Is there any software that takes set builder notations and returns roster notations? [closed]

Question

For example, if you feed {x|xεZ,0<x} to it, it returns { 1,2,3,4,5,6,7,8,9,10,11,...}

Answer 1

I don't know of any such software.

Note that no general algorithm for enumerating arbitrary sets can exist; a program that accepts any set written in set-builder notation must also be able to solve e.g. the halting problem. Moreover there exist sets that cannot be enumerated even theoretically, for example those whose construction requires use of a choice function on the reals.

Naturally the problem is easier if you restrict what kind of expressions can appear in the set-builder notation, but even then anything more complex than linear inequalities is surprisingly hard. For instance, it is known that no algorithm exists to determine whether or not a polynomial equality P(x_1, ..., x_9)=0 in nine variables has an integer solution (this is an extension of Hilbert's 10th problem), never mind actually finding some exemplar solutions.