Sage Days 13 Coding Spring Projects

Contents

  1. Sage Days 13 Coding Spring Projects
    1. Sage For Newbies
    2. Reimplement Basic Quaternion Algebra Arithmetic
    3. ZAK code integration
    4. Maps, e.g. abelian groups to set of ideals for class groups
    5. Neighbor Method
    6. Trac #4120 -- Binary Quadratic Forms
    7. Octonions and Cubes

For the main SD 13 wiki page go here

Below a list of proposed projects

Sage For Newbies

Reimplement Basic Quaternion Algebra Arithmetic

ZAK code integration

PEOPLE: M. Abshoff

To quote the Introduction of the ZAK software survey by Rainer Schulze-Pillot (linked below as PDF): 

In the 1990s Rudolf Scharlau and I had a joint project concerned with computations
for and with integral quadratic (and later also hermitian) forms over Z and also over
the rings of integers of (mainly quadratic) number fields. The project originated
in Rudolf Scharlau’s group of Diplom and doctoral students, where it also got its
name ZAK, I don’t really now why (from the German word Zahlk¨orper (number
field) perhaps?). It turned later into a project funded by Deutsche Forschungsgemeinschaft;
in this time Alexander Schiemann worked for the project, coordinated
the programming work and wrote several C++ programs. The programs developed
in the project were the basis of the articles [19, 20, 18, 22, 5] and were used for
Schiemann’s computation of tables of integral hermitian forms [23]. After Schiemann
left academia we continued to use the programs for a while on our HP-UX
workstations. When these went out of service it turned out to be difficult to adapt
the programs to other environments; I will describe some of the problems later.
All experiments I did now are under Linux (Suse 11.0) using gcc 4.3. The present
new interest in such computations, in particular in the SAGE project, raises the
question whether it is worthwhile (and possible) to revive these programs.

Two PDFs:

Maps, e.g. abelian groups to set of ideals for class groups

Neighbor Method

Trac #4120 -- Binary Quadratic Forms

Octonions and Cubes