Questions tagged [polynomials]
Questions on the functionality operating on polynomials
1,044 questions
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Avoid MonomialList applying N to coefficients containing floats
For inexact coefficients MonomialList seems to apply N.
How to avoid this?
...
- 3,516
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Accelerate Mathematica code computing visibility polynomial of one graph
Let $G$ be a graph of order $n$. Then the visibility polynomial, $\mathcal{V}(G)$, of $G$ is defined as
$$
\\
\mathcal{V}(G)=\sum_{i\geq 0} r_i x^{i}
\\
$$
where $r_i$ denote the number of mutual-...
- 2,364
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Factor polynomial with generalized root extension
Here are two examples with ordinary extensions:
Factor[1 + x^4, Extension -> Sqrt[2]]
Factor[x^2 + 2 Sqrt[3] x + 3, Extension -> Automatic]
But what about &...
- 32.8k
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How to find "minimal polynomial" of a rational number?
I suspect that 1.0982 is (close to) the root of a low degree (2 or 4) polynomial with small ...
- 1,466
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Understanding a function that finds the degree of a multi-variate polynomial
The following function finds the degree of a multi-variate polynomial.
PolyDeg[expr_]:=expr//ToList//Exponent[#,Variables[#]]&/@#&//Plus@@@#&//Max;
...
- 647
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How to improve the Mathematica implementations of q-Bessel polynomial?
I know Mathematica has implemented some QFunctions.
I have found this literature: q-Bessel polynomials, q-Laguerre polynomials, q-Charlier polynomials, etc.?
I have implemented q-Bessel polynomials in ...
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How can I reduce the degree of a polynomial in two variables by substitution?
This is similar to the how-to-replace-variable-with-power question, but here it involves two variables with different power combinations.
This quesion arises from paper forward kinematics of the 6-6 ...
- 403
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Combining like terms where the coefficients contain radicals
I need a function which combines like terms in a polynomial with multiple variables. The coefficients (constant real numbers) may contain radicals and this function must put them together.
Example: ...
- 647
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Is there a way to automate the generation of these polynomials?
The motivation of this question is pure curiosity.
Working on this problem, I tried to find the zero of function
$$f(x)=m\,(m-1)^{\frac{1}{m}-1}\, x^{1-\frac{1}{m}}+x-1 \quad \quad \text{where} \...
- 1,105
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Understanding integration of rational function which yields wrong results depending on generality
Problem
I want to evaluate the following integral:
$$\int \limits_{-1}^1\frac{x^{n}}{Q(x)} \, dx$$
where $Q(x)=\sum _{k=0}^m a_k x^k$ and $Q(x) \neq 0 \quad \forall x \in [-1,1]$.
In this specific ...
- 1,758
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How to calculate Kazhdan-Lusztig Polynomials of Coxeter groups using Mathematica? [closed]
How to calculate Kazhdan-Lusztig Polynomials using Mathematica?
References:
TABLES OF KAZHDAN-LUSZTIG POLYNOMIALS
Kazhdan-Lusztig Polynomials - Combinatorics
kazhdan-Lusztig-polynomial-calculator (of ...
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Recombining indeterminate powers in monomials [duplicate]
In an expression, I want to replace everywhere monomials, say, $x^{i-3j}y^{2j-3i}$ with $(x/y^3)^i(y^2/x^3)^j$, is there a concise way to do it?
- 2,459
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Conditions under which roots of cubic matrix polynomial are real
I've defined four $2\times 2$ matrices and a vector of size $2$:
...
- 155
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Efficient way to evaluate polynomial of matrices
I would like to evaluate a polynomial of matrix $g(A)= \sum_{m=0}^{k}e^{-i m \phi} A^{m}$ where $\phi$ is some angle provided by the user and $k$ is some positve integer. So I did a very naive thing ...
- 1,226
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Can all combination of Trigonometric functions be written in terms of spherical harmonics?
I want to write these two Expressions in terms of spin-weighted spherical harmonics:
$\cos^{2}\theta\,\cos^{2}\phi - \sin^{2}\phi$
$\cos^{2}\theta\,\sin^{2}\phi - \cos^{2}\phi$
I've written this code ...
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