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BBSGen.NonStandPoly

This function computes the non-standard polynomial generators of the vanishing ideal of border basis scheme with respect to the arrow grading.
Syntax
          
BBSGen.NonStandPoly(OO,BO,W,N); 
BBSGen.NonStandPoly(OO:LIST,BO:LIST,W:MATRIX,N:INTEGER):LIST 


          

Description
Let W be the weight matrix with respect to the arrow grading(see BBSGen.Wmat). Let tau^kl_ij be a polynomials from the generating set Tau of the vanishing ideal of border basis scheme. It is called standard, if deg_W(tau^kl_ij) has exactly one strictly positive component. If tau^kl_ij is not standard then it is called non-standard. This function computes such non-standard polynomials.

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);
XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; 
Use XX;


BBSGen.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)]]





See Also