Questions tagged [polynomials]
Questions on the functionality operating on polynomials
979
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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.
...
0
votes
0
answers
23
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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 ...
1
vote
1
answer
56
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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 ...
5
votes
2
answers
121
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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 ...
0
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0
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22
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Polynomials as an infinite sized tuple vector [migrated]
Can I consider a vector space which contains the set of polynomial functions as an infinite-sized tuple vector space?
for example, let us consider a vector space (V) (which is defined over R) which ...
0
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2
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63
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A polynomial with positive integer powers is being displayed as a transcedental function (LerchPhi)
I am defining a polynomial as follows:
...
0
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0
answers
75
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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 :
...
0
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1
answer
87
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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:
...
0
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1
answer
39
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How to factorize high-order polynomials that have only complex roots?
I have polynomials like this:
...
2
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1
answer
171
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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 ...
1
vote
1
answer
68
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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 ...
1
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2
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132
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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, ...
5
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3
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167
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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, ...
1
vote
1
answer
93
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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-...
0
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0
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53
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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 ...
4
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1
answer
315
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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 ...
0
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1
answer
40
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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 ...
3
votes
1
answer
150
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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.
...
2
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7
answers
321
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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:
$$\{1,x+y+z,x^2+y^2+z^2,xy+xz+yz,x^3+y^3+z^3,x^2y+x^2z+xy^2+y^2z+xz^2+yz^2,xyz\}$$
...
0
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1
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61
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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 ...
0
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1
answer
77
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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.
...
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0
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43
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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 ...
1
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2
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113
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How to extract coefficients of polynomial formatted like this?
I want to extract coefficients.
...
1
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3
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348
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Eliminating one variable from two simple polynomial equations
Is this really that hard to eliminate variable t? It runs forever without any result.
$$x=-\frac{t (2 t+1)}{4 t^5+1},u=-\frac{2 t}{t^2+1}$$
...
1
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0
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53
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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^...
1
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0
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71
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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 $\...
1
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3
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120
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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 ...
0
votes
1
answer
108
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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 ...
3
votes
2
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102
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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 ...
2
votes
1
answer
76
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An apparent error with Chebyshev polynomials
I am on 11.0.1.0
SeriesCoefficient[ChebyshevU[n,x],{x,0,m}] returns
...
2
votes
1
answer
72
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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 ...
1
vote
1
answer
154
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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 ...
0
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0
answers
47
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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 ...
1
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2
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155
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How do I extract terms from a complicated polynomial?
The polynomial is:
...
4
votes
3
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385
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What is the smallest degree of polynomial so that its graph includes four extreme points
Let there be four points (-2,-5), (5,-6), (6,1), (-1,2) that are extrema (maxima / minima). I am trying to find a polynomial that includes these extreme points. I ...
2
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3
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145
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How to extract specific terms from the polynomial?
Consider the following polynomial:
...
2
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0
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43
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Exact usages of the "*Coefficient*" family?
For applying some function func to the coefficients of a polynomial poly in variables vars, ...
17
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4
answers
785
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What is Mathematica's equivalent to Maple's collect with distributed option?
Given a polynomial in $x,y$, I want to collect on $x,y$ and any products of these also. As given using Maple's collect with the distributed option.
Currently Mathematica will collect on $x$ then ...
0
votes
2
answers
129
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How to prevent the computation of this polynomial sum?
In my research project, I'm working with the following polynomial
$$p(x) = 1 + 2x + 3x^2 + \ldots + nx^{n-1} + nx^n + nx^{n+1} + (n-1)x^{n+2} + (n-2)x^{n+3} + \ldots + 2x^{2n-1} + x^{2n}$$
or
$$nx^n +\...
2
votes
1
answer
82
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Relation between coefficients of polynomial to get real roots
I am trying to find a relation between coefficients $a$ and $b$ of the equation $a x^3 + b x^2 - x + 2 =0$ so that I get positive real roots of the equation (i.e. $x\geq0$). Any help on how to do this ...
1
vote
0
answers
39
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How can I transform an expression with radicals to RootSum?
I am working with the integrals like these:
...
0
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0
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146
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Factorization of 5th polynomial with Wolfram-Mathematica
I have a very complicated 5th-degree polynomial form. Using the factor function in Wolfram is impossible to make it because of the high degree. I just want to know that is it possible to factor as I ...
4
votes
1
answer
109
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How can I compute the $n$-th complete Bell polynomial?
I'm interested in computing the n-th complete Bell polynomial
$
B_n(x_1,..., x_n)
$ using the formula given as the last equation in the "Exponential Bell polynomials" section here (I tried ...
1
vote
1
answer
88
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Comparing two power series and extracting their coefficients
I have a standard mathematical problem that I was wondering how to solve efficiently by mathematica. Here is the problem.
I have two power series expansions of a function ...
0
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0
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40
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Poles of filter transfer function, fifth order equation [duplicate]
I am just trying to find the roots of the fifth-order equation. But I could get enough result from Wolfram.
Could anyone help to me about this issue?
...
3
votes
1
answer
136
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Looking for a recurrence relation for these specific polynomials?
Trying to answer this question related to the calculation of
$$I_k=\int_1^\infty x^ke^{-x}\ln(x+a)\,dx$$ which, at least to me, looks problematic.
What is missing for a complete answer is to ...
1
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0
answers
120
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Taylor series loop
I'm a beginner not only in Mathematica but also in programming in general, and so I'm not really sure where my problem lies exactly and I'd be glad to receive any guidance.
Using the Taylor series for ...
2
votes
2
answers
105
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How to get the coefficient list of their product from the coefficient list of two polynomials?
If I have the coefficient list of two polynomials
...
1
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2
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106
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Finding negative powers of polynomial expressions
Suppose I have the following expressions
...