Abstract
AbstractWe introduce and investigate an arithmetical data type designed for computation with rational numbers. Called the symmetric transrationals, this data type comes about as a more algebraically symmetric modification of the arithmetical data type of transrational numbers [9], which was inspired by the transreals of Anderson et.al. [1]. We also define a bounded version of the symmetric transrationals thereby modelling some further key semantic properties of floating point arithmetic. We prove that the bounded symmetric transrationals constitute a data type. Next, we consider the equational theory and prove that deciding the validity of equations over the symmetric transrationals is 1-1 algorithmically equivalent with deciding unsolvability of Diophantine equations over the rational numbers, which is a longstanding open problem. The algorithmic degree of the bounded case remains open.Keywordsrational numbersdata typescomputer arithmeticcommon meadowstransrationalsdiophantine problemfloating-point
Published Version
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