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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 >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > func ([`ThreeSingleVarsFunc`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > p ([`Point3`](./point#class-point3)): 点< / span > < / span >
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< 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 = "func-curry-func-multivarsfunc-args-var-onevarfunc" tabindex = "-1" > < em > < strong > func< / strong > < / em > < code > curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc< / code > < a class = "header-anchor" href = "#func-curry-func-multivarsfunc-args-var-onevarfunc" aria-label = "Permalink to "***func*** `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 (< a href = "./mp_math_typing.html#var-multivarsfunc" > < code > MultiVarsFunc< / code > < / a > ): 函数< / li > < li > *args (< a href = "./mp_math_typing.html#var-var" > < code > Var< / code > < / a > ): 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 >
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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;" > 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 >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): 函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > *args ([`Var`](./mp_math_typing#var-var)): 参数< / span > < / span >
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< 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 >
2024-09-03 22:49:39 +08:00
< 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-01c90815 data-v-28deee4a > <!-- [ --> <!-- ] --> < div class = "edit-info" data-v-28deee4a > < div class = "edit-link" data-v-28deee4a > < a class = "VPLink link vp-external-link-icon no-icon edit-link-button" href = "https://github.com/snowykami/mbcp/tree/main/mbcp//mp_math/function.py" target = "_blank" rel = "noreferrer" data-v-28deee4a > <!-- [ --> < span class = "vpi-square-pen edit-link-icon" data-v-28deee4a > < / span > 在 GitHub 上编辑此页<!-- ] --> < / a > < / div > <!-- --> < / div > < nav class = "prev-next" aria-labelledby = "doc-footer-aria-label" data-v-28deee4a > < span class = "visually-hidden" id = "doc-footer-aria-label" data-v-28deee4a > Pager< / span > < div class = "pager" data-v-28deee4a > < a class = "VPLink link pager-link prev" href = "/api/mp_math/equation.html" data-v-28deee4a > <!-- [ --> < span class = "desc" data-v-28deee4a > 上一页< / span > < span class = "title" data-v-28deee4a > mbcp.mp_math.equation< / span > <!-- ] --> < / a > < / div > < div class = "pager" data-v-28deee4a > < a class = "VPLink link pager-link next" href = "/api/mp_math/" data-v-28deee4a > <!-- [ --> < span class = "desc" data-v-28deee4a > 下一页< / span > < span class = "title" data-v-28deee4a > mbcp.mp_math< / span > <!-- ] --> < / a > < / div > < / nav > < / footer > <!-- [ --> <!-- ] --> < / div > < / div > < / div > <!-- [ --> <!-- ] --> < / div > < / div > < footer class = "VPFooter has-sidebar" data-v-3b4648ff data-v-d69bcf5d > < div class = "container" data-v-d69bcf5d > < p class = "message" data-v-d69bcf5d > 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-d69bcf5d > 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 _ i n d e x . m d \ " : \ " B O 3 O G C Z m \ " , \ " a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " D X j H P M c Z \ " , \ " a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " B _ A P a Y - d \ " , \ " a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " q a T L b d s 6 \ " , \ " a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " D 6 S k - j U O \ " , \ " a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " B f S A i 6 Y B \ " , \ " a p i _ m p _ m a t h _ l i n e . m d \ " : \ " K - H h I s v U \ " , \ " a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " D 0 j H a H h o \ " , \ " a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " D Q h j z D 0 6 \ " , \ " a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " N L p _ S g 9 U \ " , \ " a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " C 2 P E P 6 H 5 \ " , \ " a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " Q B 0 h G G M g \ " , \ " a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " B 1 W u 6 c 9 G \ " , \ " a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " B n a J l v r B \ " , \ " a p i _ p r e s e t s _ i n d e x . m d \ " : \ " C n 3 t b i U 4 \ " , \ " a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " B H 3 a z K A 8 \ " , \ " d e m o _ b e s t - p r a c t i c e . m d \ " : \ " C m Y j f r x d \ " , \ " d e m o _ i n d e x . m d \ " : \ " C V A d l a F I \ " , \ " e n _ a p i _ i n d e x . m d \ " : \ " C 0 - L R r M B \ " , \ " e n _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " B 5 t d t B i M \ " , \ " e n _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " f - 2 w Q H W 5 \ " , \ " e n _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " N 3 o P - 7 U a \ " , \ " e n _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " B T 0 N B _ 1 n \ " , \ " e n _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " B i D C W h u z \ " , \ " e n _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " 0 b B p Z M y n \ " , \ " 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 \ " : \ " A 2 o A W I N P \ " , \ " e n _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " o p 2 O K 8 n C \ " , \ " e n _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " B a _ i 7 d D C \ " , \ " e n _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " B h I G b 9 y q \ " , \ " e n _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " B z - x J h l 3 \ " , \ " e n _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " D p z q y c D g \ " , \ " e n _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " j 3 _ p 5 K t Y \ " , \ " e n _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " B j 8 H Q N _ s \ " , \ " e n _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " t R S L Y 1 0 d \ " , \ " e n _ d e m o _ b e s t - p r a c t i c e . m d \ " : \ " C m t Y 1 0 5 n \ " , \ " 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 \ " : \ " C c - N t 9 O t \ " , \ " 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 \ " : \ " C J O q v l S E \ " , \ " i n d e x . m d \ " : \ " W V p b C 1 C 1 \ " , \ " j a _ a p i _ i n d e x . m d \ " : \ " C G n g N E P X \ " , \ " j a _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " B P p e n A m _ \ " , \ " j a _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " k K A d 6 i h V \ " , \ " j a _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " C x c 2 A y G q \ " , \ " j a _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " z c K 7 s 9 - C \ " , \ " j a _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " B C R e R K f D \ " , \ " j a _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " B U E G 7 Q n 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 \ " : \ " C z E P V 5 E p \ " , \ " j a _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " D 8 l t D T I 9 \ " , \ " j a _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " B j _ w y a C j \ " , \ " j a _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " h B K U n t D s \ " , \ " j a _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " D d r b P Y - j \ " , \ " j a _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " D _ i X I 2 n w \ " , \ " j a _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " C W 1 r q a r C \ " , \ " j a _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " B F c _ P f J b \ " , \ " j a _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " B q E j Z 7 I Y \ " , \ " j a _ d e m o _ b e s t - p r a c t i c e . m d \ " : \ " C B H i F 6 e c \ " , \ " 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 \ " : \ " B v j V 8 R I J \ " , \ " 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 _ i n d e x . m d \ " : \ " B h 7 I C G 6 U \ " , \ " z h t _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " m m e c N I J M \ " , \ " z h t _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " D 9 e B w c N w \ " , \ " z h t _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " B 0 0 I W O _ d \ " , \ " z h t _ a p i _ m p _ m a t h _ f u n c t i o n . m d \ " : \ " B n U e r g l v \ " , \ " z h t _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " D V q L R Z h m \ " , \ " z h t _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " D g 3 j i _ d G \ " , \ " 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 W z R f F J e \ " , \ " z h t _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " C - 9 I g W h _ \ " , \ " z h t _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " v F M E E e V u \ " , \ " z h t _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " B u D H b w Y P \ " , \ " z h t _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " D v x T Z y 5 j \ " , \ " z h t _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " h A G 5 6 f d m \ " , \ " z h t _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " b d o u G 1 s k \ " , \ " z h t _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " 9 w d P A k K N \ " , \ " 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 \ " : \ " C y r J s c B T \ " , \ " z h t _ d e m o _ b e s t - p r a c t i c e . m d \ " : \ " C P N b D _ L g \ " , \ " 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 \ " : \ " f k O Y k Z Z e \ " , \ " 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 ) ? r . m a p ( d e s e r i a l i z e F u n c t i o n s ) : t y p e o f r = = " o b j e c t " & & r ! = = n u l l ? O b j e c t . k e y s ( r ) . r e d u c e ( ( t , n ) = > ( t [ n ] = d e s e r i a l i z e F u n c t i o n s ( r [ n ] ) , t ) , { } ) : t y p e o f r = = " s t r i n g " & & r . s t a r t s W i t h ( " _ v p - f n _ " ) ? n e w F u n c t i o n ( ` r e t u r n $ { r . s l i c e ( 7 ) } ` ) ( ) : r } ; w i n d o w . _ _ V P _ S I T E _ D A T A _ _ = d e s e r i a l i z e F u n c t i o n s ( J S O N . p a r s e ( " { \ " l a n g \ " : \ " e n - U S \ " , \ " d i r \ " : \ " l t r \ " , \ " t i t l e \ " : \ " V i t e P r e s s \ " , \ " d e s c r i p t i o n \ " : \ " A V i t e P r e s s s i t e \ " , \ " b a s e \ " : \ " / \ " , \ " h e a d \ " : [ ] , \ " r o u t e r \ " : { \ " p r e f e t c h L i n k s \ " : t r u e } , \ " a p p e a r a n c e \ " : t r u e , \ " t h e m e C o n f i g \ " : { \ " l o g o \ " : \ " / m b c p - l o g o . s v g \ " , \ " s i d e b a r \ " : { \ " / a p i / \ " : { \ " b a s e \ " : \ " / a p i / \ " , \ " i t e m s \ " : [ { \ " t e x t \ " : \ " M B C P \ " , \ " i t e m s \ " : [ { \ " t e x t \ " : \ " m p _ m a t h \ " , \ " i t e m s \ " : [ { \ " t e x t \ " : \ " m b c p . m p _ m a t h . a n g l e \ " , \ " l i n k \ " : \ " m p _ m
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