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5 votes
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Computations in Weyl algebra with rational function coefficients

I am looking for a software to perform calculations with modules over the algebra $R_n=\mathbb{C}(x_1\ldots x_n)\langle \partial_1\ldots\partial_n\rangle$ of differential operators with rational ...
Peter Kravchuk's user avatar
4 votes
0 answers
122 views

Recommendations for distributed calculations of Groebner Bases

There are many computer algebra systems available which can compute a Groebner basis, including: Mathematica Singular Macaulay2 Magma Maple CoCoA However (please correct me if I've missed something) ...
JoggingGrad's user avatar
4 votes
0 answers
98 views

Compute equalizer of maps of polynomial rings, perhaps using Gröbner bases

Suppose that $k$ is a field and I have two ring homomorphisms $$ \phi, \psi :k[x_1,...,x_m] \to k[y_1,...,y_n]. $$ How can I use Gröbner bases (or other computational tools) to compute the subring of ...
John Palmieri's user avatar
2 votes
0 answers
88 views

Gröbner implicitization with relationships between the variables

I have the following parametric equations, where cost$=\cos t$, cos2t$=\cos 2t$, and $A^2+B^2=1$: ...
Stéphane Laurent's user avatar
1 vote
0 answers
41 views

Example polynomial system where Macaulay bound is tight

I have been solving systems of polynomial equations by forming the Macaulay matrix of different degrees and computing its null space. If the degree is large enough, namely at or above the degree of ...
RaphWid's user avatar
  • 11
1 vote
0 answers
259 views

Computer algebra programs that can solve polynomial systems on algebraically closed fields besides MAGMA

I was wondering which computer algebra programs out there can solve polynomial systems on the algebraic closure of $\mathbb{Q}$ analytically and efficiently. So far, I only found MAGMA with its ...
ArminJR's user avatar
  • 21
1 vote
0 answers
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Grobner basis of the toric ideal $I_{A_P}$ with respect to $<_{rev}$ consists of those binomials $t_αt_β − t_{α\cap β} t_{α\cup β}$

I try to understand the proof of the Theorem. 10.1.3.(page 185) from ''Monomial Ideals'' by Herzog & Hibi. The reduced Grobner basis of the toric ideal $I_{A_P}$ with respect to $<_{rev}$ ...
Problemsolving's user avatar
0 votes
0 answers
71 views

Low rank approximation

Can we solve low rank approximation problem by using concept of Gröbner basis? I was trying to find it by Macaulay2 but didn't find the answer. I was trying to do by toric ideals as for them Gröbner ...
anjan samanta's user avatar