Questions tagged [groebner-bases]

Questions on the use of Gröbner basis techniques in Mathematica.

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Monitoring PolynomialReduce/Alternatives for other CAS packages

I have a large generic polynomial That looks like $N = \sum_{i_1,i_2\cdots}c_{i_1,i_2,i_3,\cdots} {x_{1}}^{i_1}{x_{2}}^{i_2}\cdots $ This could have anywhere between 3000-9000 terms with a maximum ...
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82 views

How to make GroebnerBasis Work or to speed NSolve up [closed]

I consider a set of three polynomials of two variables ...
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43 views

Same problem, different GroebnerBasis

Consider the following system of equations: $$ \begin{cases} d_0^2+d_1^2=2 \\ d_0 d_1 = -1 \end{cases} $$ Here's Mathematica solving it and producing the Gröbner Basis: ...
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1answer
51 views

Default weight matrix for EliminationOrder

For the computation of elimination ideals via Mathematica's GroebnerBasis method, e.g. grob = GroebnerBasis[eqs, {a, b, c, d, e}, {x, y}, MonomialOrder -> EliminationOrder]; what is the default ...
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1answer
104 views

Why is my GroebnerBasis = 0 in this case?

I recently asked a question: Finding Intersections Between Arbitrary Surface and A Line whose solution required me to use the GroebnerBasis function. I successfully ...
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0answers
65 views

Grobner basis calculation while keeping track of the change of basis [closed]

Can one compute a Groebner basis for a polynomial ideal in Mathematica, while simultaneously getting the change of basis matrix?
5
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1answer
103 views

How to stop GroebnerBasis from automatically normalizing?

I need to compute the Groebner basis modulus a set of prime without normalizing the Groebner basis output. Is this possible? Example: ...
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1answer
85 views

Finding a set of characteristics of a system of polynomial equations

we have an ODE system as following ...
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1answer
130 views

Define a new CoefficientDomain in PolynomialReduce function

If we have some parameter like $q_1, q_2,...,q_n$, I would like to define a new CoefficientDomain for PolynomialReduce function such that get these parameters as integers, In the other words, ...
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1answer
87 views

How to automatically find sequence of linear transformations

I have a set of three polynomials in x and y, and 9 real coefficients a1, ...
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121 views

NSolve command for underdetermined systems in Mathematica 11

I used to have Mathematica 8 previously and whenever I ran the NSolve command on underdetermined systems, NSolve[x^2 + y^2 + z^2 == 1 && x y z == 2, {x, y, z}] it used to give me a ...
5
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1answer
231 views

How to express Groebner Basis in terms of original elements?

I have polynomials {A1,B1} and then I find their Groebner basis to be {g1,g2,g3,g4}. Is there a way for me to express each polynomial g1,g2,g3,g4 in terms of A1, B1? (ie have g1= h1 A1 + h2 B1 where ...
8
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1answer
232 views

How to use Mathematica's GroebnerBasis to automate solving system of polynomials

Currently, Only way I know to use GroebnerBasis to solve system of polynomials require lots of manual steps. I'd like to know how to automate this process and if ...
7
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1answer
290 views

Using a Grobner basis to calculate common roots of a system of polynomial equations

We are trying to solve the inverse kinematics of a robot with $3$ revolute joints and one prismatic arm, link $4$, able to take lengths between $1$ and $2$. We assume all other lengths are $1$. Image ...
0
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54 views

to reduce the unknowns of a set of equations with several symbolic coefficients, e.g. using the GroebnerBasis

I have a set of $4$ equations with $4$ unknowns $\theta_1$ to $\theta_4$, and would like to eliminate the number of unknowns, to get a smaller set of equations, e.g. $n$ equations with $n$ unknowns, ...
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103 views

Operations on ideals of polynomial rings

There is GroebnerBasis to compute a Gröbner basis of an ideal in a polynomial ring, but I am looking for a package to perform operations on ideals $I,J\subseteq\Bbb ...
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31 views

Groebner bases with symbolic exponents [duplicate]

I'm trying to eliminate variables using Groebner bases or polynomial resultants with symbolic exponents. I'm wondering if it is possible to do it in general case for non-negative integers $C_{ij}$. ...
2
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2answers
133 views

Crash after long GroebnerBasis calculation

I am running a long computation of a GröbnerBasis and after some hours the kernel crashes. The memory usage increases enormous, and it crashes, when it reaches somewhat 4 GB RES, however it is ...
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108 views

Need help solving a polynomial system [closed]

I need help solving the following system of equations: ...
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284 views

How to find an algebraic representation

I want to find matrix representation of some algebra (Clifford algebra Cl(3,1) in this case). Here is an example, which I would like to get and then extend to higher dimensional matrices. Suppose we ...
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149 views

How to speed up the calculations of the Gröbner basis of the following system of equations?

Consider the following ideal: ...
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1answer
551 views

How to convert a rational parametric plane curve into implicit form?

This problem is generated from another Green's theorem related question of mine. And here is a forward of the same problem in math.stackexchange. The original equation of the plane curve is not in ...
4
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1answer
775 views

Producing a minimal Gröbner base

Mathematica has the command GroebnerBasis[{p_1,...},{x_1,...}] that returns a Gröbner base for some set of polynomials. I want to know if there is a command to do ...
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0answers
80 views

Finding related roots to a polynomial

I posted this in math.stackexchange, but this might be a better place. Assume that $f(X,Y,Z,V,W)\in \mathbb{Z}[X,Y,Z,V,W]$ is some polynomial and assume that $f(x,y,z,v,w)=0$. I would like to know if ...
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1answer
242 views

PolynomialReduce inconsistent results

I was playing around with gröbner basis and s-polynomials and I fell upon the PolynomialReduce, and I was wondering why it gives different results when I move around the polynomials in its second ...
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2answers
183 views

Number of complex roots for the system of polynomials

I have a system of algebraic equations. For example: $$ \left\{ \begin{aligned} x^2 y + 2 x y + 2 &= 0,\\ y^3 + 2 x + 1 &= 0. \end{aligned} \right. $$ (In my problem the system contains 16 ...
6
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2answers
345 views

Finding common roots of a specific system of polynomials

Some of my colleges are interested in finding common zeros of the following four polynomials: ...
4
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2answers
430 views

Dimension of an algebraic variety

I would like to compute, using Groebner bases, the dimension of the variety defined by a set of polynomials in several variables. In the wikipedia page the method is described, and an implementation ...
5
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1answer
493 views

Multivariate resultant in Mathematica?

Is there any command in Mathematica 7 which can compute the (McCaulay) resultant of a parametric system of multivariate polynomial equations? In fact, it would be great if there is also a way to ...
10
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1answer
1k views

How to express the original ideal elements in the Groebner basis?

Suppose I call GroebnerBasis[{f1, f2, ...}, {x1,x2, ...}] The output is a list {g1,g2,...} For each $g_j$, there should be ...
8
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1answer
343 views

GroebnerBasis without specifying variables

All the examples in the Mathematica documentation specify that the syntax for the GroebnerBasis command is ...
9
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1answer
759 views

Gröbner basis on a particular set of equations

This question is very similar in gist to equation solving with GroebnerBasis, but hopefully when I say that I make the system a little larger I mean little. I have ...
5
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2answers
602 views

Equation solving with GroebnerBasis

I have a system of quadratic equations defined below ...