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An objectoriented platform for distributed highperformance symbolic computation
 Mathematics and Computers in Simulation, 49:161–178
, 1999
"... We describe the distributed objectoriented threads system (DOTS), a programming environment designed to support objectoriented fork/join parallel programming in a heterogeneous distributed environment. A mixed network of Windows NT PCs and UNIX workstations is transformed by DOTS into a homogeneou ..."
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Cited by 21 (15 self)
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We describe the distributed objectoriented threads system (DOTS), a programming environment designed to support objectoriented fork/join parallel programming in a heterogeneous distributed environment. A mixed network of Windows NT PCs and UNIX workstations is transformed by DOTS into a homogeneous pool of anonymous compute servers forming together a multicomputer. DOTS is a complete redesign of the distributed threads system (DTS) using the objectoriented paradigm both in its internal implementation and in the programming paradigm it supports. It has been used for the parallelization of applications in the field of computer algebra and in the field of computer graphics. We also give a brief account of applications in the domain of symbolic computation that were developed using DTS. # 1999 IMACS/Elsevier
Distributed Symbolic Computation with DTS
 PROCEEDINGS OF PARALLEL ALGORITHMS FOR IRREGULARLY STRUCTURED PROBLEMS, LNCS 980
, 1995
"... We describe the design and implementation of the Distributed Threads System (DTS), a programming environment for the parallelization of irregular and highly datadependent algorithms. DTS extends the support for fork/join parallel programming from shared memory threads to a distributed memory enviro ..."
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Cited by 17 (6 self)
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We describe the design and implementation of the Distributed Threads System (DTS), a programming environment for the parallelization of irregular and highly datadependent algorithms. DTS extends the support for fork/join parallel programming from shared memory threads to a distributed memory environment. It is currently implemented on top of PVM, adding an asynchronous RPC abstraction and turning the net into a pool of anonymous compute servers. Each node of DTS is multithreaded using the C threads interface and is thus ready to run on a multiprocessor workstation. We give performance results for a parallel implementation of the RSA cryptosystem, parallel long integer multiplication, and parallel multivariate polynomial resultant computation.
Walking Faster
 Design and Implementation of Symbolic Computation Systems
, 1996
"... The Gröbner Walk is an algorithm that converts a given Gröbner basis of a polynomial ideal I of arbitrary dimension to a Gröbner basis of I with respect to another term order. The conversion is done in several steps (the walk) following a path in the Gröbner fan of I. We report on our experiences wi ..."
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Cited by 4 (0 self)
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The Gröbner Walk is an algorithm that converts a given Gröbner basis of a polynomial ideal I of arbitrary dimension to a Gröbner basis of I with respect to another term order. The conversion is done in several steps (the walk) following a path in the Gröbner fan of I. We report on our experiences with an implementation of the walk. We discuss several algorithmic variations as well as important implementation techniques whose combined effect is to elevate the walk to a new level of performance.
How Fast Does the Walk Run?
 5th Rhine Workshop on Computer Algebra, volume PR 801/96, pages 8.1 – 8.9. Institut Franco– Allemand de Recherches de Saint–Louis
, 1996
"... The Grobner Walk is an algorithm which converts a given Grobner basis of a polynomial ideal I of arbitrary dimension to a Grobner basis of I with respect to another term order. The conversion is done in several steps (the walk) following a path in the Grobner fan of I . We report on our experiences ..."
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Cited by 2 (1 self)
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The Grobner Walk is an algorithm which converts a given Grobner basis of a polynomial ideal I of arbitrary dimension to a Grobner basis of I with respect to another term order. The conversion is done in several steps (the walk) following a path in the Grobner fan of I . We report on our experiences with a first implementation of the walk connected with a stateoftheart Grobner basis package. Our implementation allows us to evaluate the walk on a large set of nontrivial examples. We can thus give an estimation when it is promising to apply the walk for the computation of lexicographic Grobner Bases. 1 Introduction It is well known that the form and size of a Grobner basis of a polynomial ideal [2] depends heavily on the underlying term order, and that the same is true for the complexity of its computation. Unfortunately, the lexicographic term orders needed for polynomial system solving are particularly bad in this respect. A possible strategy to overcome this difficulty is to comp...
On the Walk
, 1997
"... The Gröbner Walk is a basis conversion method proposed by Collart, Kalkbrener, and Mall. It converts a given Gröbner basis G of a (possibly positive dimensional) polynomial ideal I to a Gröbner basis G 0 of I with respect to another term order. The target Gröbner basis is approached in several steps ..."
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The Gröbner Walk is a basis conversion method proposed by Collart, Kalkbrener, and Mall. It converts a given Gröbner basis G of a (possibly positive dimensional) polynomial ideal I to a Gröbner basis G 0 of I with respect to another term order. The target Gröbner basis is approached in several steps (the Walk), each performing a simpler Gröbner basis computation. We address a host of questions associated with this method: alternative ways of presenting the main algorithm, algorithmic variations and refinements, implementation techniques, promising applications, and its practical performance, including a comparison with the FGLM conversion method. Our results show that the Walk has the potential to become a key tool for computing and manipulating ideal bases and solving systems of equations.