# ApCoCoA-1:BBSGen.LinIndepGen

## BBSGen.LinIndepGen

Let OO be an order ideal and BO be its border. Let Mu:=Len(OO) and Nu:=Len(BO). This function computes the equivalent indeterminates from K[c_11,...,c_Mu Nu] modulo m^2, where m is the maximal ideal generated by the indeterminates {c_11,...,c_Mu Nu} from the coordinate ring of the border basis scheme. As out-put, it gives every equivalence class as a list.

### Syntax

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

### Description

• @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]]
-------------------------------
-------------------------------
```