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JuliaHomotopyContinuation / HomotopyContinuation.jl

A Julia package for solving systems of polynomials via homotopy continuation.
https://www.JuliaHomotopyContinuation.org
MIT License
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Start System Complaints: Incorrect Rank Calculation #565

Closed aaronjhf closed 2 months ago

aaronjhf commented 5 months ago

Hi,

I get complaints that the start system is no good. One issue is that the rank of the Jacobian is computed incorrectly. Its entries are large numbers and rank() from LinearAlgebra computes the rank incorrectly. When I use GenericLinearAlgebra and convert the Jacobian to a BigFloat Array, then the rank is computed correctly. I have also had precision issues when rescaling things to have smaller numbers which are fractions that truncate too soon.
Here is a link to an example: https://github.com/aaronjhf/DR-Varieties/blob/main/hom.jl . It is a script where I use monodromy_solve and also calculate the jacobian.
Please let me know the best way to proceed dealing with these start system issues.

Thanks very much, aaronjhf

PBrdng commented 4 months ago

Hi,

the best way to deal with such issues is to find a formulation of your system that is numerically more feasible. In particular, I would try to find a rescaling of your polynomials which deals with coefficients in the range 10^k for k between 0 and 3. The implementation is not optimized for using BigFloat and so I do not recommend using it.

PBrdng commented 2 months ago

Closed