Survey of Symbolic Computations on the Grid

Symbolic and algebraic computations are one of the fastest growing areas of scientific computing. In this paper we present an overview of the state-of-the-art in symbolic and algebraic computations on parallel and distributed computers and on grids. We give some background information, including typical application areas, and then give a list of past and on-going projects involving symbolic computations. We also attempt at concisely summarizing our findings. This article is based on the chapter on symbolic computations on grid that will appear in 2005 the book "Engineering the Grid: status and perspective", Editors Beniamino di Martino, Jack Dongarra, Adolfy Hoisie, Laurence Yang, and Hans Zima, Nova Science Publishers, Inc..

[1]  Gary L. Miller,et al.  Sublinear Parallel Algorithm for Computing the Greatest Common Divisor of Two Integers , 1984, FOCS.

[2]  Dana Petcu PVMaple: A Distributed Approach to Cooperative Work of Maple Processes , 2000, PVM/MPI.

[3]  Menouer Diab Systolic Architectures for Multiplication over Finite Field GF(2m) , 1990, AAECC.

[4]  Paul Jackson,et al.  Finite Field Arithmetic Using the Connection Machine , 1990, CAP.

[5]  Wolfgang Küchlin,et al.  Parallel computer algebra software as a Web component , 1998 .

[6]  Joachim von zur Gathen,et al.  Modern Computer Algebra (3. ed.) , 2003 .

[7]  Dana Petcu,et al.  Extending Maple to the grid: design and implementation , 2004, Third International Symposium on Parallel and Distributed Computing/Third International Workshop on Algorithms, Models and Tools for Parallel Computing on Heterogeneous Networks.

[8]  Gene Cooperman,et al.  STAR/MPI: binding a parallel library to interactive symbolic algebra systems , 1995, ISSAC '95.

[9]  Hoon Hong,et al.  The Design of the SACLIB/PACLIB Kernels , 1995, J. Symb. Comput..

[10]  Jack Dongarra,et al.  NetSolve: Past, Present, and Future - A Look at a Grid Enabled Server , 2003 .

[11]  Richard P. Brent,et al.  Some Parallel Algorithms for Integer Factorisation , 1999, Euro-Par.

[12]  Tudor Jebelean Integer and Rational Arithmetic on MasPar , 1996, DISCO.

[13]  Christian Mittermaier,et al.  Distributed Maple: parallel computer algebra in networked environments , 2003, J. Symb. Comput..

[14]  Yuzo Takamatsu,et al.  Exponetiation in Finite Fields Using Dual Basis Multiplier , 1990, AAECC.

[15]  Mantsika Matooane Parallel systems in symbolic and algebraic computation , 2002 .

[16]  D. Fliegner,et al.  Parallelizing the Symbolic Manipulation Program FORM , 1999, hep-ph/9906426.

[17]  P. L. Montgomery,et al.  An FFT extension of the elliptic curve method of factorization , 1992 .

[18]  Laurent Bernardin,et al.  A review of symbolic solvers , 1996, SIGS.

[19]  Wolfgang Kuchlin Parsac-2: Parallel Computer Algebra On The Desk-Top , 1995 .

[20]  Erich Kaltofen,et al.  DSC: a system for distributed symbolic computation , 1991, ISSAC '91.

[21]  Erich Kaltofen,et al.  FOXBOX: a system for manipulating symbolic objects in black box representation , 1998, ISSAC '98.

[22]  John ffitch,et al.  CABAL: polynomial and power series algebra on a parallel computer , 1997, PASCO '97.

[23]  Bruno Buchberger The L-Machine: An Attempt at Parallel Hardware for Symbolic Computation , 1985, AAECC.

[24]  Takayasu Ito,et al.  Parallel Symbolic Computing: Languages, Systems, and Applications , 1992, Lecture Notes in Computer Science.

[25]  Joachim von zur Gathen,et al.  Modern Computer Algebra , 1998 .

[26]  Alyson Reeves A Parallel Implementation of Buchberger's Algorithm over Zp for p <= 31991 , 1998, J. Symb. Comput..

[27]  Mantsika Matooane,et al.  A Parallel Symbolic Computation Environment: Structures and Mechanics , 1999, Euro-Par.

[28]  Katherine A. Yelick,et al.  Implementing an irregular application on a distributed memory multiprocessor , 1993, PPOPP '93.

[29]  D. Lin,et al.  An Internet Accessible Grid Computing System : Grid-ELIMINO , .

[30]  Roberto Pirastu,et al.  Parallel Computation and Indefinite Summation: A MAPLE Application for the Rational Case , 1995, J. Symb. Comput..

[31]  Dongdai Lin,et al.  IAMC architecture and prototyping: a progress report , 2001, ISSAC '01.

[32]  Robert H. Halstead,et al.  Parallel Symbolic Computing , 1986, Computer.

[33]  Ying Chen,et al.  MATLAB*G: A Grid-Based Parallel MATLAB , 2004 .

[34]  John ffitch,et al.  The Bath concurrent LISP machine , 1983, EUROCAL.

[35]  Paul S. Wang Symbolic Computation and Parallel Software , 1991, ACPC.

[36]  Carla Limongelli,et al.  Design and Implementation of Symbolic Computation Systems , 1996, Lecture Notes in Computer Science.

[37]  Laurent Bernardin Maple on a massively parallel, distributed memory machine , 1997, PASCO '97.

[38]  Henri Casanova,et al.  Overview of GridRPC: A Remote Procedure Call API for Grid Computing , 2002, GRID.

[39]  Erich Kaltofen,et al.  Process Scheduling in DSC and the Large Sparse Linear Systems Challenge , 1995, J. Symb. Comput..

[40]  Long Yin Choy,et al.  MATLAB*P 2.0 : interactive supercomputing made practical , 2002 .

[41]  Stephen M. Watt A System for Parallel Computer Algebra Programs , 1985, European Conference on Computer Algebra.

[42]  Masanori Idesawa,et al.  Design of a Lisp machine - FLATS , 1982, LFP '82.

[43]  Wolfgang Küchlin,et al.  A case study of multi-threaded Gröbner basis completion , 1996, ISSAC '96.