# Tagged Questions

Questions on the functionality operating on polynomials

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### Implementation of the Polynomial Chinese Remainder Theorem

I would like an implementation of the Chinese Remainder Theorem for polynomials in $\mathbb{Z}[x]$, that is, a function ...
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### Points on discriminant variety?

I am trying to find a way in Mathematica to compute points on discriminant variety for modest size systems, but I couldn't find one. The system is something like: ...
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### Coefficients of a polynomial in powers of 10

Can I express a polynomial function in Mathematica in power (ScientificForm) ? I was trying: ...
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### CoefficientRules for negative powers

CoefficientRules acts like the following. ...
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### 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 ...
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### Small Issue with Chebyshev Derivative Approximation

I am trying to approximate the derivative of a function from its Chebyshev expansion. I start out with the following random function: ...
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### Efficiently strip off coefficients in front of variables?

I am working with multivariate polynomials and need a very efficient way to decompose monomials into coefficients and pure monomials. for instance consider variables ...
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### Creating a function with integral zeroes of the 0th, 1st, and 2nd derivatives

I would like to be able to randomly generate functions, each of which satisfies $f : [-10, 10] \rightarrow [-10, 10]$ All the zeroes, critical points, and inflection points have an integral ...
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### How to do the polynomial stuff over finite fields extensions fast?

This question is raised from the problem of package FiniteFields being very slow (please, see the corresponding question): I have had an evidence that Mathematica ...
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### Better use of Mathematica's PolynomialReduce[]?

I've been using scPhiDecomp[expr_]:= PolynomialReduce[expr, {x^2-y^2,2 x y}, {x,y}] which works great on ...
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### How many solutions do you get from simultaneous polynomial equations?

I have the following four simultaneous polynomial equations ...
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### How to equate coefficient of two polynomials? [closed]

Given two polynomials, How can I equate coefficients of them in Mathematica? For instance a + b x + (c+d) x^2 + (e+f)x^3 == 0
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### Relative factorisation with scalar quantities

I'd like to find a natural way to tell mathematica that a given unknown in a polynomial should be treated as a number, unlike the other variables. Typically I'd like to sum two polynomials in several ...
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### Fishing for monomials in a nested or partially factored polynomial stream

I have a problem where I'd like to be able to take a multivariate polynomial whose variables are nonscalar and is not written explicitly as a sum of it's nonzero monomial terms and determine which ...
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### How to check if a Polynomial has a specific form

I have a polynomial F[x], for example F[x] = 1 - 2x + x^2. I wanna check whether F[x] has the form of ...
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### How to reduce a quartic form to a quadratic form with equal roots

Preface: To clear the theoretical background this question is cross-posted on math.stackexchange here. I have a polynomial in $n$ variables of the form ...
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### How can I prevent a polynomial from being simplified?

I'm having a problem with polynomials. Let's say I have a polynomial "2x^2 - 5x + 6 - 3x^2" .. How can I check that this expression is not simplified ? Additionally, I would like to locate the ...
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### Solving for the roots of a trilinear system of polynomials

I have been trying to solve for the roots of the following system of trilinear polynomials: ...
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### How to solve coupled multi-variable polynomials?

The following code generates two polynomials $q_1$ and $q_2$ in complex variables p and c: ...
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### Write a function using pattern test to test whether the input is polynomial and print error message if not

I am doing this which is supposed to be an easy problem and which I think my code should be correct but for some reasons it is not working. May anyone help correcting my mistakes? How should I write ...
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### How to prevent fractions in polynomial quotients?

(This was a hard question to give a succinct title to, so feel free to edit it.) When I divide polynomials, I would like Mathematica to NOT create negative powers of variables. For example: ...
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### How to enforce mathematica to analytically evaluate roots?

I am interested in simplifying expressions involving HeavisideTheta. A simple example could be: HeavisideTheta[1 + x - x^2 + x^3] The best I can achieve is with ...