Experience with FORMAC algorithm design

Tobey, R. G.

doi:10.1145/365758.365773

Cited by 25 publications

(5 citation statements)

References 6 publications

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“…Symbolic computations often exhibit intermediate expression swell [13]. This recurring hazard requires that we implement dynamic distribution which balances storage requirements on each processing element during computation.…”

Section: Polynomial and Matrix Representationsmentioning

confidence: 99%

A Parallel Symbolic Computation Environment: Structures and Mechanics

Matooane

Norman

1999

Euro-Par’99 Parallel Processing

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We describe a set of representations for polynomials and sparse matrices suited for use with fine-grain parallelism on a distributed memory multiprocessor system. Our aim is to support use of supercomputers with this style of architecture to perform computations that would exceed the main memory capacity of more traditional computers: although such systems have very high performance communication networks it is still essential to avoid letting any one part of the network become a bottleneck. We use randomised data placement both to avoid hot-spots in the communication patterns and to balance (in a probabilistic sense) the memory load placed upon each processing element. The expected application areas for such a system will be those where intermediate expression swell means that the huge primary memory available on MPP systems will be needed if the smaller final result is to be successfully computed.

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Section: Polynomial and Matrix Representationsmentioning

confidence: 99%

A Parallel Symbolic Computation Environment: Structures and Mechanics

Matooane

Norman

1999

Euro-Par’99 Parallel Processing

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“…Such growth has caused many calculations to be aborted because the expressions filled the available computer memory. Tobey has described this phenomenon with the colorful phrase "intermediate expression swell" [32]. In many cases the final result of a symbolic calculation is quite small, but in order to get that result one generates very large intermediate expressions.…”

Section: Communications August 1971mentioning

confidence: 99%

Algebraic simplification a guide for the perplexed

Moses¹

1971

Proceedings of the Second ACM Symposium on Symbolic and Algebraic Manipulation - SYMSAC '71

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Algebraic simplification is examined first from the point of view of a user who needs to comprehend a large expression, and second from the point of view of a designer who wants to construct a useful and efficient system. First we describe various techniques akin to substitution. These techniques can be used to decrease the size of an expression and make it more intelligible to a user. Then we delineate the spectrum of approaches to the design of automatic simplification capabilities in an algebraic manipulation system. Systems are divided into five types. Each type provides different facilities for the manipulation and simplification of expressions. Finally we discuss some of the theoretical results related to algebraic simplification. We describe several positive results about the existence of powerful simplification algorithms and the number-theoretic conjectures on which they rely. Results about the nonexistence of algorithms for certain classes of expressions are included.

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“…Success with this technique depends on clever decompositions of an expression. Automatic routines for introducing labels into expressions by Baker [43 ] and Martin [ 24 ] cannot be considered great successes.…”

Section: Z86mentioning

confidence: 99%

“…Tobey has described this phenomenon with the colorful phrase "intermediate expression swell" [43 ]. In many cases the final result of a symbolic calculation is quite small, but in order to get that result one finds oneself generating very large intermediate expressions.…”

Section: Intermediate Expression Swellmentioning

confidence: 99%

Algebraic simplification

Moses¹

1971

Commun. ACM

105

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Algebraic simplification is examined first from the point of view of a user needing to comprehend a large expression, and second from the point of view of a designer who wants to construct a useful and efficient system. First we describe various techniques akin to substitution.These techniques can be used to decrease the size of an expression and make it more intelligible to a user.Then we delineate the spectrum of approaches to the design of automatic simplification capabilities in an algebraic manipulation system. Systems are divided into five types.Each type provides different facilities for the manipulation and simplification of expressions.Finally we discuss some of the theoretical results relat~ ed to algebraic simplification.We describe several positive results about the existence of powerful simplification algorithms and the number-theoretic conjectures on which they rely.

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Experience with FORMAC algorithm design

Cited by 25 publications

References 6 publications

A Parallel Symbolic Computation Environment: Structures and Mechanics

A Parallel Symbolic Computation Environment: Structures and Mechanics

Algebraic simplification a guide for the perplexed

Algebraic simplification

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