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Package invarFC0/InvFC0.SAGBI - Revision history
2024-03-28T22:40:19Z
Revision history for this page on the wiki
MediaWiki 1.35.0
http://apcocoa.uni-passau.de/wiki/index.php?title=Package_invarFC0/InvFC0.SAGBI&diff=16287&oldid=prev
Andraschko: changed wrong paranthesis
2021-02-09T16:06:53Z
<p>changed wrong paranthesis</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:06, 9 February 2021</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <item>@param <tt>G</tt> A list of matrices of size <tt>n</tt> over a ring <tt>P</tt> with <tt>n</tt> indeterminates.</item></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <item>@param <tt>G</tt> A list of matrices of size <tt>n</tt> over a ring <tt>P</tt> with <tt>n</tt> indeterminates.</item></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <item>@param <tt>d</tt> (optional) An integer describing the truncation degree.</item></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <item>@param <tt>d</tt> (optional) An integer describing the truncation degree.</item></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <item>@return A list of polynomials that form a (<tt>d</tt><del class="diffchange diffchange-inline">)</del>-truncated SAGBI basis.</item></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <item>@return A list of polynomials that form a (<tt>d</tt>-truncated<ins class="diffchange diffchange-inline">) </ins>SAGBI basis.</item></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </itemize></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </itemize></div></td></tr>
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Andraschko
http://apcocoa.uni-passau.de/wiki/index.php?title=Package_invarFC0/InvFC0.SAGBI&diff=16286&oldid=prev
Andraschko: Created page with "{{Version|2}} <command> <title>InvFC0.SAGBI</title> <short_description>This function computes a SAGBI basis of an invariant ring.</short_description> <syntax>InvFC0.S..."
2021-02-09T16:05:46Z
<p>Created page with "{{Version|2}} <command> <title>InvFC0.SAGBI</title> <short_description>This function computes a SAGBI basis of an invariant ring.</short_description> <syntax>InvFC0.S..."</p>
<p><b>New page</b></p><div>{{Version|2}}<br />
<command><br />
<title>InvFC0.SAGBI</title><br />
<short_description>This function computes a SAGBI basis of an invariant ring.</short_description><br />
<br />
<syntax>InvFC0.SAGBI(G:LIST of MAT, opt d:INT):LIST of POLY</syntax><br />
<description><br />
This function computes a (<tt>d</tt>-truncated) SAGBI basis of the invariant ring <tt>P^G</tt>.<br />
WARNING: May not terminate if <tt>P^G</tt> does not have a finite SAGBI basis.<br />
<itemize><br />
<item>@param <tt>G</tt> A list of matrices of size <tt>n</tt> over a ring <tt>P</tt> with <tt>n</tt> indeterminates.</item><br />
<item>@param <tt>d</tt> (optional) An integer describing the truncation degree.</item><br />
<item>@return A list of polynomials that form a (<tt>d</tt>)-truncated SAGBI basis.</item><br />
</itemize><br />
<br />
<!-- Examples here (also only one or more than two possible) --><br />
<!-- It is important to omit any indentation inside the example environment --><br />
<!-- may also go over more lines, but the </example>-tag should not be in a new line --><br />
<example><br />
Use P ::= QQ[x,y,z];<br />
T := matrix(P, [[0,1,0],<br />
[1,0,0],<br />
[0,0,1]]);<br />
C := matrix(P, [[0,1,0],<br />
[0,0,1],<br />
[1,0,0]]);<br />
S3 := [T*T,T,C,T*C,T*C*C,T*C*T];<br />
InvFC0.SAGBI(S3);</example><br />
<example><br />
A := Mat(P, [[0,1,0],<br />
[0,0,1],<br />
[1,0,0]]);<br />
G := [A,A^2,A^3]; // cyclic group generated by A<br />
TruncG := InvFC0.SAGBI(G,7); // has no finite DegRevLex-SAGBI basis</example><br />
</description><br />
<br />
<!-- Add related pages (also more or none possible) --><br />
<seealso><br />
<see>Package invarFC0</see><br />
<see>Package invarFC0/InvFC0.MinGens</see><br />
</seealso><br />
<br />
<!-- Add all data types used in the signature of your function (also more or none possible) --><br />
<types><br />
<type>list</type><br />
<type>poly</type><br />
<type>int</type><br />
<type>mat</type><br />
<type>sagbi</type><br />
</types><br />
<br />
<!-- Add keys here (first three are mandatory, other ones are optional) --><br />
<key>SAGBI</key><br />
<key>InvFC0.SAGBI</key><br />
<key>apcocoa/invFC0.SAGBI</key><br />
<br />
<wiki-category>Package invarFC0</wiki-category><br />
<br />
</command></div>
Andraschko