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Questions tagged [groebner-bases]

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Questions on the use of Gröbner basis techniques in Mathematica.

57 questions
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0 votes
0 answers
108 views

I want the fixed points of the following Lotka-Volterra system, which can be written in two equivalent ways, RHS, and RH: ...
florin's user avatar
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3 votes
4 answers
410 views

I wanted to solve the system with RHS ...
florin's user avatar
  • 2,380
2 votes
1 answer
179 views

So I'm trying to solve the InverseKinematics of a 7DoF robot using GrobnerBasis but it just doesn't finish. I have 19 polynomials and 14 uknowns. Here are the polynoms: ...
Dani Zsigri's user avatar
  • 35
0 votes
0 answers
101 views

I often need to compute the GroebnerBasis. Sometimes it takes a long time to respond. Sometimes changing a term to its reciprocal speeds up the computation, and sometimes modifying the elimination ...
tianzhidaosunyouyu's user avatar
  • 125
2 votes
2 answers
213 views

I have the following easy equations for positive variables and parameters ...
florin's user avatar
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2 votes
0 answers
209 views

With exactly the same code I get different Groebner bases with different versions of Mathematica. Even worse, with exactly the same code I get a Groebner basis with a version of the program but I ...
Ramon's user avatar
  • 21
1 vote
1 answer
137 views

Suppose I have a system of polynomial equations with base field $\mathbb{C}$ with $n$ equations and $n$ unknowns, how can I get the multiplicity of a certain solution? As an example, consider $$x^3=0\\...
Peter Wu's user avatar
  • 111
1 vote
1 answer
111 views

How to specify the degree or weight of variables in the computation of Gröbner bases in Mathematica? I tried something like below, but 'Weights->degrees' part doesn't work. ...
Astro Naut's user avatar
  • 55
1 vote
2 answers
191 views

Near the bottom of the page, there is "The above system of equations has only a limited number of solutions and the ideal can be calculated". But I cannot get the same GroebnerBasis, four ...
Ytrewq's user avatar
  • 199
3 votes
0 answers
79 views

Nonlinear determined systems have typically several solutions involving square or higher order roots. Instead of solving them, it may be more profitable to reduce them to smaller systems with fewer ...
florin's user avatar
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1 vote
0 answers
121 views

I have a system of five equations (Behn's model of CD4+T/APC interaction). The last four yield rational solutions in x1, so I can plug these in the first equation ...
florin's user avatar
  • 2,380
2 votes
1 answer
361 views

Given a system of polynomial equations in $\mathbb{C}$-coefficients, is there a tool in Mathematica that computes the number of solutions to this system, counted with multiplicity? (We may assume ...
Boyu Zhang's user avatar
  • 123
4 votes
3 answers
730 views

I have a bunch of two-variable polynomials and as part of a larger algorithm need to find a basis for them and express them in terms of this basis. As an illustrative example, for one case my ...
R.W's user avatar
  • 137
0 votes
1 answer
149 views

I want to transform a polynomial in Sin and Cos to AssociatedLegendrePolynomials. I have a working code, but the end result is ...
infinitezero's user avatar
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4 votes
1 answer
192 views

The documentation for PolynomialReduce points out that, to test membership in an ideal, the list of polynomials must be a Groebner basis for that ideal. But does ...
Lyle Ramshaw's user avatar
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