On Canonical Forms and Simplification
TL;DR: It is shown that canonical forms do not exist for sufficiently rich classes of mathematical expressions, but with the aid of a nmnber- theoretic conjecture, a large subclass of the negative classes is shown to possess a canonical form.
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Abstract: This paper deals with the simplification problem of symbolic mathematics. The notion of canonical form is defined and presented as a well-defined alternative to the concept of simplified form. Following Richardson it is shown that canonical forms do not exist for sufficiently rich classes of mathematical expressions. However, with the aid of a nmnber- theoretic conjecture, a large subclass of the negative classes is shown to possess a canonical form.
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Symbolic analysis for parallelizing compilers
Mohammad R. Haghighat,Constantine D. Polychronopoulos +1 more
- 01 Jan 1995
TL;DR: A methodology for capturing analyzing program properties that are essential in the effective detection and efficient exploitation of parallelism on parallel computers is described and a symbolic analysis framework is developed for the Parafrase-2 parallelizing compiler.
161
Algebraic simplification: a guide for the perplexed
Joel Moses
- 23 Mar 1971
TL;DR: The spectrum of approaches to the design of automatic simplification capabilities in an algebraic manipulation system is delineated, and several positive results about the existence of powerful simplification algorithms and the number-theoretic conjectures on which they rely are described.
Undecidability and incompleteness in classical mechanics
TL;DR: In this article, Richardson's functor from the Diophantine equations and problems into elementary real-valued functions and problems is described and a general undecidability and incompleteness result for elementary functions within ZFC set theory is derived, and applied to some problems in Hamiltonian mechanics and dynamical systems theory.
How to Recognize Zero
TL;DR: It is proved that this semi algorithm is an algorithm, i.e. that it always terminates, unless it is given a problem containing a counterexample to Schanuel?s conjecture.
73
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Automatic simplification in FORMAC
R. G. Tobey,R. J. Bobrow,S. N. Zilles +2 more
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TL;DR: This chapter discusses simplifying transformations to unwieldly mathematical expressions, which are applied "automatically" to arbitrary expressions but require special handling.
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