Difference between revisions of "ApCoCoA-1:BBSGen.NonStandPoly"
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(New page: <command> <title>BBSGen.NonStandPoly</title> <short_description> Finds the non-standard polynomials of the ring <tt>K[c_{ij}]</tt> with respect to the arrow grading. </short_descriptio...) |
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| − | BBSGen. | + | BBSGen.NonStandPoly(OO:LIST,BO:LIST,N:INT,W:MATRIX):LIST |
</syntax> | </syntax> | ||
<description> | <description> | ||
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| − | <item>@return A list of non-standard polynomials from <tt> | + | <item>@return A list of non-standard polynomials from <tt>K[c_{ij}]</tt> with their degree vectors from field <tt>K</tt>.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
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[ c[1,2]c[3,1] + c[1,4]c[4,1] - c[1,3], | [ c[1,2]c[3,1] + c[1,4]c[4,1] - c[1,3], | ||
Revision as of 19:00, 13 February 2012
BBSGen.NonStandPoly
Finds the non-standard polynomials of the ring K[c_{ij}] with respect to the arrow grading.
Syntax
BBSGen.NonStandPoly(OO:LIST,BO:LIST,N:INT,W:MATRIX):LIST
Description
@param OO A list of terms representing an order ideal.
@param BO A list of terms representing the border.
@param N The number of elements of the Polynomial ring K[x_1,...x_n].
@param W The weight matrix.
@return A list of non-standard polynomials from K[c_{ij}] with their degree vectors from field K.
Example
Use R::=QQ[x[1..2]];
OO:=BB.Box([1,1]);
BO:=BB.Border(OO);
Mu:=Len(OO);
Nu:=Len(BO);
W:=Wmat(OO,BO,N);
Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]];
BBSGen.NonStandPoly(OO,BO,N,W);
[ 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)]]
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