ApCoCoA-1:BBSGen.NonStandPoly
From ApCoCoAWiki
BBSGen.NonStandPoly
Finds the non-standard polynomials of the ring K[c_{ij}] with respect to the arrow grading.
Syntax
BBSGen.NonStand(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 BBS=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);
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)]]
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