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Solving Multivariate Polynomial Systems and an Invariant from Commutative Algebra
post-quantum cryptography multivariate cryptography Groebner basis
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2017/6/22
The security of several post-quantum cryptosystems is based on the assumption that solving a system of multivariate (quadratic) polynomial equations p1=⋯=pm=0p1=⋯=pm=0 over a finite field ...
MATH 603: INTRODUCTION TO COMMUTATIVE ALGEBRA
MATH COMMUTATIVE ALGEBRA
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2015/9/29
What is this course about? The foundations of di erential geometry (=
study of manifolds) rely on analysis in several variables as \local machinery": many
global theorems about manifolds are reduced...
Composition-Diamond Lemma for Non-associative Algebras over a Commutative Algebra
Gr¨obner-Shirshov basis non-associative algebra commutative algebra
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2010/11/26
We establish the Composition-Diamond lemma for non-associative algebras over a free commutative algebra. As an application, we prove that every countably generated non-associative algebra over an arbi...