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Questions tagged [polynomials]

Questions on the functionality operating on polynomials

1
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1answer
40 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
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2answers
72 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
179 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
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1answer
34 views

Finding constraints on polynomials from their plot

Suppose I have the following list of rational functions (fraction of polynomials): ...
-2
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1answer
53 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
56 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
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1answer
37 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
27 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
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2answers
89 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 ...
1
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1answer
49 views

Simplifying elliptic functions

I am working with (long) elliptic functions, which are rational functions in WeierstrassP and WeierstrassPPrime. As expressed in ...
3
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1answer
90 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
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0answers
54 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 ...
2
votes
1answer
39 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
52 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
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5answers
163 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
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1answer
69 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
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3answers
81 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
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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
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0answers
64 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
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1answer
49 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
80 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
70 views
5
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3answers
184 views

Factor polynomial of degree n+3

I'm considering a polynom poly[n,v] in v ...
1
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2answers
77 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
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1answer
45 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
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1answer
53 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
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1answer
40 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
79 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, ...
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0answers
49 views

Solve polynomial system

I am trying to solve ...
0
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0answers
93 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
48 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
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2answers
80 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: ...
0
votes
1answer
58 views

Collect terms in Fourier Transform

I want to collect terms in x from a product of polynomials and Fourier transform. So I try following code: ...
0
votes
1answer
61 views

Recurrences with some relation to Dedekind eta functions

Dedekind eta functions are know to satisfy certain difference equations/recurrence relations. The same is true for ratios of eta functions. Suppose some ratio of eta functions, say $A(q)$ satisfies ...
1
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1answer
47 views

Get coefficients of specified variables of polynomial, including zeros

In general I want to extract coefficients of specific variables of a polynomial (even of variables whose coefficients are zero). I try to explain it step by step: 1) I have a first polynomial. ...
0
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0answers
56 views

Simplify not acting smart on a sum of 10 rational functions

Rather by accident I discovered that throwing Simplify at the following "harmless" expression ...
6
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4answers
722 views
0
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2answers
74 views

Verify polynomial equation for set of 3D data [closed]

Goodmorning, I mean to this link: Find polynomial equation for set of 3D data I tried to verify the result, namely if the interpolation is correct, but I found something that I don't understand. I ...
4
votes
4answers
114 views

Approximate GCD

I have several pairs of bivariate polynomials that I want to find if they have common factors. The polynomials, however, have numerical errors because the coefficients are some algebraic numbers that ...
0
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0answers
49 views

How to write a nonlinear polynomial system in matrix form

I have a nonlinear system like the following example ...
1
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0answers
49 views

Reconstructing a partition from its character

Given a solid partition $\rho=\{\pi_1, \pi_2, ..\}$, where $\pi_a$ are plane partitions such that $\pi_{a+1} \subset \pi_a$, we can compute its character, which is a sum of monomials with non-negative ...
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1answer
45 views
2
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2answers
60 views

Grouping terms in Taylor expansion

I have this code: ...
1
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2answers
63 views

Solving a 4th order polynomial [closed]

I have a fourth order polynomial of the form: $$y = a_{0} + a_1 x + a_{2}x^{2} + a_{3}x^{3} + a_{4}x^{4}$$ Where the coefficients $a_{0}$, $a_{1}$, $a_{2}$, $a_{3}$ and $a_{4}$ are determined from the ...
2
votes
1answer
141 views

Solving for coefficients in a polynominal

I've the following problem: how can I solve for the coefficients in a polynominal? So, I mean the following: I've the following expression: $$\left(56-85689\cdot x\right)^2-3136\tag1$$ And I ...
9
votes
2answers
265 views

Finding the condition for root of a third degree polynominal

I've a third degree polynominal (in $s$): $$as^3+bs^2+cs+d\tag1$$ I need to find the roots of the polynominal, so I can use the code: ...
2
votes
2answers
66 views

Want to generate picture of all the algebraic integers for all the polynomials of a given degree

So I'm looking for a function that takes in the degree of the polynomial and the range of coefficients from -c to c, and outputs a list of all the monic polynomials of that degree and with ...
0
votes
1answer
98 views

Define a new CoefficientDomain in PolynomialReduce function

If we have some parameter like $q_1, q_2,...,q_n$, I would like to define a new CoefficientDomain for PolynomialReduce function such that get these parameters as integers, In the other words, ...
6
votes
2answers
96 views

Efficient way to partition list of expressions based on its contents

I have a list of polynomials polys linear in a set of variables vars. How do I partition the list based on successive dependence ...
0
votes
2answers
86 views

Finding the roots of a polynomial that meet specified conditions

Find the largest real root and the largest real part of a root of the polynomial below. Clearly indicate which is which. $f(x) = 5 -\sum\limits_{k=1}^{100}k^2x^k$. To get all roots, solve ...