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About this product
- Author(s)Murray R. Bremner,Vladimir Dotsenko
- PublisherApple Academic Press Inc.
- Date of Publication01/04/2016
- Place of PublicationOakville
- Country of PublicationCanada
- ImprintApple Academic Press Inc.
- Content Note18 black & white illustrations
- Weight657 g
- Width156 mm
- Height235 mm
- Spine25 mm
- Table Of ContentsNormal Forms for Vectors and Univariate Polynomials Standard Forms Normal Forms Noncommutative Associative Algebras Introduction Free Associative Algebras Normal Forms Computing Grobner Bases Examples of Grobner Bases and Their Applications Rewriting Systems and Grobner Bases Exercises Nonsymmetric Operads Introduction Nonsymmetric Operads Free Nonsymmetric Operads Normal Forms Computing Grobner Bases Examples of Grobner Bases for Nonsymmetric Operads Normal Forms for Algebras over Nonsymmetric Operads Exercises Twisted Associative Algebras and Shuffle Algebras Introduction Twisted Associative Algebras and Shuffle Algebras Free Shuffle Algebras Normal Forms Computing Grobner Bases Examples of Shuffle Algebras and their Applications Exercises Symmetric Operads and Shuffle Operads Introduction Symmetric Operads and Shuffle Operads Free Shuffle Operads Normal Forms Computing Grobner Bases Examples of Grobner Bases for Shuffle Operads Exercises Operadic Homological Algebra and Grobner Bases Introduction First Instances of Koszul Signs for Graded Operads Koszul Duality for Operads Models for Operads from Grobner Bases Exercises Commutative Grobner Bases Introduction Commutative Associative Polynomials Equivalent Definitions of Commutative Grobner Bases Classification of Commutative Monomial Orders Zero-Dimensional Ideals Complexity of Grobner Bases: A Historical Survey Exercises Linear Algebra over Polynomial Rings Introduction Rank of a Polynomial Matrix; Determinantal Ideals Some Elementary Examples Algorithms for Linear Algebra over Polynomial Rings Bibliographical Comments Exercises Case Study of Nonsymmetric Binary Cubic Operads Introduction Toy Model: The Quadratic Case The Cubic Case Exercises Case Study of Nonsymmetric Ternary Quadratic Operads Introduction Generalities on Nonsymmetric Operads with One Generator Nonsymmetric Ternary Operads Further Directions Exercises Appendices: Maple Code for Buchberger's Algorithm First Block: Initialization Second Block: Monomial Orders Third Block: Sorting Polynomials Fourth Block: Standard Forms of Polynomials Fifth Block: Reduce and Self-Reduce Sixth Block: Main Loop - Buchberger's Algorithm
- Author BiographyMurray R. Bremner, PhD, is a professor at the University of Saskatchewan in Canada. He attended that university as an undergraduate, and received an M. Comp. Sc. degree at Concordia University in Montreal. He obtained a doctorate in mathematics at Yale University with a thesis entitled On Tensor Products of Modules over the Virasoro Algebra. Prior to returning to Saskatchewan, he held shorter positions at MSRI in Berkeley and at the University of Toronto. Dr. Bremner authored the book Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications and is a co-translator with M. V. Kotchetov of Selected Works of A. I. Shirshov in English Translation. His primary research interests are algebraic operads, nonassociative algebra, representation theory, and computer algebra. Vladimir Dotsenko, PhD, is an assistant professor in pure mathematics at Trinity College Dublin in Ireland. He studied at the Mathematical High School 57 in Moscow, Independent University of Moscow, and Moscow State University. His PhD thesis is titled Analogues of Orlik-Solomon Algebras and Related Operads. Dr. Dotsenko also held shorter positions at Dublin Institute for Advanced Studies and the University of Luxembourg. His collaboration with Murray started in February 2013 in CIMAT (Guanajuato, Mexico), where they both lectured in the research school Associative and Nonassociative Algebras and Dialgebras: Theory and Algorithms. His primary research interests are algebraic operads, homotopical algebra, combinatorics, and representation theory.
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