Questions tagged [polynomials]

Questions on the functionality operating on polynomials

0
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1answer
36 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
27 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
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1answer
54 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
58 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
241 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
56 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
32 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
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0answers
28 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
48 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
88 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
377 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
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1answer
84 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
40 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
49 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
29 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
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0answers
29 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
253 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
83 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
50 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
38 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
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0answers
79 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
157 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
67 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
69 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
83 views

Find $\text{k}$ such that $:$ $\text{discriminant}= 0$ [closed]

I tried to find $\text{k}$ such that $:$ $$\text{discriminant}\left [ \text{discriminant}\left [ z^{\,2}\left ( z^{\,2}- 1 \right )^{\,2}\left ( z^{\,2}+ 1 \right )+ \left ( y^{\,2}- z^{\,2} \...
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
89 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
74 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
88 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
82 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
83 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
42 views

Ranking polynomials based on global maxima

Suppose I have the following polynomials in an association i.e. <|...|>, they are: ...
0
votes
1answer
81 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 ...
0
votes
3answers
60 views

Simplifying polynomial Roots with assumptions

I have acquired the following root from a minimization problem: ...
0
votes
0answers
94 views

Create a polynomial from a list of coefficients [duplicate]

First I have to extract coefficients from a polynomial.Then I have to make a polynomial from by given list and show that they are identical. So I tried like this: ...
1
vote
2answers
41 views

How to reduce the residue in NSolve for a system of 3 non-linear equations

I have written the following snippet in Mathematica to solve a system of 3 non-linear equations? ...
0
votes
1answer
48 views

Computing subresultants

Let $f=f(x), g=g(x) \in \mathbb{C}[x]$ Write $f=(x-a_1)\cdots(x-a_n)$ and $g=(x-b_1)\cdots(x-b_m)$, where $n,m$ are natural numbers (distinct or not). Let $\lambda,\mu \in \mathbb{C}$. How do we ...
0
votes
1answer
55 views

How to avoid polynomial roots solution to be in a “power m/n” form?

How to find complex polynomial roots not in a weird "power m/n" form but in an "a+ib" form (e.g. for x^2+x+1==0)?
3
votes
4answers
225 views

Continuous non-piecewise equivalent of smoothstep function?

I have a smooth step function given by the piecewise function ...
0
votes
1answer
77 views

Convert a piecewise definition of a single impulse into an impulse train

NOTE: See update at end of question I have a function smoothstep (based on the derivative of a smoothstep function) that gives a single impulse as follows: ...
5
votes
2answers
90 views

Basic 3D Interpolation Failing

I've seen a few other posts asking about the "unstructured grid" error in Interpolation. Here's a minimal (non)working example of the issue: ...
6
votes
1answer
93 views

Loss of accuracy in orthogonalisation of polynomials using Orthogonalize

Context As a mean to understand the growth of structure in the universe, I am interested in characterising the curvature of random fields such as this one: For this purpose I start with a PDF of the ...
0
votes
2answers
99 views

Roots of a polynomial

In Mathematica I have represented the following polynomial $a x^4 + b x^2 + c x+2$ using the Plot command and, through the ...
4
votes
2answers
208 views

How to check whether Laguerre polynomials are orthogonal?

I've got the problem with checking if Laguerre polynomials for n=1,...,10 are orthogonal. I have to create the list of these polynomials, then create the matrix of integrals from 0 to infinity. ...
1
vote
1answer
38 views

Finding constraints on polynomials from their plot

Suppose I have the following list of rational functions (fraction of polynomials): ...
-2
votes
1answer
63 views

Plot a polynomial of two variables without giving the variables' limits [closed]

How to do make Plot automatically figure out a domain interval? what I mean to say is "I have a cubic polynomial with two variables "lambda" and "k".where as lambda is a function of "k". i.e lamda(k) ...
0
votes
3answers
133 views

how to get coefficient list from a polynomial with negative powers

Say a polynomial x^2-x^(-2), I need to extract its coefficient. I tried the command CoefficientList[x^2-x^(-2)], but no result ...
0
votes
2answers
95 views

Finding the best representation of a numerically-inverted function via InterpolatingPolynomial and/or variations

Below is the routine I am using to sort of represent the numerically-inverted function TP. Basically I am finding a necessary interpolating polynomial ...