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A language for computational algebra

Authors:

Richard D. Jenks,

Barry M. TragerAuthors Info & Claims

SYMSAC '81: Proceedings of the fourth ACM symposium on Symbolic and algebraic computation

Pages 6 - 13

https://doi.org/10.1145/800206.806363

Published: 05 August 1981 Publication History

Abstract

This paper reports ongoing research at the IBM Research Center on the development of a language with extensible parameterized types and generic operators for computational algebra. The language provides an abstract data type mechanism for defining algorithms which work in as general a setting as possible. The language is based on the notions of domains and categories. Domains represent algebraic structures. Categories designate collections of domains having common operations with stated mathematical properties. Domains and categories are computed objects which may be dynamically assigned to variables, passed as arguments, and returned by functions. Although the language has been carefully tailored for the application of algebraic computation, it actually provides a very general abstract data type mechanism. Our notion of a category to group domains with common properties appears novel among programming languages (cf. image functor of RUSSELL) and leads to a very powerful notion of abstract algorithms missing from other work on data types known to the authors.

References

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Cited By

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A language for computational algebra

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cover image ACM Conferences

SYMSAC '81: Proceedings of the fourth ACM symposium on Symbolic and algebraic computation

August 1981

248 pages

ISBN:0897910478

DOI:10.1145/800206

Copyright © 1981 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

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Association for Computing Machinery

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Published: 05 August 1981

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Cited By

Stefanov EDijk MShi EChan TFletcher CRen LYu XDevadas S(2018)Path ORAMJournal of the ACM10.1145/317787265:4(1-26)Online publication date: 12-Apr-2018
https://dl.acm.org/doi/10.1145/3177872
Chierichetti FGiakkoupis GLattanzi SPanconesi A(2018)Rumor Spreading and ConductanceJournal of the ACM10.1145/317304365:4(1-21)Online publication date: 12-Apr-2018
https://dl.acm.org/doi/10.1145/3173043
Watt S(2011)Computational Tools for Mathematical CollaborationProceedings of the 2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing10.1109/SYNASC.2011.64(16-18)Online publication date: 26-Sep-2011
https://dl.acm.org/doi/10.1109/SYNASC.2011.64
Siek J(2010)The c++0x "concepts" effortProceedings of the 2010 international spring school conference on Generic and Indexed Programming10.1007/978-3-642-32202-0_4(175-216)Online publication date: 22-Mar-2010
https://dl.acm.org/doi/10.1007/978-3-642-32202-0_4
Coppersmith D(2006)Fast evaluation of logarithms in fields of characteristic twoIEEE Transactions on Information Theory10.1109/TIT.1984.105694130:4(587-594)Online publication date: 1-Sep-2006
https://dl.acm.org/doi/10.1109/TIT.1984.1056941
Andreica A(2006)Implementing Parameterized Type Algorithm Definitions in MathematicaProceedings of the Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing10.1109/SYNASC.2006.45(35-40)Online publication date: 26-Sep-2006
https://dl.acm.org/doi/10.1109/SYNASC.2006.45
Fortenbacher A(2005)Efficient type inference and coercion in computer algebraDesign and Implementation of Symbolic Computation Systems10.1007/3-540-52531-9_124(56-60)Online publication date: 5-Jun-2005
https://doi.org/10.1007/3-540-52531-9_124
Burge WWatt S(2005)Infinite structures in scratchpad IIEurocal '8710.1007/3-540-51517-8_103(138-148)Online publication date: 31-May-2005
https://doi.org/10.1007/3-540-51517-8_103
Watt S(2005)A fixed point method for power series computationSymbolic and Algebraic Computation10.1007/3-540-51084-2_19(206-217)Online publication date: 27-May-2005
https://doi.org/10.1007/3-540-51084-2_19
Jenks RSutor RWatt S(2005)Scratchpad II: An abstract datatype system for mathematical computationTrends in Computer Algebra10.1007/3-540-18928-9_3(12-37)Online publication date: 26-May-2005
https://doi.org/10.1007/3-540-18928-9_3
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