Thanks, it works!
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| how to check that an ideal is a monomial ideal? https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1795 |
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| Author: | Dmitry [ Tue Jan 19, 2010 10:34 am ] |
| Post subject: | how to check that an ideal is a monomial ideal? |
Dear Users, is there a way to check in Singular that an ideal in a polynomial ring (say in two variables) has a monomial basis? Maybe even to see this basis explicitly? (My knowledge of Groebner bases is infinitesimal, sorry if the question is stupid.) |
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| Author: | greuel [ Tue Jan 19, 2010 3:18 pm ] |
| Post subject: | Re: how to check that an ideal is a monomial ideal? |
If an ideal I is generated by monomials then these monomials are a GB of I with respect to any monomial ordering. Since the reduced GB of an ideal is unique (only depending on the ordering), I is a monomial ideal iff the reduced GB of I w.r.t. any monomial ordering consists of monomials. |
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| Author: | Dmitry [ Tue Jan 19, 2010 7:30 pm ] |
| Post subject: | Re: how to check that an ideal is a monomial ideal? |
Thanks, it works!
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