Questions tagged [polynomials]
Questions on the functionality operating on polynomials
-4
votes
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
vote
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
vote
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
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
votes
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
votes
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
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
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:
...
