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ApCoCoA-1:CharP.MNLASolve - Revision history
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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><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>This function computes the unique zero in <tt>F_2^n</tt> of a polynomial system over <tt>F_2 </tt>. It uses Mutant NLA-Algorithm to find the unique zero. The Mutant NLA-Algorithm generates a sequence of linear systems to solve the given system. The Mutant NLA-Algorithm can find the unique zero only. If the given polynomial system has more than one zeros in <tt>F_2^n </tt> then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound. In fact Mutant NLA-Algorithm is the NLA-Algorithm with mutant strategy. It uses <ref>LinAlg.EF</ref> for gaussian elimination.</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>This function computes the unique zero in <tt>F_2^n</tt> of a polynomial system over <tt>F_2 </tt>. It uses Mutant NLA-Algorithm to find the unique zero. The Mutant NLA-Algorithm generates a sequence of linear systems to solve the given system. The Mutant NLA-Algorithm can find the unique zero only. If the given polynomial system has more than one zeros in <tt>F_2^n </tt> then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound. In fact Mutant NLA-Algorithm is the NLA-Algorithm with mutant strategy. It uses <ref><ins class="diffchange diffchange-inline">ApCoCoA-1:LinAlg.EF|</ins>LinAlg.EF</ref> for gaussian elimination.</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;"><div> <seealso></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> <seealso></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>CharP.MXLSolve</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:CharP.MXLSolve|</ins>CharP.MXLSolve</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>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>Introduction to Groebner Basis in CoCoA</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 Groebner Basis in CoCoA|</ins>Introduction to Groebner Basis in CoCoA</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>CharP.GBasisF2</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:CharP.GBasisF2|</ins>CharP.GBasisF2</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>CharP.XLSolve</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:CharP.XLSolve|</ins>CharP.XLSolve</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>CharP.IMXLSolve</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:CharP.IMXLSolve|</ins>CharP.IMXLSolve</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>CharP.IMNLASolve</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:CharP.IMNLASolve|</ins>CharP.IMNLASolve</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> </seealso></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> </seealso></div></td></tr>
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AndraschkoBot: Bot: Category moved
2020-10-02T16:03:11Z
<p>Bot: Category moved</p>
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132.231.10.53 at 11:28, 28 April 2011
2011-04-28T11:28:21Z
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132.231.10.53 at 11:24, 28 April 2011
2011-04-28T11:24:51Z
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132.231.10.53
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Stadler at 14:23, 14 December 2010
2010-12-14T14:23:35Z
<p></p>
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Stadler
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Stadler at 14:15, 14 December 2010
2010-12-14T14:15:19Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:15, 14 December 2010</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</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><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="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> <title>CharP.<del class="diffchange diffchange-inline">GBasisF2</del></title></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> <title>CharP.<ins class="diffchange diffchange-inline">MNLASolve</ins></title></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> <short_description><del class="diffchange diffchange-inline">Computing </del>the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description></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> <short_description><ins class="diffchange diffchange-inline">Computes </ins>the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description></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><syntax></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><syntax></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>CharP.MNLASolve(F:LIST):LIST</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>CharP.MNLASolve(F:LIST):LIST</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l9" >Line 9:</td>
<td colspan="2" class="diff-lineno">Line 9:</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;"></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="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>This function computes the unique zero in <tt>F_2^n</tt> of a polynomial system over <tt>F_2 </tt>. It uses Mutant NLA<del class="diffchange diffchange-inline"><tt></del>-<del class="diffchange diffchange-inline"></tt></del>Algorithm to find the unique zero. The Mutant NLA<del class="diffchange diffchange-inline"><tt></del>-<del class="diffchange diffchange-inline"></tt></del>Algorithm generates a sequence of linear systems to solve the given system. The Mutant NLA<del class="diffchange diffchange-inline"><tt></del>-<del class="diffchange diffchange-inline"></tt></del>Algorithm can find the unique zero only. If the given polynomial system has more than one zeros in <tt>F_2^n </tt> then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound. In fact Mutant NLA<del class="diffchange diffchange-inline"><tt></del>-<del class="diffchange diffchange-inline"></tt></del>Algorithm is the NLA<del class="diffchange diffchange-inline"><tt></del>-<del class="diffchange diffchange-inline"></tt></del>Algorithm with mutant strategy. It uses <ref><del class="diffchange diffchange-inline">linalg</del>.EF</ref> for gaussian elimination.</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>This function computes the unique zero in <tt>F_2^n</tt> of a polynomial system over <tt>F_2 </tt>. It uses Mutant NLA-Algorithm to find the unique zero. The Mutant NLA-Algorithm generates a sequence of linear systems to solve the given system. The Mutant NLA-Algorithm can find the unique zero only. If the given polynomial system has more than one zeros in <tt>F_2^n </tt> then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound. In fact Mutant NLA-Algorithm is the NLA-Algorithm with mutant strategy. It uses <ref><ins class="diffchange diffchange-inline">LinAlg</ins>.EF</ref> for gaussian elimination.</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;"></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="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 colspan="2" class="diff-lineno" id="mw-diff-left-l363" >Line 363:</td>
<td colspan="2" class="diff-lineno">Line 363:</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> <see>CharP.IMXLSolve</see></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> <see>CharP.IMXLSolve</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> <see>CharP.IMNLASolve</see></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> <see>CharP.IMNLASolve</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><del style="font-weight: bold; text-decoration: none;"> </del></div></td><td colspan="2"> </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><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </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><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </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> </seealso></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> </seealso></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;"></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 colspan="2" class="diff-lineno" id="mw-diff-left-l374" >Line 374:</td>
<td colspan="2" class="diff-lineno">Line 371:</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>
<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> <key>charP.<del class="diffchange diffchange-inline">GBasisF2</del></key></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> <key>charP.<ins class="diffchange diffchange-inline">mnlasolve</ins></key></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> <key><del class="diffchange diffchange-inline">GBasisF2</del></key></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> <key><ins class="diffchange diffchange-inline">mnlasolve</ins></key></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> <key>finite field</key></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> <key>finite field</key></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> <wiki-category>Package_charP</wiki-category></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> <wiki-category>Package_charP</wiki-category></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> </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>
</table>
Stadler
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:CharP.MNLASolve&diff=11437&oldid=prev
132.231.10.53 at 11:18, 7 December 2010
2010-12-07T11:18:18Z
<p></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<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 11:18, 7 December 2010</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l363" >Line 363:</td>
<td colspan="2" class="diff-lineno">Line 363:</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> <see>CharP.IMXLSolve</see></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> <see>CharP.IMXLSolve</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> <see>CharP.IMNLASolve</see></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> <see>CharP.IMNLASolve</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> <del class="diffchange diffchange-inline"><see>CharP.MNLASolve</see></del></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> </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;"></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="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>
</table>
132.231.10.53
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:CharP.MNLASolve&diff=11436&oldid=prev
132.231.10.53: New page: <command> <title>CharP.GBasisF2</title> <short_description>Computing the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description> <synt...
2010-12-07T11:14:14Z
<p>New page: <command> <title>CharP.GBasisF2</title> <short_description>Computing the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description> <synt...</p>
<p><b>New page</b></p><div><command><br />
<title>CharP.GBasisF2</title><br />
<short_description>Computing the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description><br />
<syntax><br />
CharP.MNLASolve(F:LIST):LIST<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 />
<br />
<par/><br />
This function computes the unique zero in <tt>F_2^n</tt> of a polynomial system over <tt>F_2 </tt>. It uses Mutant NLA<tt>-</tt>Algorithm to find the unique zero. The Mutant NLA<tt>-</tt>Algorithm generates a sequence of linear systems to solve the given system. The Mutant NLA<tt>-</tt>Algorithm can find the unique zero only. If the given polynomial system has more than one zeros in <tt>F_2^n </tt> then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound. In fact Mutant NLA<tt>-</tt>Algorithm is the NLA<tt>-</tt>Algorithm with mutant strategy. It uses <ref>linalg.EF</ref> for gaussian elimination.<br />
<br />
<br />
<br />
<itemize><br />
<item>@param <em>F:</em> List of polynomials of given system.</item><br />
<item>@return The unique solution of the given system in <tt>F_2^n</tt>. </item><br />
</itemize><br />
<br />
<example><br />
Use Z/(2)[x[1..4]];<br />
F:=[<br />
x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1, <br />
x[1]x[2] + x[1]x[3] + x[1]x[4] + x[3]x[4] + x[2] + x[3] + 1, <br />
x[1]x[2] + x[1]x[3] + x[2]x[3] + x[3]x[4] + x[1] + x[4] + 1, <br />
x[1]x[3] + x[2]x[3] + x[1]x[4] + x[2]x[4] + 1<br />
];<br />
<br />
<br />
-- Then we compute the solution with<br />
CharP.MNLASolve(F);<br />
<br />
-- And we achieve the following information on the screen together with the solution at the end.<br />
----------------------------------------<br />
<br />
Finding Variable: x[4]<br />
The size of Matrix is:<br />
No. of Rows=4<br />
No. of Columns=11<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=4<br />
No. of Columns=11<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=11<br />
No. of Columns=5<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The size of Matrix is:<br />
No. of Rows=11<br />
No. of Columns=5<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The No. of Mutants found = 0<br />
The size of Matrix is:<br />
No. of Rows=8<br />
No. of Columns=11<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=11<br />
No. of Columns=8<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0.015<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The size of Matrix is:<br />
No. of Rows=11<br />
No. of Columns=8<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The No. of Mutants found = 1<br />
The size of Matrix is:<br />
No. of Rows=11<br />
No. of Columns=11<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0.016<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=11<br />
No. of Columns=10<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The size of Matrix is:<br />
No. of Rows=11<br />
No. of Columns=10<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
x[4] = 1<br />
Finding Variable: x[3]<br />
The size of Matrix is:<br />
No. of Rows=4<br />
No. of Columns=7<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=4<br />
No. of Columns=7<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=7<br />
No. of Columns=5<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The size of Matrix is:<br />
No. of Rows=7<br />
No. of Columns=5<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The No. of Mutants found = 0<br />
The size of Matrix is:<br />
No. of Rows=7<br />
No. of Columns=7<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=7<br />
No. of Columns=7<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
x[3] = 0<br />
Finding Variable: x[2]<br />
The size of Matrix is:<br />
No. of Rows=3<br />
No. of Columns=4<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=3<br />
No. of Columns=4<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=4<br />
No. of Columns=4<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The size of Matrix is:<br />
No. of Rows=4<br />
No. of Columns=4<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
x[2] = 1<br />
[0, 1, 0, 1]<br />
<br />
</example><br />
<br />
<br />
<example><br />
Use Z/(2)[x[1..4]];<br />
F:=[ <br />
x[2]x[3] + x[1]x[4] + x[2]x[4] + x[3]x[4] + x[1] + x[2] + x[3] + x[4], <br />
x[2]x[3] + x[2]x[4] + x[3]x[4] + x[2] + x[3] + x[4], <br />
x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[2], <br />
x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[2]<br />
];<br />
<br />
-- Solution is not unique i.e. [0, 1, 1, 1], [0, 0, 0, 0], and [1, 1, 1, 1] are solutions <br />
<br />
-- Then we compute the solution with<br />
CharP.MNLASolve(F);<br />
<br />
-- And we achieve the following information on the screen.<br />
----------------------------------------<br />
<br />
Finding Variable: x[4]<br />
The size of Matrix is:<br />
No. of Rows=4<br />
No. of Columns=9<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=3<br />
No. of Columns=9<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=9<br />
No. of Columns=4<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The size of Matrix is:<br />
No. of Rows=9<br />
No. of Columns=4<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The No. of Mutants found = 0<br />
The size of Matrix is:<br />
No. of Rows=15<br />
No. of Columns=14<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=14<br />
No. of Columns=12<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The size of Matrix is:<br />
No. of Rows=14<br />
No. of Columns=12<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The No. of Mutants found = 4<br />
The size of Matrix is:<br />
No. of Rows=27<br />
No. of Columns=14<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=14<br />
No. of Columns=13<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The size of Matrix is:<br />
No. of Rows=14<br />
No. of Columns=13<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The No. of Mutants found = 0<br />
The size of Matrix is:<br />
No. of Rows=12<br />
No. of Columns=14<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=14<br />
No. of Columns=13<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0.016<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The size of Matrix is:<br />
No. of Rows=14<br />
No. of Columns=13<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The No. of Mutants found = 0<br />
The size of Matrix is:<br />
No. of Rows=19<br />
No. of Columns=15<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=15<br />
No. of Columns=14<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The size of Matrix is:<br />
No. of Rows=15<br />
No. of Columns=14<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The No. of Mutants found = 0<br />
The size of Matrix is:<br />
No. of Rows=14<br />
No. of Columns=15<br />
Appling Gaussian Elimination for finding Mutants...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Compeleted<br />
The size of Matrix is:<br />
No. of Rows=15<br />
No. of Columns=14<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
The size of Matrix is:<br />
No. of Rows=15<br />
No. of Columns=14<br />
Appling Gaussian Elimination to check solution coordinate...<br />
-- CoCoAServer: computing Cpu Time = 0<br />
-------------------------------<br />
Gaussian Elimination Completed.<br />
x[4] = NA<br />
Please Check the uniqueness of solution.<br />
The Given system of polynomials does not<br />
seem to have a unique solution or it has<br />
no solution over the finite field F2.<br />
<br />
<br />
</example><br />
<br />
<br />
</description><br />
<seealso><br />
<see>CharP.MXLSolve</see><br />
<see>Introduction to CoCoAServer</see><br />
<see>Introduction to Groebner Basis in CoCoA</see><br />
<see>CharP.GBasisF2</see><br />
<see>CharP.XLSolve</see><br />
<see>CharP.IMXLSolve</see><br />
<see>CharP.IMNLASolve</see><br />
<see>CharP.MNLASolve</see><br />
<br />
<br />
</seealso><br />
<br />
<types><br />
<type>apcocoaserver</type><br />
<type>ideal</type><br />
<type>groebner</type><br />
</types><br />
<br />
<key>charP.GBasisF2</key><br />
<key>GBasisF2</key><br />
<key>finite field</key><br />
<wiki-category>Package_charP</wiki-category><br />
</command></div>
132.231.10.53