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class="content" data-v-01c90815><div class="content-container" data-v-01c90815><!--[--><!--]--><main class="main" data-v-01c90815><div style="position:relative;" class="vp-doc _ja_api_mp_math_function" data-v-01c90815><div><h1 id="モジュール-mbcp-mp-math-function" tabindex="-1"><strong>モジュール</strong> <code>mbcp.mp_math.function</code> <a class="header-anchor" href="#モジュール-mbcp-mp-math-function" aria-label="Permalink to "**モジュール** `mbcp.mp_math.function`""></a></h1><p>AAA</p><h3 id="func-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3" tabindex="-1"><em><strong>func</strong></em> <code>cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3</code> <a class="header-anchor" href="#func-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3" aria-label="Permalink to "***func*** `cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3`""></a></h3><p><strong>説明</strong>: 计算三元函数在某点的梯度向量。</p><div class="tip custom-block github-alert"><p class="custom-block-title">TIP</p><p>已知一个函数<mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="8.471ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3744.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D453" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z" style="stroke-width:3;"></path></g><g data-mml-node="mo" transform="translate(550,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z" style="stroke-width:3;"></path></g><g data-mml-node="mi" transform="translate(939,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 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-443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z" style="stroke-width:3;"></path></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∇</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>,</mo><msub><mi>y</mi><mn>0</mn></msub><mo>,</mo><msub><mi>z</mi><mn>0</mn></msub><mo stretchy="false">)</mo><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mfrac><mrow><mi>∂</mi><mi>f</mi></mrow><mrow><mi>∂</mi><mi>x</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>∂</mi><mi>f</mi></mrow><mrow><mi>∂</mi><mi>y</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>∂</mi><mi>f</mi></mrow><mrow><mi>∂</mi><mi>z</mi></mrow></mfrac><mo data-mjx-texclass="CLOSE">)</mo></mrow></math></mjx-assistive-mml></mjx-container></p></div><p><strong>引数</strong>:</p><blockquote><ul><li>func (<a href="./mp_math_typing.html#var-threesinglevarsfunc"><code>ThreeSingleVarsFunc</code></a>): 三元函数</li><li>p (<a href="./point.html#class-point3"><code>Point3</code></a>): 点</li><li>epsilon: 偏移量</li></ul></blockquote><p><strong>戻り値</strong>: 梯度</p><details><summary><b>ソースコード</b> または <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/function.py#L11" target="_blank">GitHubで表示</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;"> cal_gradient_3vf</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(func: ThreeSingleVarsFunc, p: Point3, epsilon: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">float</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">EPSILON</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -> Vector3:</span></span>
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<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> """</span></span>
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<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>
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<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> > [!tip]</span></span>
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<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>
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<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>
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<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>
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<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>
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<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> Returns:</span></span>
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<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 梯度</span></span>
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<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> """</span></span>
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<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>
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<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>
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<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>
|
||
<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>説明</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(Currying)</a></p></div><p><strong>引数</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>戻り値</strong>: 柯里化后的函数</p><p><strong>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>ソースコード</b> または <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/function.py#L30" target="_blank">GitHubで表示</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(Currying)](https://zhuanlan.zhihu.com/p/355859667)</span></span>
|
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<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 ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): 函数</span></span>
|
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<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> *args ([`Var`](./mp_math_typing#var-var)): 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>
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<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> Examples:</span></span>
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||
<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>
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<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> return a + b + c</span></span>
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<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>
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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;"> """</span></span>
|
||
<span class="line"></span>
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<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>
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<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> """@litedoc-hide"""</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;"> 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-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> このページをGitHubで編集する<!--]--></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="/ja/api/mp_math/equation.html" data-v-28deee4a><!--[--><span class="desc" data-v-28deee4a>前のページ</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="/ja/api/mp_math/" data-v-28deee4a><!--[--><span class="desc" data-v-28deee4a>次のページ</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><a href="https://vitepress.dev/">VitePress</a> で構築されたドキュメント | <a href="https://github.com/LiteyukiStudio/litedoc">litedoc</a> によって生成されたAPIリファレンス</p><p class="copyright" data-v-d69bcf5d>Copyright (C) 2020-2024 SnowyKami. All Rights Reserved</p></div></footer><!--[--><!--]--></div></div>
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