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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 >
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< 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 > 或 < a href = "https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/function.py#L30" target = "_blank" > 在GitHub上查看< / a > < / 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 >
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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;" > 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 >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#6F42C1;--shiki-dark:#B392F0;" > curried_func< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args2: Var) -> Var:< / span > < / span >
< 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 >
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< 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 \ " : \ " C M v A M n 4 b \ " , \ " a p i _ i n d e x . m d \ " : \ " B Y C W C W D w \ " , \ " a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " Z H Q L V Z i 6 \ " , \ " a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " D P f W D l O C \ " , \ " a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " D N L 3 R h R T \ " , \ " a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " l F d 1 g u d y \ " , \ " a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " C B a W j 2 T G \ " , \ " a p i _ m p _ m a t h _ l i n e . m d \ " : \ " D j f Q - B 5 i \ " , \ " a p i _ m p _ m a t h _ m p _ m a t h . m d \ " : \ " C p Q n g d P n \ " , \ " a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " u e X w U e 7 x \ " , \ " a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " C X p U 2 f 7 r \ " , \ " a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " J b Q s _ F q s \ " , \ " a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " B k j s i F Z K \ " , \ " a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " C - G f - q 7 v \ " , \ " a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " B m e q j m - R \ " , \ " a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " e l M k n 6 t v \ " , \ " a p i _ p a r t i c l e _ p a r t i c l e . m d \ " : \ " j e i n d v 3 k \ " , \ " a p i _ p r e s e t s _ i n d e x . m d \ " : \ " D A n s 7 u V y \ " , \ " a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " B V 3 c g l v I \ " , \ " a p i _ p r e s e t s _ m o d e l _ m o d e l . m d \ " : \ " C k T 5 A 2 V x \ " , \ " a p i _ p r e s e t s _ p r e s e t s . m d \ " : \ " D K v f M d j r \ " , \ " d e m o _ i n d e x . m d \ " : \ " C V A d l a F I \ " , \ " e n _ a p i _ a p i . m d \ " : \ " D N V 4 3 N d 2 \ " , \ " e n _ a p i _ i n d e x . m d \ " : \ " r I v J - t I - \ " , \ " e n _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " B W p D h X E 0 \ " , \ " e n _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " C 7 R P r 8 Y w \ " , \ " e n _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " Q 3 e d A l T b \ " , \ " e n _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " s T y Z Q 9 K p \ " , \ " e n _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " D R j W G 5 h d \ " , \ " e n _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " B e v e A f E c \ " , \ " e n _ a p i _ m p _ m a t h _ m p _ m a t h . m d \ " : \ " B g 5 e F I M k \ " , \ " 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 \ " : \ " B y 9 a l 4 4 H \ " , \ " e n _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " D S 5 O U S g Q \ " , \ " e n _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " m I U s 1 I A B \ " , \ " e n _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " l 3 K D D W f s \ " , \ " e n _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " B r P H v G Z 2 \ " , \ " e n _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " B k O b 6 w 9 W \ " , \ " e n _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " L U 1 i J 7 C h \ " , \ " e n _ a p i _ p a r t i c l e _ p a r t i c l e . m d \ " : \ " B F O r 8 q j E \ " , \ " e n _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " B r Q 3 P k 9 2 \ " , \ " e n _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " D - C 7 z M 8 U \ " , \ " e n _ a p i _ p r e s e t s _ m o d e l _ m o d e l . m d \ " : \ " D a W J c W m r \ " , \ " e n _ a p i _ p r e s e t s _ p r e s e t s . m d \ " : \ " O K z O d e y i \ " , \ " e n _ g u i d e _ i n d e x . m d \ " : \ " C 3 k I 8 f 8 A \ " , \ " e n _ i n d e x . m d \ " : \ " D 5 C d d O W - \ " , \ " e n _ r e f e r _ i n d e x . m d \ " : \ " C q 6 G W i 0 V \ " , \ " g u i d e _ i n d e x . m d \ " : \ " B V h Q 0 k P y \ " , \ " i n d e x . m d \ " : \ " D J W B R k U z \ " , \ " j a _ a p i _ a p i . m d \ " : \ " a s J Z C X i e \ " , \ " j a _ a p i _ i n d e x . m d \ " : \ " B k N - p Z - z \ " , \ " j a _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " Q 4 K O k l 4 D \ " , \ " j a _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " q n e r s N f K \ " , \ " j a _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " C r 5 p O v e T \ " , \ " j a _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " x y b s 8 K o c \ " , \ " j a _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " C R j x 8 T k H \ " , \ " j a _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " B 0 6 T Z x O j \ " , \ " j a _ a p i _ m p _ m a t h _ m p _ m a t h . m d \ " : \ " B B R k f U b W \ " , \ " 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 4 8 J O b 2 8 \ " , \ " j a _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " B s I 6 A c c W \ " , \ " j a _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " B a R a B 4 F 7 \ " , \ " j a _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " S G T K z H C - \ " , \ " j a _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " B 0 A u G U a q \ " , \ " j a _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " Z V 6 g 6 C q y \ " , \ " j a _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " l Q M 7 6 p h s \ " , \ " j a _ a p i _ p a r t i c l e _ p a r t i c l e . m d \ " : \ " B l Q t 6 - 7 L \ " , \ " j a _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " b R V 3 3 r r M \ " , \ " 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 U 3 t c R O p \ " , \ " j a _ a p i _ p r e s e t s _ m o d e l _ m o d e l . m d \ " : \ " C a 8 3 7 h 0 t \ " , \ " j a _ a p i _ p r e s e t s _ p r e s e t s . m d \ " : \ " B 4 N I H C 5 7 \ " , \ " j a _ g u i d e _ i n d e x . m d \ " : \ " w 1 T f 2 A d m \ " , \ " j a _ i n d e x . m d \ " : \ " D n s q Z i 7 i \ " , \ " j a _ r e f e r _ i n d e x . m d \ " : \ " D a m U s c s 8 \ " , \ " r e f e r _ f u n c t i o n _ c u r r y . m d \ " : \ " D _ o q R D d 3 \ " , \ " r e f e r _ f u n c t i o n _ f u n c t i o n . m d \ " : \ " B i _ 8 2 l I J \ " , \ " r e f e r _ i n d e x . m d \ " : \ " y F Z W 0 k I 4 \ " , \ " z h t _ a p i _ a p i . m d \ " : \ " D i H U k C Y v \ " , \ " z h t _ a p i _ i n d e x . m d \ " : \ " B E o H S 6 e Y \ " , \ " z h t _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " C U X s 1 f 3 L \ " , \ " z h t _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " B R b O g - i k \ " , \ " z h t _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " D k F 2 3 w Z v \ " , \ " z h t _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " H x 5 F v 7 y g \ " , \ " z h t _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " d k T u U 5 S c \ " , \ " z h t _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " C h B w W N 5 h \ " , \ " z h t _ a p i _ m p _ m a t h _ m p _ m a t h . m d \ " : \ " C 2 f K j 2 U - \ " , \ " 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 \ " : \ " D R n E B E 4 1 \ " , \ " z h t _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " C s q Z z 8 A P \ " , \ " z h t _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " D d P n y 4 E p \ " , \ " z h t _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " C G l D P y I d \ " , \ " z h t _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " q R r y p Z k K \ " , \ " z h t _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " B g u y f Q 9 I \ " , \ " z h t _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " C 3 u v y f W b \ " , \ " z h t _ a p i _ p a r t i c l e _ p a r t i c l e . m d \ " : \ " B V p 5 w R X c \ " , \ " z h t _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " D 5 b U O R c 4 \ " , \ " 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 A B Y o P v x \ " , \ " 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 \ " : \ " D 7 U O T u j b \ " , \ " z h t _ a p i _ p r e s e t s _ p r e s e t s . m d \ " : \ " C R L 6 J o 8 B \ " , \ " z h t _ g u i d e _ i n d e x . m d \ " : \ " B N n M V i C 8 \ " , \ " z h t _ i n d e x . m d \ " : \ " C U R 8 - Q X m \ " , \ " z h t _ r e f e r _ i n d e x . m d \ " : \ " B 7 C Q S 2 U W \ " } " ) ; 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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