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ApCoCoA-1:NCo.MRLC - Revision history
2024-03-29T07:37:11Z
Revision history for this page on the wiki
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AndraschkoBot: replaced <quotes> tag by real quotes
2020-10-29T13:42:17Z
<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 13:42, 29 October 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l15" >Line 15:</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>X:</em> a finite alphabet (or set of indeterminates). It is of STRING type. Note that every letter in X MUST appear only once.The order of letters in X induces word orderings.</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>X:</em> a finite alphabet (or set of indeterminates). It is of STRING type. Note that every letter in X MUST appear only once.The order of letters in X induces word orderings.</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="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>Ordering:</em> a word ordering induced by the order of letters in X. It is a STRING, which is a shortened-form of the name of corresponding word ordering. Note that <del class="diffchange diffchange-inline"><quotes></del>LLEX<del class="diffchange diffchange-inline"></quotes> </del>(the length-lexicographic ordering), <del class="diffchange diffchange-inline"><quotes></del>ELIM<del class="diffchange diffchange-inline"></quotes> </del>(an elimination ordering) and <del class="diffchange diffchange-inline"><quotes></del>LRLEX<del class="diffchange diffchange-inline"></quotes> </del>(the length-reverse-lexicographic ordering) are supported currently. See <ref>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</ref> for more details.</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>Ordering:</em> a word ordering induced by the order of letters in X. It is a STRING, which is a shortened-form of the name of corresponding word ordering. Note that <ins class="diffchange diffchange-inline">"</ins>LLEX<ins class="diffchange diffchange-inline">" </ins>(the length-lexicographic ordering), <ins class="diffchange diffchange-inline">"</ins>ELIM<ins class="diffchange diffchange-inline">" </ins>(an elimination ordering) and <ins class="diffchange diffchange-inline">"</ins>LRLEX<ins class="diffchange diffchange-inline">" </ins>(the length-reverse-lexicographic ordering) are supported currently. See <ref>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</ref> for more details.</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="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>Relations:</em> a finite set of relations. It is of LIST type. Each element in Relations is of the form [W1, W2], where W1 and W2 are words in <tt>&lt;X&gt;</tt>. Each word is represented as a STRING. For example, the word <tt>xy^2x</tt> is represented as <del class="diffchange diffchange-inline"><quotes></del>xyyx<del class="diffchange diffchange-inline"></quotes></del>, and the identity is represented as the empty string <del class="diffchange diffchange-inline"><quotes></quotes></del>. Thus, the relation <tt>(yx, xy)</tt> is represented as [<del class="diffchange diffchange-inline"><quotes></del>yx<del class="diffchange diffchange-inline"></quotes></del>, <del class="diffchange diffchange-inline"><quotes></del>xy<del class="diffchange diffchange-inline"></quotes></del>], and the set of relations <tt>{(yx, xy),(zx,xz),(zy,yz)}</tt> is represented as [[<del class="diffchange diffchange-inline"><quotes></del>yx<del class="diffchange diffchange-inline"></quotes></del>, <del class="diffchange diffchange-inline"><quotes></del>xy<del class="diffchange diffchange-inline"></quotes></del>],[<del class="diffchange diffchange-inline"><quotes></del>zx<del class="diffchange diffchange-inline"></quotes></del>, <del class="diffchange diffchange-inline"><quotes></del>xz<del class="diffchange diffchange-inline"></quotes></del>],[<del class="diffchange diffchange-inline"><quotes></del>zy<del class="diffchange diffchange-inline"></quotes></del>, <del class="diffchange diffchange-inline"><quotes></del>yz<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>Relations:</em> a finite set of relations. It is of LIST type. Each element in Relations is of the form [W1, W2], where W1 and W2 are words in <tt>&lt;X&gt;</tt>. Each word is represented as a STRING. For example, the word <tt>xy^2x</tt> is represented as <ins class="diffchange diffchange-inline">"</ins>xyyx<ins class="diffchange diffchange-inline">"</ins>, and the identity is represented as the empty string <ins class="diffchange diffchange-inline">""</ins>. Thus, the relation <tt>(yx, xy)</tt> is represented as [<ins class="diffchange diffchange-inline">"</ins>yx<ins class="diffchange diffchange-inline">"</ins>, <ins class="diffchange diffchange-inline">"</ins>xy<ins class="diffchange diffchange-inline">"</ins>], and the set of relations <tt>{(yx, xy),(zx,xz),(zy,yz)}</tt> is represented as [[<ins class="diffchange diffchange-inline">"</ins>yx<ins class="diffchange diffchange-inline">"</ins>, <ins class="diffchange diffchange-inline">"</ins>xy<ins class="diffchange diffchange-inline">"</ins>],[<ins class="diffchange diffchange-inline">"</ins>zx<ins class="diffchange diffchange-inline">"</ins>, <ins class="diffchange diffchange-inline">"</ins>xz<ins class="diffchange diffchange-inline">"</ins>],[<ins class="diffchange diffchange-inline">"</ins>zy<ins class="diffchange diffchange-inline">"</ins>, <ins class="diffchange diffchange-inline">"</ins>yz<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;"></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><item>@param <em>F:</em> a polynomial in the finitely presented monoid ring. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the 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>F:</em> a polynomial in the finitely presented monoid ring. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the 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 INT or RAT which represents the leading coefficient of F with respect to the word ordering Ordering. If F=0, the function returns 0.</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 INT or RAT which represents the leading coefficient of F with respect to the word ordering Ordering. If F=0, the function returns 0.</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>X := <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>X := <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>Ordering := <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>Ordering := <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>Relations := [[<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>Relations := [[<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>F := [[1.1,<del class="diffchange diffchange-inline"><quotes></del>a<del class="diffchange diffchange-inline"></quotes></del>],[2.2,<del class="diffchange diffchange-inline"><quotes></del>abc<del class="diffchange diffchange-inline"></quotes></del>],[3.3,<del class="diffchange diffchange-inline"><quotes></del>cc<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>F := [[1.1,<ins class="diffchange diffchange-inline">"</ins>a<ins class="diffchange diffchange-inline">"</ins>],[2.2,<ins class="diffchange diffchange-inline">"</ins>abc<ins class="diffchange diffchange-inline">"</ins>],[3.3,<ins class="diffchange diffchange-inline">"</ins>cc<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.MRLC(X, Ordering, Relations, F);</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.MRLC(X, Ordering, Relations, F);</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>11/2</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>11/2</div></td></tr>
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AndraschkoBot
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:NCo.MRLC&diff=15597&oldid=prev
AndraschkoBot: insert version info
2020-10-07T10:22:33Z
<p>insert version info</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:22, 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.MRLC</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.MRLC</title></div></td></tr>
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AndraschkoBot
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:NCo.MRLC&diff=15233&oldid=prev
AndraschkoBot: fixed links to namespace ApCoCoA
2020-10-07T08:31:37Z
<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 08:31, 7 October 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l10" >Line 10:</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 coefficient field via the function <ref>NCo.SetFp</ref> (or <ref>NCo.UnsetFp</ref>) before calling this function. The default coefficient field is the field of rational numbers, i.e. RAT in CoCoAL. 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 coefficient field via the function <ref><ins class="diffchange diffchange-inline">ApCoCoA-1:NCo.SetFp|</ins>NCo.SetFp</ref> (or <ref><ins class="diffchange diffchange-inline">ApCoCoA-1:NCo.UnsetFp|</ins>NCo.UnsetFp</ref>) before calling this function. The default coefficient field is the field of rational numbers, i.e. RAT in CoCoAL. 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>X:</em> a finite alphabet (or set of indeterminates). It is of STRING type. Note that every letter in X MUST appear only once.The order of letters in X induces word orderings.</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>X:</em> a finite alphabet (or set of indeterminates). It is of STRING type. Note that every letter in X MUST appear only once.The order of letters in X induces word orderings.</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="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>Ordering:</em> a word ordering induced by the order of letters in X. It is a STRING, which is a shortened-form of the name of corresponding word ordering. Note that <quotes>LLEX</quotes> (the length-lexicographic ordering), <quotes>ELIM</quotes> (an elimination ordering) and <quotes>LRLEX</quotes> (the length-reverse-lexicographic ordering) are supported currently. See <ref>NCo.SetOrdering</ref> for more details.</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>Ordering:</em> a word ordering induced by the order of letters in X. It is a STRING, which is a shortened-form of the name of corresponding word ordering. Note that <quotes>LLEX</quotes> (the length-lexicographic ordering), <quotes>ELIM</quotes> (an elimination ordering) and <quotes>LRLEX</quotes> (the length-reverse-lexicographic ordering) are supported currently. See <ref><ins class="diffchange diffchange-inline">ApCoCoA-1:NCo.SetOrdering|</ins>NCo.SetOrdering</ref> for more details.</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>@param <em>Relations:</em> a finite set of relations. It is of LIST type. Each element in Relations is of the form [W1, W2], where W1 and W2 are words in <tt>&lt;X&gt;</tt>. Each word is represented as a STRING. For example, the word <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, and the identity is represented as the empty string <quotes></quotes>. Thus, the relation <tt>(yx, xy)</tt> is represented as [<quotes>yx</quotes>, <quotes>xy</quotes>], and the set of relations <tt>{(yx, xy),(zx,xz),(zy,yz)}</tt> is represented as [[<quotes>yx</quotes>, <quotes>xy</quotes>],[<quotes>zx</quotes>, <quotes>xz</quotes>],[<quotes>zy</quotes>, <quotes>yz</quotes>]].</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>Relations:</em> a finite set of relations. It is of LIST type. Each element in Relations is of the form [W1, W2], where W1 and W2 are words in <tt>&lt;X&gt;</tt>. Each word is represented as a STRING. For example, the word <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, and the identity is represented as the empty string <quotes></quotes>. Thus, the relation <tt>(yx, xy)</tt> is represented as [<quotes>yx</quotes>, <quotes>xy</quotes>], and the set of relations <tt>{(yx, xy),(zx,xz),(zy,yz)}</tt> is represented as [[<quotes>yx</quotes>, <quotes>xy</quotes>],[<quotes>zx</quotes>, <quotes>xz</quotes>],[<quotes>zy</quotes>, <quotes>yz</quotes>]].</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.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.UnsetFp</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.UnsetFp|</ins>NCo.UnsetFp</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>
<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>
</table>
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AndraschkoBot: Bot: Category moved
2020-10-02T16:28:42Z
<p>Bot: Category moved</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:28, 2 October 2020</td>
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Xiu: New page: <command> <title>NCo.MRLC</title> <short_description> The leading coefficient of a polynomial in a finitely presented monoid ring. </short_description> <syntax> NCo.MRLC(X:STRING, Ordering...
2013-05-01T14:57:38Z
<p>New page: <command> <title>NCo.MRLC</title> <short_description> The leading coefficient of a polynomial in a finitely presented monoid ring. </short_description> <syntax> NCo.MRLC(X:STRING, Ordering...</p>
<p><b>New page</b></p><div><command><br />
<title>NCo.MRLC</title><br />
<short_description><br />
The leading coefficient of a polynomial in a finitely presented monoid ring.<br />
</short_description><br />
<syntax><br />
NCo.MRLC(X:STRING, Ordering:STRING, Relations:LIST, F:LIST):INT or RAT<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 coefficient field via the function <ref>NCo.SetFp</ref> (or <ref>NCo.UnsetFp</ref>) before calling this function. The default coefficient field is the field of rational numbers, i.e. RAT in CoCoAL. For more information, please check the relevant functions.<br />
<itemize><br />
<item>@param <em>X:</em> a finite alphabet (or set of indeterminates). It is of STRING type. Note that every letter in X MUST appear only once.The order of letters in X induces word orderings.</item><br />
<br />
<item>@param <em>Ordering:</em> a word ordering induced by the order of letters in X. It is a STRING, which is a shortened-form of the name of corresponding word ordering. Note that <quotes>LLEX</quotes> (the length-lexicographic ordering), <quotes>ELIM</quotes> (an elimination ordering) and <quotes>LRLEX</quotes> (the length-reverse-lexicographic ordering) are supported currently. See <ref>NCo.SetOrdering</ref> for more details.</item><br />
<br />
<item>@param <em>Relations:</em> a finite set of relations. It is of LIST type. Each element in Relations is of the form [W1, W2], where W1 and W2 are words in <tt>&lt;X&gt;</tt>. Each word is represented as a STRING. For example, the word <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, and the identity is represented as the empty string <quotes></quotes>. Thus, the relation <tt>(yx, xy)</tt> is represented as [<quotes>yx</quotes>, <quotes>xy</quotes>], and the set of relations <tt>{(yx, xy),(zx,xz),(zy,yz)}</tt> is represented as [[<quotes>yx</quotes>, <quotes>xy</quotes>],[<quotes>zx</quotes>, <quotes>xz</quotes>],[<quotes>zy</quotes>, <quotes>yz</quotes>]].</item><br />
<br />
<item>@param <em>F:</em> a polynomial in the finitely presented monoid ring. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the 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 INT or RAT which represents the leading coefficient of F with respect to the word ordering Ordering. If F=0, the function returns 0.</item><br />
</itemize><br />
<example><br />
X := <quotes>abc</quotes>; <br />
Ordering := <quotes>LLEX</quotes>; <br />
Relations := [[<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 />
F := [[1.1,<quotes>a</quotes>],[2.2,<quotes>abc</quotes>],[3.3,<quotes>cc</quotes>]]; <br />
NCo.MRLC(X, Ordering, Relations, F);<br />
11/2<br />
-------------------------------<br />
NCo.MRLC(X, Ordering, Relations, []);<br />
0<br />
-------------------------------<br />
</example><br />
</description><br />
<seealso><br />
<see>NCo.SetFp</see><br />
<see>NCo.SetOrdering</see><br />
<see>NCo.UnsetFp</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.MRLC</key><br />
<key>NCo.MRLC</key><br />
<key>MRLC</key><br />
<wiki-category>Package_gbmr</wiki-category><br />
</command></div>
Xiu