MAGMA: One-sided ideals in finitely presented algebras

Question

So I have the following code in MAGMA to obtain a right ideal in the free algebra:

K := RationalField();
F<x> := FreeAlgebra(K,1);
I := rideal<F|x^2>;

I would like to be able to do the same for a finitely-presented algebra, for example:

K := RationalField();
F<x> := FreeAlgebra(K,1);
A<x> := quo<F|x^3>;

I := rideal<A|x^2>;

However, I get the following error Runtime error in ideal< ... >: Rhs argument 1 is invalid for this constructor. Does anyone know a method to do this?

Answer 1

Try the following:

K := RationalField();
F<x> := FreeAlgebra(K,1);
A := quo<F|x^3>;
I := ideal<A|x^2>;

MAGMA sometimes gives problems if you redefine the x. Also, since your algebra is commutative, the rideal and lideal constructors are not available.