Ordered algebraic structures in the open-source mathematics system Sage
by
Peter Jipsen
Chapman University

Several computer algebra systems, such as Maple and Mathematica, have packages for doing calculations with posets and lattices. Recently the free open-source mathematics system Sage (sagemath.org) has also acquired some built-in support for such calculations. I will demonstrate some extensions of these features to several classes of ordered algebraic structures, including residuated lattices, idempotent semirings (with domain operator), modal lattices, and allegories. This aids with illustrating a structure theorem for n-potent divisible residuated lattices as Heyting products of MV-chains. Extensions of this result to some classes of idempotent semirings, distributive modal lattices and distributive allegories will also be discussed.

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Date received: June 9, 2008