# Questions tagged [groebner-bases]

Questions on the use of Gröbner basis techniques in Mathematica.

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### Groebner Basis for Functions

We can use Reduce to solve the following Reduce[1 - Sqrt[a^(-1)] + Sqrt*Sqrt[(a + a^2)^(-1)] - Sqrt[2 - 2/(1 + a)] == -1 + Sqrt, a, Reals] We can also do ...
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### Solving a system of polynomial equations - can I be sure that the number of solutions, and the solutions are correct?

I need to solve a system of two polynomials with integer coefficients in two variables, $\{Q_1(w,z)=0,\,Q_2(w,z)=0\}$, and want to compute all real solutions. I'm able to run ...
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### Why are some symbols recognized by Mathematica but nowhere in the documentation? [duplicate]

I was trying to calculate a Groebner basis for a given set of polynomials, and I did it successfully. But I wanted to calculate the conversion matrix between the original basis and the Groebner basis....
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### How to find the regular chain?

How do we find the regular chain from the Gröbner basis ...
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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: ...
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### Default weight matrix for EliminationOrder

For the computation of elimination ideals via Mathematica's GroebnerBasis method, e.g. ...
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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?
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### 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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### Finding a set of characteristics of a system of polynomial equations

we have an ODE system as following ...
140 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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### How to automatically find sequence of linear transformations

I have a set of three polynomials in x and y, and 9 real coefficients a1, ...
134 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 ...
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### 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 ...
278 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 ...
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### 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 ...