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Dec
15
awarded  Enlightened
Dec
15
awarded  Nice Answer
Dec
15
revised Is an ideal generated by multilinear, irreducible, homogeneous polynomials of different degrees always radical?
it's Proposition 23 not Theorem 23.
Dec
15
comment Is an ideal generated by multilinear, irreducible, homogeneous polynomials of different degrees always radical?
It's Proposition 23. I fixed the answer, thanks.
Dec
11
awarded  Nice Answer
Sep
4
revised Graded-irreducible ideals are irreducible?
expand a lot on different gradings.
Sep
4
comment How can I include irreducibility in a Groebner basis calculation?
And 3) The irreducibility is hard to model in this framework, but over an algebraically closed field there is of course the Nullstellensatz which can give infeasibility certificates.
Sep
4
awarded  Custodian
Sep
4
comment How can I include irreducibility in a Groebner basis calculation?
Two comments: 1) This depends very much on the field you want your solutions from. Real root finding for instance is a branch of real algebraic geometry. 2) Gröbner bases can't help you since you can't use them to decide if a single polynomial is irreducible. You need factorization algorithms and then 1) comes into play.
Sep
4
reviewed Reviewed Help with notations from 2D to 3D FFT representations as 1D FFT
Sep
3
answered Graded-irreducible ideals are irreducible?
Aug
31
revised Is an irreducible ideal in $R$ also irreducible in $R[x]$?
Streamline many small details, fix typos, make proof understandable to me.
Aug
31
accepted Is an irreducible ideal in $R$ also irreducible in $R[x]$?
Aug
31
comment Is an irreducible ideal in $R$ also irreducible in $R[x]$?
Thank you! I've taken the liberty to edit your proof a little. As you say, it's not short, but quite elementary. Nice.
Aug
31
suggested approved edit on Is an irreducible ideal in $R$ also irreducible in $R[x]$?
Aug
31
comment Lattice Flatness Measure
Can you give some more examples: How should that flatness measure be different from just height?
Aug
31
awarded  Quorum
Aug
31
awarded  Nice Question
Aug
31
comment Is an irreducible ideal in $R$ also irreducible in $R[x]$?
Thank you for your answer. There are a number of things that I don't understand yet. Can you please explain: Why can you saturate at X ("since X is indeterminate")? In Claim 1, are you saying that you want to choose f,g so that Claim 1 is satisfied? What do you mean by "then we replace"/why can you replace $f$? And then David Lamperts comment. It would be great if you could fill in some more detail. Thanks!
Aug
27
asked Is an irreducible ideal in $R$ also irreducible in $R[x]$?