Is there any software which does Ring Computations?

Question

Are there any software that is able to compute the following problems:

1. Verifying if or not a subset of a ring is an ideal.
2. Generating all ideals of a given finite ring.
3. Finding maximal multiplicative closed subset of a finite ring, etc.

I found this question previously posted, but this deals with Groups.

Answer 1

For one thing, you can work with rings in GAP! Documentation

If this isn't powerful enough, maybe look into Sage or Magma. These are general-purpose computer algebra systems that have some built-in support for rings and such.

Macaulay2 and Singular are also popular software tools, but I think they're more focused towards commutative algebra and algebraic geometry (I've never used them, though -- perhaps they do have what you're looking for).

Answer 2

Macaulay2 is good for these problems. For example for the first one, after defining the Ring, you can check is Ideal or not with "isIdeal" command.