IntBasis is a maple package which contains a number of algorithms for computing with algebraic curves. The purpose of this html page is to give additional documentation for this package. The main algorithm in IntBasis is integral_basis. It computes an integral basis of an algebraic function field using Puiseux expansions. An application is to compute normal forms for algebraic curves of genus 0 and genus 1.

Version Dec 1995 version of IntBasis for Maple 5.3. Additional code "ratpar", date: Jan 3 1996, for rational parametrizations and a file with test examples . The new version (Sep 28 1996) of this code, called algcurves. Available as a tar.gz file containing the source files (make .m files out of these, and then the code can be used after the command with(algcurves) in Maple). Also available (this takes less time to install) as a single text file which is more or less just the concatenation of the source files in the tar.gz file (to use this just read the file in Maple). This code works under Maple 5.3 and Maple 5.4, but unfortunately the help pages only work under Maple 5.3. It will be shipped with the next release of maple in the package algcurves. Examples

Some comments on the implementation

IntBasis Graphics: Have a look at the 3D singularity knot animations!

Future changes in IntBasis

Integral basis for algebraic number fields

Other sources of software: the algebraic geometry package CASA.

If you have any questions or comments, please mail them to hoeij@math.fsu.edu