ApCoCoA-1:BBSGen.PurPow

BBSGen.PurPow

This function finds the pure power indeterminates in the ring K[c].

Syntax

BBSGen.PurPow(OO);
BBSGen.PurPow(OO:LIST):LIST

Description

If b_j=x_i^d_i where x_i is an indeterminate of the base ring K[x_1,...,x_N] and d_i is some power, then c_ij is called a pure power indeterminate.

This function computes the indices [i,j] of the pure power indterminates c_ij in the coordinate ring of the border basis scheme.

• @param The order ideal OO.

• @return List of the indices [i,j] of the pure powers c_ij.

Example

Use R::=QQ[x,y];
OO:=[1,x,y,xy];
BO:=$apcocoa/borderbasis.Border(OO);
Mu:=Len(OO);
Nu:=Len(BO);

BBSGen.PurPow(OO);
[[1, 2], [2, 2], [3, 2], [4, 2], 
[1, 3], [2, 3], [3, 3], [4, 3]]

Class:=BBSGen.PurPow(OO);

Use BBS::=CoeffRing[c[1..Mu,1..Nu]]; 

BBSGen.IndFinder(Class,Mu,Nu);
[c[1,2],  c[1,3],  c[2,2], c[2,3], 
c[3,2], c[3,3], c[4,2],  c[4,3]]

BBSGen.LinIdepGen