# Subproject A2: Parallelization of Algebraic Program Systems

Project leader:

Prof. Dr. Johann
Kühn, Institute of Theoretical Particle
Physics, Karlsruhe Institute of Technology (KIT)
and

Prof. Dr. Matthias Steinhauser, Institute of Theoretical Particle
Physics, Karlsruhe Institute of Technology (KIT)

** Short Summary:**

In modern theoretical particle physics computer algebra systems (CAS) are
indispensable. They are very important tools for the manipulation of formulae.
The main focus of this project is the further development of
` ParFORM` and ` TFORM`, the parallel
versions of ` FORM` designed to handle huge algebraic expressions. In
particular, the combination of the two different parallelization concepts
is considered.
In addition we develop in this project efficient programs for the reduction of
Feynman integrals to master integrals and their numerical evaluation.

**Summary:**

The symbolic manipulation of complicated formulae has a long tradition in
particle physics. Computer algebra systems (CAS) have been used already quite
early in order to evaluate, e.g., traces over γ matrices. Among the
first CAS there are ` REDUCE` and ` SCHOONSCHIP`, the latter has been
designed by M. Veltman.
Afterwards ` Mathematica`, ` Maple` and others have been developed which
are still in use nowadays. However, their field of application is limited to
small and medium sized problems since it is not possible to work with very
large intermediate expressions. On the other hand, there are quite a lot of
problems which produce intermediate
expression of the order of a few hundred giga bytes up tera bytes to
be manipulated by the CAS. The only CAS currently available in order to cope
with such tasks is ` FORM`.

Although ` FORM` is very powerful, there are many
important physical applications where even ` FORM` requires several weeks
or even months of CPU time. Furthermore the resources as far as CPU speed,
memory and disk
space are concerned are often not sufficient. An obvious solution is
the parallelization of ` FORM` which makes simultaneously available
the resources of several computers and furthermore significantly reduces
the wall clock time.

In recent years two concepts for parallel versions of ` FORM`
have been successfully implemented:
` ParFORM`, essentially based on MPI (message passing interface), and `
TFORM` which uses threads for the parallelization and has been developed in
the current funding period. Both programs run
stable, show a good speedup and are complete in the sense that all programs
written for the serial version of ` FORM` can now be used with `
ParFORM` and ` TFORM`}.
For the next funding period we aim at the combination of both
parallelization concepts allowing for the efficient use of clusters build from
multi-core nodes. Furthermore, an improvement of the speedup behaviour is
on the agenda.

In this project there are also activities concerned with the reduction of
families of Feynman integrals to a small set of basis elements (master
integrals) and their
numerical evaluation. These two topics are covered in two
program packages, ` FIRE` and ` FIESTA`, which have been published
within this project.
In the next period we plan to rewrite ` FIRE` in ` C++` and to extend
` FIESTA` to additional kinematical regions.

Last Change : 14th June 2011