Invariant relations
نویسندگان
چکیده
منابع مشابه
Invariant assertions, invariant relations, and invariant functions
Invariant assertions play an important role in the analysis and documentation of while loops of imperative programs. Invariant functions and invariant relations are alternative analysis tools that are distinct from invariant assertions but are related to them. In this paper we discuss these three concepts and analyze their relationships. The study of invariant functions and invariant relations ...
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Whereas the analysis of loops in imperative programs is, justifiably, dominated by the concept of invariant assertion, we submit a related but different concept, of invariant relation, and show how it can be used to compute or approximate the function of a while loop. We also introduce the concept of invariant function, which is used to generate a broad class of invariant relations.
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Let f ∈ Q[x] be an irreducible polynomial of degree n. Then the splitting field L ≥ Q of f is a normal extension. We want to determine the Galois group G = Gal(f) = Gal(L/Q) of f which is the group of all field automorphisms of this extension. This task is basic in computational number theory [Coh93] as the Galois group determines a lot of properties of the field extension defined by f . Becaus...
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We investigate characterizations of the Galois connection sInv–Aut between sets of finitary relations on a base set A and their automorphisms. In particular, for A = ω1, we construct a set R of relations that is closed under all invariant operations on relations and under arbitrary intersections, but is not closed under sInv Aut.
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Every order invariant subset of Q[0,n] has a maximal square whose sections at any (i,...,n1),(i+1,...,n) agree below i. Every order invariant graph on Q[0,n] has a maximal clique whose sections at any (i,...,n-1),(i+1,...,n) agree below i. We prove these and closely related statements, including a finite form, in extensions of the usual ZFC axioms for mathematics with standard large cardinal hy...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1927
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1927-04352-x