Questions tagged [polynomials]
Questions on the functionality operating on polynomials
1
vote
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
votes
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
votes
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
vote
1answer
34 views
Finding constraints on polynomials from their plot
Suppose I have the following list of rational functions (fraction of polynomials):
...
-2
votes
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
votes
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
votes
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
votes
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
vote
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
votes
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
votes
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
votes
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
votes
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
votes
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
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
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
vote
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
votes
3answers
184 views
1
vote
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
votes
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
vote
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
votes
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,
...
1
vote
0answers
49 views
0
votes
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
votes
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
vote
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
votes
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
votes
4answers
722 views
0
votes
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
votes
0answers
49 views
How to write a nonlinear polynomial system in matrix form
I have a nonlinear system like the following example
...
1
vote
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 ...
-1
votes
1answer
45 views
NSolve and Solve are unable to Solve System of Polynomials with methods available to them
Is this number to big to work with
...
2
votes
2answers
60 views
1
vote
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 ...
