# How to create an object representing the set {a*S + b*T | a,b in ZZ}?

I would like to construct an object which represents the following set {a*S + b*T | a,b in ZZ} where S, T are given. If S and T are two linearly independent vectors, I can manage to do it by constructing a submodule and then changing its base ring to ZZ, if the ambient field of the vector space is QQ.

```
sage: V = VectorSpace(QQ,2)
sage: S = V.submodule_with_basis([[1,1],[2,1]])
sage: S = S.change_ring(ZZ)
sage: S
```

However, I would like to have S = 1 and T equal to some irrational algebraic. In this case, I am unable to construct my set using a submodule of a vector space as above (the changing of ring expects the entries of elements of the vector space to be elements of QQ...). Is there some good way to use the SageMath's structures to produce this set?

I can construct a generic free module and map from and to QQ(T), but I was wondering if there is a better way.