Abstract and concrete categories
Abstract and concrete categories
An introduction to functional programming systems using Haskell
An introduction to functional programming systems using Haskell
ML for the working programmer (2nd ed.)
ML for the working programmer (2nd ed.)
Clifford Algebraic Calculus for Geometric Reasoning with Application to Computer Vision
Selected Papers from the International Workshop on Automated Deduction in Geometry
Object-Oriented Concurrent Constraint Programming in Oz
Grundlagen und Anwendungen der Künstlichen Intelligenz, 17. Fachtagung für Künstliche Intelligenz, Humboldt-Universität zu
Geometry Machines: From AI to SMC
AISMC-3 Proceedings of the International Conference AISMC-3 on Artificial Intelligence and Symbolic Mathematical Computation
Proving Geometric Theorems Using Clifford Algebra and Rewrite Rules
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
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The category of noncommutative geometric spaces is a rather new and wide field in geometry that provides a rich source of hard computer applications. In this contribution we give a short summary of the basic notions of geometric spaces. The so-called parallel map that describes a space will play a fundamental role because, in terms of the parallel map, a geometric space can be represented in such a way that geometric conditions/axioms (which form the structure of a space) are expressible by certain equations. To verify a configuration amounts to showing the solvability of a corresponding equation or a system of equations, respectively. This is a computational aspect that opens the whole field naturally to computer applications by means of “automated deduction in geometry,” verification of geometric constraints, computer-aided construction of finite geometries. We give motivation why we use specific declarative programming languages for doing all the implementations and computer applications.