Questions tagged [polynomials]
Questions on the functionality operating on polynomials
814
questions
2
votes
0answers
41 views
Mathematica package for computing Macdonald polynomials
I want to implement computation of Macdonald polynomials in mathematica. A similar question was raised in another question 5 years ago (Macdonald-Koornwinder polynomials?), but received no clear ...
2
votes
0answers
51 views
Extracting variables [closed]
Similar to this perhaps, but I prefer a built-in function.
I have defined the expression L = a*b*c.
Is there a Mathematica function that can identify and extract ...
2
votes
1answer
84 views
Factoring a polynomial over a number field
Consider a polynomial x^3-x-1 and let $\alpha$, $\beta$, $\gamma$ be three zeros of the polynomial where $\alpha \in \mathbb{R}$. Since $\beta \not \in \mathbb{Q}[\alpha]$ and the degree of the ...
1
vote
2answers
41 views
System of rules transformingn a multivariate polynomial onto corresponding partial derivative operator
I take a complex multivariate polynomial, and I want to transform it into the corresponding differential operator. I.e., I am looking for the set of rules transforming variables to derivation, ...
2
votes
2answers
100 views
Find relationship between parameters to prove conditions of eigenvalues
I have the following 3-by-3 matrix. I need to find condition(s) on the parameters 'a' and 'b' such that this matrix has exactly 1 eigenvalue bigger than 1 in absolute value and other two eigenvalues ...
0
votes
1answer
50 views
The list of coefficients of the "polynomial", which has the order of derivatives instead of degrees
I have some equation
eqn = (A + B).x''[t] + Transpose[x'[t]].(2 A - 3 B + 1).x'[t] +(СС - 5).y'[t]+ Sin[x[t]+y[t]]
I need to collect all the coefficients at ...
1
vote
1answer
68 views
How to factor real polynomials over complex field
I'd like to factor polynomials over the complex field. For example, how do I factor x^2+1 over $\mathbb{C}$?
Factor[x^2+1] and <...
1
vote
1answer
55 views
0
votes
1answer
120 views
Minimization of a very simple polynomial
1. I get a very strange output for this minimization
Minimize[(1 - x y)^2 + x^2, {x, y}]
(*{0, {x -> Indeterminate, y -> Indeterminate}}*)
Is it correct? Can ...
2
votes
1answer
70 views
How to Write a matrix Laurent polynomial $A_{-5}t^{-5} + A_{-4}t^{-4} + ...+ A_0 + A_1 t + A_2 t^2....$ in mathematica [closed]
I need to write in mathematica programming language a matrix Laurent Polynomial
$$ T = \sum_{i=-5}^{5} A_i t ^i $$
where the $A_i$ are $n \times n$ matrices (I want the entries to be symbolic) which ...
1
vote
1answer
25 views
Want to realize this operation (multiplication of divergent integrals of polynomials) in Mathematica [closed]
I am currently researching divergent integrals.
Definition. An extended number is an expression of the form $\int_a^b f(x)dx$, where function $f(x)$ is defined almost everywhere at $(a,b)$. Generally ...
1
vote
0answers
36 views
How to extract the coefficient all the monomials of an arbitrary polynomial efficiently?
At present I know 3 efficient function to generate a list of all the monomials and the corresponding coefficients of an arbitrary polynomial. They are CoefficientRule, MonomialList and GroebnerBasis`...
3
votes
1answer
111 views
Pick up certain terms in multiplication [closed]
Suppose I have the following expression:
(2a + 3b)^2
when expanded, it gives
4a^2 + 9b^2 +6a*b
I want to pick up only the terms involving a* b, that is the term 6a*b. Is there an automatic way to pick ...
1
vote
1answer
103 views
Associated Legendre polynomials in Mathematica
I'm trying to look at the Associated Legendre Polynomial, so I plugged it into Mathematica to see the values for different input.
From wikipedia:
$$
p_l(x)=\frac{1}{2^l l!}\frac{\partial ^l}{\partial ...
0
votes
1answer
33 views
Simple Question: Cut Number in Transfer function
Given transfer function:
$W=\frac{10 (s+100)}{2 s^4+219 s^3+1909 s^2+900 s+1000}$
W=(1000 + 10 s)/(1 (1000 + 900 s + 1909 s^2 + 219 s^3 + 2 s^4))
Which command to ...
0
votes
0answers
56 views
Discriminant of n-degree polynomial
The discriminants of polynomials $f(x)=x^n+a_1x^{n-1}+\cdots+a_n, 1\leq n\leq 4$ are
degree-n
discriminant-$\Delta_n$
1
1
2
$a_1^2-4a_2$
3
$a_1^2a_2^2-27a_3^2-4a_1^3a_3-4a_2^3+18a_1a_2a_3$
4
$a_1^...
0
votes
2answers
73 views
Order multivariable polynomial terms in order of total degree
Given a polynomial, lets say for example $f(x,y) = (1+x+y)^2 = 1+2x+x^2+2y+2xy+y^2$, I'd like to be able to order the terms of the polynomial by total degree, either in increasing or decreasing order (...
1
vote
3answers
95 views
Given f[b,d,k]=0 and g[b,d,k]=0, I need to find a branch (provided it exists) of k[b,d] such that this system has a solution in b,d
I have two polynomials in k given by f[b,d,k] and g[b,d,k]. I know that there exists a ...
2
votes
1answer
46 views
Extract only a few coefficients of the multiple of extremely many polynomials
I want to extract some informations, say the coefficients of $x^{500}$ and $x^{1000}$ terms (numerical values are acceptable), of the multiple of
...
1
vote
2answers
51 views
How to reorganize a polynomial including exponents to the simplest form?
I want to reorganize a polynomial including exponents as the following Figure 1 to the form showing as Figure 2. Failed to realize it after several times trying such as Figure 3. Can you help me to ...
0
votes
1answer
47 views
Reduce coefficients from constraints in a set of equations
Total beginner here. I am chaining 4 quadratic equations $f_i(x)$ at 4 knots $k_i$ (where $0 < k_i < 1$ and $k_{i+1} > k_i$) on a wrapped unit interval (i.e. $0 \leq x \leq 1$):
$$ f_i(x) = ...
1
vote
1answer
69 views
Finding the absolute value of the roots of a polynomial
So I am trying to find the absolute value of the roots of a polynomial in Mathematica. I am quite new to this software and I am having a hard time how to figure out the absolute value of the roots of ...
1
vote
1answer
83 views
Reduce/Resolve without roots/radicals
Is there a way to convince Mathematica to perform quantifier elimination on a semialgebraic set and yield a resulting semialgebraic set whose representation does not involve any roots or radicals, i.e....
2
votes
3answers
115 views
How to collect a polynomial with a specific power
Suppose I have got this polynomial
u=x^12-3x^8-x^4+3
Now, I am trying to collect this polynomial with x^4 terms.
I need to write it like this: (-1+x^4) (-3 + x^4) (1 + x^4)
To evaluate it, I used
...
0
votes
0answers
45 views
Problems with NSolve[] finding zeros of a 32-degree polynomial
I have the following calculation in Mathematica:
...
0
votes
1answer
61 views
Plot real zeros regions of the polynomial
Good morning everyone! One problem have appeared. I'm trying to plot regions with different number of real zeros of the polynomial. I have this code:
...
1
vote
2answers
43 views
Collect all terms containing the same powers of a function in a polynomial
I have a polynomial including powers of \[CapitalPhi][\[Xi]]
I want to collect all terms containing the same powers of ...
1
vote
1answer
73 views
Factorize the multivariate polynomial [closed]
I came across the following problem:
Factorize the multivariate polynomial given by:
$$w*(A^2-2l*A+1)*f+v*(B^2-2m*B+1)g+u*(C^2-2n*C+1)*h+(w*(x+2A*l+A*s-l*s-A^2-1)+v*(y+2B*m+B*t-m*t-B^2-1)+u*(z+2C*n+C*...
4
votes
1answer
83 views
To find the combinational coefficients of vectors in polynomials
Simply put, I have a few vectors of polynomials $\{d_i\}$ and I know one of their combinations gives $x$, which is also a vector of polynomials. How do I find the combinational coefficients $a_i$, ...
1
vote
2answers
36 views
A list of the exponents of the irreducible factors in a factored polynomial
I have a list of factored polynomials:
{x^3, x^2 (1 + x), x (1 + x)^2, x (1 + x + x^2), (1 + x) (1 + x + x^2), 1 + x^2 + x^3, 1 + x + x^3, (1 + x)^3}
I want a ...
0
votes
3answers
92 views
Find order of polynomial approximation and LeastSquares for given datapoints
I have a set of data, where I'd like to find the order of the polynomial that approximates the data, and also know what the Least squares is.
My data:
...
0
votes
1answer
85 views
All real and complex roots of 10 degree polynomial [closed]
I am trying on
${\rm poly} =x^{10} + 7 x^9 - 38 x^8 - 192 x^7 + 209 x^6 - 1009 x^5 + 5768 x^4 - 19002 x^3 - 2580 x^2 - 99792 x^1 - 120960$;
I was trying "FindRoot & NRoots" to find real ...
1
vote
2answers
60 views
How to delete certain terms in a polynomial with variables in subscript?
I have a polynomial in the following style,
...
1
vote
0answers
31 views
Custom multiplication operation between variables
I am constructing polynomial expressions in the variables $s[0],s[1],...,s[n]$ and I'm trying to define a new operation to simplify the expression:
...
0
votes
1answer
60 views
1
vote
1answer
47 views
Apply a function to all coefficients of a polynomial
I would like to apply a given function $f$ to each one of the coefficients of a polynomial.
For example if $P=(x - 2) (y^2 + 1)= -2 + x - 2 y^2 + x y^2$ and $f(c)=c^2$, I would like to obtain the ...
0
votes
1answer
34 views
Is it possible to automatically check a polynomial to determine whether it has integer coefficients?
Given a polynomial f, I want to determine whether f has integer coefficients. More specifically, define
M[f_]:=MonomialList[f].
Is it possible to determine ...
0
votes
1answer
42 views
Extract coefficients and terms in polynomial expansion [closed]
I have a polynomial in $a$ and $b$:
$$(Aa^2 + Bb^2 + Ca + Db + E)^m$$
How can I construct a table of coefficients corresponding to all different products $a^i b^j$ in the expansion for a defined $m$, ...
0
votes
2answers
90 views
Forcing mathematica to solve polynomials exactly
It used to be the default behavior that Mathematica would solve polynomials of degree 4 exactly. In the current version I have (12.2.2.0) it sometimes gives numerical answers. Is there a way to change ...
1
vote
1answer
49 views
Matching polynomial coefficients when solving an equation
Two polynomials of the same degree are equal if the they have the same coefficients. I would like to use that to find all coefficients of a polynomial:
...
1
vote
2answers
82 views
Fittind data with shifted Chebyshev polynomials
I am trying to fit data from a simulation to a particular class of polynomials, according to least squares approach.
...
2
votes
2answers
69 views
Checking if a polynomial contains a certain monomial
I want to check if a given polynomial contains a certain monomial while ignoring ordering of the variables. For example:
$$P(a,b,c)=abc + bca$$
And then I want to check if $P$ contains $bac$ (should ...
2
votes
0answers
31 views
Convolution for large arrays went wrong [closed]
I am trying to use ListConvolve[a, b, {1, -1}, 0] for large arrays a and b (1024 length) to ...
2
votes
2answers
87 views
Does Mathematica have build-in function to compute dimension of square polynomial system?
I'm working with square polynomial systems and wish to know if a (small) system has a finite number of solutions. That is, if it's zero-dimensional. I'm not aware of any built-in function to do this ...
1
vote
1answer
44 views
Guess the next number formula [closed]
I have a sequence of numbers such as {1,2,4,8,16}
The goal is to create a polynomial f(x) such that:
f(0)=1, f(1)=2, f(2)=4, f(n)=nth item on the list
I found this function which claims to do exactly ...
0
votes
0answers
27 views
Watching Intermediate Calculations or Estimate Remaining Time in Eliminate Command
I want to use Eliminate commands to 70 coupled multivariable polynomial equations, but the code is too slow. (It does not show result after 30 minutes in my laptop.)...
3
votes
1answer
65 views
Return the factors of a partially-factored polynomial, without factoring
Suppose I have an integer polynomial f that is in a factored form, say f = (1 + x) * (2 + x + x^3) * (2 + x^5). I want a ...
1
vote
1answer
45 views
Idiomatic way to express a polynomial in terms of a shifted variable
I have a polynomial of known degree, $f(x) = \sum_{n = 0}^N a_n x^n$ and I' d like to express it in terms of a shifted variable $x - x_ 0$, so that $f(x) = \sum_{n = 0}^N b_n (x - x_ 0)^n$.
I can do ...
4
votes
1answer
144 views
Solve efficiently large system of $N$ quadratic equations
I am trying to find all $\lambda$ given a tensor $T$ such that $\sum_{jk}^N T_{ijk}x_jx_k=\lambda x_i$ with $1\leq i \leq N$ and $\sum_i x_i^2=1$. $T$ is known but $x$ is unknown.
This boils down to ...
5
votes
1answer
105 views
Check if polynomial is in factored form, without factoring
I have a large list list of integer polynomials, all of which are the output of Factor. So my list looks something like this: <...