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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?

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Global section of what? –  Qiaochu Yuan Mar 6 '13 at 2:54
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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 '13 at 2:59
    
@Steven: I am curious what algorithm does that command use? –  minimax Mar 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... –  minimax Mar 6 '13 at 6:41

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