Questions tagged [polynomials]
Questions on the functionality operating on polynomials
1,044 questions
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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-...
CommunityBot
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"How to determine the conditions for a polynomial to always be positive?
I have a polynomial of the type p(x)=a0+a1x+a2x^2+a3x^3+ ... +a6x^6, I want conditions so that p(x) is always positive, knowing that x> or = 0.
How can I implement this in wolfran in order to put ...
CommunityBot
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Avoid MonomialList applying N to coefficients containing floats
For inexact coefficients MonomialList seems to apply N.
How to avoid this?
...
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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 ...
- 39.3k
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Solving quintic in radicals
I need to find an explicit expression in radicals for the real root of the quintic equation
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Build a Companion Matrix of a Polynomial?
The eigenvalues of a square matrix $A$ are the roots of its characteristic polynomial $\chi(\lambda)$. Conversely, if we have a monic polynomial
$p(\lambda)=a_0 + a_1 \lambda + \cdots + a_{n-1}\lambda^...
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Express polynomials as sum of squares
Well, while SOStools of Matlab can express a polynomials as SOS (Sum Of Squares) by the following theorem:
A multivariate polynomial p in n variables and of degree 2d is a sum of squares if
and only ...
- 647
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Are there any bugs in the `SubresultantPolynomials` and `SubresultantPolynomialRemainders`?
Bug introduced in 14.0 or earlier and fixed in 14.2.
Try the following code
...
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Kernel crash in PolynomialMod [closed]
Bug introduced in 14.1 or earlier and fixed in 14.3.
The following code runs correctly
PolynomialMod[1-2x+x^(3/2)+I x^2, x^(3/2)]
PolynomialMod[1-2x+I x^2, x]
The ...
- 41.5k
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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 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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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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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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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: ...
- 259k