Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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5
votes
3answers
98 views

Optimal way to extract “positive part” of a multivariate polynomial

I've got multivariate polynomials with numerical coefficients, like e. g. p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3 and ...
5
votes
2answers
319 views

Plotting Chebyshev polynomials using PolarPlot and FilledCurve

This question is related to this answer. What should I change in the following code to replace black color with blue color in the second image? ...
0
votes
1answer
42 views

Generalize polynomial coefficients from multiple equations

I have following equations: $$\frac{1}{((a_1 - 1) f + 1)} + \frac{1}{((a_2 - 1) f + 1)} -k = 0$$ $$\frac{1}{((a_1 - 1) f + 1)} + \frac{1}{((a_1 - 1) f + 1)} + ... + \frac{1}{((a_n - 1) f + 1)} -k = 0$...
1
vote
1answer
71 views

How to extract only real part of 2nd root solution to C code?

I have this cubic polynomial: ...
2
votes
2answers
171 views

NSolve gives weird result for $n=101$ with NSolve[$\frac{d}{dx}\prod \limits_{k=1}^n (x-k)$==0,x]

Coming from this post: What would be the roots of the derivate of this polynom I did a quick check with Mathematica and arrived at a wrong result. I was initially confused but chose to trust ...
5
votes
3answers
352 views

Mathematica function equivalent to Matlab's residue function (partial fraction expansion)

I am looking for a Mathematica function equivalent to Matlab's residue function. If there is no Mathematica equivalent, I would like to write a function that given the coefficients of two polynomials ...
5
votes
2answers
372 views

Turning arguments into exponents

I'd like to replace every instance of L[stuff], e.g., L[-1,-2,-2] in an expression with ...
1
vote
1answer
30 views

Factorization of multivariable polynomial

I have a polynomials of multivariable for instance: $P=yx+2^4xy+3+5^2xz+3^4zx $ Now I would like to do the following: extract those temrs that only has $z$ . extract terms that only has $y$ express ...
4
votes
2answers
53 views

Making polynomials representing frequency of a character in a list

Suppose I have the following list: l={{"a"}, {"a", "h"}, {"a", "d", "k", "r", "v"}, {"a", "b", "c", "k"}, {"a", "b", "c", "s", "u"}} this list made of the ...
3
votes
2answers
57 views

Simplify the cubic root of cube assuming real and positive variable

I know this is very simple but I couldn't find a reasonable solution for it in the archive. It seems that my Mathematica does not take into account the assumptions when it wants to simplify the ...
0
votes
1answer
62 views

Find roots of a polynomial equation or simplify

I have an equation like below: ...
1
vote
4answers
130 views

How to fit polynomial curve using Mathematica for multiple inputs?

I am new to mathematica. I have 3 inputs and 1 output. I want to find the 'N' th degree of polynomial which would approimately fit my dataset. I tried FindFit but it does not solve my problem. I also ...
4
votes
1answer
54 views

How to do arbitrary non-negative powered polynomial division in Mathematica?

Suppose I have a simple polynomial in $\{a,b\}$, defined as $a^k-b^k \ \forall \ k\in \mathbb{Z}^{\geq0}$. If I know one of the factor is $(a-b)$, is there a way to get a representation of its ...
1
vote
2answers
77 views

Zeros of high degree polynomials

I am working with Hermite polynomials in Mathematica with the built-in function HermiteH. I want to compute the zeros of the polynomial ...
2
votes
4answers
89 views

Sorting polynomials based on their y value and finding their intersection

I've got the following list of polynomials, ...
0
votes
1answer
42 views

Symbolic Resultant Too Slow/Keeps Running

Evalutation of the following cell, which includes the symbolic resultant, of two univariate polynomials in $x$, with parameters $a,b,c$ for the first polynomial (of degree 4) and parameters $d,e,f,g$ ...
3
votes
1answer
29 views

Collect more than one symbol and series

I have a complicated expression in function of 2 variables A and f that appears in all the possible combination. For example ...
0
votes
1answer
60 views

How to find the largest degree of a polynomial?

I have a huge polynomial, and I am having the following issues 1. I wanted to find the largest and smallest degree of that polynomial. 2. How to truncate the lower order terms, sometimes higher order ...
0
votes
1answer
65 views

How do I treat polynomials as vectors?

From time to time I find myself in the following situation. I have generated a list of polynomials from some ring $R=\mathbb R[x_1,\ldots,x_n]$ and now I wish to view these polynomials as vectors in ...
4
votes
3answers
243 views

Alias for root of a polynomial

I need to work with a variable $u$ such that $u^2 + u + 1 = 0$. I don't want to find a root of the polynomial $u^2 + u + 1$. Rather, I have to work with $u$ symbolically so that a (polynomial) ...
0
votes
1answer
58 views

How to substitute integral operators into polynomials?

Suppose I have a polynomial $a_0+a_1 f(x,t) + a_2 f(x,t)^2 + ....$. In code, a0 + a1 y + a2 y^2 + a3 y^3 /. y :> Integrate[Subscript[y, k] E^(I k y), k] <...
0
votes
1answer
35 views

Resultant running too slow

I have a system of equations all linear in one variable X with many parameters. I am trying to separate the variable in these equations by taking the pairwise resultants of one of the equation with ...
1
vote
1answer
65 views

Have I found bugs in Solve and Reduce? [closed]

f[x_] := x^3 - 2 x + 1; Solve[f[x] == 0, x] {{x -> 1}, {x -> 1/2 (-1 - Sqrt[5])}, {x -> 1/2 (-1 + Sqrt[5])}} But ...
0
votes
0answers
30 views

Optimisation in the solution of Newton Interpolation

I have an exercise in which I have to solve the following Problem: Given Newton formula for the representation of a polynomial $q(x)$ given the values $y_j$ of $q(x)$ for $j$ between 0 and 5 $q(x)= \...
1
vote
1answer
50 views

Parametric solution of a system of polynomial equations

I have the following system of equations, 1+x+y+z==0, 1+x*y+y*z+x*z==0 which I want to solve in the extension field of GF(2), the algebraic closure of GF(2) for ...
0
votes
1answer
105 views

Fastest way to simplify rational functions

I am using Series to approximate function of two variables: Series[f[x,y],{x,0,m}] the function is a complicated sum of ...
3
votes
1answer
392 views

How to write the shifted Chebyshev polynomials (the first kind) in mathematica?

Is it possible to write the shifted Chebyshev polynomials (the first kind) in Mathematica? The formula is: $$P_n(x)=\sum_{k=0}^{\left\lfloor\tfrac{n}{2}\right\rfloor}(-1)^k 2^{n-2k-1}\frac{n}{n-k}\...
1
vote
1answer
86 views

How to expand a composite function into series?

I need to expand such a function $$g[y,z(x,y)]=\frac{-y (z+1)^4-z^4-4 z^3+8 z+8}{z+1},\tag{1}$$ into powers of $x$ and $y$. Among $x,y,z$ there is a constraint equation, for example $$(3 y+3) z^4+z^...
0
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0answers
41 views

Discrete convolution power

In my previous question we have discussed the posibility of various definition of convolution of power function within Mathematica. Now the question is "How to define convolution power in Mathematica ?...
0
votes
2answers
51 views

Factor not factoring quadratic polynomial [closed]

I'm using version 11.3 Expand[(Sqrt[2] - t)^2] 2 - 2 Sqrt[2] t + t^2, but ...
1
vote
1answer
30 views

(Ir)reducible polynomials over some field

When I want to factor a polynomial, say $p(x)$ over $\mathbb{Q}[\sqrt{2}]$, I can do Factor[p(x), Extension -> {Sqrt[2]}] what if I want to factor a ...
0
votes
0answers
30 views

Solving Polynomial Functions [duplicate]

How would I code the solution to this problem? Let P be a polynomial satisfying P(x + 1) + P(x − 1) = x^3 for all real numbers x. I am trying to find P(x)
5
votes
5answers
270 views

How to factor all coefficients of a multivariable into prime factors

I have several polynomials in 2 variables with integer coefficients, e.g., poly= -10 x - 10240 y^3 - 1520 x y^4; I'd like to convert all such polynomials into a ...
2
votes
0answers
87 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 ...
1
vote
1answer
59 views

Splitting a general rational polynomial ansatz into powers

EDIT This question is completely wrong and useless. It is mathematically incorrect. I think something like Series is sufficient if you're trying to do something ...
0
votes
1answer
46 views

Constant term of Laurent polynomial in many variables

What is the quickest way to extract the constant term from a Laurent polynomial in two variables? For example $x+1 +x^{-2}y+x/y$ has constant term $+1$.
3
votes
0answers
81 views

How to make GroebnerBasis Work or to speed NSolve up [closed]

I consider a set of three polynomials of two variables ...
2
votes
1answer
161 views

Rewrite the power sum in terms of convolution

Let be an identity $$n^{2m+1}=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1}k^r(n-k)^r,$$ where $A_{m,r}$ are real coefficients, see A302971 for numerators and formula of $A_{m,r}$. Here we can notice that $\...
0
votes
2answers
71 views

How to write a function of a polynomial

I will illustrate my problem with this example: I want to make a function which, given a polynomial, gives me the value of the integral $\int_0^1(ax+bx^2)dx=a/2+b/3$. Therefore, in this example, I ...
1
vote
1answer
76 views

Polynomial PowerMod

Is there equivalent of PowerMod for polynomials in Mathematica? We have Mod[a^e,m]==PowerMod[a,e,m], $a$, $e$ and $m$ all ...
0
votes
2answers
96 views

Find $k= constant$ so that $disc= 0$ [closed]

Find $k= constant$ so that $\lceil$ https://www.wolframalpha.com/input/?i=discriminant%5By%5E6%2By%5E2z%5E6%2Bz%5E2-y%5E2z%5E2(1%2By%5E2%2Bz%5E2)-k(1%2Bz%5E2)z%5E2(y%2Bz)(y-z)(z-1)(z%2B1)%5D,z%5D $\...
1
vote
2answers
43 views

Collect term in a distributive way

Consider P = x (a2 b2 v^a2-1+a3 b3 v^a3-1+d1+d2-2 y)-(y-d1)(y-d2)-x I would like to collect terms in (x,y,z) in a distributive way, that is to get an expression ...
1
vote
2answers
94 views

Polynomial fit and Fourier transform plot

I'm pretty new to Mathematica so excuse me for obvious questions. I have a dataset, second column contains invoice amount and the first column contains days passed between each invoice date starting ...
0
votes
1answer
76 views

Algebraic substitution for polynomial simplification

Consider a polynomial $p(x,y)$ and we want to simplify $p(x,y_0)$ where $y_0$ is a root of some other polynomial $q(y)$. In Maple I would use something like: ...
1
vote
2answers
101 views

Simplifying polynomials [closed]

I have noticed a strange behaviour in Mathematica regarding simplifying polynomial expressions. Take the following polynomials pol1=3-8s+4s^2 pol2=(2s-1)(2s-3) ...
3
votes
2answers
176 views

Maximum point of a rational function

Suppose I have the following rational function: ...
6
votes
2answers
89 views

How to make Orthogonalize simplify each new vector before using it to orthogonalize the next one?

I'm trying to construct a set of orthogonal polynomials, starting from a specially-prepared initial polynomials: ...
4
votes
2answers
88 views

The set of polynomials under the action by a symmetric group

Let $$f(x_1,x_2,x_3)=\frac{x_1^r x_2^r \left(1-x_1 x_3\right) \left(1-x_2 x_3\right)}{\left(1-\frac{x_2}{x_1}\right) \left(1-\frac{x_3}{x_1}\right)\left(1-\frac{x_3}{x_2}\right)},$$ where $r$ is a ...
3
votes
1answer
43 views

Ranking polynomials based on global maxima

Suppose I have the following polynomials in an association i.e. <|...|>, they are: ...
0
votes
1answer
83 views

Finding the inverse of a function

I am to solve for $r(\rho)$ given the function, \[Rho]Asymp[r_,b_,q_] := 1/(1 - q) Gamma[1/(1 - q)]/Gamma[(q - 2)/(q - 1)] r Sqrt[1 - (b/r)^(1 - q)] This can be ...