# 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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### 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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### 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: ...
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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### 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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### 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?
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: ...
85 views

### Finding a set of characteristics of a system of polynomial equations

we have an ODE system as following ...
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, ...
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, ...
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 ...
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 ...
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 ...
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 ...
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### 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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### GroebnerBasis without specifying variables

All the examples in the Mathematica documentation specify that the syntax for the GroebnerBasis command is ...