I have a different series of papers on algorithms for computational algebra
for which I will add pointers as I become more ambitious.
For pointers to me, personally,
see my home page.

*(last modified, Oct. 8, 1997)*

This has three separate C libraries, allowing identical end-user code to run on either a sequential machine, a NOW (network of workstations), or a SMP (Symmetric MultiProcessing -- shared memory). The NOW version runs on top of MPI, and the SMP version runs on top of threads (evolving toward POSIX threads).

G. Cooperman,
``TOP-C: A Task-Oriented Parallel C Interface'',
* 5-th International Symposium on High Performance
Distributed Computing* (HPDC-5), IEEE Press, 1996, pp. 141--150.
(N.B.: The paper on Gaussian elimination provides
a good illustration of the principles of TOP-C.)

G. Cooperman,
``GAP/MPI: Facilitating Parallelism'',
*Proc. of DIMACS Workshop on Groups and
Computation II* **28**, *DIMACS Series in
Discrete Mathematics and Theoretical Computer Science*,
L. Finkelstein and W.M. Kantor (eds.), AMS, Providence, RI,
1997, pp. 69--84.

G. Cooperman,
``STAR/MPI: Binding a Parallel Library to
Interactive Symbolic Algebra Systems'',
* Proc. of International Symposium on Symbolic and Algebraic Computation
(ISSAC '95)*, ACM Press, pp. 126--132.

G. Cooperman and V. Greenberg,
``TOP-WEB: Task-Oriented Metacomputing on the Web'',
G. Cooperman and V. Grinberg, * International
Journal of Parallel and Distributed Systems and
Networks* **1**, 1998,
pp.~184--192

G. Cooperman and M. Tselman,
``Using Tadpoles to Reduce Memory and Communication Requirements
for Exhaustive, Breadth-First Search Using Distributed Computers'',
* Proc. of ACM Symposium on Parallel
Architectures and Algorithms* (SPAA-97), ACM Press, 1997,
pp. 231--238; also N.U. Tech. Rept. NU-CCS-97-02, 1997.

G. ooperman, G. Hiß, K. Lux, and J. Müller,
``The Brauer tree of the principal 19-block of the sporadic simple
Thompson group'',
*J. of Experimental
Mathematics* **6**(4), 1997, pp& 293-300.

G. Cooperman,
``Practical Task-Oriented Parallelism for
Gaussian Elimination in Distributed Memory'',
*Linear Algebra Applications* **275-276**,
1998, pp. 107-120.

G. Cooperman and G. Havas, ``Practical Parallel Coset Enumeration'',
*Proc. of Workshop on High Performance Computation and Gigabit
Local Area Networks}* G.& Cooperman, G.& Michler
and H.& Vinck (eds.),
Lecture notes in control and information
sciences& **226**, Springer Verlag, pp.& 15--27.

G. Cooperman, L. Finkelstein, M.& Tselman and B.& York,
``Constructing Permutation Representations for Matrix Groups'',
*J. of Symbolic Computation*& **24**, 1997,
pp.& 1--18.

To date, there have been a number of notable successes in computational
algebra, which provided the initial testbeds. These successes include:
finding a permutation representation of Lyons's group of degree 9,606,125
(GCL/MPI, 8 SPARC-2's, 12 hours, joint
with Finkelstein
and Tselman,
Northeastern U.);
condensation of a permutation matrix representation of *J_4* from
dimension
173,067,389 to a matrix representation for an algebra of dimension
5,693 (GCL/MPI, 14 heavily loaded Alpha's, 2-1/2 days, joint with Tselman,
Northeastern U.); and enumeration of 8,835,156 cosets in order to determine a
permutation representation of Lyons's group from a presentation (TOP-C,
4-processor Convex, 6 hours,
joint with Havas,
U. of Queensland, Australia).

Each of these algebraic computations were the largest of their kind at that
time,
and in each case, almost linear speedup with the number of processors was
seen. Each example has begun with a sequential algorithm and used the
parallel methodology to parallelize the algorithm in a natural manner. For
example, the coset enumeration used sequential code written 6-1/2 years
earlier by Schönert with no thought for parallelization. Approximately
30 lines of a 1400 line C program were modified, and the program was then
linked with the TOP-C library to achieve the parallelization. Each of these
tests on larger problems has stressed further the general parallelization
methodology and led to new ideas. Ongoing work in this spirit includes
condensation of a permutation matrix representation of *Th* from
dimension
976,841,775 to a matrix representation for an algebra of dimension 1,403
(GCL/MPI, 7 Alpha 3000's, 3 weeks expected time, joint with Lux, RWTH, Aachen,
Germany and Mueller, Heidelberg, Germany) and construction of a permutation
representation of dimension 173,067,389 for *J_4*
over *GL(1333,11)*
(TOP-C, about 200 nodes of SP-2, under 2 days expected, joint with
Michler's group)
at Essen, Germany.