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ApCoCoA-1:Weyl.Inw - Revision history
2024-03-29T10:18:59Z
Revision history for this page on the wiki
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AndraschkoBot: insert version info
2020-10-07T10:35:33Z
<p>insert version info</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:35, 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><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>Weyl.Inw</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>Weyl.Inw</title></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><short_description>Computes the initial form of a polynomial in Weyl algebra <tt>A_n</tt> with respect to the weight vector <tt>W=(u_i,v_i)</tt>.</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>Computes the initial form of a polynomial in Weyl algebra <tt>A_n</tt> with respect to the weight vector <tt>W=(u_i,v_i)</tt>.</short_description></div></td></tr>
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AndraschkoBot
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:Weyl.Inw&diff=15303&oldid=prev
AndraschkoBot: fixed links to namespace ApCoCoA
2020-10-07T08:43:18Z
<p>fixed links to namespace ApCoCoA</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:43, 7 October 2020</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <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>Weyl.InIw</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:Weyl.InIw|</ins>Weyl.InIw</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>Weyl.WNormalForm</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:Weyl.WNormalForm|</ins>Weyl.WNormalForm</see></div></td></tr>
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AndraschkoBot
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AndraschkoBot: Bot: Category moved
2020-10-02T16:41:13Z
<p>Bot: Category moved</p>
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AndraschkoBot
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:Weyl.Inw&diff=9846&oldid=prev
Stadler at 13:22, 10 July 2009
2009-07-10T13:22:40Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:22, 10 July 2009</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><title>Weyl.Inw</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>Weyl.Inw</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>Computes the initial form of a polynomial in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i).</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>Computes the initial form of a polynomial in Weyl algebra <ins class="diffchange diffchange-inline"><tt></ins>A_n<ins class="diffchange diffchange-inline"></tt> </ins>with respect to the weight vector <ins class="diffchange diffchange-inline"><tt></ins>W=(u_i,v_i)<ins class="diffchange diffchange-inline"></tt></ins>.</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>Weyl.Inw(P:POLY,W:LIST):POLY</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>Weyl.Inw(P:POLY,W:LIST):POLY</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><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>Computes the initial form of a normally ordered Weyl polynomial P in the Weyl algebra D with respect to weight vector W=(u,v) such that u+v<del class="diffchange diffchange-inline">></del>=0. Here u=(u1,...,un) and v=(v1,...,vn) are weights of indeterminates [x1,...,xn] and [y1,...,yn] respectively. Note that Inw(P,W) is a <del class="diffchange diffchange-inline">polynomail </del>in the graded ring of D with <del class="diffchange diffchange-inline">respet </del>to weight vector W.</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>Computes the initial form of a normally ordered Weyl polynomial P in the Weyl algebra D with respect to weight vector <ins class="diffchange diffchange-inline"><tt></ins>W=(u,v)<ins class="diffchange diffchange-inline"></tt> </ins>such that <ins class="diffchange diffchange-inline"><tt></ins>u+v <ins class="diffchange diffchange-inline">&gt;</ins>= 0<ins class="diffchange diffchange-inline"></tt></ins>. Here <ins class="diffchange diffchange-inline"><tt></ins>u=(u1,...,un)<ins class="diffchange diffchange-inline"></tt> </ins>and <ins class="diffchange diffchange-inline"><tt></ins>v=(v1,...,vn)<ins class="diffchange diffchange-inline"></tt> </ins>are weights of indeterminates <ins class="diffchange diffchange-inline"><tt></ins>[x1,...,xn]<ins class="diffchange diffchange-inline"></tt> </ins>and <ins class="diffchange diffchange-inline"><tt></ins>[y1,...,yn]<ins class="diffchange diffchange-inline"></tt> </ins>respectively. Note that <ins class="diffchange diffchange-inline"><tt></ins>Inw(P,W)<ins class="diffchange diffchange-inline"></tt> </ins>is a <ins class="diffchange diffchange-inline">polynomial </ins>in the graded ring of D with <ins class="diffchange diffchange-inline">respect </ins>to weight vector <ins class="diffchange diffchange-inline"><tt></ins>W<ins class="diffchange diffchange-inline"></tt></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><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>P</em> A polynomial in the Weyl algebra.</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>P</em> A polynomial in the Weyl algebra.</item></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><item>@param <em>W</em> A list of n positive integers, where n = number of indeterminates.</item></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><item>@param <em>W</em> A list of n positive integers, where n = number of indeterminates.</item></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><item>@return A polynomial, which is the initial form of P with respect to W.</item></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><item>@return A polynomial, which is the initial form of <ins class="diffchange diffchange-inline"><tt></ins>P<ins class="diffchange diffchange-inline"></tt> </ins>with respect to <ins class="diffchange diffchange-inline"><tt></ins>W<ins class="diffchange diffchange-inline"></tt></ins>.</item></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></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><em>Beta Warning:</em> This method, package or class is a beta version. It may not work as intended or its interface may change in the next version! So please be careful when you're intending to use it.</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>Beta Warning:</em> This method, package or class is a beta version. It may not work as intended or its interface may change in the next version! So please be careful when you're intending to use it.</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> </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;"><div> <key>weyl.Inw</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>weyl.Inw</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> </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><ins class="diffchange diffchange-inline"> <key>inw</key></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> <wiki-category>Package_weyl</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_weyl</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:Weyl.Inw&diff=9841&oldid=prev
Rashid: New page: <command> <title>Weyl.Inw</title> <short_description>Computes the initial form of a polynomial in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i).</short_description> <syn...
2009-07-09T11:18:50Z
<p>New page: <command> <title>Weyl.Inw</title> <short_description>Computes the initial form of a polynomial in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i).</short_description> <syn...</p>
<p><b>New page</b></p><div> <command><br />
<title>Weyl.Inw</title><br />
<short_description>Computes the initial form of a polynomial in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i).</short_description><br />
<syntax><br />
Weyl.Inw(P:POLY,W:LIST):POLY<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 />
Computes the initial form of a normally ordered Weyl polynomial P in the Weyl algebra D with respect to weight vector W=(u,v) such that u+v>=0. Here u=(u1,...,un) and v=(v1,...,vn) are weights of indeterminates [x1,...,xn] and [y1,...,yn] respectively. Note that Inw(P,W) is a polynomail in the graded ring of D with respet to weight vector W.<br />
<itemize><br />
<item>@param <em>P</em> A polynomial in the Weyl algebra.</item><br />
<item>@param <em>W</em> A list of n positive integers, where n = number of indeterminates.</item><br />
<item>@return A polynomial, which is the initial form of P with respect to W.</item><br />
</itemize><br />
<em>Beta Warning:</em> This method, package or class is a beta version. It may not work as intended or its interface may change in the next version! So please be careful when you're intending to use it.<br />
<br />
<example><br />
Use A2::=QQ[x[1..2],d[1..2]];<br />
W:=[0,0,1,1];<br />
Weyl.Inw(x[1]d[1]+x[1],W);<br />
x[1]d[1]<br />
-------------------------------<br />
Weyl.Inw(x[1]d[1]+d[1],W);<br />
x[1]d[1] + d[1]<br />
-------------------------------<br />
Weyl.Inw(x[1]d[1]+x[2]d[2]+d[2]^2,W);<br />
d[2]^2<br />
-------------------------------<br />
Weyl.Inw(3x[1]d[1]^2+4x[2]d[1]+d[2]^2,W);<br />
3x[1]d[1]^2 + d[2]^2<br />
-------------------------------<br />
W2:=[-1,-1,1,1];<br />
Weyl.Inw(3x[1]d[1]+4x[2]d[1]+6x[2]d[2],W2);<br />
3x[1]d[1] + 4x[2]d[1] + 6x[2]d[2]<br />
-------------------------------<br />
Weyl.Inw(0,W);<br />
0<br />
-------------------------------<br />
<br />
<br />
</example><br />
</description><br />
<seealso><br />
<see>Weyl.InIw</see><br />
<see>Weyl.WNormalForm</see><br />
</seealso><br />
<types><br />
<type>apcocoaserver</type><br />
<type>poly</type><br />
<type>groebner</type><br />
</types><br />
<key>weyl.Inw</key><br />
<br />
<wiki-category>Package_weyl</wiki-category><br />
</command></div>
Rashid