ApCoCoA-1:BBSGen.JacobiLin

BBSGen.TraceSyzStep

This function computes the polynomial entries of the Jacobi identity [ A_i[A_k,A_l ] ]+[ A_k[ A_l,A_i]] +[ A_l[A_i,A_k ] ]=0 , where i,k,l is from {1...n} , which has constant coeficients.

Syntax

JacobiLin(OO,BO,N);
JacobiLin(OO:LIST,BO:LIST,N:INTEGER):MATRIX

Description

Let R=K[x_1,...,x_n] and A_i is the generic multiplication matrix for x_i. Let Tau^kl_ij :=t[k,l,i,j] be the (i,j) ^th entry of matrix the operation [A_k,A_l]. This function computes the entries of the Jacobi identity [ A_i[A_k,A_l ] ]+[ A_k[ A_l,A_i]] +[ A_l[A_i,A_k ] ]=0 , where i,k,l is from {1...n} , which has constant coeficients.

Please note that this function does not work for the case, where n=2.

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

  
  

• @return The K[c]-linear entries of the Jacobi Identity J^{ikl}. .

Example

Use R::=QQ[x[1..3]];

OO:=[1,x[1]];
BO:=BB.Border(OO);
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]]; 

BoxJacobiLin(OO,BO,N);

[[[0,0],
  [t[2,3,1,1], t[2,3,1,2]]]]

BB.Border

BB.Box

BBSGen.JacobiFull

BBSGen.JacobiLin