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Rounding coefficients and artificially underflowing terms in non-numeric expressions

Authors:

Robert Corless,

David R. StoutemyerAuthors Info & Claims

ACM Communications in Computer Algebra, Volume 45, Issue 1/2

Pages 17 - 48

https://doi.org/10.1145/2016567.2016570

Published: 25 July 2011 Publication History

Abstract

This article takes an analytical viewpoint to address the following questions:

1. How can we justifiably beautify an input or result sum of non-numeric terms that has some approximate coefficients by deleting some terms and/or rounding some coefficients to simpler floating-point or rational numbers?

2. When we add two expressions, how can we justifiably delete more non-zero result terms and/or round some result coefficients to even simpler floating-point, rational or irrational numbers?

The methods considered in this paper provide a justifiable scale-invariant way to attack these problems for subexpressions that are multivariate sums of monomials with real exponents.

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Cited By

Stoutemyer DNagasaka KWinkler FSzanto A(2014)Fuzzy simplification of non-numeric expressions containing some intervals and/or floating point numbersProceedings of the 39th International Symposium on Symbolic and Algebraic Computation10.1145/2608628.2627489(9-16)Online publication date: 23-Jul-2014
https://dl.acm.org/doi/10.1145/2608628.2627489
Corless RPostma EStoutemyer DKotsireas I(2012)GCD of multivariate approximate polynomials using beautification with the subtractive algorithmProceedings of the 2011 International Workshop on Symbolic-Numeric Computation10.1145/2331684.2331709(153-154)Online publication date: 7-Jun-2012
https://dl.acm.org/doi/10.1145/2331684.2331709

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Rounding coefficients and artificially underflowing terms in non-numeric expressions

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Published In

cover image ACM Communications in Computer Algebra

ACM Communications in Computer Algebra Volume 45, Issue 1/2

March/June 2011

138 pages

ISSN:1932-2232

EISSN:1932-2240

DOI:10.1145/2016567

Issue’s Table of Contents

Copyright © 2011 Authors.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 July 2011

Published in SIGSAM-CCA Volume 45, Issue 1/2

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Cited By

Stoutemyer DNagasaka KWinkler FSzanto A(2014)Fuzzy simplification of non-numeric expressions containing some intervals and/or floating point numbersProceedings of the 39th International Symposium on Symbolic and Algebraic Computation10.1145/2608628.2627489(9-16)Online publication date: 23-Jul-2014
https://dl.acm.org/doi/10.1145/2608628.2627489
Corless RPostma EStoutemyer DKotsireas I(2012)GCD of multivariate approximate polynomials using beautification with the subtractive algorithmProceedings of the 2011 International Workshop on Symbolic-Numeric Computation10.1145/2331684.2331709(153-154)Online publication date: 7-Jun-2012
https://dl.acm.org/doi/10.1145/2331684.2331709

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