000580| 75 6d 65 6e 74 20 61 6e | 64 0d 72 65 74 75 72 6e |ument an|d.return|
|00000590| 20 61 20 70 61 69 72 20 | 6f 66 20 76 61 6c 75 65 | a pair |of value|
|000005a0| 73 2c 20 72 61 74 68 65 | 72 20 74 68 61 6e 20 72 |s, rathe|r than r|
|000005b0| 65 74 75 72 6e 69 6e 67 | 20 74 68 65 69 72 20 73 |eturning| their s|
|000005c0| 65 63 6f 6e 64 20 72 65 | 74 75 72 6e 0d 76 61 6c |econd re|turn.val|
|000005d0| 75 65 20 74 68 72 6f 75 | 67 68 20 61 6e 20 60 6f |ue throu|gh an `o|
|000005e0| 75 74 70 75 74 20 70 61 | 72 61 6d 65 74 65 72 27 |utput pa|rameter'|
|000005f0| 20 28 74 68 65 72 65 20 | 69 73 20 6e 6f 20 73 75 | (there |is no su|
|00000600| 63 68 20 74 68 69 6e 67 | 20 69 6e 20 50 79 74 68 |ch thing| in Pyth|
|00000610| 6f 6e 29 2e 0d 0d 54 68 | 65 20 6d 6f 64 75 6c 65 |on)...Th|e module|
|00000620| 20 61 6c 73 6f 20 64 65 | 66 69 6e 65 73 20 74 77 | also de|fines tw|
|00000630| 6f 20 6d 61 74 68 65 6d | 61 74 69 63 61 6c 20 63 |o mathem|atical c|
|00000640| 6f 6e 73 74 61 6e 74 73 | 3a 0d 5c 69 66 74 65 78 |onstants|:.\iftex|
|00000650| 69 0d 5c 62 65 67 69 6e | 7b 64 61 74 61 64 65 73 |i.\begin|{datades|
|00000660| 63 7d 7b 70 69 7d 0d 5c | 64 61 74 61 6c 69 6e 65 |c}{pi}.\|dataline|
|00000670| 7b 65 7d 0d 5c 65 6e 64 | 7b 64 61 74 61 64 65 73 |{e}.\end|{datades|
|00000680| 63 7d 0d 5c 65 6c 73 65 | 0d 5c 63 6f 64 65 7b 70 |c}.\else|.\code{p|
|00000690| 69 7d 20 61 6e 64 20 5c | 63 6f 64 65 7b 65 7d 2e |i} and \|code{e}.|
|000006a0| 0d 5c 66 69 0d | |.\fi. | |
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