Suppose given an inclusion $A\subset B$ of finitely-presented commutative algebras over a field. Is there a CAS which can decide whether $B$ is a finite $A$-module?
What if instead of f.p. k-algebras, I have an extension of DVRs (discrete valuation rings)?
Alternatively, is there a CAS that can compute the integral closure of a dvr or f.p. k-algebra in a finite separable extension of its field of fractions?
Macaulay2 has the method isModuleFinite.
Magma has a function IntegralClosure, but it seems to only work over function fields. Macaulay2 allow you to normalize certain integral domains in their fields of fractions, but Magma allows you to take the integral closure in an extension of the field of fractions.