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Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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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., ...
Orders's user avatar
  • 1,247
8 votes
0 answers
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 ...
Pavithran Iyer's user avatar
7 votes
0 answers
184 views

Why is Resultant so slow?

I need to calculate the discriminant of a polynomial $f$ ...
lapcal's user avatar
  • 531
6 votes
0 answers
101 views

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 ...
bbgodfrey's user avatar
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5 votes
0 answers
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 ...
Per Alexandersson's user avatar
5 votes
0 answers
169 views

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 ...
Claretta's user avatar
  • 283
4 votes
0 answers
591 views

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 ...
physioConfusio's user avatar
4 votes
0 answers
122 views

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

I have a big polynomial expression, like this: ...
user43259's user avatar
4 votes
0 answers
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 ...
Nicholas Gaffney-Henderson's user avatar
3 votes
0 answers
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 ...
hipHopMetropolisHastings's user avatar
3 votes
0 answers
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 ...
Nugi's user avatar
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3 votes
0 answers
42 views

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?
Gerald Cargo's user avatar
3 votes
0 answers
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 ...
user57467's user avatar
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3 votes
0 answers
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: ...
jjstankowicz's user avatar
3 votes
0 answers
393 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 ...
Jesko Hüttenhain's user avatar
3 votes
0 answers
469 views

Integrating the Associated Legendre Polynomials

I know the following identity: $\qquad \int_{-1}^1 P_l^m(t)^2dt=\frac{2(m+n)!}{(2n+1)(n-m)!}$ I would like to verify this result using Mathematica. This is what I entered: ...
Soby's user avatar
  • 131
3 votes
0 answers
383 views

Least squares approximation

I have data points which is mydata = {{0, 0}, {1, 1}, {2, 0}}; From this data, I need to do the least squares approximation by using Bernstein polynomials to produce a set of Bezier points. Before ...
BayWilson's user avatar
  • 347
3 votes
0 answers
456 views

Polynomial kernel expansion

I am trying to calculate the polynomial kernel expansion using Mathematica. I have tried the Expand and Simplify functions with ...
JC1's user avatar
  • 131
3 votes
1 answer
413 views

Mathematica is unreliable about recognizing orthogonal functions

Hermite polynomials should be orthogonal over a Gaussian measure. However when the orders of the polynomials are larger than a few, Mathematica gets this wrong. Strangely, it seems to hinge on whether ...
Yakimo's user avatar
  • 31
3 votes
1 answer
129 views

PolynomialRemainder memory

This calculation makes the kernel crash because it needs so much memory. Thoughts on how to get around this? ...
Katie's user avatar
  • 31
2 votes
0 answers
43 views

Exact usages of the "*Coefficient*" family?

For applying some function func to the coefficients of a polynomial poly in variables vars, ...
user688486's user avatar
2 votes
0 answers
99 views

Guessing patterns of symbolic series

I have a system of 2s+1 equations, where s can take integer values of {1,2,3,....,n}. Here ...
Monire Jalili's user avatar
2 votes
0 answers
119 views

How to solve this equation analytically?

Why can't Mathematica 13 solve this equation in radicals? Solve[x^5 - 5*x^4 - 10*x^3 - 10*x^2 - 5*x - 1 == 0, x] // ToRadicals I also tried to use ...
user avatar
2 votes
0 answers
125 views

Real solutions of third and fourth degree equations

A few hours ago I "discovered" that if a third or fourth degree equation has distinct real solutions, it's possible to calculate them avoiding complex numbers. In particular, we have: ...
πρόσεχε's user avatar
2 votes
0 answers
64 views

Approximation of roots using Series

I am solving a fifth degree polynomial using Series. My equation looks like ...
Gaurav Maurya's user avatar
2 votes
0 answers
315 views

Root finding over finite field extension

I'd like to know if there exists any method on Mathematica, third-party coded resource or library that can compute roots of a polynomial over an extension $\mathbb{E}$ where $E=F_p[x]/f(x)$ and $f(x)$ ...
kub0x's user avatar
  • 203
2 votes
0 answers
189 views

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 ...
2010jetta's user avatar
2 votes
0 answers
75 views

Solve polynomial system

I am trying to solve ...
dan's user avatar
  • 21
2 votes
0 answers
83 views

Expand a big product efficiently

I would like a fast way of expanding the following product: $$\prod_{i=1}^{N_1} \prod_{j=1}^{N_2}(\partial_{z_i} - w_j) (z_i - \partial_{w_j})$$ with the rule that the derivatives are moved all the ...
Marius Ladegård Meyer's user avatar
2 votes
0 answers
180 views

Check Zagier theorem about Mahler's measure

I want to check the following theorem by using Mathematica: (from Heights of Polynomials and Entropy in Algebraic Dynamics, page 22) $\textbf{Theorem}.$ Let $\omega$ denote a primitive $6th$ root ...
vito's user avatar
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2 votes
0 answers
88 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 ...
JT1's user avatar
  • 121
2 votes
0 answers
1k views

Polynomial factorization over finite fields with non-prime order

One can easily factor a polynomial over finite fields of prime order, using Factor command: ...
Sadeq Dousti's user avatar
1 vote
0 answers
46 views

How to `Collect` where `var` is one expression?

Edit: Clear["Global`*"]; expr1 = (a + c - b + 1)^3 + (-b + a + c + 2)^4 // Expand For test case expr1, this is the ...
138 Aspen's user avatar
  • 1,519
1 vote
0 answers
67 views

Problems with implementation of subresultant pseudo-remainder sequence in Sturm's theorem

I've implemented the subresultant pseudo-remainder sequences ( https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor#Pseudo-remainder_sequences ) as described in Wikipedia. However, when ...
Moonwalker's user avatar
1 vote
0 answers
37 views

Performing difference in extracting coefficients from a sum

I have an expression ...
Lelouch's user avatar
  • 543
1 vote
0 answers
48 views

Is it possible to use the Finite Fields package to define the elements of GF(4) in terms of the irreducible polynomial $P$?

I am new to the Finite Fields package and am finding the package tutorial confusing. I am wondering, if I am working over GF[4], is there a way of finding the elements of GF[4] in terms of the ...
am567's user avatar
  • 547
1 vote
0 answers
73 views

Solving a linear algebra problem containing minimal polynomial degree

Consider a set of three-dimensional points ${\left\{{\left(a,ab,abc\right)}~\middle\vert~a,b,c\in\mathbb{N_+}\land a+b+c\leqslant2023\right\}}$. If there exists a non-zero real polynomial $\...
user688486's user avatar
1 vote
0 answers
41 views

How can I transform an expression with radicals to RootSum?

I am working with the integrals like these: ...
Igor Kotelnikov's user avatar
1 vote
0 answers
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 ...
milf_and_cookies's user avatar
1 vote
0 answers
73 views

Putting everything with the same power together

I'm doing some computations wich involves a lot of big polynomials, for example: ...
User0212's user avatar
1 vote
0 answers
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 ...
user2966584's user avatar
1 vote
0 answers
78 views

Can one collect with respect to two groups of variables?

Here is a toy example of what I want: given ...
მამუკა ჯიბლაძე's user avatar
1 vote
0 answers
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 ...
Gert's user avatar
  • 1,580
1 vote
0 answers
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 ...
Bogdan Grechuk's user avatar
1 vote
0 answers
48 views

Question about NSolve

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: ...
Александр Миллер's user avatar
1 vote
0 answers
81 views

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

Consider the following matrix: ...
Math's user avatar
  • 407
1 vote
0 answers
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 ...
crabtree's user avatar
1 vote
0 answers
59 views

Reduce returning redundant solutions

When I call reduce on the following system: ...
David's user avatar
  • 159
1 vote
0 answers
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`...
Rui Yu's user avatar
  • 63
1 vote
0 answers
40 views

Custom multiplication operation between variables

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: ...
David's user avatar
  • 159