ApCoCoA-1:BBSGen.TraceSyzLinStep

BBSGen.TraceSyzStep

This function only computes the K[c_ij-]linear summand of trace syzygy polynomial for the degree of the given monomial.

Syntax

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

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 only the K[c_ij]-linear summand of the trace syzygy polynomial for the degree of the given monomial.

@param The Monomial Mon, the distinguished indterminate of choice, order ideal OO, border BO, the number of Indeterminates of the Polynomial.
@return K[c_ij]-linear summand of the trace syzygy polynomial which is computed by help of the given monomial.

Example

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

OO:=BB.Box([1,1]);
BO:=BB.Border(OO);
Mu:=Len(OO);
Nu:=Len(BO);

Mon:=x[1]^2x[2];--------Target Monomial

X:=x[1];   ------------Choice of the Indeterminate

Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; 
 
 BBSGen.TraceSyzLinStep(Mon,X,OO,BO,N);
  
 
 t[1,2,1,3] + t[1,2,2,4]

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