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 0dimensional, is there an algorithm to compute a monomial basis for this ring?
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1$\begingroup$ Global section of what? $\endgroup$ – Qiaochu Yuan Mar 6 '13 at 2:54

1$\begingroup$ If you're presenting it as a quotient of a polynomial ring, then the "basis" command in Macaulay2 does this for you. $\endgroup$ – Steven Sam Mar 6 '13 at 2:59

$\begingroup$ @Steven: I am curious what algorithm does that command use? $\endgroup$ – minimax Mar 6 '13 at 4:29

$\begingroup$ @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... $\endgroup$ – minimax Mar 6 '13 at 6:41