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2 changes: 1 addition & 1 deletion previews/PR1305/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.11.0","generation_timestamp":"2024-10-12T15:27:01","documenter_version":"1.7.0"}}
{"documenter":{"julia_version":"1.11.0","generation_timestamp":"2024-10-12T20:54:12","documenter_version":"1.7.0"}}
2 changes: 1 addition & 1 deletion previews/PR1305/comparison/index.html
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2 changes: 1 addition & 1 deletion previews/PR1305/examples/perturbation/index.html
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- (𝜀 + 4*𝜀^2 + 10*𝜀^3)*𝑀^3/6
+ (𝜀 + 16*𝜀^2 + 91*𝜀^3)*𝑀^5/120</code></pre><p>Comparing the formula to the one for 𝐸 in the <a href="https://en.wikipedia.org/wiki/Kepler%27s_equation">Wikipedia article on the Kepler&#39;s equation</a>:</p><p class="math-container">\[ E = \frac{1}{1-\epsilon}M
-\frac{\epsilon}{(1-\epsilon)^4} \frac{M^3}{3!} + \frac{(9\epsilon^2
+ \epsilon)}{(1-\epsilon)^7}\frac{M^5}{5!}\cdots\]</p><p>The first deviation is in the coefficient of <span>$\epsilon^3 M^5$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../tutorials/converting_to_C/">« Automatic Conversion of Julia Code to C Functions</a><a class="docs-footer-nextpage" href="../../manual/variables/">Variable and Equation Types »</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><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 12 October 2024 15:27">Saturday 12 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ \epsilon)}{(1-\epsilon)^7}\frac{M^5}{5!}\cdots\]</p><p>The first deviation is in the coefficient of <span>$\epsilon^3 M^5$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../tutorials/converting_to_C/">« Automatic Conversion of Julia Code to C Functions</a><a class="docs-footer-nextpage" href="../../manual/variables/">Variable and Equation Types »</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><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 12 October 2024 20:54">Saturday 12 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
14 changes: 7 additions & 7 deletions previews/PR1305/getting_started/index.html
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\end{equation}
\]</p><h2 id="Registering-Functions"><a class="docs-heading-anchor" href="#Registering-Functions">Registering Functions</a><a id="Registering-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Registering-Functions" title="Permalink"></a></h2><p>One of the benefits of a one-language Julia symbolic stack is that the primitives are all written in Julia, and therefore it&#39;s trivially extendable from Julia itself. By default, new functions are traced to the primitives and the symbolic expressions are written on the primitives. However, we can expand the allowed primitives by registering new functions. For example, let&#39;s register a new function <code>h</code>:</p><pre><code class="language-julia hljs">h(x, y) = x^2 + y
@register_symbolic h(x, y)</code></pre><p>When we use <code>h(x, y)</code>, it is a symbolic expression and doesn&#39;t expand:</p><pre><code class="language-julia hljs">h(x, y) + y^2</code></pre><p class="math-container">\[ \begin{equation}
h\left( x\left( t \right), y\left( t \right) \right) + y\left( t \right)^{2}
h\left( x\left( t \right), y\left( t \right) \right) + \left( y\left( t \right) \right)^{2}
\end{equation}
\]</p><p>To use it with the differentiation system, we need to register its derivatives. We would do it like this:</p><pre><code class="language-julia hljs"># Derivative w.r.t. the first argument
Symbolics.derivative(::typeof(h), args::NTuple{2,Any}, ::Val{1}) = 2args[1]
Expand Down Expand Up @@ -233,9 +233,9 @@
out = sparse(rows, cols, zeros(length(cols)), size(sj)...) # pre-allocate, and correct structure
myf = eval(last(f_expr))
myf(out, rand(N)) # note that out matches the sparsity structure of sj
out</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">20×10 SparseArrays.SparseMatrixCSC{Float64, Int64} with 24 stored entries:
⎡⠁⠁⢀⠀⠂⎤
⎢⡈⠃⡀⠀⠀⎥
⎢⠠⡀⠈⠀⠨⎥
⎢⠄⢀⠀⡀⠈⎥
⎣⠁⢀⢃⠈⠀⎦</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../tutorials/auto_parallel/">Automated Sparse Parallelism of Julia Functions via Tracing »</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><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 12 October 2024 15:27">Saturday 12 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
out</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">20×10 SparseArrays.SparseMatrixCSC{Float64, Int64} with 18 stored entries:
⎡⡡⠊⢀⡀⠅⎤
⎢⠀⡂⠀⠀⠀⎥
⎢⠀⠀⢁⠀⠀⎥
⎢⠐⠂⠀⠀⠀⎥
⎣⠀⠈⠀⠠⠐⎦</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../tutorials/auto_parallel/">Automated Sparse Parallelism of Julia Functions via Tracing »</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><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 12 October 2024 20:54">Saturday 12 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.59.0+0
[3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`</code></pre></details><p>You can also download the <a href="https://github.com/SciML/Symbolics.jl/tree/gh-pages/v6.14.0/assets/Manifest.toml">manifest</a> file and the <a href="https://github.com/SciML/Symbolics.jl/tree/gh-pages/v6.14.0/assets/Project.toml">project</a> file.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="getting_started/">Getting Started with Symbolics.jl »</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><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 12 October 2024 15:27">Saturday 12 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`</code></pre></details><p>You can also download the <a href="https://github.com/SciML/Symbolics.jl/tree/gh-pages/v6.14.0/assets/Manifest.toml">manifest</a> file and the <a href="https://github.com/SciML/Symbolics.jl/tree/gh-pages/v6.14.0/assets/Project.toml">project</a> file.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="getting_started/">Getting Started with Symbolics.jl »</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><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 12 October 2024 20:54">Saturday 12 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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A_{2,1} A_{3,1} + A_{2,2} A_{3,2} + A_{2,3} A_{3,3}
\end{equation}
\]</p><pre><code class="language-julia hljs">@syms i::Int j::Int
Symbolics.scalarize(AAt[i,j])</code></pre><p>In general, any scalar expression which is derived from array expressions can be scalarized.</p><pre><code class="language-julia hljs">#sum(A[:,1]) + sum(A[2,:])#latexify not working</code></pre><pre><code class="language-julia hljs">Symbolics.scalarize(sum(A[:,1]) + sum(A[2,:]))</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../solver/">« Solver</a><a class="docs-footer-nextpage" href="../build_function/">Function Building and Compilation (build_function) »</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><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 12 October 2024 15:27">Saturday 12 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
Symbolics.scalarize(AAt[i,j])</code></pre><p>In general, any scalar expression which is derived from array expressions can be scalarized.</p><pre><code class="language-julia hljs">#sum(A[:,1]) + sum(A[2,:])#latexify not working</code></pre><pre><code class="language-julia hljs">Symbolics.scalarize(sum(A[:,1]) + sum(A[2,:]))</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../solver/">« Solver</a><a class="docs-footer-nextpage" href="../build_function/">Function Building and Compilation (build_function) »</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><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 12 October 2024 20:54">Saturday 12 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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