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Questions tagged [polynomials]

Questions on the functionality operating on polynomials

-4
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0answers
21 views

Finding and solving polynomial inequalities in scilab [on hold]

First I would thank the Mathematica community. i have a system like this: ...
1
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2answers
40 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
77 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
62 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
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2answers
66 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
174 views

Maximum point of a rational function

Suppose I have the following rational function: ...
5
votes
1answer
40 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
66 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
40 views

Ranking polynomials based on global maxima

Suppose I have the following polynomials in an association i.e. <|...|>, they are: ...
0
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1answer
55 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
49 views

Simplifying polynomial Roots with assumptions

I have acquired the following root from a minimization problem: ...
0
votes
0answers
10 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
38 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
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
votes
1answer
39 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
185 views

Continuous non-piecewise equivalent of smoothstep function?

I have a smooth step function given by the piecewise function ...
0
votes
1answer
67 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
72 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: ...
5
votes
1answer
81 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
81 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
192 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
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) ...
0
votes
3answers
69 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
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 ...
0
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1answer
32 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? ...
3
votes
2answers
98 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 ...
2
votes
1answer
56 views

Simplifying elliptic functions

I am working with (long) elliptic functions, which are rational functions in WeierstrassP and WeierstrassPPrime. As expressed in ...
3
votes
1answer
93 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....
0
votes
0answers
58 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
votes
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
votes
1answer
54 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 ...
5
votes
5answers
169 views

For a polynomial F with dependence on a parameter beta, find the value of beta for which F has 2 positive roots

Good morning, I have the following polynomial with degree 4 and its coefficients are quadratic functions of a parameter beta: ...
2
votes
1answer
74 views

Symmetrize a polynomial forgetting the commutativity property of multiplication

I need a script to authomatically symmetrize a given polynomial. For example, if the input is xy the output should be ...
0
votes
3answers
86 views

How to solve this 4th degree polynomial equation with complex coefficients numerically in Mathematica?

I have a polynomial equation: $-(a-ib)e^{(4\pi i/3)}(\sqrt{2}i+x^3/\sqrt{3})x- (a+ib) e^{(2\pi i/3)}(\sqrt{2}ix^3+1/\sqrt{3})=0$ (which in code is): ...
1
vote
0answers
27 views

How do I maximise the first real root of a multi-variable polynomial in x?

I have a polynomial in x, that also depends on {y1,y2,y3,y4,y5}. It always has 10 (not necessarily distinct) real roots. It's top coefficient is (1*x^10) I aim to find the y's that maximize the ...
0
votes
0answers
67 views

Packing binomial functions in a list

I would like to pack binomial functions with different parameters in a list. Here the binomial functions are defined as follows: ...
1
vote
1answer
51 views

How to generate addition table for $GF(2)[x] \mod x^3 + 1 = 0$ [closed]

I have been playing with Mathematica for a while. I tried generating addition table for a simple ring $R$ such that $R = \mathbb{Z}_{15}$ as asked in my last question. However, I am completely ...
3
votes
0answers
84 views

The actual polynomial behind a BezierFunction

Let's say I have the following Mathematica code pts = {{0, 0}, {1, 1}, {2, -1}, {3, 0}}; F = BezierFunction[pts] How can I find the actual polynomial of the <...
2
votes
1answer
72 views
5
votes
3answers
188 views

Factor polynomial of degree n+3

I'm considering a polynom poly[n,v] in v ...
1
vote
2answers
78 views

Integration using assumption in Mathematica

I want to reproduce the solution of the following integral, using Mathematica: $$\int_0^1duu(1-u)^2\frac{1}{(1-u)(1-v)}\left(\frac{1-u}{u}(1+\frac{1}{1-v})\theta(u-v)+\frac{1-v}{v}(1+\frac{1}{1-u})\...
0
votes
1answer
47 views

Choice of variables name affects the behavior of expression evaluation

I tried to expand this polynomials. With x, it is increasing with the right order, however with b it is in a random order. The only difference is that I change b to x and it works. ...
1
vote
1answer
55 views

How can I compute how many primes of this kind are up to $N$?

In the following link: https://oeis.org/A079796/b079796.txt we can see the first 10,000 prime numbers $p$ with the property that both $(3p)^2 + p^2 + 3^2$ and $(3p)^2 - p^2 - 3^2$ are primes ...
3
votes
1answer
42 views

Generate multivariate monomials with constraints

I'm trying to generate multivariate monomials in variables $p_1, \ldots, p_n$. Each monomial has either $p_i$ as a factor, otherwise $(1-p_i)$. I need to generate all monomials which have exactly $k$ ...
2
votes
3answers
80 views

Change the negative exponentials to the positive exponentials of a polynomial

$1)$ For the polynomial p = x^(-4) - x^(-3) - 2x^(-2) + 2 + 3x + x^2 + 2x^4 How to change the negative exponentials into the positive exponentials, ...
1
vote
0answers
50 views

Solve polynomial system

I am trying to solve ...
0
votes
0answers
112 views

PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD.Error

Not exactly sure whats wrong with my code but it keeps giving me a PolynomialGCD: Exponent is out of bounds for function PolynomialGCD error. The equation that I do NSolve for is very big and it takes ...
3
votes
0answers
55 views

Accuracy of Chebyshev Interpolation

I have been looking at how to interpolate a function using Chebyshev polynomials. There are several good posts such as this one by Michael E2 and this one by J.M needs help. There is also an example ...
0
votes
2answers
104 views

Why does my Solve output contain this symbol? [duplicate]

I have a pair of coupled polynomial equations that I need to solve, so I tried using Mathematica's solve tool. This is the code that I wrote: ...