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@ -4,17 +4,17 @@
This is a library for computing homotopy continuation of a given root of one This is a library for computing homotopy continuation of a given root of one
dimensional sections of bivariate complex polynomials. dimensional sections of bivariate complex polynomials.
The output is a piecewise linear aproximation of the path followed by the root, The output is a piecewise linear approximation of the path followed by the root,
with the property that there is a tubular neighborhood, with square transversal with the property that there is a tubular neighborhood, with square transversal
section, that contains the actual path, and there is a three times thicker tubular section, that contains the actual path, and there is a three times thicker tubular
neigborhood guaranted to contain no other root of the polynomial. This second neighborhood guaranted to contain no other root of the polynomial. This second
property ensures that the piecewise linear approximation computed from all roots property ensures that the piecewise linear approximation computed from all roots
of a polynomial form a topologically correct deformation of the actual braid, of a polynomial form a topologically correct deformation of the actual braid,
since the inner tubular neighborhoods cannot intersect. since the inner tubular neighborhoods cannot intersect.
The first version of the library was written in C, and provided only double The first version of the library was written in C, and provided only double
precission. This is the second version, rewritten in C++, and provides the precission. This is the second version, rewritten in C++, and provides the
possibility of using arbitrary precission computations. Hence, it deppends on possibility of using arbitrary precission computations. Hence, it depends on
the [MPFR](http://www.mpfr.org/) and [GMP](https://gmplib.org/) libraries. the [MPFR](http://www.mpfr.org/) and [GMP](https://gmplib.org/) libraries.
## Authors: ## Authors:
@ -105,7 +105,7 @@ library from a [sagemath](https://www.sagemath.org) session. The relevant files
for that are `sage-sirocco_interface.pyx` and `ZVK.py`. The first one contains for that are `sage-sirocco_interface.pyx` and `ZVK.py`. The first one contains
the interface code, and the second one several functions to compute the the interface code, and the second one several functions to compute the
fundamental group of the complement of a curve in the complex plane, using this fundamental group of the complement of a curve in the complex plane, using this
library. Reffer to the comments in `ZVK.py` for a more detailed explanation of library. Refer to the comments in `ZVK.py` for a more detailed explanation of
the functions available there. the functions available there.
An example of session using this library can be the following An example of session using this library can be the following