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0 votes
1 answer
190 views

Solving a polynomial with NumPy

I'm trying to do something that I thought would be very straightforward but somehow I'm struggling. I have a time series and I want to extrapolate it, assuming a linear trend, to forecast when will it ...
user avatar
2 votes
0 answers
102 views

Is the numerical resolution of this huge sparse polynomial system tractable?

I'd like to find numerically a solution to a sparse system of 2000000 polynomial equations of degree 3 with 50000 variables and integer coefficients (or at least to decide whether or not a solution ...
Sebastien Palcoux's user avatar
6 votes
1 answer
509 views

roots of polynomials with small coefficients

I would like to compute the roots of a polynomial with exponentially small coefficients. $$ \sum_{n=0}^N a_n \frac{z^n}{\sqrt{n!}} \tag{$\ast$}$$ where $a_n$ are Normal random variables with mean $0$...
john mangual's user avatar
0 votes
1 answer
928 views

roots of polynomials of high degree: LinAlgError: Eigenvalues did not converge

I wrote a simple script to generate random polynoimals $\displaystyle f(z)= \sum_{k=0}^N a_k \frac{z^k}{\sqrt{k!}} $ of high degree and find their roots. For more discussion on random polyomials see ...
john mangual's user avatar
5 votes
1 answer
2k views

Rational functions in Python

I would like use Python to verify the following identities: $ \frac{1}{1-z} = 1 + z + z^2 + z^3 + \dots $ $ \frac{1}{1-z - z^2} = 1 + z + 2z^2 + 3z^3 + \dots $ $ q \prod_{n \geq 1} (1 - q^n)^{24} = ...
john mangual's user avatar