ApCoCoA-1:BBSGen.NonStandPoly

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)]]

BB.Border

BB.Box