Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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2
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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
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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
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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 ...
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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
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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
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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
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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 <...
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1answer
55 views

Understanding plot of Root[] object

I'm trying to understand the plot of this Root object ...
0
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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
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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
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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 ...
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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
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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 ...
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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 ...
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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
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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
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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 (...
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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
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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
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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
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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
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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
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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
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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 ...
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0answers
45 views

Problems with NSolve[] finding zeros of a 32-degree polynomial

I have the following calculation in Mathematica: ...
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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: ...
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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 ...
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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*...
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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 $a_i$, ...
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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 ...
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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
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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 ...
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2answers
60 views

How to delete certain terms in a polynomial with variables in subscript?

I have a polynomial in the following style, ...
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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
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1answer
60 views

Using a Groebner Basis to show Bijectivity

I have a set of n polynomials over n variables, like ...
1
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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
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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
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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
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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
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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: ...
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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
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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
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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
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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
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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
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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
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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
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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
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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: <...

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