ApCoCoA-1:BBSGen.TraceSyzLin

BBSGen.TraceSyzLin

This function computes the K[c]-linear summand of trace syzygy polynomials.

Syntax

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

Description

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 only computes the summands of trace syzygy, which has constant and non-zero coefficient.

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

• @return List of Tau^kl_i s, which have constant coefficients in the trace syzygy polynomial.

  
  

Example

 
Use R::=QQ[x[1..2]];

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

Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; 
 N:=2; 
BBSGen.TraceSyzLin(OO,BO,N); 

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

BB.Border

BB.Box

BBSGen.Wmat

BBSGen.TraceSyzStep

BBSGen.TraceSyzFull