


Mailing address:
 Mathematisch Instituut
Universiteit Utrecht
P.O.Box 80.010
3508 TA UTRECHT
The Netherlands
Location:

"Hans Freudenthal" building.

Email:
 W.vanderKallen@uu.nl

 Wilberd van der Kallen,
 Computing some KLpolynomials for the poset
of B×Borbits in
group compactifications (July 2002) PDF
 Wilberd van der Kallen,

Complexity of an extended lattice reduction algorithm (19971998)

Hecke eigenforms
The programs used for the paper
Hecke eigenforms in the Cuspidal
Cohomology of Congruence Subgroups of SL(3,Z),
Experimental Mathematics
6 (1997), 163174,
have been packed in
a
zipped tar file
(cf. the
instructions to unpack
)
Intersection Cohomology
We have
implemented the recursions in the paper
T.A. Springer,
Intersection Cohomology of
B×B orbits in group compactifications,
Journal of Algebra 258 (2002) 71111.
Lenstra Lenstra Lovász
Our
implementations
of the extended Lenstra Lenstra Lovász algorithm (with integer
arithmetic and allowing dependent generators) try to use smaller integers than,
say,
the implementation in
GP/PARI Version
1.38.71.
One can prove complexity bounds
for our algorithm that are similar to those
proved for the original LLL algorithm.
One can also do such an analysis
for the Hermite Normal Form algorithm of
Havas, Majewski, Matthews. One may use the same principles
to avoid coefficient explosion in a straightforward
GCD based
Hermite Normal Form algorithm. It is just a matter of understanding
where the explosion is produced. Severe countermeasures like modular
arithmetic are quite unnecessary.
Shortest vector in a lattice
The Mathematica Package
ShortestVector
depends on the Mathematica Package
LLLalgorithm.
Style file for LaTeX
To make an Index with pagerefs under LaTeX
Chladni plates
These pictures have been made with
a Mathematica
package for a
simple model of round and square Chladni plates. Note that plates are
not membranes, so that the wave equation does not apply.
Wilberd van der Kallen