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?

Global section of what?
– Qiaochu YuanMar 6 '13 at 2:54

1

If you're presenting it as a quotient of a polynomial ring, then the "basis" command in Macaulay2 does this for you.
– Steven SamMar 6 '13 at 2:59

@Steven: I am curious what algorithm does that command use?
– minimaxMar 6 '13 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...
– minimaxMar 6 '13 at 6:41