Algorithm for computing basis of zero dimensional ring?

If given a zero dimensional ring over a field, for example, a polynomial ring $A=k[x_1,\ldots,x_n]/(f_1,\ldots,f_n)$ such that $A$ is 0-dimensional, is there an algorithm to compute a monomial basis for this ring?

edited Mar 6 at 6:40

asked Mar 6 at 2:49

minimax
557●2●10

Global section of what? – Qiaochu Yuan Mar 6 at 2:54

If you're presenting it as a quotient of a polynomial ring, then the "basis" command in Macaulay2 does this for you. – Steven Sam Mar 6 at 2:59

@Steven: I am curious what algorithm does that command use? – minimax Mar 6 at 4:29

@Qiaochu: I just meant the global section of Spec of that ring, i.e. the ring itself.... It seems unnecessary to use that language so I have changed the working. Sorry for the confusion... – minimax Mar 6 at 6:41