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Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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How to `Collect` where `var` is one expression?

Edit: Clear["Global`*"]; expr1 = (a + c - b + 1)^3 + (-b + a + c + 2)^4 // Expand For test case expr1, this is the ...
138 Aspen's user avatar
  • 1,519
6 votes
3 answers
310 views

PolynomialQ behaviour

I am crafting some functions on polynomials that must be in x. But I checked that it is always True whatever variable I use: ...
Giovanni Russo's user avatar
2 votes
2 answers
79 views

Unstable work of PolynomialMod

I tried to use PolynomialMod for my calculation and i need some help on working with it, because i'll need to use it several hundred times. I made such a request ...
greg's user avatar
  • 23
1 vote
3 answers
96 views

How to sort the terms in a polynomial according to their degree?

I have the polynomial ...
youthdoo's user avatar
  • 251
0 votes
1 answer
125 views

How to execute this code? [closed]

I want to plot the following equation: ...
vijay's user avatar
  • 47
1 vote
0 answers
55 views

Replacement rule runs for a long time [duplicate]

I have a simple expression that reads (some expression in b) q^(8/3): ...
Lelouch's user avatar
  • 543
1 vote
1 answer
56 views

How to get the multiplicity of a certain root in a system of polynomial equation

Suppose I have a system of polynomial equations with base field $\mathbb{C}$ with $n$ equations and $n$ unknowns, how can I get the multiplicity of a certain solution? As an example, consider $$x^3=0\\...
Peter Wu's user avatar
  • 111
0 votes
0 answers
34 views

How to prevent factorization of polynomials in output

The output of my program is a matrix with polynomial entries. Most often Mathematica rearranges the polynomials with some partial or full factorization, as in $p^2q+q^2(p+q)$ or $p(p+q)$. I would like ...
Maesumi's user avatar
  • 807
0 votes
1 answer
31 views

Extracting matrix coefficients from multivariate matrices

Suppose we have a multivariate polynomial matrix $P(\mathbf x) = \sum_\alpha A_\alpha\mathbf x^\alpha$ (in multi-index notation) where the $A_\alpha$ are constant coefficient matrices. I am looking ...
GBaardink's user avatar
0 votes
3 answers
89 views

How to find the maximum value of coefficient k that satisfies the condition?

The known equation is: (1 + 62 x)^99 + (62 - x)^99 == a0 + a1 x + a2 x^2 + a3 x^3 + ... + a99 x^99 And ...
csn899's user avatar
  • 4,339
3 votes
2 answers
137 views

How to divide a known root out of a polynomial?

Consider this simple 5th order polynomial: pol=x^5+x^4+1 Factor[pol] (* (1+x+x^2)(1-x+x^3) *) root=FindInstance[pol==0, x] (* -1/2 -I/2 Sqrt[3] *) ...
Jos Bergervoet's user avatar
5 votes
3 answers
369 views

How to get the analytical form of a solution to an algebraic equation?

The real analytical solution of the algebraic equation $x^5 + 10 x^3 + 20 x == 4$ is $x=-2^{2/5} + 2^{3/5}$, how to get it with Mathematica? I've tried with ...
SHBooKP's user avatar
  • 370
1 vote
2 answers
82 views

Ordering of solutions of NSolve

I want to compute the solution to an equation with a parameter. It turns out that this solution is a sextic polynomial and mathematica outputs the solutions in a root form. Here's my code ...
Geigercounter's user avatar
1 vote
0 answers
67 views

Problems with implementation of subresultant pseudo-remainder sequence in Sturm's theorem

I've implemented the subresultant pseudo-remainder sequences ( https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor#Pseudo-remainder_sequences ) as described in Wikipedia. However, when ...
Moonwalker's user avatar
1 vote
0 answers
37 views

Performing difference in extracting coefficients from a sum

I have an expression ...
Lelouch's user avatar
  • 543
1 vote
1 answer
52 views

How to convert a list of polynomials with different degrees into a list of lists?

I asked a question about converting a polynomial into a list. Now I have a list of polynomials. For example, ...
Jianrong Li's user avatar
5 votes
4 answers
289 views

How to convert a polynomial into a list?

I have a list of polynomials. Each polynomial looks like: p[1, 2, 5] p[3, 6, 9] p[4, 7, 8] - 3 p[1, 2, 4] p[3, 6, 9] p[5, 7, 8] How to convert each of these ...
Jianrong Li's user avatar
2 votes
1 answer
74 views

How to write a^2 - a b + b^2 - a c - b c + c^2 has the form a^2 + b^2 + c^2 - a b - b c - c a?

I tried ...
vector's user avatar
  • 243
1 vote
1 answer
43 views

Solve polynomial functions with four unknown variables [duplicate]

I want to make curve with polynominal function like this figure but only 2 known point to solve this one. I try to used solve function for this one. but the result is not the same like the figure. ...
葉柏樂's user avatar
  • 157
0 votes
0 answers
25 views

How to Factor Out Polynomial Terms which Have Same Coefficient Differing Only by Sign

I'm new to the Mathematica StackExchange. I am trying to simplify a polynomial in Mathematica. In the following, I only show a part of the polynomial Here I want to combine terms with the same ...
Kazuki's user avatar
  • 1
1 vote
1 answer
62 views

Finding constant term in product expression

I've an expression which is product of 20 or more factors of polynomial, something like $$\left(1-\frac{pq}{z^i}\right)(1+pq z^j+z^k)$$ and I want to find coefficient of $z^0$. SeriesCoefficient works ...
xandar's user avatar
  • 13
5 votes
2 answers
127 views

Simplifying a logical expression with multivariate polynomials

I have several expressions similar to a (a b + c d) != 0 || b (a b + c d) != 0 || c (a b + c d) != 0 || d (a b + c d) != 0 and I would like to reduce them ...
მამუკა ჯიბლაძე's user avatar
0 votes
2 answers
63 views

A polynomial with positive integer powers is being displayed as a transcedental function (LerchPhi)

I am defining a polynomial as follows: ...
Mohit Kumar's user avatar
0 votes
0 answers
81 views

How can I approximate a function with composite polynomials?

I know that to approximate a function with for example $f(x) = \sin(x)$ using polynomials with degrees up to 4, I can use the Fit function : ...
何子钦's user avatar
0 votes
1 answer
89 views

Finding the solution for the cubic formula over NonNegativeReals

The standard cubic polynomial is: $ax^3+bx^2+cx + d$. And when I used my function: ...
Teg Louis's user avatar
0 votes
1 answer
43 views

How to factorize high-order polynomials that have only complex roots?

I have polynomials like this: ...
homocomputeris's user avatar
2 votes
1 answer
194 views

How to verify a solution of an ordinary differential equation?

Given an ordinary differential equation with initial conditions eq = u a[u] + (16 + u^2 + 2 u a[u] (12 + u a[u] (6 + u a[u]))) a'[u] == 0 ic = a[0] == -1/2 How can ...
yarchik's user avatar
  • 19k
1 vote
1 answer
70 views

Expanding polynomials using valuation

I would like to expand the polynomial $p(\lambda) = \sum_{i=0}^{d} a_{i} \lambda^{i}$, as $F(p(\lambda), \lambda_{0})= \min_{j} [ val(a_{j}) + j \lambda_{0} ] $ with $\lambda_{0}$ being a real ...
Shasa's user avatar
  • 1,043
1 vote
2 answers
139 views

Elegant way to restrict PolynomialMod to non-negatives

Update at the bottom! PolynomialMod[4 + 10x, 1 + 2x] returns -1. Instead, I'd like to get 4, ...
Andreas Lauschke's user avatar
5 votes
3 answers
177 views

Calculating the basis set of quotient spaces

Having a polynomial $f(x,y)$, I would like to compute the following quantity \begin{equation*} {\mathbb C}[X,Y,Z]/\langle f_{x}, f_{y}, f_{z} \rangle, \end{equation*} where $f_{x},f_{y},f_{z}$ are, ...
Shasa's user avatar
  • 1,043
1 vote
1 answer
95 views

Rearranging a simple algebraic expression

I have a polynomial of variables $x,y$, where $|x|<1$ and $|y|<1$. When I apply the Simplify function to this expression, I get an expression of the form $(x-...
akr's user avatar
  • 177
0 votes
0 answers
54 views

Solving polynomial roots of any degree only by Vieta's formula

I have already wrote the code that solves it for quadratic formula and I'm curious if this is possible to make that function work with any kind of polynomial(higher degrees) and solving roots only ...
Karol Bargieł's user avatar
4 votes
1 answer
316 views

How to make a polynomial so that f(i) = 1/(2^i)?

I know that, sequence has formula $f(n) = \dfrac{1}{2^n}$ satifying the conditions $f(1)=\dfrac{1}{2}$, $f(2)=\dfrac{1}{4}$, $f(3)=\dfrac{1}{8}$, $f(4)=\dfrac{1}{16}$. Now I am trying to find a ...
John Paul Peter's user avatar
0 votes
1 answer
41 views

How to make MMA distinguish between symbolic coefficients and variables when doing factorization? [closed]

I what to factor a polynomial with complicated symbolic coefficients Factor[p0^2 + k^2 r^2 \[Tau]^2 - 2 k p0 r \[Tau]^2 \[Omega] + p0^2 \[Tau]^2 \[Omega]^2] In ...
Haiqin Tang's user avatar
3 votes
1 answer
151 views

Cannot solve this polynomial equation

I'm trying to solve the following polynomial equation for $x$: $$ (qx)^\alpha (1-qx)^{1-\alpha} = [(1-q)x]^\beta [1-(1-q)x]^{1-\beta} $$ where $\alpha, \beta, q, x$ are all strictly between 0 and 1. ...
raving-bandit's user avatar
2 votes
7 answers
329 views

How can I get a list of symmetric polynomials?

Q1: Suppose I have an expression like this one: $(1+x+y+z)^3$ How can I transform it into the following expression: $$\{1,x+y+z,x^2+y^2+z^2,xy+xz+yz,x^3+y^3+z^3,x^2y+x^2z+xy^2+y^2z+xz^2+yz^2,xyz\}$$ ...
deltaxxkkk's user avatar
0 votes
1 answer
61 views

Is it possible to get rid of the square root in the solutions of the following symbolic quadratic equation?

I have a quadratic equation, which I want to solve, but don't want the square root to appear within the solutions. I tried converting the discriminant into a quadratic form but failed, not sure if ...
larry's user avatar
  • 735
0 votes
1 answer
83 views

How to make a polynomial output be used as function for input?

I basically made a code interpolating a set of data that gives me the polynomial for the interpolation. Here's the sample interpolation I did. ...
Mule's user avatar
  • 43
1 vote
0 answers
48 views

Is it possible to use the Finite Fields package to define the elements of GF(4) in terms of the irreducible polynomial $P$?

I am new to the Finite Fields package and am finding the package tutorial confusing. I am wondering, if I am working over GF[4], is there a way of finding the elements of GF[4] in terms of the ...
am567's user avatar
  • 547
1 vote
2 answers
120 views

How to extract coefficients of polynomial formatted like this?

I want to extract coefficients. ...
138 Aspen's user avatar
  • 1,519
1 vote
3 answers
348 views

Eliminating one variable from two simple polynomial equations

Is this really that hard to eliminate variable t? It runs forever without any result. $$x=-\frac{t (2 t+1)}{4 t^5+1},u=-\frac{2 t}{t^2+1}$$ ...
azerbajdzan's user avatar
  • 19.7k
1 vote
0 answers
53 views

How to solve quartic equation modulo a composite? [closed]

I have an univariate polynomial equation over a composite moduli. Namely the composite is of for $q=(2p)^{2}-1$ where $p$ is odd and $2p-1$ and $2p+1$ are distinct primes. The modular equation is $$ax^...
Turbo's user avatar
  • 145
1 vote
0 answers
73 views

Solving a linear algebra problem containing minimal polynomial degree

Consider a set of three-dimensional points ${\left\{{\left(a,ab,abc\right)}~\middle\vert~a,b,c\in\mathbb{N_+}\land a+b+c\leqslant2023\right\}}$. If there exists a non-zero real polynomial $\...
user688486's user avatar
1 vote
3 answers
124 views

Selecting coefficients of multivariable polynomial

We have polynomial in three variables x, y, z. How to list all coefficients of odd powers of z or ...
azerbajdzan's user avatar
  • 19.7k
0 votes
1 answer
117 views

How to implement the Vieta's formula in Mathematica in the general case? [closed]

I have list of $N$ roots ($r_1, r_2, ..., r_N$) and would like to restore some coefficient $a_k$ of the original polynomial. Vieta's formula is what I need, but I don't understand how to implement it ...
Nikolai Gerasimenyk's user avatar
3 votes
2 answers
103 views

Check if polynomial is subtraction free

I have several very long, factorised polynomials in several variables, e.g. x1^4 x2^3 x3 x4^3 x5 x6 x7^2 x8 (1 + x2 + x2 x3 + x5 + x1 x5) I want an easy way to ...
Facieod's user avatar
  • 175
2 votes
1 answer
78 views

An apparent error with Chebyshev polynomials

I am on 11.0.1.0 SeriesCoefficient[ChebyshevU[n,x],{x,0,m}] returns ...
მამუკა ჯიბლაძე's user avatar
2 votes
1 answer
77 views

Computing symbolic continued fractions for rational functions with respect to a variable

There are quite a few questions here about continued fractions, so this might be a duplicate, but I honestly could not find what I want. What I want is, having two polynomials ...
მამუკა ჯიბლაძე's user avatar
1 vote
1 answer
157 views

How to factor a quartic equation whose coefficient has unknown parameters?

i'm trying to see if a quartic equation I obtained can be factored into simpler forms, such as the product of two quadratics. The problem is that their coefficients are some complex expressions in ...
larry's user avatar
  • 735
0 votes
0 answers
48 views

how to get the set of coefficient of a trig function in terms of the sines and cosines of a given angle

Say I have an expression like this a Sin[\[Theta]]^4 + b Cos[\[Theta]]^4 + c Sin[\[Theta]]^3 Cos[\[Theta]] + d Sin[\[Theta]]^2 + e=0 My ultimate goal is to solve ...
larry's user avatar
  • 735

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