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Abstract: The algebraic structure of combinatory differential fields is constructed to provide a semantics for computations in analysis. In this setting programs, approximations, limits and operations of analysis are represented as algebraic terms. Analytic algorithms can be derived by algebraic methods. The main tool in this construction are combinatory models which are inner algebras of Engeler graph models. As an universal domain of denotational semantics the lattice structure of the graph models... (Update)
Context of citations to this paper: More
...introducing the notion of combinatory models. The reader interested in the relations to graph models is advised to refer to [Aberer, 1991A, Aberer, 1991B] 2 Operations of Symbolic Computation We distinguish the following three types of operations used in computer algebra. 1....
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BibTeX entry: (Update)
Aberer, K.(1991). Combinatory Differential Fields: An Algebraic ApproachtoApproximate Computation and Constructive Analysis. TR-91-061, International Computer Science Institute, Berkeley.. http://citeseer.ist.psu.edu/aberer91combinatory.html More
@techreport{ aberer91combinatory,
author = "Karl Aberer",
title = "Combinatory Differential Fields: An Algebraic Approach to Approximate Computation and Constructive Analysis",
number = "TR-91-061",
address = "Berkeley, CA",
year = "1991",
url = "citeseer.ist.psu.edu/aberer91combinatory.html" }
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134 Information Based Complexity (context) - Traub, Wasilkowski et al. - 1988
60 Computability in Analysis and Physics (context) - -El, Richards - 1989
33 An Introduction to Differential Algebra (context) - Kaplansky - 1957
32 Computer Algebra-Symbolic and Algebraic Computation (context) - Buchberger, Collins et al. - 1983
30 Algebras and Combinators (context) - Engeler - 1981
26 Computer Algebra (context) - Davenport, Siret - 1988
7 Finding a Zero by Means of Successive Linear Interpolation (context) - Dekker - 1969
4 Scratchpad II: An Abstract Datatype System for Mathematical .. (context) - Jenks, Sutor et al. - 1988
4 A Critique of Numerical Analysis (context) - Linz - 1988
3 Combinatory Differential Fields and Constructive Analysis (context) - Aberer - 1991
3 Metamathematik der Elementarmathematik (context) - Engeler - 1981
3 Normal Forms in Function Fields - Aberer - 1990
3 A Combinatory Representation of Varieties and Universal Clas.. (context) - Engeler - 1988
2 Theorie und Anwendung des Graphmodells der kombinatorischen .. (context) - Fehlmann - 1981
2 A Kind of Difference Methods for Enclosing Solutions of Ordi.. (context) - Weissinger - 1988
2 Solving Function Space Problems with Guaranteed Close Bounds (context) - Kaucher - 1983
1 Extension of Combinatory Logic to a Theory of Combinatory Re.. (context) - Weibel - 1990
1 Nonstandard Computation Theory (context) - Richter, Szaeo - 1983
1 Freiburger Intervall Berichte (context) - Krawczyk - 1983
1 Rekursionstheorie und Komplexitatstheorie auf effektiven CPO.. (context) - Weihrauch - 1980
1 Normal Forms in Combinatory Differential Fields (context) - Aberer - 1989
1 Equations in Combinatory Algebras (context) - Engeler - 1984
1 A Computer Oriented Version of Nonstandard Analysis in: Cont.. (context) - Jensen - 1972
1 Nichtstandard Erweiterungen von Differentialkorpern (context) - di Primo - 1991
1 Graph Algebras (context) - Mader - 1986
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