Difference between revisions of "ApCoCoA-1:BBSGen.Wmat"

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{{Version|1}}
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<command>
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  <title>BBSGen.WMat</title>
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  <short_description>This function computes the Weight Matrix with respect to the arrow grading. </short_description>
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<syntax>
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BBSGen.WMat(OO,BO,N):
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BBSGen.WMat(OO:LIST,BO:LIST,N:INTEGER):MATRIX
  
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</syntax>
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  <description>
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Let c_ij be an indeterminate from the Ring K[c_ij]. Let OO be an order ideal and BO be its border. Let Mu:=Len(OO) and Nu:=Len(BO). Let m be an integer that is equal to Mu*Nu.  The ring K[c_ij] is Z^m-graded if we define  deg_{W}(c_ij)=log(b_j)-log(t_i)=(u_1,...,u_m)=u in Z^m,  where W is the grading matrix.
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We shall name this  grading the arrow grading. The Function <tt>BBSGen.Wmat(OO,BO,N)</tt> computes the grading matrix with respect to this grading.
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<itemize>
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  <item>@param The order ideal OO, the border BO and the number of indeterminates of the polynomial ring K[x_1,...,x_N].
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</item>
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  <item>@return Weight Matrix.</item>
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</itemize>
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<example>
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Use R::=QQ[x[1..2]];
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OO:=$apcocoa/borderbasis.Box([1,1]);
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BO:=$apcocoa/borderbasis.Border(OO);
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N:=Len(Indets());
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----------------------
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W:=BBSGen.Wmat(OO,BO,N);
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W;
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Mat([
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  [0, 2, 1, 2, 0, 2, 1, 2, -1, 1, 0, 1, -1, 1, 0, 1],
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  [2, 0, 2, 1, 1, -1, 1, 0, 2, 0, 2, 1, 1, -1, 1, 0]
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])
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</example>
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  </description>
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  <types>
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    <type>bbsmingensys</type>
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    <type>Mat</type>
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    <type>apcocoaserver</type>
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  </types>
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  <key>Wmat</key>
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  <key>BBSGen.Wmat</key>
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  <key>bbsmingensys.Wmat</key>
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  <wiki-category>ApCoCoA-1:Package_bbsmingensys</wiki-category>
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</command>

Latest revision as of 09:52, 7 October 2020

This article is about a function from ApCoCoA-1.

BBSGen.WMat

This function computes the Weight Matrix with respect to the arrow grading.

Syntax

BBSGen.WMat(OO,BO,N):
BBSGen.WMat(OO:LIST,BO:LIST,N:INTEGER):MATRIX

Description

Let c_ij be an indeterminate from the Ring K[c_ij]. Let OO be an order ideal and BO be its border. Let Mu:=Len(OO) and Nu:=Len(BO). Let m be an integer that is equal to Mu*Nu. The ring K[c_ij] is Z^m-graded if we define deg_{W}(c_ij)=log(b_j)-log(t_i)=(u_1,...,u_m)=u in Z^m, where W is the grading matrix.

We shall name this grading the arrow grading. The Function BBSGen.Wmat(OO,BO,N) computes the grading matrix with respect to this grading.

  • @param The order ideal OO, the border BO and the number of indeterminates of the polynomial ring K[x_1,...,x_N].

  • @return Weight Matrix.


Example

Use R::=QQ[x[1..2]];
OO:=$apcocoa/borderbasis.Box([1,1]); 
BO:=$apcocoa/borderbasis.Border(OO);
N:=Len(Indets());
----------------------
W:=BBSGen.Wmat(OO,BO,N); 
W;

Mat([
  [0, 2, 1, 2, 0, 2, 1, 2, -1, 1, 0, 1, -1, 1, 0, 1],
  [2, 0, 2, 1, 1, -1, 1, 0, 2, 0, 2, 1, 1, -1, 1, 0]
])





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