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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 计算三元函数在某点的梯度向量。< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > > [!tip]< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > $< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > nabla f(x_0, y_0, z_0) = < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > left(< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > frac{< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > partial f}{< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > partial x}, < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > frac{< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > partial f}{< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > partial y}, < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > frac{< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > partial f}{< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > partial z}< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > \\< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > right)$< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Args:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > func: 三元函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > p: 点< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > epsilon: 偏移量< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Returns:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 梯度< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > dx < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (func(p.x < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > +< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon, p.y, p.z) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > -< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > func(p.x < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > -< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon, p.y, p.z)) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > /< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 2< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > dy < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (func(p.x, p.y < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > +< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon, p.z) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > -< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > func(p.x, p.y < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > -< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon, p.z)) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > /< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 2< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > dz < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (func(p.x, p.y, p.z < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > +< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > -< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > func(p.x, p.y, p.z < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > -< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon)) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > /< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 2< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon)< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > Vector3(dx, dy, dz)< / span > < / span > < / code > < / pre > < / div > < / details > < h3 id = "def-curry-func-multivarsfunc-args-var-onevarfunc" tabindex = "-1" > < em > < strong > def< / strong > < / em > < code > curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc< / code > < a class = "header-anchor" href = "#def-curry-func-multivarsfunc-args-var-onevarfunc" aria-label = "Permalink to "***def*** `curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc`"" > < / a > < / h3 > < p > < strong > 说明< / strong > : 对多参数函数进行柯里化。< / p > < div class = "tip custom-block github-alert" > < p class = "custom-block-title" > TIP< / p > < p > 有关函数柯里化，可参考< a href = "https://zhuanlan.zhihu.com/p/355859667" target = "_blank" rel = "noreferrer" > 函数式编程--柯理化（ ） < / a > < / p > < / div > < p > < strong > 参数< / strong > :< / p > < blockquote > < ul > < li > func: 函数< / li > < li > *args: 参数< / li > < / ul > < / blockquote > < p > < strong > 返回< / strong > : 柯里化后的函数< / p > < p > < strong > 示例< / strong > :< / p > < div class = "language-python vp-adaptive-theme" > < button title = "Copy Code" class = "copy" > < / button > < span class = "lang" > python< / span > < pre class = "shiki shiki-themes github-light github-dark vp-code" tabindex = "0" > < code > < span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#6F42C1;--shiki-dark:#B392F0;" > add< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (a: < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > int< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > , b: < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > int< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > , c: < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > int< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ) -> < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > int< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > :< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > a < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > +< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > b < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > +< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > c< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > add_curried < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > curry(add, < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 1< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > , < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 2< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > )< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > add_curried(< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 3< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ) < / span > < span style = "--shiki-light:#6A737D;--shiki-dark:#6A737D;" > # 6< / span > < / span > < / code > < / pre > < / div > < details > < summary > < b > 源代码< / b > < / summary > < div class = "language-python vp-adaptive-theme" > < button title = "Copy Code" class = "copy" > < / button > < span class = "lang" > python< / span > < pre class = "shiki shiki-themes github-light github-dark vp-code" tabindex = "0" > < code > < span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#6F42C1;--shiki-dark:#B392F0;" > curry< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (func: MultiVarsFunc, < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args: Var) -> OneVarFunc:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 对多参数函数进行柯里化。< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > > [!tip]< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > > 有关函数柯里化，可参考[函数式编程--柯理化（ ） < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Args:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > func: 函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > *args: 参数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Returns:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 柯里化后的函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Examples:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > ```python< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > def add(a: int, b: int, c: int) -> int:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > return a + b + c< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > add_curried = curry(add, 1, 2)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > add_curried(3) # 6< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > ```< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " @litedoc-hide" " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > func(< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args, < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args2)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > curried_func< / span > < / span > < / code > < / pre > < / div > < / details > < / div > < / div > < / main > < footer class = "VPDocFooter" data-v-40342069 data-v-a4b38bd6 > <!-- [ --> <!-- ] --> <!-- --> < nav class = "prev-next" aria-labelledby = "doc-footer-aria-label" data-v-a4b38bd6 > < span class = "visually-hidden" id = "doc-footer-aria-label" data-v-a4b38bd6 > Pager< / span > < div class = "pager" data-v-a4b38bd6 > < a class = "VPLink link pager-link prev" href = "/api/mp_math/equation.html" data-v-a4b38bd6 > <!-- [ --> < span class = "desc" data-v-a4b38bd6 > 上一页< / span > < span class = "title" data-v-a4b38bd6 > mbcp.mp_math.equation< / span > <!-- ] --> < / a > < / div > < div class = "pager" data-v-a4b38bd6 > < a class = "VPLink link pager-link next" href = "/api/mp_math/" data-v-a4b38bd6 > <!-- [ --> < span class = "desc" data-v-a4b38bd6 > 下一页< / span > < span class = "title" data-v-a4b38bd6 > mbcp.mp_math< / span > <!-- ] --> < / a > < / div > < / nav > < / footer > <!-- [ --> <!-- ] --> < / div > < / div > < / div > <!-- [ --> <!-- ] --> < / div > < / div > < footer class = "VPFooter has-sidebar" data-v-22f859ac data-v-e3ca6860 > < div class = "container" data-v-e3ca6860 > < p class = "message" data-v-e3ca6860 > 文档由 < a href = "https://vitepress.dev/" > VitePress< / a > 构建 | API引用由 < a href = "https://github.com/LiteyukiStudio/litedoc" > litedoc< / a > 生成< / p > < p class = "copyright" data-v-e3ca6860 > Copyright (C) 2020-2024 SnowyKami. All Rights Reserved< / p > < / div > < / footer > <!-- [ --> <!-- ] --> < / div > < / div >
< script > w i n d o w . _ _ V P _ H A S H _ M A P _ _ = J S O N . p a r s e ( " { \ " a p i _ a p i . m d \ " : \ " D _ B 0 H l c p \ " , \ " a p i _ i n d e x . m d \ " : \ " C _ w E S r r Y \ " , \ " a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " v K Q L L q T S \ " , \ " a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " B A f 8 m K 4 W \ " , \ " a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " B 2 F e M 0 M H \ " , \ " a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " B n S M o I o o \ " , \ " a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " B N f 7 b Q q L \ " , \ " a p i _ m p _ m a t h _ l i n e . m d \ " : \ " D P W L 9 O - M \ " , \ " a p i _ m p _ m a t h _ m p _ m a t h . m d \ " : \ " G l F M k W i Q \ " , \ " a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " D l n J m k o s \ " , \ " a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " D T A J A b 0 P \ " , \ " a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " v t g I d e d 6 \ " , \ " a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " D - 8 a R B 8 W \ " , \ " a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " D a a o R 6 3 4 \ " , \ " a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " B T n P e A K R \ " , \ " a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " C m 3 V k - e s \ " , \ " a p i _ p a r t i c l e _ p a r t i c l e . m d \ " : \ " y D 6 t c N S r \ " , \ " a p i _ p r e s e t s _ i n d e x . m d \ " : \ " C D 6 2 I 2 g v \ " , \ " a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " g O 0 N o t p 6 \ " , \ " a p i _ p r e s e t s _ m o d e l _ m o d e l . m d \ " : \ " s 8 f 6 8 j _ n \ " , \ " a p i _ p r e s e t s _ p r e s e t s . m d \ " : \ " 4 R 0 V R b Q o \ " , \ " d e m o _ i n d e x . m d \ " : \ " D - H 9 z R U E \ " , \ " e n _ a p i _ a p i . m d \ " : \ " B S g r C X 1 d \ " , \ " e n _ a p i _ i n d e x . m d \ " : \ " D j _ 5 n F T t \ " , \ " e n _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " B u 0 7 w j n V \ " , \ " e n _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " g G p X U S h q \ " , \ " e n _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " v E M I O I T c \ " , \ " e n _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " B W h q j _ 9 Y \ " , \ " e n _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " B E j L B M p H \ " , \ " e n _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " B G q 0 9 m c o \ " , \ " e n _ a p i _ m p _ m a t h _ m p _ m a t h . m d \ " : \ " D 6 i h Y P a v \ " , \ " e n _ a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " D n l 2 a J Q 4 \ " , \ " e n _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " C 3 K P G K E 4 \ " , \ " e n _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " D 7 Z d R 7 V M \ " , \ " e n _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " D M W - Y U f w \ " , \ " e n _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " B 3 i 5 g z _ 2 \ " , \ " e n _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " C g t I o M 4 A \ " , \ " e n _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " B f y N Q i R g \ " , \ " e n _ a p i _ p a r t i c l e _ p a r t i c l e . m d \ " : \ " B N k f E y J n \ " , \ " e n _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " B W b 2 f p T g \ " , \ " e n _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " p b E u - 6 6 9 \ " , \ " e n _ a p i _ p r e s e t s _ m o d e l _ m o d e l . m d \ " : \ " C L 5 u K Z b j \ " , \ " e n _ a p i _ p r e s e t s _ p r e s e t s . m d \ " : \ " C C U z s Y o g \ " , \ " e n _ g u i d e _ i n d e x . m d \ " : \ " D r D H T Y C Z \ " , \ " e n _ i n d e x . m d \ " : \ " B S T S O H 3 9 \ " , \ " e n _ r e f e r _ i n d e x . m d \ " : \ " a l w 4 L - b p \ " , \ " g u i d e _ i n d e x . m d \ " : \ " C f m z k 2 I H \ " , \ " i n d e x . m d \ " : \ " C N F 8 L J a 0 \ " , \ " j a _ a p i _ a p i . m d \ " : \ " C P z 5 8 q I w \ " , \ " j a _ a p i _ i n d e x . m d \ " : \ " C n U e u i f x \ " , \ " j a _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " D T K 1 P N u J \ " , \ " j a _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " D G X A g D f n \ " , \ " j a _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " D - 4 B B s n Q \ " , \ " j a _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " B v f 1 U 0 9 A \ " , \ " j a _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " C T Z Z - p 9 Z \ " , \ " j a _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " D Y J V 4 K N E \ " , \ " j a _ a p i _ m p _ m a t h _ m p _ m a t h . m d \ " : \ " D - p r C 0 U O \ " , \ " j a _ a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " B N y m g r C T \ " , \ " j a _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " D - y H a x P - \ " , \ " j a _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " D j H R k H I 5 \ " , \ " j a _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " 3 7 V 8 k A c 1 \ " , \ " j a _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " B b d h M 1 t p \ " , \ " j a _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " B B V n C w J a \ " , \ " j a _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " J r 4 1 Y 3 T S \ " , \ " j a _ a p i _ p a r t i c l e _ p a r t i c l e . m d \ " : \ " e x T t 4 6 p q \ " , \ " j a _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " C Q q d Q b I Z \ " , \ " j a _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " C - Y p f - q h \ " , \ " j a _ a p i _ p r e s e t s _ m o d e l _ m o d e l . m d \ " : \ " D w b c 1 q I c \ " , \ " j a _ a p i _ p r e s e t s _ p r e s e t s . m d \ " : \ " D w z X d D q R \ " , \ " j a _ g u i d e _ i n d e x . m d \ " : \ " B x G n Z Y w R \ " , \ " j a _ i n d e x . m d \ " : \ " D C W i T E N z \ " , \ " j a _ r e f e r _ i n d e x . m d \ " : \ " C O D W 6 i M X \ " , \ " r e f e r _ f u n c t i o n _ c u r r y . m d \ " : \ " D w K Z a w p 5 \ " , \ " r e f e r _ f u n c t i o n _ f u n c t i o n . m d \ " : \ " D 3 I g f Z X 2 \ " , \ " r e f e r _ i n d e x . m d \ " : \ " C c z Y T l 3 j \ " , \ " z h t _ a p i _ a p i . m d \ " : \ " D y U S H A 0 S \ " , \ " z h t _ a p i _ i n d e x . m d \ " : \ " C g Z H 6 a H Q \ " , \ " z h t _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " l z c X w n W 6 \ " , \ " z h t _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " x w Q v u Y c k \ " , \ " z h t _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " B A r _ k t N P \ " , \ " z h t _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " C 2 G p 7 z 0 v \ " , \ " z h t _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " m m e M M r i u \ " , \ " z h t _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " D X 6 2 b g j Z \ " , \ " z h t _ a p i _ m p _ m a t h _ m p _ m a t h . m d \ " : \ " C 3 0 2 r x K c \ " , \ " z h t _ a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " C N i S n u M w \ " , \ " z h t _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " D J _ 9 N Q F z \ " , \ " z h t _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " D 1 n A i R P 0 \ " , \ " z h t _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " C M R e y - M G \ " , \ " z h t _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " B D p W 2 F d 4 \ " , \ " z h t _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " D G V O Q o 3 Y \ " , \ " z h t _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " 8 G a G B 1 u l \ " , \ " z h t _ a p i _ p a r t i c l e _ p a r t i c l e . m d \ " : \ " h u u R T E b 9 \ " , \ " z h t _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " D v O V i S o x \ " , \ " z h t _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " B J W X _ k 6 K \ " , \ " z h t _ a p i _ p r e s e t s _ m o d e l _ m o d e l . m d \ " : \ " C N I 4 u b O h \ " , \ " z h t _ a p i _ p r e s e t s _ p r e s e t s . m d \ " : \ " C s D H j R b K \ " , \ " z h t _ g u i d e _ i n d e x . m d \ " : \ " C s u F V F x u \ " , \ " z h t _ i n d e x . m d \ " : \ " V M j J 0 l p j \ " , \ " z h t _ r e f e r _ i n d e x . m d \ " : \ " B z 6 v o x E Q \ " } " ) ; f u n c t i o n d e s e r i a l i z e F u n c t i o n s ( r ) { r e t u r n A r r a y . i s A r r a y ( r )
2024-08-30 13:46:30 +08:00
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