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Questions on the functionality operating on polynomials

1
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0answers
6 views

Calculating Hermite Expansion Coefficents of |x| [migrated]

I`m struggling to calculate the coefficents for the Hermite Expansion of the absolute value function and the indicator function $x \mapsto \mathbb{1}_{|x-u|\leq \delta}$ Background: I know, that for ...
2
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1answer
66 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
80 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
58 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
41 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
74 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
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1answer
67 views
5
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3answers
178 views

Factor polynomial of degree n+3

I'm considering a polynom poly[n,v] in v ...
1
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2answers
75 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
42 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
51 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
37 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
78 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
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0answers
48 views

Solve polynomial system

I am trying to solve ...
0
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0answers
53 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
44 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
67 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
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1answer
56 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
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1answer
58 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
42 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
55 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
707 views
0
votes
2answers
65 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
109 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 ...
-1
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1answer
38 views
2
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2answers
57 views

Grouping terms in Taylor expansion

I have this code: ...
1
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2answers
60 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
138 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
260 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
94 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
83 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 ...
2
votes
1answer
50 views

Get polynomial terms

Is there a command equivalent to that of Coefficient to get the terms of a polynomial which are a power of the variables? For example: func[(x^3 + x)^2] {x^2, ...
1
vote
1answer
79 views

How to automatically find sequence of linear transformations

I have a set of three polynomials in x and y, and 9 real coefficients a1, ...
1
vote
1answer
84 views

Plot the critical points of degree $d$ polynomials with zeros randomly chosen in given region

I wish to be able to scatter slightly (by at most some fixed $\varepsilon>0$) the zeros of a given complex polynomial $p(z)$ in a random way, and then see the effect on the critical points. For ...
0
votes
1answer
94 views
1
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1answer
160 views

How to draw Lemniscate of Bernoulli type curves for higher degree polynomials

The lemniscate of Bernoulli is a curve in the complex plane given by $|z^2-1|=1$ that has the shape of $\infty.$: This is a special case of the Cassini ovals that has the form $|z^2-1|=r^2$ for $r\in\...
0
votes
1answer
70 views

Factoring the Quadratic Polynomial $a x^2 +b x +c$

I want mathematica to factor the quadratic polynomial $a x^2 +b x +c$ into this standard form $a(x-r_1)(x-r_2)$ with $r_1=-\frac{b}{2a}+\frac{\sqrt{b^2-4ac}}{2a}$ and $r_2=-\frac{b}{2a}-\frac{\sqrt{b^...
0
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0answers
51 views
1
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2answers
89 views

Polynomial factorization over number fields that are extensions of the rationals [duplicate]

I want to factor some polynomials into irreducible terms, but not only limited to integers. If I evaluate Factor[x^4+1], it will generate nothing. But in fact I ...
3
votes
2answers
203 views

Factor out constant terms with square roots

I would like to use FactorTerms to factor out constant numerical terms out of an expression, this works as follows: ...
0
votes
1answer
65 views

Pull the variable out of the fraction

I have a code which outputs a polynomial, the last line is of the form: K[f[#]/g[#] &, 6], with f and g being some functions. The coefficients are fractions, ...
0
votes
0answers
93 views

Prime factorization of numerator and denominator of rationals

I am completely new to Mathematica and I need some help (sorry if it is trivial, but I haven't found the answer). I have this code ...
0
votes
0answers
21 views

Solving in terms of polynomials for F,G such that Ff+Gg=c

I'm pretty new to mathematica and am trying to solve the following: I have two explicit polynomials $f(x), g(x)$ with integer coefficients and a constant $c$ and I'm looking for two polynomials $F(x),...
2
votes
1answer
65 views

problem in finding roots of a large polynomial

I have a problem with finding the roots of a huge polynomial with mathematica: it finds the roots but they are wrong! I tried to use both "NSolve" as well as "Roots", but I always get the same wrong ...
1
vote
1answer
45 views

How can I expand a rational expressions of polynomials? [closed]

I am trying to expand $$-\frac{2}{(x+2)^3}$$ into $$-\frac{2}{x^3+6 x^2+12 x+8}$$ How would I do this? Also, How can I extended this to fractions of the form $$\frac{P(x)}{Q(x)}$$ where $P(x)$ and $...