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-{"documenter":{"julia_version":"1.10.3","generation_timestamp":"2024-05-09T16:52:14","documenter_version":"1.4.1"}}
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dev/differentiation/index.html

@@ -3,7 +3,7 @@
 differentiate(p, x) # should return 6xy + 1
 differentiate(p, x, Val{1}()) # equivalent to the above
 differentiate(p, (x, y)) # should return [6xy+1, 3x^2+1]
-differentiate( [x^2+y, z^2+4x], [x, y, z]) # should return [2x 1 0; 4 0 2z]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaAlgebra/MultivariatePolynomials.jl/blob/a5b893116ef2981d76189f8121dedca33dd9b4d2/src/differentiation.jl#L1-L30">source</a></section></article><h1 id="Antidifferentiation"><a class="docs-heading-anchor" href="#Antidifferentiation">Antidifferentiation</a><a id="Antidifferentiation-1"></a><a class="docs-heading-anchor-permalink" href="#Antidifferentiation" title="Permalink"></a></h1><p>Given a polynomial, say <code>p(x, y) = 3x^2y + x + 2y + 1</code>, we can antidifferentiate it by a variable, say <code>x</code> and get <span>$\int_0^x p(X, y)\mathrm{d}X = x^3y + 1/2x^2 + 2xy + x$</span>. We can also antidifferentiate it by both of its variable and get the vector <code>[x^3y + 1/2x^2 + 2xy + x, 3/2x^2y^2 + xy + y^2 + y]</code>.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="MultivariatePolynomials.antidifferentiate" href="#MultivariatePolynomials.antidifferentiate"><code>MultivariatePolynomials.antidifferentiate</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">antidifferentiate(p::AbstractPolynomialLike, v::AbstractVariable, deg::Union{Int, Val}=1)</code></pre><p>Antidifferentiate <code>deg</code> times the polynomial <code>p</code> by the variable <code>v</code>. The free constant involved by the antidifferentiation is set to 0.</p><pre><code class="nohighlight hljs">antidifferentiate(p::AbstractPolynomialLike, vs, deg::Union{Int, Val}=1)</code></pre><p>Antidifferentiate <code>deg</code> times the polynomial <code>p</code> by the variables of the vector or tuple of variable <code>vs</code> and return an array of dimension <code>deg</code>. It is recommended to pass <code>deg</code> as a <code>Val</code> instance when the degree is known at compile time, e.g. <code>antidifferentiate(p, v, Val{2}())</code> instead of <code>antidifferentiate(p, x, 2)</code>, as this will help the compiler infer the return type.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">p = 3x^2*y + x + 2y + 1
+differentiate( [x^2+y, z^2+4x], [x, y, z]) # should return [2x 1 0; 4 0 2z]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaAlgebra/MultivariatePolynomials.jl/blob/05574bb8c80560f53394cba4ca24f2006770db43/src/differentiation.jl#L1-L30">source</a></section></article><h1 id="Antidifferentiation"><a class="docs-heading-anchor" href="#Antidifferentiation">Antidifferentiation</a><a id="Antidifferentiation-1"></a><a class="docs-heading-anchor-permalink" href="#Antidifferentiation" title="Permalink"></a></h1><p>Given a polynomial, say <code>p(x, y) = 3x^2y + x + 2y + 1</code>, we can antidifferentiate it by a variable, say <code>x</code> and get <span>$\int_0^x p(X, y)\mathrm{d}X = x^3y + 1/2x^2 + 2xy + x$</span>. We can also antidifferentiate it by both of its variable and get the vector <code>[x^3y + 1/2x^2 + 2xy + x, 3/2x^2y^2 + xy + y^2 + y]</code>.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="MultivariatePolynomials.antidifferentiate" href="#MultivariatePolynomials.antidifferentiate"><code>MultivariatePolynomials.antidifferentiate</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">antidifferentiate(p::AbstractPolynomialLike, v::AbstractVariable, deg::Union{Int, Val}=1)</code></pre><p>Antidifferentiate <code>deg</code> times the polynomial <code>p</code> by the variable <code>v</code>. The free constant involved by the antidifferentiation is set to 0.</p><pre><code class="nohighlight hljs">antidifferentiate(p::AbstractPolynomialLike, vs, deg::Union{Int, Val}=1)</code></pre><p>Antidifferentiate <code>deg</code> times the polynomial <code>p</code> by the variables of the vector or tuple of variable <code>vs</code> and return an array of dimension <code>deg</code>. It is recommended to pass <code>deg</code> as a <code>Val</code> instance when the degree is known at compile time, e.g. <code>antidifferentiate(p, v, Val{2}())</code> instead of <code>antidifferentiate(p, x, 2)</code>, as this will help the compiler infer the return type.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">p = 3x^2*y + x + 2y + 1
 antidifferentiate(p, x) # should return 3x^3* + 1/2*x + 2xy + x
 antidifferentiate(p, x, Val{1}()) # equivalent to the above
-antidifferentiate(p, (x, y)) # should return [3x^3* + 1/2*x + 2xy + x, 3/2x^2*y^2 + xy + y^2 + y]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaAlgebra/MultivariatePolynomials.jl/blob/a5b893116ef2981d76189f8121dedca33dd9b4d2/src/antidifferentiation.jl#L1-L24">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../substitution/">« Substitution</a><a class="docs-footer-nextpage" href="../division/">Division »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Thursday 9 May 2024 16:52">Thursday 9 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+antidifferentiate(p, (x, y)) # should return [3x^3* + 1/2*x + 2xy + x, 3/2x^2*y^2 + xy + y^2 + y]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaAlgebra/MultivariatePolynomials.jl/blob/05574bb8c80560f53394cba4ca24f2006770db43/src/antidifferentiation.jl#L1-L24">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../substitution/">« Substitution</a><a class="docs-footer-nextpage" href="../division/">Division »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Thursday 9 May 2024 16:52">Thursday 9 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>