# Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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### 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 ...
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### 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 ...
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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### 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, ...
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### 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 ...
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### 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 ...
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### 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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### Understanding plot of Root[] object

I'm trying to understand the plot of this Root object ...
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### 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 ...
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### 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 ...
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### 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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### 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`...
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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### 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 ...
83 views

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

I have the following calculation in Mathematica: ...
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### 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: ...
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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### 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 ...
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 ...
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### 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 ...
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.)...
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### 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 ...
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### 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 ...
### 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 ...