ApCoCoA-1:BBSGen.LinIndepGen

BBSGen.LinIndepGen

This function computes the equivalent indeterminates modulo m^2 of BBS where m is the maximal ideal generated by the indeterminates {c_11,...,c_\mu \nu} .

Syntax

BBSGen.LinIndepGen(OO):
BBSGen.LinIndepGen(OO:LIST):LIST

Description

This function computes the equivalent indeterminates in the cotangent space m\m^2 of BBS and gives these equivalent indeterminates in one list(if they are not equivalent to 0) and additionally the K-linearly independent ones. The base ring can be K[x_1,..,x_n].

• @param The order ideal OO.

• @return The list of classes of indeterminates modulo m^2.

Example

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

BBSGen.LinIndepGen(OO); 


[[[3, 3], [1, 1]], [[1, 2], [2, 4]], [[4, 3], [2, 1]], [[2, 2]], [[3, 1]], [[4, 4], [3, 2]], [4, 2], [4, 1]]

Class:=BBSGen.LinIndepGen(OO); 

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

BBSGen.IndFinder(Class,Mu,Nu);

[[c[3,3], c[1,1]], [c[1,2], c[2,4]], [c[4,3], c[2,1]], c[2,2], c[3,1], [c[4,4], c[3,2]], c[4,1], c[4,2]]
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BBSGen.InFinder

BBSGen.PurPow