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ApCoCoA-1:LinAlg.Solve - Revision history
2024-03-29T05:57:19Z
Revision history for this page on the wiki
MediaWiki 1.35.0
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AndraschkoBot: replaced <quotes> tag by real quotes
2020-10-29T13:33:16Z
<p>replaced <quotes> tag by real quotes</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:33, 29 October 2020</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 <em>M</em> A matrix with components either of type INT, ZMOD or RAT.</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 <em>M</em> A matrix with components either of type INT, ZMOD or RAT.</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 <em>B</em> A matrix with components either of type INT, ZMOD or RAT.</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 <em>B</em> A matrix with components either of type INT, ZMOD or RAT.</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>@param <em>BACKEND</em> Either the string <del class="diffchange diffchange-inline"><quotes></del>IML<del class="diffchange diffchange-inline"></quotes> </del>or <del class="diffchange diffchange-inline"><quotes></del>LINBOX<del class="diffchange diffchange-inline"></quotes></del>.</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>@param <em>BACKEND</em> Either the string <ins class="diffchange diffchange-inline">"</ins>IML<ins class="diffchange diffchange-inline">" </ins>or <ins class="diffchange diffchange-inline">"</ins>LINBOX<ins class="diffchange diffchange-inline">"</ins>.</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>@return A matrix X representing a solution vector of the linear equation system M*X = B if a solution exists or the empty matrix otherwise.</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>@return A matrix X representing a solution vector of the linear equation system M*X = B if a solution exists or the empty matrix otherwise.</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>
<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>The following parameter is optional.</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>The following parameter is optional.</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>
<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>@param <em>METHOD</em> A string specifying the solution method to use. Available methods are <del class="diffchange diffchange-inline"><quotes></del>Wiedemann<del class="diffchange diffchange-inline"></quotes> </del>and <del class="diffchange diffchange-inline"><quotes></del>BlasElim<del class="diffchange diffchange-inline"></quotes></del>. Please read the detailed description about this parameter, too.</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>@param <em>METHOD</em> A string specifying the solution method to use. Available methods are <ins class="diffchange diffchange-inline">"</ins>Wiedemann<ins class="diffchange diffchange-inline">" </ins>and <ins class="diffchange diffchange-inline">"</ins>BlasElim<ins class="diffchange diffchange-inline">"</ins>. Please read the detailed description about this parameter, too.</item></div></td></tr>
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AndraschkoBot
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AndraschkoBot: insert version info
2020-10-07T10:11:12Z
<p>insert version info</p>
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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><command></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><command></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> <title>LinAlg.Solve</title></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> <title>LinAlg.Solve</title></div></td></tr>
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AndraschkoBot: fixed links to namespace ApCoCoA
2020-10-07T08:20:26Z
<p>fixed links to namespace ApCoCoA</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:20, 7 October 2020</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><em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.</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><em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.</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><par/></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><par/></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>Let <tt>M</tt> and <tt>B</tt> be matrices defined over the ring of integers, a finite field or the field of rationals. This function tries to solve the linear equation system <tt>M*X = B</tt> by using the ApCoCoAServer supported by the IML or LinBox library (depending on the value of parameter <tt>BACKEND</tt>). Possible values for <tt>BACKEND</tt> are <tt>IML</tt> and <tt>LINBOX</tt>. If <tt>BACKEND</tt> is set to <tt>LINBOX</tt>, a fourth optional parameter <tt>METHOD</tt> may be specified. Please refer to <ref>LinBox.Solve</ref> for further details about this parameter.</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>Let <tt>M</tt> and <tt>B</tt> be matrices defined over the ring of integers, a finite field or the field of rationals. This function tries to solve the linear equation system <tt>M*X = B</tt> by using the ApCoCoAServer supported by the IML or LinBox library (depending on the value of parameter <tt>BACKEND</tt>). Possible values for <tt>BACKEND</tt> are <tt>IML</tt> and <tt>LINBOX</tt>. If <tt>BACKEND</tt> is set to <tt>LINBOX</tt>, a fourth optional parameter <tt>METHOD</tt> may be specified. Please refer to <ref><ins class="diffchange diffchange-inline">ApCoCoA-1:LinBox.Solve|</ins>LinBox.Solve</ref> for further details about this parameter.</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><par/></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><par/></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>The return value will be a solution vector of the linear equation system or an empty matrix if no solution has been found.</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>The return value will be a solution vector of the linear equation system or an empty matrix if no solution has been found.</div></td></tr>
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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;"></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;"></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> <see>Introduction to CoCoAServer</see></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> <see><ins class="diffchange diffchange-inline">ApCoCoA-1:Introduction to CoCoAServer|</ins>Introduction to CoCoAServer</see></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> <see>IML.Solve</see></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> <see><ins class="diffchange diffchange-inline">ApCoCoA-1:IML.Solve|</ins>IML.Solve</see></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> <see>LinBox.Solve</see></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> <see><ins class="diffchange diffchange-inline">ApCoCoA-1:LinBox.Solve|</ins>LinBox.Solve</see></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> <see>LinKer</see></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> <see><ins class="diffchange diffchange-inline">ApCoCoA-1:LinKer|</ins>LinKer</see></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> <types></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> <types></div></td></tr>
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AndraschkoBot: Bot: Category moved
2020-10-02T16:17:22Z
<p>Bot: Category moved</p>
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AndraschkoBot
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:LinAlg.Solve&diff=11334&oldid=prev
Skaspar: Initial version.
2010-11-19T18:07:27Z
<p>Initial version.</p>
<p><b>New page</b></p><div><command><br />
<title>LinAlg.Solve</title><br />
<short_description>Solves a system of linear equations.</short_description><br />
<br />
<syntax><br />
LinAlg.Solve(M:MAT, B:MAT, BACKEND:STRING):MAT<br />
LinAlg.Solve(M:MAT, B:MAT, BACKEND:STRING, METHOD:STRING):MAT<br />
</syntax><br />
<description><br />
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.<br />
<par/><br />
Let <tt>M</tt> and <tt>B</tt> be matrices defined over the ring of integers, a finite field or the field of rationals. This function tries to solve the linear equation system <tt>M*X = B</tt> by using the ApCoCoAServer supported by the IML or LinBox library (depending on the value of parameter <tt>BACKEND</tt>). Possible values for <tt>BACKEND</tt> are <tt>IML</tt> and <tt>LINBOX</tt>. If <tt>BACKEND</tt> is set to <tt>LINBOX</tt>, a fourth optional parameter <tt>METHOD</tt> may be specified. Please refer to <ref>LinBox.Solve</ref> for further details about this parameter.<br />
<par/><br />
The return value will be a solution vector of the linear equation system or an empty matrix if no solution has been found.<br />
<itemize><br />
<item>@param <em>M</em> A matrix with components either of type INT, ZMOD or RAT.</item><br />
<item>@param <em>B</em> A matrix with components either of type INT, ZMOD or RAT.</item><br />
<item>@param <em>BACKEND</em> Either the string <quotes>IML</quotes> or <quotes>LINBOX</quotes>.</item><br />
<item>@return A matrix X representing a solution vector of the linear equation system M*X = B if a solution exists or the empty matrix otherwise.</item><br />
</itemize><br />
The following parameter is optional.<br />
<itemize><br />
<item>@param <em>METHOD</em> A string specifying the solution method to use. Available methods are <quotes>Wiedemann</quotes> and <quotes>BlasElim</quotes>. Please read the detailed description about this parameter, too.</item><br />
</itemize><br />
<example><br />
Use ZZ/(19)[x];<br />
M := BringIn(Mat([[1,3,4], [0,2,1]]));<br />
B := BringIn(Mat([[1], [2]]));<br />
LinAlg.Solve(M, B, "IML");<br />
<br />
-------------------------------<br />
Mat([<br />
[-2 % 19],<br />
[1 % 19],<br />
[0 % 19]<br />
])<br />
-------------------------------<br />
</example><br />
<example><br />
Use QQ[x];<br />
M := Mat([ [1,3,4], [0,2,1], [1,3,4] ]);<br />
B := Mat([ [1], [2], [0] ]);<br />
LinAlg.Solve(M, B, "IML");<br />
<br />
-------------------------------<br />
Mat([<br />
[ ]<br />
])<br />
-------------------------------<br />
</example><br />
</description><br />
<br />
<see>Introduction to CoCoAServer</see><br />
<see>IML.Solve</see><br />
<see>LinBox.Solve</see><br />
<see>LinKer</see><br />
<types><br />
<type>matrix</type><br />
<type>apcocoaserver</type><br />
</types><br />
<key>Solve</key><br />
<key>LinAlg.Solve</key><br />
<key>linalg.Solve</key><br />
<key>solve linear equation system</key><br />
<key>solve linear equation</key><br />
<wiki-category>Package_linalg</wiki-category><br />
</command></div>
Skaspar