HomologyOfDerivation(d):: Derivation --> List

Inputs a derivation d\colon E \rightarrow E on a quotient E=R/I of a polynomial ring R=\mathbb F[x_1,\ldots,x_m] over a field \mathbb F. It returns a list [S,J,h] where S is a polynomial ring and J is a list of generators for an ideal in $S$ such that there is an isomorphism \alpha\colon S/J \rightarrow \ker d/{\rm im~} d. This isomorphism lifts to the ring homomorphism h\colon S \rightarrow \ker d.

This function was written by Paul Smith. It uses the Singular commutative algebra package.