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Topic review - how to check that an ideal is a monomial ideal?
Author Message
Dmitry
  Post subject:  Re: how to check that an ideal is a monomial ideal?  Reply with quote
Thanks, it works! :D
Post Posted: Tue Jan 19, 2010 7:30 pm
greuel
  Post subject:  Re: how to check that an ideal is a monomial ideal?  Reply with quote
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.
Post Posted: Tue Jan 19, 2010 3:18 pm
Dmitry
  Post subject:  how to check that an ideal is a monomial ideal?  Reply with quote
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.)
Post Posted: Tue Jan 19, 2010 10:34 am


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