ApCoCoA-1:BBSGen.TraceSyzFull

BBSGen.TraceSyzFull

This function computes the trace syzygy polynomials.

Syntax

TraceSyzFull(OO,BO,N);
TraceSyzFull(OO:LIST,BO:LIST,N:INTEGER):LIST

Description

Let Tau^kl_ij :=t[k,l,i,j] be the (i,j) ^th entry of matrix the operation [A_k,A_l]. The result of the Trace Syzygy computation is K[c]-linear combination of Tau^kl_ij that is equal to 0. This function computes such Trace Syzygy polynomials. This function, because of the growth of the polynomials during the computation,may not give result for every ring with three indeterminates. In that case we recommend the functions TraceSyzLin or TraceSyzStep.

• @param The order ideal OO, border BO, the number of Indeterminates of the Polynomial.

• @return The list of Trace Syzygy polynomials.

Example

    
Use R::=QQ[x[1..2]];
OO:=BB.Box([1,1]);
BO:=BB.Border(OO);
 W:=BBSGen.Wmat(OO,BO,N);
Mu:=Len(OO);
Nu:=Len(BO);
N:=Len(Indets());

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


BBSGen.TraceSyzFull(OO,BO,N);

[c[1,2]t[1,2,3,1] + c[2,2]t[1,2,3,2] + c[3,2]t[1,2,3,3] + c[4,2]t[1,2,3,4] +
 c[1,4]t[1,2,4,1] + c[2,4]t[1,2,4,2] + c[3,4]t[1,2,4,3] + c[4,4]t[1,2,4,4] + 
t[1,2,1,3] + t[1,2,2,4],
  2c[1,1]t[1,2,2,1] + 2c[2,1]t[1,2,2,2] + 2c[3,1]t[1,2,2,3] + 2c[4,1]t[1,2,2,4]+ 
2c[1,3]t[1,2,4,1] + 2c[2,3]t[1,2,4,2] + 2c[3,3]t[1,2,4,3] + 2c[4,3]t[1,2,4,4] 
+ 2t[1,2,1,2] + 2t[1,2,3,4],
  c[1,2]t[1,2,3,1] + c[2,2]t[1,2,3,2] + c[3,2]t[1,2,3,3] + c[4,2]t[1,2,3,4] + 
c[1,4]t[1,2,4,1] + c[2,4]t[1,2,4,2] + c[3,4]t[1,2,4,3] + c[4,4]t[1,2,4,4] + 
t[1,2,1,3] + t[1,2,2,4],
  2c[1,2]c[3,1]t[1,2,2,1] + 2c[1,4]c[4,1]t[1,2,2,1] + 2c[2,2]c[3,1]t[1,2,2,2] +
 2c[2,4]c[4,1]t[1,2,2,2] + 2c[3,1]c[3,2]t[1,2,2,3] + 2c[3,4]c[4,1]t[1,2,2,3] +
 2c[3,1]c[4,2]t[1,2,2,4] + 2c[4,1]c[4,4]t[1,2,2,4] + 2c[1,2]c[3,3]t[1,2,4,1] +
 2c[1,4]c[4,3]t[1,2,4,1] + 2c[2,2]c[3,3]t[1,2,4,2] + 2c[2,4]c[4,3]t[1,2,4,2] +
 2c[3,2]c[3,3]t[1,2,4,3] + 2c[3,4]c[4,3]t[1,2,4,3] + 2c[3,3]c[4,2]t[1,2,4,4] + 
2c[4,3]c[4,4]t[1,2,4,4] + 2c[1,1]t[1,2,2,3] + 2c[2,1]t[1,2,2,4] + 2c[1,4]t[1,2,3,1] + 
2c[2,4]t[1,2,3,2] + 2c[3,4]t[1,2,3,3] + 2c[4,4]t[1,2,3,4] + 2c[1,3]t[1,2,4,3] +
 2c[2,3]t[1,2,4,4] + 2t[1,2,1,4]]

BB.Border

BB.Box

BBSGen.Wmat

BBSGen.TraceSyzStep

BBSGen.TraceSyzLin