## Homepage of the **VKCURVE** package

**VKCURVE** is a joint project of

which we undertook in order to do the computations described in
our paper
"explicit presentations for exceptional braid groups" (see the file
contrib/readme in the package for details).
**VKCURVE** is a computer algebra package which computes a
presentation of the fundamental group of the complement in the complex
plane of an algebraic curve, following Van Kampen's method. It is
written in GAP3.
If, when using this package, you find any bugs, misdesigns, problems etc...
(or if you just make an interesting use of the package), please send Email
to us
(David Bessis
or Jean Michel).

Here is brief example of the package in action:

gap> FundamentalGroup(x^2-y^3);
#I there are 2 generators and 1 relator of total length 6
1: bab=aba
gap> FundamentalGroup((x+y)*(x-y)*(x+2*y));
#I there are 3 generators and 2 relators of total length 12
1: cab=abc
2: bca=abc

For more information you look at the manual
online.
You can also try VKCURVE
online, an (experimental) web interface where you can directly enter
a curve and get a result.

## How to install **VKCURVE** onto your computer

To help people who are interested in VKCURVE or other GAP3 packages not
ported to GAP4 I have prepared an easy-to install GAP3
distribution. I recommend to use this rather than trying to install
VKCURVE separately, especially since VKCURVE depends for some
functionalities on some other packages being up to date.
## History of the package

First release 0.99 on 15-2-2002
Version 1.0 on 1-3-2002. Now curves with Gaussian rational
coefficients are accepted:
gap> FundamentalGroup(x^2-E(4)*y^3);
#I there are 2 generators and 1 relator of total length 6
1: bab=aba

Version 1.2 on 3-2009. Some bug fixes.