I am looking for software which helps me do straightforward tasks in combinatorial algebra. Let me give an example of what I mean by a straightforward task:
I have two graded (generally noncommutative!) algebras $A$ and $B$ given by generators and homogeneous relations. Given two graded algebra homomorphisms $f,g:A\to B$ which are given by their values on the generators. I want to be able, for every fixed $n\in\mathbb N$, to know whether the kernel of $A$ in degree $n$ is contained in the kernel of $B$ in degree $n$.
This is a completely elementary linear-algebraic problem, in the sense that no Gröbner bases are required (because everything is graded), so it shouldn't be hard to do for a computer. I would like to be able to do this and many similar tasks with the least possible amount of work. In particular, I don't want to have to write scripts that translate my problem into linear algebra in order to feed them to the software (that should be done by the software), and I don't want to have to install experimental and undocumented extensions/libraries. I am not sure whether Singular does all I want in the commutative case, but it's certainly the right direction. Plural (the noncommutative algebra module of Singular) is not the right direction.