Questions tagged [polynomials]
Questions on the functionality operating on polynomials
1,048 questions
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Expand product of polynomials with display of intermediate terms
The question is best explained by an example:
Expand[(a+b)(a-b)] results in a^2-b^2.
How to avoid summation to get also the ...
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Why is `CoefficientRules` significantly slower than `CoefficientList`, and how to efficiently get sparse rules for multivariate polynomials?
I have noticed a significant performance gap between CoefficientList and CoefficientRules. While ...
- 1,087
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Why doesn't NSolve return any real solution although FindRoot can find some?
I'm trying to run this relatively simple code. I have five polynomial equations (I read that NSolve should work fine with these) and five variables. I need to find ...
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Why is PrimitivePolynomialQ[x + 1, 2] False?
Why does PrimitivePolynomialQ[x + 1, 2] yield False ?
Why does PrimitivePolynomialQ[x, 2] ...
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Writing cyclic polynomial as a cyclic sum
I need to write a cyclic polynomial of $a$, $b$, $c$ as a cyclic sum $\sum\limits_{\rm cyc}$ of another polynomial. The problem is rigorously stated as follows.
Input: A polynomial $f(a,b,c)$.
Output:...
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Replace constant term of polynomial
Given is a polynomial with an arbitrary number of variables. How can I replace the constant term of the polynomial by another expression? The constant term is a number but the value 0 is not ...
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Is it possible to find the parametric root of $x$ in $25 x^4 + x^2 (5 - 7 y^2) + 3 x y + 4=0 $ for which $\text{Re(x)}<0$?
I have this quartic equation 25 x^4 + x^2 (5 - 7 y^2) + 3 x y + 4 == 0 for real $y>0$. I use Reduce and get four parametric ...
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Avoid MonomialList applying N to coefficients containing floats
For inexact coefficients MonomialList seems to apply N.
How to avoid this?
...
- 3,546
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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-...
- 2,434
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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 &...
- 38.5k
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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;
...
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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 ...
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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: ...
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