JuliaHomotopyContinuation/HomotopyContinuation.jl: Version 1.0

We are very happy to announce the first stable release of HomotopyContinuation.jl.

• Support for polyhedral homotopies. This is an advanced algorithm to construct good start systems and usually results in a much smaller number of paths to track compared to the total degree homotopy. This homotopy is for now optional and can be enabled by calling solve(f; start_system=:polyhedral). Note that compared to total degree homotopy this is so far not multi-threaded.
• More robust path tracking by implementing a new endgame algorithm. We should now be able to handle in more challenging situations to find the correct number of solutions. Many thanks to @TorkelE for providing helpful test cases. Due to the new algorithm some keywords changed.
• Singular solutions are now grouped by their multiplicities and only counted once.
• Much improved performance for tracking overdetermined solutions (~10x speed up) by using LAPACK more efficiently.
• We finally also have a nice progress bar in Jupyer notebooks! So no more need to set show_progress=false in notebooks.
• We track now by default in affine rather than projective space where possible. This results in much improved numerical stability.
• It is now possible to increase the precision of the evaluation of the residual in Newton's method to 128 bit. With this it is possible to track more numerically challenging paths. The precision can be fixed to 64 bit, 128 bit or change adaptively.

• We took 1.0 as a chance to make the naming of the provided functions and keywords more consistent. If a function or keyword consists out of multiple words it now should be separated by an _. See https://github.com/JuliaHomotopyContinuation/HomotopyContinuation.jl/pull/274 for a list of changed functions and keywords.