Questions on the functionality operating on polynomials

learn more… | top users | synonyms (1)

4
votes
1answer
74 views

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: ...
0
votes
0answers
35 views

Numerically finding a single root of a polynomial system

I may be off base, but from the documentation, it sounds like NSolve is specifically tailored to finding (all) roots of a polynomial system. On the other hand, ...
1
vote
1answer
153 views

How can I calculate all irreducible polynomials of 31 degree in $\mathbb Z_2[x]$?

How can I calculate all binary irreducible polynomials of degree 31? or how i calculate all irreducible $f$ in $\mathbb Z_2[x]$? (The irreducible polynomial in $\mathbb Z_2[x]$ and $\mathbb R$ are ...
2
votes
1answer
54 views

RootReduce-Part of Solve

I have given the following expression in $M$ and $z$: \begin{equation} a = \frac{-4 M^2+M (-3 z-5)+\frac{1.1875 z}{\sqrt{\frac{0.015625 z}{M+1}-1.5625} \sqrt{\frac{0.765625 ...
3
votes
4answers
58 views

CoefficientList with multivariable [closed]

Consider: t = (1 + x)^3 (1 - y - x)^2 Expand[t] Now: CoefficientList[t, {x, y}] The output is: {{1, -2, 1}, {1, -4, 3}, ...
10
votes
5answers
2k views

How to get exact roots of this polynomial?

The equation $$ 64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0 $$ has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
3
votes
1answer
126 views

Solving a system of generated equations?

I would like to generate a function in the following form, where the number of terms can be specified arbitrarily: ...
6
votes
6answers
2k views

Series expansion in terms of Hermite polynomials

I am trying to expand a polynomial in terms of orthogonal polynomials (in my case, Hermite). Maple has a nice built-in function for this, ChangeBasis. Is there a ...
3
votes
1answer
117 views

Factorize and find the null space of a polynomial in several variables [duplicate]

I've been asked to factor the following polynomial: poly = 6 x^3 + x^2 y - 11 xy^2 - 6 y^3 - 5 x^2 z + 11 xyz + 11 y^2 z - 2 xz^2 - 6 yz^2 + z^3 And to solve for z so that poly = 0 Can anyone help ...
7
votes
4answers
133 views

Unexpected behavior using FromDigits to reconstruct polynomial

I have an issue with the reconstruction of a polynomial using FromDigits. The documentation of the function CoefficientList says: Fold the operation for multivariate polynomials: ...
1
vote
1answer
66 views

How to rearrange CharacteristicPolynomial[ ] terms?

I have a symbolic matrix A, which I need to find the characteristic polynomial, then order the polynomial in greatest-to-least form. (Ultimately to find the matrix inversion via Cayley-Hamilton ...
2
votes
1answer
128 views

Computing Poincaré symbolic solution for an arbitrary integer order polynomial

In the 1880s, Poincaré created functions which give the solution to the nth order polynomial equation in finite form. These functions turned out to be "natural" generalizations of the elliptic ...
1
vote
1answer
59 views

Recurrence relation for multivariate polynomials

I am trying to define a function which recursively computes a polynomial associated to every binary string: ComputePoly[s_]:=(** Recurse on the string s**) For ...
2
votes
1answer
188 views

Issue with Coefficient command [closed]

I'm trying to used the Coefficient command to extract the numerical values in front of a Chebyshev polynomial. I know that there is a numerical way to do this, presented in numerical recipes, which I ...
4
votes
1answer
108 views

Counting the number of terms in a polynomial using Length command

I have the following polynomial which depends on $n$: poly = (Sum[(i - 1) y[i], {i, 1, n, 1}])^2 - Sum[(i - 1)^2 y[i]^2, {i, 2, n, 1}] // Expand; The ...
8
votes
1answer
232 views

Speed up MinimalPolynomial

My Mathematica code runs slowly MinimalPolynomial[Sqrt[2] + Sqrt[3]+ Sqrt[5]+ Sqrt[7]+ Sqrt[11]+ Sqrt[13], x] runs slowly, but the Maple version ...
2
votes
1answer
58 views

Efficient way to apply linear function to multivariate polynomial [closed]

Suppose I start with an expression that is a multivariate polynomial in $x_k$'s, $$W = a + b \cdot x_1^{n_1} x_2^{n_2} x_3^{n_3} x_4^{n_4} + c \cdot x_1^{m_1} x_2^{m_2} x_3^{m_3} x_4^{m_4}$$ where ...
0
votes
1answer
42 views

Primitive polynomials of a field [closed]

I would like to know how I can get the primitive polynomials to generate the points of the fields GF(7) and GF(9) using Mathematica. Any help is appreciated.
6
votes
7answers
260 views

What is the inverse of CoefficientList?

I have numbers in vector notation. I need to get polynomial notation from them. My numbers are {0, 1, 23, 5, 15, 0, 0, 0}. I want to get $x + 23x^2 + 5x^3 + ...
-1
votes
0answers
28 views

Coefficients to Polynomial expression [duplicate]

How could I create a polynomial function from a list of coefficients. ...
0
votes
0answers
33 views

Timing of associated Legendre polynomials

I encountered a strange issue with the associated Legendre polynomials implemented with LegendreP[l,m,z]. Quite simply, the time used for the numerical computation of those quantities depends on ...
3
votes
0answers
71 views

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: ...
6
votes
2answers
157 views

How does Mathematica calculate LaguerreL

About the function LaguerreL[n,a,x], the helping documents in Mathematica only say that this function satisfies equation $xy^{\prime\prime}+(a+1-x)y^\prime+ny=0$. ...
1
vote
0answers
55 views

How can I find the formal derivative of a polynomial w.r.t. to its coefficients [duplicate]

I want to define a function $f(x)$ as in $\quad \quad f(x) = \sum^{n}_{i=0} c_i x^i$ as a symbolic expression. Then I'd like to do operations on it. For example, take derivatives of it with respect ...
0
votes
0answers
79 views

NIntegrate Polynomial of high degree

I want to integrate a polynomial of degree 100 and higher over a domain that is the intersection of two balls like ...
3
votes
1answer
52 views

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 ...
7
votes
1answer
152 views

Trouble with polynomial multiplication

Bug introduced in 10.1.0 and persisting through 10.2.0 or later ...
2
votes
0answers
61 views

Funny behavior when computing dot product of coefficients with high-order polynomials

I have a similar problem to Funny behaviour when plotting a polynomial of high degree and large coefficients. However, the thing being evaluated is not just a polynomial but a dot product of some ...
3
votes
2answers
261 views

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 ...
3
votes
1answer
116 views

Bug in associated Legendre Polynomials?

Mathematica's definition of the connection of associated Legendre polynomials with $m$ and $-m$ is: $P_l^{-m}=(-1)^m \frac{(l-m)!}{(l+m)!} P_l^m$. We also now that $|m|>l \Rightarrow P_l^m=0$. ...
4
votes
1answer
33 views

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 ...
7
votes
2answers
2k views

Gram-Schmidt Process for Polynomials

I want to implement the Gram Schimdt procedure to the vector space of polynomials of degree up to 5, i.e. I want to find an orthogonal basis from the set of vectors $v=(1,x,x^2,x^3,x^4,x^5)$. The ...
3
votes
0answers
62 views

Memory Management for Large Datasets [closed]

I've written some Mathematica code to generate polynomial roots. The code take an argument n as the highest degree of polynomial to solve for and then exports a file containing a list of the roots: ...
2
votes
1answer
47 views

Polynomials with integer coefficients vs. polynomials with rational coefficients

My problem is very simple. From two different functions $f_1$ and $f_2$, I create two multivariate polynomials. Because of theoretical reasons those two functions (evaluated with the same input $x$) ...
1
vote
2answers
308 views

How to know form of plotted Bézier function

Simple scenario is to see the Bézier function, but how to know which polynomial approximate it? ...
13
votes
1answer
315 views

ToNumberField won't recognize Root as an explicit algebraic number

Bug fixed in 10.0.0 In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an ...
16
votes
4answers
881 views

How to keep Collect[] result in order?

For example, Collect[(1 + x + Cos[s] x^2)^3, x] gives the result ...
14
votes
4answers
2k views

Is there a way to Collect[] for more than one symbol?

Oftentimes you find yourself looking for polynomials in multiple variables. Consider the following expression: a(x - y)^3 + b(x - y) + c(x - y) + d as you can ...
5
votes
1answer
61 views

Is there a way to Collect[] for more than one symbol in Mathematica 10.0?

This question has already been asked three years ago (Is there a way to Collect[] for more than one symbol?) but I'm not allowed to comment since I'm new at Mathematica StackExchange. The first ...
14
votes
0answers
149 views

Undocumented fourth parameter of Collect; how long has it been there?

While tinkering with How to get a list of monomials of a polynomial without coefficients? on a whim I tried a fourth argument in Collect and found: ...
4
votes
3answers
275 views

How to get a list of monomials of a polynomial without coefficients?

Giving a polynomial, say a x^2 + b x y + c y^2 MonomialList[a x^2 + b x y + c y^2, {x, y}] just gives ...
7
votes
2answers
211 views

On the definition of the associated Legendre polynomials

Mathematica computes for n = 1,2,...: (-1)^n (LegendreP[n, -1, -3]/Sqrt[2]) -I, -3 I, -11 I, -45 I, -197 I, ... Maple ...
-2
votes
1answer
45 views

Generic approaches for multivariable polynomials across different domains [closed]

Mathematica newbie here. So I don't have a lot of time to read through the whole library of functions and language rules. So I'm trying to settle in on generic ways of doing the math that I'm going to ...
2
votes
3answers
117 views

Question on alternate forms of polynomial output

EDIT: Would it be possible to do something like let $y=ax+b$ then use Collect[] or Apart[] on the new expression? How would I go about this. I've tried using Collect[%,ax+b], Collect[%,{ax+b}], and ...
6
votes
2answers
132 views

NSolve erroneously gives no solution to a polynomial system

I have a polynomial system with three equations in three unknowns, the maximum degree is 26. Two equations are symmetric, i.e. eq1(x,y,z)=eq2(y,x,z). If I search ...
4
votes
2answers
141 views

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 ...
4
votes
3answers
294 views

What is the best way to write a polynomial in the Bernstein basis?

The Bernstein basis of polynomials of degree $n$ is the set of polynomials of the form $$\binom{n}{k} t^{n-k}(1-t)^k$$ where $0 \leq k \leq n$. What is the best way to transform a given polynomial ...
0
votes
2answers
68 views

Generating polynomials with conditions on coefficients

I want to define polynomials with coefficients given in some range. Namely, let $p$ be a prime number and $n$ be a positive integer. For all positive integer $k\leq n$ I want to generate all ...
2
votes
4answers
142 views

Symbolic cut-off of high-order terms

I know that I can cut-off high-order terms of a $1$-variable polynomial P = a0 + a1*x + a2*x^2 + a3*x^3 + a4*x^4 + a5*x^5; simply by doing for example ...