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diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json
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-{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-05T09:06:01","documenter_version":"1.1.0"}}
+{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-05T09:06:37","documenter_version":"1.1.0"}}
diff --git a/dev/direct_sum/index.html b/dev/direct_sum/index.html
diff --git a/dev/euclidean_interface/index.html b/dev/euclidean_interface/index.html
diff --git a/dev/extending_abstractalgebra/index.html b/dev/extending_abstractalgebra/index.html
diff --git a/dev/field_introduction/index.html b/dev/field_introduction/index.html
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diff --git a/dev/fraction/index.html b/dev/fraction/index.html
@@ -113,7 +113,7 @@
 x^2 + x + 1
 
 julia&gt; 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="Base.gcd-Union{Tuple{T}, Tuple{FracElem{T}, FracElem{T}}} where T&lt;:RingElem" href="#Base.gcd-Union{Tuple{T}, Tuple{FracElem{T}, FracElem{T}}} where T&lt;:RingElem"><code>Base.gcd</code></a> — <span class="docstring-category">Method</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/77ac268fa30692304bdc741a19af52df82afba96/src/Fraction.jl#L713-L720">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(QQ, &quot;x&quot;)
+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="Base.gcd-Union{Tuple{T}, Tuple{FracElem{T}, FracElem{T}}} where T&lt;:RingElem" href="#Base.gcd-Union{Tuple{T}, Tuple{FracElem{T}, FracElem{T}}} where T&lt;:RingElem"><code>Base.gcd</code></a> — <span class="docstring-category">Method</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/e1c902fc1d45281d65a7cb7b4dda4bb55a3f77d4/src/Fraction.jl#L713-L720">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(QQ, &quot;x&quot;)
 (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="AbstractAlgebra.is_square-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem" href="#AbstractAlgebra.is_square-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem"><code>AbstractAlgebra.is_square</code></a> — <span class="docstring-category">Method</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/77ac268fa30692304bdc741a19af52df82afba96/src/Fraction.jl#L675-L679">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="Base.sqrt-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem" href="#Base.sqrt-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem"><code>Base.sqrt</code></a> — <span class="docstring-category">Method</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/77ac268fa30692304bdc741a19af52df82afba96/src/Fraction.jl#L684-L689">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(QQ, &quot;x&quot;)
+</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="AbstractAlgebra.is_square-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem" href="#AbstractAlgebra.is_square-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem"><code>AbstractAlgebra.is_square</code></a> — <span class="docstring-category">Method</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/e1c902fc1d45281d65a7cb7b4dda4bb55a3f77d4/src/Fraction.jl#L675-L679">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="Base.sqrt-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem" href="#Base.sqrt-Union{Tuple{FracElem{T}}, Tuple{T}} where T&lt;:RingElem"><code>Base.sqrt</code></a> — <span class="docstring-category">Method</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/e1c902fc1d45281d65a7cb7b4dda4bb55a3f77d4/src/Fraction.jl#L684-L689">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(QQ, &quot;x&quot;)
 (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="AbstractAlgebra.remove-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem" href="#AbstractAlgebra.remove-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem"><code>AbstractAlgebra.remove</code></a> — <span class="docstring-category">Method</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/77ac268fa30692304bdc741a19af52df82afba96/src/Fraction.jl#L740-L745">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="AbstractAlgebra.valuation-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem" href="#AbstractAlgebra.valuation-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem"><code>AbstractAlgebra.valuation</code></a> — <span class="docstring-category">Method</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/77ac268fa30692304bdc741a19af52df82afba96/src/Fraction.jl#L754-L758">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(ZZ, &quot;x&quot;)
+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="AbstractAlgebra.remove-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem" href="#AbstractAlgebra.remove-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem"><code>AbstractAlgebra.remove</code></a> — <span class="docstring-category">Method</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/e1c902fc1d45281d65a7cb7b4dda4bb55a3f77d4/src/Fraction.jl#L740-L745">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="AbstractAlgebra.valuation-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem" href="#AbstractAlgebra.valuation-Union{Tuple{T}, Tuple{FracElem{T}, T}} where T&lt;:RingElem"><code>AbstractAlgebra.valuation</code></a> — <span class="docstring-category">Method</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/e1c902fc1d45281d65a7cb7b4dda4bb55a3f77d4/src/Fraction.jl#L754-L758">source</a></section></article><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; R, x = polynomial_ring(ZZ, &quot;x&quot;)
 (Univariate polynomial ring in x over integers, x)
 
 julia&gt; f = (x + 1)//(x^3 + 3x + 1)