ApCoCoA-1:BBSGen.NonStand

BBSGen.NonStand

This function computes the non-standard indeterminates from K[c] with respect to the arrow grading.

Syntax

BBSGen.NonStand(OO,BO,N,W);
BBSGen.NonStand(OO:LIST,BO:LIST,N:INTEGER,W:MATRIX):LIST

Description

Let W be the weight matrix with respect to the arrow grading(see BBSGen.Wmat).

An indeterminate c_ij in K[c] is called standard, if deg_W(c_ij)=log(b_j)-log(t_i) has exactly one strictly positive component. If c_ij is not standard then it is called non-standard. This function computes such non-standard indeterminates from ring K[c].

• @param The order ideal OO, the border BO the number of indeterminates of the polynomial ring K[x_1,...,x_N] and the weight matrix(BBSGen.Wmat).

• @return List of Indeterminates and their degree with respect to the arrow grading.

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.NonStand(OO,BO,N,W);

[[c[1,3], [R :: 1, R :: 2]], 
[c[1,4], [R :: 2, R :: 1]],
[c[2,3], [R :: 1, R :: 1]], 
[c[3,4], [R :: 1, R :: 1]]]
  

BBSGen.Wmat