build based on 05c6ffc

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-10-09T15:44:26","documenter_version":"1.7.0"}}
+{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-10-15T08:23:49","documenter_version":"1.7.0"}}

dev/AbstractAlgebra/fraction/index.html

@@ -113,7 +113,7 @@
 x^2 + x + 1
 
 julia> d = denominator(g)
-x^3 + 3*x + 1</code></pre><h3 id="Greatest-common-divisor"><a class="docs-heading-anchor" href="#Greatest-common-divisor">Greatest common divisor</a><a id="Greatest-common-divisor-1"></a><a class="docs-heading-anchor-permalink" href="#Greatest-common-divisor" title="Permalink"></a></h3><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="gcd-Union{Tuple{T}, Tuple{FracElem{T}, FracElem{T}}} where T&lt;:RingElem" href="#gcd-Union{Tuple{T}, Tuple{FracElem{T}, FracElem{T}}} where T&lt;:RingElem"><code>gcd</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">gcd(a::FracElem{T}, b::FracElem{T}) where {T &lt;: RingElem}</code></pre><p>Return a greatest common divisor of <span>$a$</span> and <span>$b$</span> if one exists. N.B: we define the GCD of <span>$a/b$</span> and <span>$c/d$</span> to be gcd<span>$(ad, bc)/bd$</span>, reduced to lowest terms. This requires the existence of a greatest common divisor function for the base ring.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Nemocas/AbstractAlgebra.jl/blob/v0.43.5/src/Fraction.jl#L725-L732">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(QQ, :x)
+x^3 + 3*x + 1</code></pre><h3 id="Greatest-common-divisor"><a class="docs-heading-anchor" href="#Greatest-common-divisor">Greatest common divisor</a><a id="Greatest-common-divisor-1"></a><a class="docs-heading-anchor-permalink" href="#Greatest-common-divisor" title="Permalink"></a></h3><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="gcd-Union{Tuple{T}, Tuple{FracElem{T}, FracElem{T}}} where T&lt;:RingElem" href="#gcd-Union{Tuple{T}, Tuple{FracElem{T}, FracElem{T}}} where T&lt;:RingElem"><code>gcd</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">gcd(a::FracElem{T}, b::FracElem{T}) where {T &lt;: RingElem}</code></pre><p>Return a greatest common divisor of <span>$a$</span> and <span>$b$</span> if one exists. N.B: we define the GCD of <span>$a/b$</span> and <span>$c/d$</span> to be gcd<span>$(ad, bc)/bd$</span>, reduced to lowest terms. This requires the existence of a greatest common divisor function for the base ring.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Nemocas/AbstractAlgebra.jl/blob/v0.43.6/src/Fraction.jl#L725-L732">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(QQ, :x)
 (Univariate polynomial ring in x over rationals, x)
 
 julia&gt; f = (x + 1)//(x^3 + 3x + 1)
@@ -124,7 +124,7 @@
 
 julia&gt; h = gcd(f, g)
 (x + 1)//(x^5 + x^4 + 4*x^3 + 4*x^2 + 4*x + 1)
-</code></pre><h3 id="Square-root"><a class="docs-heading-anchor" href="#Square-root">Square root</a><a id="Square-root-1"></a><a class="docs-heading-anchor-permalink" href="#Square-root" title="Permalink"></a></h3><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="is_square-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem" href="#is_square-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem"><code>is_square</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">is_square(a::FracElem{T}) where T &lt;: RingElem</code></pre><p>Return <code>true</code> if <span>$a$</span> is a square.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Nemocas/AbstractAlgebra.jl/blob/v0.43.5/src/Fraction.jl#L687-L691">source</a></section></article><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="sqrt-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem" href="#sqrt-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem"><code>sqrt</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Base.sqrt(a::FracElem{T}; check::Bool=true) where T &lt;: RingElem</code></pre><p>Return the square root of <span>$a$</span>. By default the function will throw an exception if the input is not square. If <code>check=false</code> this test is omitted.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Nemocas/AbstractAlgebra.jl/blob/v0.43.5/src/Fraction.jl#L696-L701">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(QQ, :x)
+</code></pre><h3 id="Square-root"><a class="docs-heading-anchor" href="#Square-root">Square root</a><a id="Square-root-1"></a><a class="docs-heading-anchor-permalink" href="#Square-root" title="Permalink"></a></h3><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="is_square-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem" href="#is_square-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem"><code>is_square</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">is_square(a::FracElem{T}) where T &lt;: RingElem</code></pre><p>Return <code>true</code> if <span>$a$</span> is a square.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Nemocas/AbstractAlgebra.jl/blob/v0.43.6/src/Fraction.jl#L687-L691">source</a></section></article><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="sqrt-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem" href="#sqrt-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem"><code>sqrt</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Base.sqrt(a::FracElem{T}; check::Bool=true) where T &lt;: RingElem</code></pre><p>Return the square root of <span>$a$</span>. By default the function will throw an exception if the input is not square. If <code>check=false</code> this test is omitted.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Nemocas/AbstractAlgebra.jl/blob/v0.43.6/src/Fraction.jl#L696-L701">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(QQ, :x)
 (Univariate polynomial ring in x over rationals, x)
 
 julia&gt; S = fraction_field(R)
@@ -138,7 +138,7 @@
 (21//4*x^6 - 15*x^5 + 27//14*x^4 + 9//20*x^3 + 3//7*x + 9//10)//(x + 3)
 
 julia&gt; is_square(a^2)
-true</code></pre><h3 id="Remove-and-valuation"><a class="docs-heading-anchor" href="#Remove-and-valuation">Remove and valuation</a><a id="Remove-and-valuation-1"></a><a class="docs-heading-anchor-permalink" href="#Remove-and-valuation" title="Permalink"></a></h3><p>When working over a Euclidean domain, it is convenient to extend valuations to the fraction field. To facilitate this, we define the following functions.</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="remove-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem" href="#remove-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem"><code>remove</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">remove(z::FracElem{T}, p::T) where {T &lt;: RingElem}</code></pre><p>Return the tuple <span>$n, x$</span> such that <span>$z = p^nx$</span> where <span>$x$</span> has valuation <span>$0$</span> at <span>$p$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Nemocas/AbstractAlgebra.jl/blob/v0.43.5/src/Fraction.jl#L752-L757">source</a></section></article><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="valuation-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem" href="#valuation-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem"><code>valuation</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">valuation(z::FracElem{T}, p::T) where {T &lt;: RingElem}</code></pre><p>Return the valuation of <span>$z$</span> at <span>$p$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Nemocas/AbstractAlgebra.jl/blob/v0.43.5/src/Fraction.jl#L766-L770">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(ZZ, :x)
+true</code></pre><h3 id="Remove-and-valuation"><a class="docs-heading-anchor" href="#Remove-and-valuation">Remove and valuation</a><a id="Remove-and-valuation-1"></a><a class="docs-heading-anchor-permalink" href="#Remove-and-valuation" title="Permalink"></a></h3><p>When working over a Euclidean domain, it is convenient to extend valuations to the fraction field. To facilitate this, we define the following functions.</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="remove-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem" href="#remove-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem"><code>remove</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">remove(z::FracElem{T}, p::T) where {T &lt;: RingElem}</code></pre><p>Return the tuple <span>$n, x$</span> such that <span>$z = p^nx$</span> where <span>$x$</span> has valuation <span>$0$</span> at <span>$p$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Nemocas/AbstractAlgebra.jl/blob/v0.43.6/src/Fraction.jl#L752-L757">source</a></section></article><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="valuation-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem" href="#valuation-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem"><code>valuation</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">valuation(z::FracElem{T}, p::T) where {T &lt;: RingElem}</code></pre><p>Return the valuation of <span>$z$</span> at <span>$p$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Nemocas/AbstractAlgebra.jl/blob/v0.43.6/src/Fraction.jl#L766-L770">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(ZZ, :x)
 (Univariate polynomial ring in x over integers, x)
 
 julia&gt; f = (x + 1)//(x^3 + 3x + 1)
@@ -187,4 +187,4 @@
 julia&gt; collect(f)
 2-element Vector{Tuple{BigInt, Int64}}:
  (10, 10)
- (42, -8)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../Hecke/manual/number_fields/class_fields/">« Class Field Theory</a><a class="docs-footer-nextpage" href="../../Nemo/padic/">Padics »</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="Wednesday 9 October 2024 15:44">Wednesday 9 October 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ (42, -8)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../Hecke/manual/number_fields/class_fields/">« Class Field Theory</a><a class="docs-footer-nextpage" href="../../Nemo/padic/">Padics »</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="Tuesday 15 October 2024 08:23">Tuesday 15 October 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>