# Questions tagged [polynomials]

Questions on the functionality operating on polynomials

119 questions with no upvoted or accepted answers
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### Changes to Coefficient function in v10.2

In the version Mathemaica 10.4, I am very surprised that the core function Coefficient has changed, e.g., ...
• 1,247
601 views

### Computing Ehrhart's polynomial for a convex polytope

Is there a Mathematica implementation for computing the Ehrhart polynomial of a convex polytope which is specified either by its vertices or by a set of inequalities? I am interested in knowing this ...
184 views

### Why is Resultant so slow?

I need to calculate the discriminant of a polynomial $f$ ...
• 531
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### When does Root have a third argument

In Mathematica "11.0.1 for Microsoft Windows (64-bit) (September 20, 2016)", Root[#^4 + 1 &, 2]; actually has three arguments, as can be seen from ...
• 61.7k
580 views

### Change of basis of polynomials

Suppose I have a favourite basis for polynomials in $x_1,\dotsc,x_n$, say non-symmetric Macdonald polynomials to be specific. I can easily compute these, and thus the change-of-basis matrix that takes ...
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### Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
• 283
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### Homotopy Continuation solution of system of polynomials

I have very large systems (>20) of polynomial (max degree 3) equations that I would like to find a solution to. I'm not interested in all solutions as presumably there are too many (a huge number ...
122 views

### How do I reassign the ordering of symbols in a polynomial expression?

I have a big polynomial expression, like this: ...
518 views

### Extracting an equation from an interpolated function

Im trying to use LibraryLink to do some calculations in C but part of the expression i want to calculate is an Interpolating Function. C cant use that obviously so I'm trying to shift it to a data ...
80 views

### Computing First Moment of TransformedDistribution slow. Is there a way to speed things up? If not, can you help me understand why its slow?

I'm a novice Mathematica program, toying with the idea of solving for the first four moments of a linear combination of a multivariate Gaussian mixture distribution. The first two moments I have ...
123 views

### Mathematica package for computing Macdonald polynomials

I want to implement computation of Macdonald polynomials in mathematica. A similar question was raised in another question 5 years ago (Macdonald-Koornwinder polynomials?), but received no clear ...
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### Irreducibility of polynomials in two variables

Mathematica tests polynomials in several variables for irreduciblity. How can I find out what sufficient conditions for irreducibilty it uses?
414 views

### How to invert Expand

How do I invert Expand? I have lis={1 + x^2, 2 + 2 x^2 + x^4, 5 + 8 x^2 + 8 x^4 + 4 x^6 + x^8} and want to get ...
• 2,738
92 views

### Matrix elements in terms of Minors?

Is there a simple way to rewrite a rectangular $m \times n$ matrix in terms of its maximal minors? For a few small cases, $(m,n)$ = $(2,3),(2,4),(3,4)$ I can brute force by explicitly solving: ...
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1 vote
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### How can I transform an expression with radicals to RootSum?

I am working with the integrals like these: ...
1 vote
127 views

### Taylor series loop

I'm a beginner not only in Mathematica but also in programming in general, and so I'm not really sure where my problem lies exactly and I'd be glad to receive any guidance. Using the Taylor series for ...
1 vote
73 views

### Putting everything with the same power together

I'm doing some computations wich involves a lot of big polynomials, for example: ...
• 95
1 vote
103 views

### How to speed up Resultant?

I am experimenting with the polynomials Y and T: i1 = 9; i2 = 4; Y = Sum[ x^i y[i], {i, 0, i1}]; T = Sum[ x^i t[i], {i, 0, i2}]; Timing[Resultant[Y, T, x]] Whith ...
• 161
1 vote
78 views

### Can one collect with respect to two groups of variables?

Here is a toy example of what I want: given ...
• 2,066
1 vote
125 views

### Mathematica doesn't simplify 1. x

I'm debugging a program that uses polynomials with numerical coefficients and it turns out that mathematica does not simplify 1. x[1]^2 x[2]^2 to ...
• 1,580
1 vote
187 views

### Easy upper and lower bounds for curve genus in Mathematica

I am writing a Mathematica code in which I need, at some point, to compute genus of a lot of curves given by polynomial equations in 2 variables in affine coordinates. Unfortunately, this is possible ...
1 vote
48 views

there! For some purposes I need to be able to write a code in C# that could find all roots of the equations system, consisting of two-variable polynomial expressions, like the folliwing: ...
1 vote
81 views

### How to solve this quintic polynomial with the solutions in its simplest final form?

Consider the following matrix: ...
• 407
1 vote
166 views

### Algorithms or Mathematica definition for functions ideals of polynomial Rings

This question was well posed four years ago without answer at Operations on ideals of polynomial rings. I asked again in Nov 2021 and posted possible function defininitions. Lichtblau commented ...
• 71
1 vote
59 views

### Reduce returning redundant solutions

When I call reduce on the following system: ...
• 159
1 vote
87 views

### How to extract the coefficient all the monomials of an arbitrary polynomial efficiently?

At present I know 3 efficient function to generate a list of all the monomials and the corresponding coefficients of an arbitrary polynomial. They are CoefficientRule, MonomialList and GroebnerBasis...
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I am constructing polynomial expressions in the variables $s[0],s[1],...,s[n]$ and I'm trying to define a new operation to simplify the expression: ...