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» Formal Theories for Linear Algebra
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ACS
2010
14 years 9 months ago
Graded and Koszul Categories
Koszul algebras have arisen in many contexts; algebraic geometry, combinatorics, Lie algebras, non-commutative geometry and topology. The aim of this paper and several sequel paper...
Roberto Martínez-Villa, Øyvind Solbe...
AISC
2010
Springer
15 years 26 days ago
A Formal Quantifier Elimination for Algebraically Closed Fields
We prove formally that the first order theory of algebraically closed fields enjoy quantifier elimination, and hence is decidable. This proof is organized in two modular parts. We ...
Cyril Cohen, Assia Mahboubi
AISC
1998
Springer
15 years 1 months ago
Reasoning About Coding Theory: The Benefits We Get from Computer Algebra
The use of computer algebra is usually considered beneficial for mechanised reasoning in mathematical domains. We present a case study, in the application domain of coding theory, ...
Clemens Ballarin, Lawrence C. Paulson
78
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STACS
1997
Springer
15 years 1 months ago
Methods and Applications of (MAX, +) Linear Algebra
Exotic semirings such as the “(max, +) semiring” (R ∪ {−∞}, max, +), or the “tropical semiring” (N ∪ {+∞}, min, +), have been invented and reinvented many times s...
Stephane Gaubert, Max Plus
79
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FOIS
2006
14 years 11 months ago
Formalizing Ontology Alignment and its Operations with Category Theory
An ontology alignment is the expression of relations between different ontologies. In order to view alignments independently from the language expressing ontologies and from the te...
Antoine Zimmermann, Markus Krötzsch, Jé...