ApCoCoA-1:BBSGen.Wmat: Difference between revisions
From ApCoCoAWiki
No edit summary |
m insert version info |
||
| (21 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
{{Version|1}} | |||
<command> | <command> | ||
<title>BBSGen. | <title>BBSGen.WMat</title> | ||
<short_description>This function computes the Weight Matrix with respect to the arrow grading. </short_description> | <short_description>This function computes the Weight Matrix with respect to the arrow grading. </short_description> | ||
<syntax> | <syntax> | ||
WMat(OO,BO,N): | BBSGen.WMat(OO,BO,N): | ||
WMat(OO:LIST,BO:LIST,N:INTEGER):MATRIX | BBSGen.WMat(OO:LIST,BO:LIST,N:INTEGER):MATRIX | ||
</syntax> | </syntax> | ||
<description> | <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 The order ideal OO, the border BO and the number of | <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> | ||
<item>@return Weight Matrix.</item> | <item>@return Weight Matrix.</item> | ||
| Line 19: | Line 22: | ||
<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; | ||
| Line 36: | Line 39: | ||
</description> | </description> | ||
<types> | <types> | ||
<type> | <type>bbsmingensys</type> | ||
<type> | <type>Mat</type> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
<key>Wmat</key> | <key>Wmat</key> | ||
<key>BBSGen.Wmat</key> | <key>BBSGen.Wmat</key> | ||
<key> | <key>bbsmingensys.Wmat</key> | ||
<wiki-category> | <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] ])
