All Questions
Tagged with mathematica polynomials
15
questions
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Definite Integral involving polynomial and Meijer G-function
I am trying to solve the following integral involving Meijer-g function
$\int_0^{\infty} \left(\varrho x + \nu\right)^{p+\frac{1}{2}-\frac{k}{2}} G_{1,3}^{3,0}\left(\begin{matrix} \frac{\...
- 31
1
vote
1
answer
60
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Simplifying a particular expression
I have the expression
$$ \frac{x(-c z^{n+1} (-1)^k + c x^{n+1})}{(x-ze^{i \theta})(x - ze^{-i\theta})},$$
where $b$ and $c$ are non-zero complex numbers, $z = \frac{b}{\sqrt{bc}}$ and $\theta = \frac{...
- 43
1
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0
answers
52
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Do you recognize these polynomials?
Consider the integral
$$f_k (x) := \int_{- \infty}^{+ \infty} dt \, t^k \, e^{-t^2 + x t} \, , \quad k \in \mathbb{N}.$$
According to Mathematica:
$$f_k(x) = \frac{1 -(-1)^k}{2} \, x \, \Gamma \left(...
- 759
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0
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139
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Finding Roots of a Polynomial in a Given Range
I want to be able to analyze complicated polynomials (degree $6,7$ etc.) and find out if they have roots in a given range. How do I proceed to do this using Mathematica, Matlab, or analytically(if ...
user911589
0
votes
1
answer
455
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Is there a way to solve a very complicated equation in one variable? [closed]
Essentially solving for x in this equation:
$\frac{(631.60353-0.078408πx^3-3.44416x^2)[π(\sin31.72778)+2]}{6.54928x+0.22365x^2} + 15.4-\frac{x(\sin31.72778+2)+7.7}{6.54928x+0.22365x^2}(0.235224πx^2+6....
- 25
7
votes
1
answer
294
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Basis of factors for large degree polynomials
In $\mathbb{Z}_2$, the polynomial $x^{2^6}+x+1$ or $x^{64}+x+1$ factors into $x^4+x+1$, $x^{12}+x^9+x^5+x^2+1$, $x^{12}+x^9+x^5+x^4+x^2+x+1$, $x^{12}+x^9+x^8+x^5+1$, $x^{12}+x^9+x^8+x^5+x^4+x+1$, $x^{...
- 21.4k
3
votes
1
answer
428
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Help me understand Gröbner basis result please
I'm practicing a bit with Gröbner bases but I'm not understanding the following result I obtain from Mathematica:
...
- 7,305
0
votes
1
answer
424
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Best program for multiplying many multivariable polynomials
I want to make a table with two columns:
The first column will consist of many(possibly hundreds) of polynomials in two variables.
The second column will be a function applied to all of the ...
- 1
1
vote
2
answers
1k
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Practical applications of Graeffe's root finding method
What are the practical applications of Graeffe's root finding method? I searched a lot but couldn't find any. I found that it is used in aerodynamics and electric circuit analysis. But I don't know ...
2
votes
1
answer
1k
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Newton backward interpolation in Mathematica [closed]
I have the following task:
Create a function (in Wolfram Mathematica), called $\mathrm{NewtonBackward}$[n_,x0_,h_,f_] which interpolates backwards the function $f(x)$ with nodes {x_i = x_0 + $i$$\...
- 21
2
votes
1
answer
2k
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Automatic calculation of the intersection of discrete curves
first of all, let me apologize for a poor math-english translation, I'll try my very best.
I have the following situation:
I have over 16.000 data files which I generated from a biometric verification ...
- 133
2
votes
3
answers
1k
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Finding root of a polynomial
Let's say I've got $ax^3 + bx^2 + cx + d = 0$
I want to find x for a general-case.
Mathematica gave me a very long solution, and even longer for one which has $kx^4$.
Can you please help me ...
- 191
2
votes
2
answers
201
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Computation of characteristic polynomial fails for me
For a matrix $A\in\mathbb{K}^{n\times n}$ where $\mathbb{K}\in\{\mathbb{R},\mathbb{C}\}$ the characteristic polynomial is defined as
$$\chi_A(\lambda) := \text{det}(A-\lambda I_n) = \sum_{k=0}^n c_k \...
- 3,153
1
vote
2
answers
257
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Help need in Mathematica or Sage
I want to find the common positive solutions of two polynomials $f_{a,b}(x,y)$, $g_{a,b}(x,y)$ where $a,b$ runs from 0 to 1 with an interval 0.01. Let $(x_0,y_0)$ be a common positive solution. Then ...
- 1,305
4
votes
2
answers
1k
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Integrate in Mathematica takes forever
I'm trying to calculate the length of a curve from a polynomial in Mathematica and for some reason Integrate doesn't complete, it just runs until I abort the execution.
The polynom:
...
- 143