This package computes Whitney stratifications of real and complex algebraic varieties using the algorithms described in [1, 2]. For varieties considered over the complex numbers the output is indexed by the strata dimension. When wishing to treat the variety over the reals, the same output may be used, but the dimensions of the strata may differ (and some strata may be empty), see [2] for more details. This post processing in the real case is currently left to the user.
A method is also provided to stratify polynomial maps $f:X\to Y$ between algebraic varieties, the output is a Whitney stratification of both $X$ and $Y$, such that for each (open, connected) strata $M$ of $X$ there is an (open, connected) strata $N$ of $Y$ such that $f(M) \subset N$ and such that the restriction of $f$ to $M$ is a submersion.
Computing the Conormal variety of a variety is an important step in these algorithms, so a method for this is also provided.
References:
[1] Martin Helmer and Vidit Nanda. "Conormal Spaces and Whitney Stratifications", Foundations of Computational Mathematics, DOI: 10.1007/s10208-022-09574-8.
[2] Martin Helmer and Vidit Nanda "Effective Whitney stratification of real algebraic varieties", arXiv:2307.05427v2, 2023.
This documentation describes version 2.03 of WhitneyStratifications.
The source code from which this documentation is derived is in the file WhitneyStratifications.m2.
The object WhitneyStratifications is a package.