OutOfMemoryError in HomotopyContinuation

General Usage
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1

Hi all,
I’m trying to use HomotopyContinuation.jl to find all of the solutions a polynomial system of equations with 14 polynomials in 14 variables.
Each polynomial is sum of monomials of degree from 10 to 13 (like f1=2x13^2x14x15x16x24x25x26x34x35x36 +
12x14x15x16x23x24x25x26x34x35x36+…).

After receiving the error

ERROR: OverflowError: Cannot compute a start system.

I tried to use the option

start_system=:total_degree

in solve, but now I am received the error message

ERROR: OutOfMemoryError()

even without Julia allocating a large amount of memory. What to do in this case?

2

The start system with total degree homotopy should be z_j = e^{i2\pi n / p}, for n=0,...,p-1 and for each j. Hence for 14 polynomials in 14 variables that means a starting system with 10^{14} initial starting vectors if p=10. Pretty large given that each path solves a multivariate differential equation of dimension 14. This is highly parallelizable though so it should be possible to deploy machines in parallel to follow each path.