ApCoCoA-1:BBSGen.Wmat: Difference between revisions
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New page: <command> <title>BBSGens.Wmat</title> <short_description>This function computes the weight matrix with respect to the arrow grading. </short_description> <syntax>BBSGens.WMat(OO:LIST,BO... |
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<command> | <command> | ||
<title>BBSGen.WMat</title> | |||
<short_description>This function computes the | <short_description>This function computes the Weight Matrix with respect to the arrow grading. </short_description> | ||
<syntax> | |||
<syntax> | |||
BBSGen.WMat(OO,BO,N): | |||
BBSGen.WMat(OO:LIST,BO:LIST,N:INTEGER):MATRIX | |||
</syntax> | |||
<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 <tt>BBSGen.Wmat(OO,BO,N)</tt> computes the grading matrix with respect to this grading. | |||
<itemize> | <itemize> | ||
<item>@param | <item>@param The order ideal OO, the border BO and the number of indeterminates of the polynomial ring K[x_1,...,x_N]. | ||
</item> | |||
<item>@return Weight Matrix.</item> | |||
<item>@return | |||
</itemize> | </itemize> | ||
<example> | <example> | ||
Use R::=QQ[x[1..2]]; | Use R::=QQ[x[1..2]]; | ||
OO:= | OO:=$apcocoa/borderbasis.Box([1,1]); | ||
BO:= | BO:=$apcocoa/borderbasis.Border(OO); | ||
N:=Len(Indets()); | N:=Len(Indets()); | ||
---------------------- | ---------------------- | ||
W:=Wmat(OO,BO,N); | W:=BBSGen.Wmat(OO,BO,N); | ||
W; | W; | ||
Mat([ | Mat([ | ||
[0, 2, 1, 2, 0, 2, 1, 2, -1, 1, 0, 1, -1, 1, 0, 1], | [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]]) | [2, 0, 2, 1, 1, -1, 1, 0, 2, 0, 2, 1, 1, -1, 1, 0] | ||
]) | |||
</example> | </example> | ||
</description> | </description> | ||
<types> | |||
<type>bbsmingensys</type> | <type>bbsmingensys</type> | ||
<wiki-category>Package_bbsmingensys</wiki-category> | <type>Mat</type> | ||
<type>apcocoaserver</type> | |||
</types> | |||
<key>Wmat</key> | |||
<key>BBSGen.Wmat</key> | |||
<key>bbsmingensys.Wmat</key> | |||
<wiki-category>ApCoCoA-1:Package_bbsmingensys</wiki-category> | |||
</command> | </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] ])
