ideal

ideal

Philosophy

a. of or relating to a highly desirable and possible state of affairs

b. of or relating to idealism

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ideal [ī′dēl]

(mathematics)

A subsetIof a ringRwherex-yis inIfor everyx,yinIand eitherrxis inIfor everyrinRandxinIorxris inIfor everyrinRandxinI; in the first caseIis called a left ideal, and in the second a right ideal; an ideal is two-sided if it is both a left and a right ideal.

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1.		IDEAL - Ideal DEductive Applicative Language. A language by Pier Bosco and Elio Giovannetti combining Miranda and Prolog. Function definitions can have a guard condition (introduced by ":-") which is a conjunction of equalities between arbitrary terms, including functions. These guards are solved by normal Prolog resolution and unification. It was originally compiled into C-Prolog but was eventually to be compiled to K-leaf.
2.		IDEAL - A numerical constraint language written by Van Wyk of Stanford in 1980 for typesetting graphics in documents. It was inspired partly by Metafont and is distributed as part of Troff. ["A High-Level Language for Specifying Pictures", C.J. Van Wyk, ACM Trans Graphics 1(2):163-182 (Apr 1982)].
3.	(theory)	ideal - In domain theory, a non-empty, downward closed subset which is also closed under binary least upper bounds. I.e. anything less than an element is also an element and the least upper bound of any two elements is also an element.