ApCoCoA-1:BBSGen.NonStandPoly: Difference between revisions
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<command> | |||
<title>BBSGen.Wmat</title> | |||
<short_description>This function computes the non-standard polynomials among the generators of the vanishing ideal of border basis | |||
scheme. | |||
</short_description> | |||
<syntax> | |||
NonStandPoly(OO,BO,W,N); | |||
NonStandPoly(OO:LIST,BO:LIST,W:MATRIX,N:INTEGER):LIST | |||
</syntax> | |||
<description> | |||
<itemize> | |||
<item>@param The order ideal OO, BO border of OO , the number of indeterminates of the polynomial ring N and the Weight Matrix. | |||
</item> | |||
<item>@return List of polynomials and their degree wrt. the arrow grading. .</item> | |||
</itemize> | |||
<example> | |||
Use R::=QQ[x[1..2]]; | |||
OO:=BB.Box([1,1]); | |||
BO:=BB.Border(OO); | |||
W:=Wmat(OO,BO,N); | |||
XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; | |||
Use XX; | |||
NonStandPoly(OO,BO,W,N); | |||
[ c[1,2]c[3,1] + c[1,4]c[4,1] - c[1,3], | |||
R :: Vector(1, 2)], | |||
[ c[1,1]c[2,2] + c[1,3]c[4,2] - c[1,4], | |||
R :: Vector(2, 1)], | |||
[ c[1,1]c[2,4] - c[1,2]c[3,3] - c[1,4]c[4,3] + c[1,3]c[4,4], | |||
R :: Vector(2, 2)], | |||
[c[2,2]c[3,1] + c[2,4]c[4,1] - c[2,3], | |||
R :: Vector(1, 1)], | |||
[c[2,1]c[2,4] - c[2,2]c[3,3] - c[2,4]c[4,3] + c[2,3]c[4,4] + c[1,4], | |||
R :: Vector(2, 1)], | |||
[c[2,2]c[3,1] + c[3,3]c[4,2] - c[3,4], | |||
R :: Vector(1, 1)], | |||
[c[2,4]c[3,1] - c[3,2]c[3,3] - c[3,4]c[4,3] + c[3,3]c[4,4] - c[1,3], | |||
R :: Vector(1, 2)], | |||
[c[2,4]c[4,1] - c[3,3]c[4,2] - c[2,3] + c[3,4], | |||
R :: Vector(1, 1)]] | |||
</example> | |||
</description> | |||
<types> | |||
<type>borderbasis</type> | |||
<type>ideal</type> | |||
<type>apcocoaserver</type> | |||
</types> | |||
<see>BB.Border</see> | |||
<see>BB.Box</see> | |||
<key>Wmat</key> | |||
<key>BBSGen.Wmat</key> | |||
<key>bbsmingensys.Wmat</key> | |||
<wiki-category>Package_bbsmingensys</wiki-category> | |||
</command> | |||
Revision as of 16:12, 31 May 2012
BBSGen.Wmat
This function computes the non-standard polynomials among the generators of the vanishing ideal of border basis
scheme.
Syntax
NonStandPoly(OO,BO,W,N); NonStandPoly(OO:LIST,BO:LIST,W:MATRIX,N:INTEGER):LIST
Description
@param The order ideal OO, BO border of OO , the number of indeterminates of the polynomial ring N and the Weight Matrix.
@return List of polynomials and their degree wrt. the arrow grading. .
Example
Use R::=QQ[x[1..2]];
OO:=BB.Box([1,1]);
BO:=BB.Border(OO);
W:=Wmat(OO,BO,N);
XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]];
Use XX;
NonStandPoly(OO,BO,W,N);
[ c[1,2]c[3,1] + c[1,4]c[4,1] - c[1,3],
R :: Vector(1, 2)],
[ c[1,1]c[2,2] + c[1,3]c[4,2] - c[1,4],
R :: Vector(2, 1)],
[ c[1,1]c[2,4] - c[1,2]c[3,3] - c[1,4]c[4,3] + c[1,3]c[4,4],
R :: Vector(2, 2)],
[c[2,2]c[3,1] + c[2,4]c[4,1] - c[2,3],
R :: Vector(1, 1)],
[c[2,1]c[2,4] - c[2,2]c[3,3] - c[2,4]c[4,3] + c[2,3]c[4,4] + c[1,4],
R :: Vector(2, 1)],
[c[2,2]c[3,1] + c[3,3]c[4,2] - c[3,4],
R :: Vector(1, 1)],
[c[2,4]c[3,1] - c[3,2]c[3,3] - c[3,4]c[4,3] + c[3,3]c[4,4] - c[1,3],
R :: Vector(1, 2)],
[c[2,4]c[4,1] - c[3,3]c[4,2] - c[2,3] + c[3,4],
R :: Vector(1, 1)]]
