Introduction to computer algebra systems

Mini-workshop in Saarbrücken, 28 - 30 November, 2017

Funded by SFB-TRR 195 Symbolic Tools in Mathematics and their Applications.
Part of the graduate programme of the Integrated Research Training Group of the SFB-TRR 195.
Organized by Moritz Weber.
How to get to the math building of Saarland University

This mini-workshop serves as an introduction to the computer algebra systems GAP and SINGULAR.
If you want to take part, please send an email to Moritz Weber.


Speakers

Thomas Breuer (RWTH Aachen)
Christian Eder (TU Kaiserslautern)
Andreas Steenpaß (TU Kaiserslautern)


Participants

If you want to take part, please send an email to Moritz Weber.
Aslam Ali
Marwa Banna
Jessica Cologna
Arved Frommberger
Daniel Gromada
Stefan Jung
Luca Junk
Pascal Kattler
Matias Klimpel
Felix Leid
Tobias Mai
Alexander Mang
Christian Mauz
Martin Michajlow
Miguel Angel Pluma Rodriguez
Julien Schanz
Simon Schmidt
Gabriela Weitze-Schmithüsen
Ricardo Schnur
Carlo Sircana
Mirko Stappert
Christian Steinhart
Jayantha Suranimalee
Andrea Thevis
Nikolaos Tsakanikas
Moritz Weber
Andreas Widenka
Sheng Yin
Mang Zhao


Schedule

All lectures take place in building E2 4.

The schedule consists in introductory lectures open for all participants, and some time for discussions about
individual computer algebra problems mainly between the speakers and the participants of the Integrated
Research Training Group.

Tuesday, 28 November
12:00 - 16:00   Introduction to GAP (Thomas Breuer), HS IV
Slides
16:00   Coffee break, Konferenzraum (103)
from 16:30   Individual discussions on GAP (for members of the Integrated Research Training Group), SR8 (318)

Wednesday, 29 November
10:00 - 13:00   Introduction to SINGULAR (Christian Eder and Andreas Steenpaß), HS IV
Slides
from 14:00   Continuation of the introduction to SINGULAR, SR10 (316)
or individual discussions on SINGULAR and GAP (for members of the Integrated Research Training Group) ,
SR9 (319) and SR10 (316)
16:00   Coffee break, Klassenzimmer (216)
19:00   Dinner (downtown)

Thursday, 30 November
until 12:00   individual discussions on SINGULAR and GAP (for members of the Integrated Research Training Group), SR9 (319)
from 14:00   individual discussions on SINGULAR and GAP (for members of the Integrated Research Training Group), SR8 (318)
16:00   Coffee break, Klassenzimmer (216)


Preparation from the participant's side

Please make sure to have GAP and/or SINGULAR on your laptop. If you have any problems with installing the software, please contact one of the speakers or the organizer as soon as possible. Also, please send a message to Moritz Weber with the information which system you are using (Linux, Windows,...).

If you have any particular questions or problems regarding GAP and/or SINGULAR or if you are interested in learning about any specific features of these softwares, please contact Moritz Weber as soon as possible as we are collecting a list of questions to the speakers (see below).

Some useful links:
GAP:
   Homepage
   Documentation
   Manual
   Tutorial

SINGULAR:
   Homepage
   Manual
   Source code
   testing SINGULAR online/tutorials


Some concrete questions from the participant's side

  • How does the profiling package of GAP work?
  • Could you please describe more in detail the difference between the structure "matrix" and "module" in SINGULAR? What are the differences between implementation. In which cases it is convenient to use "matrix" and in which it is convenient to use "module"? How efficient is the retyping from one to another? (My particular problem is following. I need to describe a vector subspace. I suppose, it is convenient to use "module" for this purpose. However, I want the basis vectors to be as simple as possible, for which I use the Gauss elimination in the matrix package. Am I doing it correctly? Is there a more efficient way?)
  • How to find the documentation of software and packages, how to document self written packages?
  • How to work with free groups, the free group algebra, congruence groups, actions of groups, linear algebra?
  • How to work with noncommutative polynomials and rational functions in SINGULAR?
  • How to work with the symmetric group in GAP?
  • How to work with Gröbner basis in SINGULAR, in particular regarding efficiency? Also, how much is implemented regarding p-adic numbers?
  • Is it possible to do some programming in the kernel of SINGULAR (without knowing C++)?



Updated: 29 November 2017   Moritz Weber Impressum