http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:NCo.PrefixInterreduction&feed=atom&action=history
ApCoCoA-1:NCo.PrefixInterreduction - Revision history
2024-03-29T10:46:54Z
Revision history for this page on the wiki
MediaWiki 1.35.0
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:NCo.PrefixInterreduction&diff=16150&oldid=prev
AndraschkoBot: replaced <quotes> tag by real quotes
2020-10-29T13:43:57Z
<p>replaced <quotes> tag by real quotes</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 13:43, 29 October 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13" >Line 13:</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>Please set ring environment coefficient field <tt> K</tt>, alphabet (or set of indeterminates) <tt>X</tt>, rewrite relations <tt>Relations</tt> and word ordering <tt>Ordering</tt> through the functions <ref>ApCoCoA-1:NCo.SetFp|NCo.SetFp</ref>, <ref>ApCoCoA-1:NCo.SetX|NCo.SetX</ref>, <ref>ApCoCoA-1:NCo.SetRelations|NCo.SetRelations</ref> and <ref>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</ref>, respectively, before using this function. The default coefficient field is the field of rational numbers, i.e. RAT in CoCoAL, and the default ordering is the length-lexicographic ordering <del class="diffchange diffchange-inline"><quotes></del>LLEX<del class="diffchange diffchange-inline"></quotes></del>. For more information, please check the relevant functions.</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>Please set ring environment coefficient field <tt> K</tt>, alphabet (or set of indeterminates) <tt>X</tt>, rewrite relations <tt>Relations</tt> and word ordering <tt>Ordering</tt> through the functions <ref>ApCoCoA-1:NCo.SetFp|NCo.SetFp</ref>, <ref>ApCoCoA-1:NCo.SetX|NCo.SetX</ref>, <ref>ApCoCoA-1:NCo.SetRelations|NCo.SetRelations</ref> and <ref>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</ref>, respectively, before using this function. The default coefficient field is the field of rational numbers, i.e. RAT in CoCoAL, and the default ordering is the length-lexicographic ordering <ins class="diffchange diffchange-inline">"</ins>LLEX<ins class="diffchange diffchange-inline">"</ins>. For more information, please check the relevant functions.</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>G:</em> a LIST of non-zero polynomials in the monoid ring. Each polynomial is represented as a LIST of LISTs, i.e. as <tt>[[C1,W1],...,[Cs,Ws]]</tt> where, for each i, Wi is a term represented as a STRING and Ci is the coefficient of Wi. For example, polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,<del class="diffchange diffchange-inline"><quotes></del>xy<del class="diffchange diffchange-inline"></quotes></del>], [-1, <del class="diffchange diffchange-inline"><quotes></del>y<del class="diffchange diffchange-inline"></quotes></del>], [1,<del class="diffchange diffchange-inline"><quotes></quotes></del>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</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>G:</em> a LIST of non-zero polynomials in the monoid ring. Each polynomial is represented as a LIST of LISTs, i.e. as <tt>[[C1,W1],...,[Cs,Ws]]</tt> where, for each i, Wi is a term represented as a STRING and Ci is the coefficient of Wi. For example, polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,<ins class="diffchange diffchange-inline">"</ins>xy<ins class="diffchange diffchange-inline">"</ins>], [-1, <ins class="diffchange diffchange-inline">"</ins>y<ins class="diffchange diffchange-inline">"</ins>], [1,<ins class="diffchange diffchange-inline">""</ins>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</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;"></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><item>@return: a LIST of prefix interreduced polynomials.</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 LIST of prefix interreduced polynomials.</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><example></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><example></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>NCo.SetX(<del class="diffchange diffchange-inline"><quotes></del>abc<del class="diffchange diffchange-inline"></quotes></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>NCo.SetX(<ins class="diffchange diffchange-inline">"</ins>abc<ins class="diffchange diffchange-inline">"</ins>);</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>NCo.SetOrdering(<del class="diffchange diffchange-inline"><quotes></del>LLEX<del class="diffchange diffchange-inline"></quotes></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>NCo.SetOrdering(<ins class="diffchange diffchange-inline">"</ins>LLEX<ins class="diffchange diffchange-inline">"</ins>);</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>NCo.SetRelations([[<del class="diffchange diffchange-inline"><quotes></del>aa<del class="diffchange diffchange-inline"></quotes></del>,<del class="diffchange diffchange-inline"><quotes></quotes></del>], [<del class="diffchange diffchange-inline"><quotes></del>bb<del class="diffchange diffchange-inline"></quotes></del>,<del class="diffchange diffchange-inline"><quotes></quotes></del>], [<del class="diffchange diffchange-inline"><quotes></del>ab<del class="diffchange diffchange-inline"></quotes></del>,<del class="diffchange diffchange-inline"><quotes></del>c<del class="diffchange diffchange-inline"></quotes></del>], [<del class="diffchange diffchange-inline"><quotes></del>ac<del class="diffchange diffchange-inline"></quotes></del>, <del class="diffchange diffchange-inline"><quotes></del>b<del class="diffchange diffchange-inline"></quotes></del>], [<del class="diffchange diffchange-inline"><quotes></del>cb<del class="diffchange diffchange-inline"></quotes></del>, <del class="diffchange diffchange-inline"><quotes></del>a<del class="diffchange diffchange-inline"></quotes></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>NCo.SetRelations([[<ins class="diffchange diffchange-inline">"</ins>aa<ins class="diffchange diffchange-inline">"</ins>,<ins class="diffchange diffchange-inline">""</ins>], [<ins class="diffchange diffchange-inline">"</ins>bb<ins class="diffchange diffchange-inline">"</ins>,<ins class="diffchange diffchange-inline">""</ins>], [<ins class="diffchange diffchange-inline">"</ins>ab<ins class="diffchange diffchange-inline">"</ins>,<ins class="diffchange diffchange-inline">"</ins>c<ins class="diffchange diffchange-inline">"</ins>], [<ins class="diffchange diffchange-inline">"</ins>ac<ins class="diffchange diffchange-inline">"</ins>, <ins class="diffchange diffchange-inline">"</ins>b<ins class="diffchange diffchange-inline">"</ins>], [<ins class="diffchange diffchange-inline">"</ins>cb<ins class="diffchange diffchange-inline">"</ins>, <ins class="diffchange diffchange-inline">"</ins>a<ins class="diffchange diffchange-inline">"</ins>]]);</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>G:=[[[1,<del class="diffchange diffchange-inline"><quotes></del>b<del class="diffchange diffchange-inline"></quotes></del>],[1,<del class="diffchange diffchange-inline"><quotes></quotes></del>]], [[1,<del class="diffchange diffchange-inline"><quotes></del>c<del class="diffchange diffchange-inline"></quotes></del>]],[[1,<del class="diffchange diffchange-inline"><quotes></del>ba<del class="diffchange diffchange-inline"></quotes></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>G:=[[[1,<ins class="diffchange diffchange-inline">"</ins>b<ins class="diffchange diffchange-inline">"</ins>],[1,<ins class="diffchange diffchange-inline">""</ins>]], [[1,<ins class="diffchange diffchange-inline">"</ins>c<ins class="diffchange diffchange-inline">"</ins>]],[[1,<ins class="diffchange diffchange-inline">"</ins>ba<ins class="diffchange diffchange-inline">"</ins>]]];</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>NCo.PrefixInterreduction(G);</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>NCo.PrefixInterreduction(G);</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>[[[1, <del class="diffchange diffchange-inline"><quotes></del>b<del class="diffchange diffchange-inline"></quotes></del>], [1, <del class="diffchange diffchange-inline"><quotes></quotes></del>]], [[1, <del class="diffchange diffchange-inline"><quotes></del>c<del class="diffchange diffchange-inline"></quotes></del>]], [[1, <del class="diffchange diffchange-inline"><quotes></del>a<del class="diffchange diffchange-inline"></quotes></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>[[[1, <ins class="diffchange diffchange-inline">"</ins>b<ins class="diffchange diffchange-inline">"</ins>], [1, <ins class="diffchange diffchange-inline">""</ins>]], [[1, <ins class="diffchange diffchange-inline">"</ins>c<ins class="diffchange diffchange-inline">"</ins>]], [[1, <ins class="diffchange diffchange-inline">"</ins>a<ins class="diffchange diffchange-inline">"</ins>]]]</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>-------------------------------</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>-------------------------------</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></example></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></example></div></td></tr>
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AndraschkoBot
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:NCo.PrefixInterreduction&diff=15607&oldid=prev
AndraschkoBot: insert version info
2020-10-07T10:24:13Z
<p>insert version info</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:24, 7 October 2020</td>
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<tr><td colspan="2"> </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><ins style="font-weight: bold; text-decoration: none;">{{Version|1}}</ins></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>
<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>NCo.PrefixInterreduction</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>NCo.PrefixInterreduction</title></div></td></tr>
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AndraschkoBot
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:NCo.PrefixInterreduction&diff=15243&oldid=prev
AndraschkoBot: fixed links to namespace ApCoCoA
2020-10-07T08:33:17Z
<p>fixed links to namespace ApCoCoA</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 08:33, 7 October 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12" >Line 12:</td>
<td colspan="2" class="diff-lineno">Line 12:</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><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>Please set ring environment coefficient field <tt> K</tt>, alphabet (or set of indeterminates) <tt>X</tt>, rewrite relations <tt>Relations</tt> and word ordering <tt>Ordering</tt> through the functions <ref>NCo.SetFp</ref>, <ref>NCo.SetX</ref>, <ref>NCo.SetRelations</ref> and <ref>NCo.SetOrdering</ref>, respectively, before using this function. The default coefficient field is the field of rational numbers, i.e. RAT in CoCoAL, and the default ordering is the length-lexicographic ordering <quotes>LLEX</quotes>. For more information, please check the relevant functions.</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>Please set ring environment coefficient field <tt> K</tt>, alphabet (or set of indeterminates) <tt>X</tt>, rewrite relations <tt>Relations</tt> and word ordering <tt>Ordering</tt> through the functions <ref><ins class="diffchange diffchange-inline">ApCoCoA-1:NCo.SetFp|</ins>NCo.SetFp</ref>, <ref><ins class="diffchange diffchange-inline">ApCoCoA-1:NCo.SetX|</ins>NCo.SetX</ref>, <ref><ins class="diffchange diffchange-inline">ApCoCoA-1:NCo.SetRelations|</ins>NCo.SetRelations</ref> and <ref><ins class="diffchange diffchange-inline">ApCoCoA-1:NCo.SetOrdering|</ins>NCo.SetOrdering</ref>, respectively, before using this function. The default coefficient field is the field of rational numbers, i.e. RAT in CoCoAL, and the default ordering is the length-lexicographic ordering <quotes>LLEX</quotes>. For more information, please check the relevant functions.</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><item>@param <em>G:</em> a LIST of non-zero polynomials in the monoid ring. Each polynomial is represented as a LIST of LISTs, i.e. as <tt>[[C1,W1],...,[Cs,Ws]]</tt> where, for each i, Wi is a term represented as a STRING and Ci is the coefficient of Wi. For example, polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</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>G:</em> a LIST of non-zero polynomials in the monoid ring. Each polynomial is represented as a LIST of LISTs, i.e. as <tt>[[C1,W1],...,[Cs,Ws]]</tt> where, for each i, Wi is a term represented as a STRING and Ci is the coefficient of Wi. For example, polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item></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></description></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></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><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>NCo.PrefixGB</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:NCo.PrefixGB|</ins>NCo.PrefixGB</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>NCo.PrefixNR</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:NCo.PrefixNR|</ins>NCo.PrefixNR</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>NCo.PrefixReducedGB</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:NCo.PrefixReducedGB|</ins>NCo.PrefixReducedGB</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>NCo.PrefixSaturation</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:NCo.PrefixSaturation|</ins>NCo.PrefixSaturation</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>NCo.SetFp</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:NCo.SetFp|</ins>NCo.SetFp</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>NCo.SetOrdering</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:NCo.SetOrdering|</ins>NCo.SetOrdering</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>NCo.SetRelations</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:NCo.SetRelations|</ins>NCo.SetRelations</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>NCo.SetX</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:NCo.SetX|</ins>NCo.SetX</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="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
2020-10-02T16:30:22Z
<p>Bot: Category moved</p>
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<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><wiki-category>Package_gbmr</wiki-category></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><wiki-category><ins class="diffchange diffchange-inline">ApCoCoA-1:</ins>Package_gbmr</wiki-category></div></td></tr>
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AndraschkoBot
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Stadler at 20:04, 14 May 2013
2013-05-14T20:04:42Z
<p></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
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</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3" >Line 3:</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><short_description></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><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>Prefix interreduction of a LIST of polynomials in a finitely presented monoid ring.</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>Prefix interreduction of a LIST of polynomials in a finitely presented monoid ring.</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;"><par/></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;">Let <tt>P=K&lt;X|R&gt;</tt> be a finitely presented monoid ring. A subset set <tt>G</tt> of non-zero polynomials in <tt>P</tt> is said to be <em>prefix interreduced</em> if no element of Supp(g) is a multiply of the leading word of any element in <tt>R</tt>, and if no element of Supp(g) contains the leading word of any elements in <tt>{G\{g}}</tt> as a prefix.</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></short_description></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></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>
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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></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><description></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><description></div></td></tr>
<tr><td colspan="2"> </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><ins style="font-weight: bold; text-decoration: none;">Let <tt>P=K&lt;X|R&gt;</tt> be a finitely presented monoid ring. A subset set <tt>G</tt> of non-zero polynomials in <tt>P</tt> is said to be <em>prefix interreduced</em> if no element of Supp(g) is a multiply of the leading word of any element in <tt>R</tt>, and if no element of Supp(g) contains the leading word of any elements in <tt>{G\{g}}</tt> as a prefix.</ins></div></td></tr>
<tr><td colspan="2"> </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><ins style="font-weight: bold; text-decoration: none;"><par/></ins></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><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>
</table>
Stadler
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:NCo.PrefixInterreduction&diff=13291&oldid=prev
Xiu at 18:45, 1 May 2013
2013-05-01T18:45:37Z
<p></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 18:45, 1 May 2013</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><see>NCo.PrefixReducedGB</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>NCo.PrefixReducedGB</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>NCo.PrefixSaturation</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>NCo.PrefixSaturation</see></div></td></tr>
<tr><td colspan="2"> </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><ins style="font-weight: bold; text-decoration: none;"><see>NCo.SetFp</see></ins></div></td></tr>
<tr><td colspan="2"> </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><ins style="font-weight: bold; text-decoration: none;"><see>NCo.SetOrdering</see></ins></div></td></tr>
<tr><td colspan="2"> </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><ins style="font-weight: bold; text-decoration: none;"><see>NCo.SetRelations</see></ins></div></td></tr>
<tr><td colspan="2"> </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><ins style="font-weight: bold; text-decoration: none;"><see>NCo.SetX</see></ins></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>Introduction to CoCoAServer</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>Introduction to CoCoAServer</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>
</table>
Xiu
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:NCo.PrefixInterreduction&diff=13285&oldid=prev
Xiu: New page: <command> <title>NCo.PrefixInterreduction</title> <short_description> Prefix interreduction of a LIST of polynomials in a finitely presented monoid ring. <par/> Let <tt>P=K<X|R></tt>...
2013-05-01T17:36:23Z
<p>New page: <command> <title>NCo.PrefixInterreduction</title> <short_description> Prefix interreduction of a LIST of polynomials in a finitely presented monoid ring. <par/> Let <tt>P=K<X|R></tt>...</p>
<p><b>New page</b></p><div><command><br />
<title>NCo.PrefixInterreduction</title><br />
<short_description><br />
Prefix interreduction of a LIST of polynomials in a finitely presented monoid ring.<br />
<par/><br />
Let <tt>P=K&lt;X|R&gt;</tt> be a finitely presented monoid ring. A subset set <tt>G</tt> of non-zero polynomials in <tt>P</tt> is said to be <em>prefix interreduced</em> if no element of Supp(g) is a multiply of the leading word of any element in <tt>R</tt>, and if no element of Supp(g) contains the leading word of any elements in <tt>{G\{g}}</tt> as a prefix.<br />
</short_description><br />
<syntax><br />
NCo.PrefixInterreduction(G: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 />
<par/><br />
Please set ring environment coefficient field <tt> K</tt>, alphabet (or set of indeterminates) <tt>X</tt>, rewrite relations <tt>Relations</tt> and word ordering <tt>Ordering</tt> through the functions <ref>NCo.SetFp</ref>, <ref>NCo.SetX</ref>, <ref>NCo.SetRelations</ref> and <ref>NCo.SetOrdering</ref>, respectively, before using this function. The default coefficient field is the field of rational numbers, i.e. RAT in CoCoAL, and the default ordering is the length-lexicographic ordering <quotes>LLEX</quotes>. For more information, please check the relevant functions.<br />
<itemize><br />
<item>@param <em>G:</em> a LIST of non-zero polynomials in the monoid ring. Each polynomial is represented as a LIST of LISTs, i.e. as <tt>[[C1,W1],...,[Cs,Ws]]</tt> where, for each i, Wi is a term represented as a STRING and Ci is the coefficient of Wi. For example, polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item><br />
<br />
<item>@return: a LIST of prefix interreduced polynomials.</item><br />
</itemize><br />
<example><br />
NCo.SetX(<quotes>abc</quotes>);<br />
NCo.SetOrdering(<quotes>LLEX</quotes>);<br />
NCo.SetRelations([[<quotes>aa</quotes>,<quotes></quotes>], [<quotes>bb</quotes>,<quotes></quotes>], [<quotes>ab</quotes>,<quotes>c</quotes>], [<quotes>ac</quotes>, <quotes>b</quotes>], [<quotes>cb</quotes>, <quotes>a</quotes>]]);<br />
G:=[[[1,<quotes>b</quotes>],[1,<quotes></quotes>]], [[1,<quotes>c</quotes>]],[[1,<quotes>ba</quotes>]]];<br />
NCo.PrefixInterreduction(G);<br />
<br />
[[[1, <quotes>b</quotes>], [1, <quotes></quotes>]], [[1, <quotes>c</quotes>]], [[1, <quotes>a</quotes>]]]<br />
-------------------------------<br />
</example><br />
</description><br />
<seealso><br />
<see>NCo.PrefixGB</see><br />
<see>NCo.PrefixNR</see><br />
<see>NCo.PrefixReducedGB</see><br />
<see>NCo.PrefixSaturation</see><br />
<see>Introduction to CoCoAServer</see><br />
</seealso><br />
<types><br />
<type>apcocoaserver</type><br />
<type>polynomial</type><br />
<type>non_commutative</type><br />
</types><br />
<key>gbmr.PrefixInterreduction</key><br />
<key>NCo.PrefixInterreduction</key><br />
<key>PrefixInterreduction</key><br />
<wiki-category>Package_gbmr</wiki-category><br />
</command></div>
Xiu