Questions tagged [polynomials]
Questions on the functionality operating on polynomials
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How to solve quartic equation modulo a composite?
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^...
- 145
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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 $\...
- 385
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3
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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 ...
- 7,094
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1
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96
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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
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2
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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 ...
- 175
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1
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73
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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
...
- 1,770
1
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1
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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 ...
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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 ...
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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 ...
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4
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3
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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 ...
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3
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2
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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, ...
- 385
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4
answers
767
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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 ...
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2
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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 +\...
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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 ...
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How can I transform an expression with radicals to RootSum?
I am working with the integrals like these:
...
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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
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answer
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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 ...
- 45
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1
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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 ...
- 417
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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?
...
2
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1
answer
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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 ...
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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
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2
answers
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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
...
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2
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4
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4
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Extract monomials with a certain structure from a given polynomial
I have a long polynomial such as
a x^2+ bx^2y+cx^2y^2 +d x^3y^4+e x^4y^3+f y^2+g xy^2
Consider an example problem as follows: I want to output the monomials (along ...
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Solving a complicated equation of order 5. completely parametrically
I have this equation and it takes so much time to solve. i would appreciate some guidance how to solve it. 0<l<1 and 0<gamma<1 and -Pi/2<theta<Pi/2 and w is real and positive. other ...
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Reducing roots of power sums
Often I encounter expressions like for example
Root[ 1 - # + #^2 - #^3 + #^4 - #^5 + #^6 &, 3 ] or
...
- 1,460
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Collect with rational powers
I need a function, which will collect terms next to the same rational power of a given variable. For the input
RCollect[3xy^(3/2)+2/y+zx/y-y/x+2*x^z y^(3/2),y]
the ...
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3
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Intersection points of two-variable polynomials
Let $h$ and $g$ designate two multivariable polynomials:
$$\!\!h(x,y)=-96\! \left(32 x^2\!+\!8 x (3\!-\!8 y)\!+\!40 y^2-28 y+5\right) \left(10 x^2+x (4 y-2)+\quad\quad\quad\\ \quad\quad+(1-2 y)^2\...
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On the solution of systems equations with exact coefficients
It all starts with the following system of equations that I can't solve by hand:
...
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How to simplify the formula under the quadratic root sign? [duplicate]
The following formula is given：
...
- 2,695
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Solving polynomial equation of 4th order with more than 1 variable
I have this equation but it takes so long and no answer comes out. Could you please suggest me what to do or should I just wait more. Even if you could help me understand different numerical solves, ...
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Is there a function in Mathematica that computes the number of solutions to polynomial systems?
Given a system of polynomial equations in $\mathbb{C}$-coefficients, is there a tool in Mathematica that computes the number of solutions to this system, counted with multiplicity? (We may assume ...
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How to apply a function to coefficients of a polynomial?
I found Apply a function to all coefficients of a polynomial but I could not understand
I want to apply Round to the coeffricients of $x^2 + 3.1x^3 + 5.4x^4$. The <...
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2
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Attempting to verify if real roots of a polynomial produce the value "true" when plugged back in [closed]
Given the polynomial
poly = 1-6 x-3 x^4+x^7
and having already found the list of real roots, I now need to Check that the numerical values in the list ...
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0
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Polynomial GCD over a ring with composite modulus [duplicate]
I need the gcd of two polynomials,
...
3
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3
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470
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Polynomial approximation of max function
Let me just say upfront I'm not a mathematician, I'm rather looking for a practical answer to my question. I was wondering if there is a polynomial approximation for the function
$$\max(0,x)=\left\{\...
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3
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Basis for multivariable polynomials
I have a bunch of two-variable polynomials and as part of a larger algorithm need to find a basis for them and express them in terms of this basis.
As an illustrative example, for one case my ...
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0
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96
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Guessing patterns of symbolic series
I have a system of 2s+1 equations, where s can take integer values of {1,2,3,....,n}. Here ...
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How to solve Equation for different variable in Mathematica?
I want to solve the given equation for $(n=m=3)$ and I want the output variable $q_{1,1}, q_{1,2}, q_{2,1}, q_{2,2}$
Given Equation
Given Equation-2
The output should be
required Output
Here is my ...
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0
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Expanding a large dynamic expression involving roots of a degree 4 polynomial
I am trying to find the eigenvalues of a 4x4 Matrix symbolically. Below is the code I am using,
...
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76
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How to arrange the obtained results according to the descending power of x?
The function of the code is to obtain a univariate quadratic equation about x by simultaneous equation
the code is this：
...
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Stepped Infinite Square Well [closed]
Here is the link for making the above graph for the Stepped infinite square well.
The problem here is, all the eigenfunctions and energy eigenvalues are previously defined. Whereas, I want to use this ...
- 1,502
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Compute all bivariate polynomials over GF(2) of degree d or less and evaluate them at certain polynomial input
I want to compute all $<=d$ degree bivariate polynomials of form $f_1(x)g_1(y) + f_2(x)g_2(y)$, over field $GF(2)$, and evaluate them at a certain polynomial input
for eg $d = 1$, evaluation at $(p^...
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How can I verify that the function $f$ and its simplified version are same?
I have the function $f=f(x,y,z)$ and rewrite it in the PolynomialForm and TraditionalOrder ; then, I try to verify the result by ...
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How to calculate Intermediate fields of Galois group in Hasse diagram?
I can easily calculate the Hasse diagram of an equation in maple, for example for the equation $x^4 + 8x + 12$(It's Galois group is $A4$):
...
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Drawing the roots of polynomials on the complex plane [duplicate]
I have a polynomial $f(x)=x^2(x + 1)^{2n} + 2x^{n + 1}(x + 1)^n + x^{2n}$.
Then I want to show the roots of $f(x)$ from $2\leq n\leq 30$ in the complex plane. I have tried lots of methods but don't ...
3
votes
3
answers
209
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How do I adjust the form of the inequality?
I have some inequality ,like this
$$
\left\{\begin{array}{l}
x+y+z \geqslant 1 \\
2 x+6 y+3 z \geqslant 6 \\
a x+b y+c z \geqslant d
\end{array}\right.
$$
I want to put all the y's in this inequality ...
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How to convert a polynomial into monic form of a polynomial
The function ResourceFunction["StauduharGaloisGroup"] can get a Galois Group about a monic irreducible integer polynomial. But I want to know the Galois ...
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