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Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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1answer
63 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 ...
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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
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1answer
44 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 ...
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1answer
66 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 ...
2
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1answer
359 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}\...
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1answer
72 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^...
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0answers
36 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 ?...
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2answers
48 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
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1answer
28 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 ...
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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)
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5answers
151 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 ...
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0answers
64 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
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1answer
46 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 ...
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1answer
27 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 $+1$.
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0answers
76 views

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

I consider a set of three polynomials of two variables ...
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1answer
146 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 $\...
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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 ...
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1answer
56 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 ...
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2answers
80 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} \...
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2answers
41 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 ...
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2answers
87 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 ...
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1answer
66 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: ...
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2answers
74 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) ...
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2answers
175 views

Maximum point of a rational function

Suppose I have the following rational function: ...
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2answers
74 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
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2answers
75 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
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1answer
41 views

Ranking polynomials based on global maxima

Suppose I have the following polynomials in an association i.e. <|...|>, they are: ...
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1answer
58 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 ...
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3answers
54 views

Simplifying polynomial Roots with assumptions

I have acquired the following root from a minimization problem: ...
0
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0answers
43 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
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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? ...
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1answer
46 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
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1answer
42 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)?
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4answers
196 views

Continuous non-piecewise equivalent of smoothstep function?

I have a smooth step function given by the piecewise function ...
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1answer
72 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: ...
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2answers
82 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: ...
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1answer
89 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 ...
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2answers
93 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
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2answers
202 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. ...
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1answer
38 views

Finding constraints on polynomials from their plot

Suppose I have the following list of rational functions (fraction of polynomials): ...
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1answer
62 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) ...
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3answers
97 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 ...
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1answer
51 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 $TPint$ that fits with the data points given by ...
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1answer
38 views

Coercing FullSimplify to groups results

Is there a way to coerce FullSimplify to group the second result (below) to be similar to the first result? ...
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2answers
103 views

Programming with Mathematica Syntax - Dunford decomposition

I am always amazed while I am reading some solutions of problems in mathematical problems of this site with Mathematica. For instance, look at the problem 48. Whereas I am writing 100 lines of code ...
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1answer
72 views

Simplifying elliptic functions

I am working with (long) elliptic functions, which are rational functions in WeierstrassP and WeierstrassPPrime. As expressed in ...
4
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1answer
95 views

rational parameterization of a plane curve

Say one has a plane curve defined by a polynomial equation $$P(x,y)=0$$ and one knows that the curve has genus 0. Is there an implementation in Mathematica of a (proper) rational parameterization, i.e....
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0answers
60 views

Solving a real polynomial system takes forever, am I asking the impossible?

I want to find all stationary points of a particular 3 dimensional polynomial function. Sounds easy enough, right? Just get the gradient with Grad[], and solve the ...
4
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1answer
42 views

Default weight matrix for EliminationOrder

For the computation of elimination ideals via Mathematica's GroebnerBasis method, e.g. grob = GroebnerBasis[eqs, {a, b, c, d, e}, {x, y}, MonomialOrder -> EliminationOrder]; what is the default ...
0
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1answer
58 views

how to color edges of a convex polygon,say a square, using interpolation with respect to the color in Mathematica

How do I color edges of a convex polygon, say a square, using interpolation with respect to the color (to form parametric polynomials) in Mathematica, so that the colors displayed on the 4 edges would ...