Title  
HighPerformance Computer Algebra 

Organizers  
Jeremy Johnson(jjohnson@cs.drexel.edu) and Werner Krandick(krandick@cs.drexel.edu) 

Aim and Scope  
Improved algorithms, better implementations, and faster computers have
enabled many previously timeconsuming computer algebra computations to
be performed routinely and have extended the range of what is practically
possible to compute. However, there remains many computations that still
require excessive computing time, and there are many cases where the performance
achieved by an implementation could be dramatically improved. Tuning algorithms
to perform well on modern computer architectures can be a difficult and
time consuming process. Simply reducing the number of arithmetic operations
is insufficient. It is necessary to take into account the memory hierarchy,
pipelining, and instruction level parallelism. Compilers attempt to produce
code that utilize these features, however, even for highly structured numeric
computations such as matrix multiplication, compilers are far from achieving
optimal performance. The scientific computing community has devoted considerable
effort to producing (recently using automated techniques  see the Special
Issue of the Proceedings of the IEEE on Program Generation, Optimization,
and Platform Adaptation, Vol.93, No. 2, Feb. 2005 ) highperformance libraries
of key kernel computations such as matrix multiplication, linear solve,
and the FFT. Similar work has been initiated in a few cases by the computer
algebra community (largely fundamental arithmetic operations and some work
on matrix and polynomial computations); however, the effort is still at
a primitive state compared to the numeric community. There are many challenges
if achieving highperformance in computer algebra algorithm implementations
due to their irregular structure and higher level data types. It is not
enough to rely on optimizing compilers and the use of optimized implementations
of basic arithmetic operations. This session will focus on techniques for obtaining highperformance implementations of computer algebra algorithms. Potential Topics:
Call for Submissions: This session is a last minute addition to the ACA program; however, submissions for presentations will still be considered. Please contact either of the session organizers 

List of Talks  
