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Article Dans Une Revue Transmathematica Année : 2020

The Transrational Numbers as an Abstract Data Type

Résumé

In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. We define an enlargement of a field to a transfield, in which division is totalised by setting 1/0 equal to the positive infinite value and-1/0 equal to its opposite, and which also contains an error element to help control their effects. We construct the transrational numbers as a transfield of the field of rational numbers and consider it as an abstract data type. We give it an equational specification under initial algebra semantics.
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hal-03184954 , version 1 (30-03-2021)

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Jan A Bergstra, Jan Aldert Bergstra, John Tucker. The Transrational Numbers as an Abstract Data Type. Transmathematica, 2020, ⟨10.36285/tm.47⟩. ⟨hal-03184954⟩
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