Algebraic operads : an algorithmic companion /: an algorithmic companion. (2016)

• Record Type: Book
• Further Information: Note: Murray R. Bremner and Vladimir Dotsenko.
• Authors: Bremner, Murray R; Dotsenko, Vladimir, 1981-
• Contents: Normal Forms for Vectors and Univariate Polynomials; Standard Forms; Normal Forms; ; Noncommutative Associative Algebras; Introduction; Free Associative Algebras; Normal Forms; Computing Gröbner Bases; Examples of Gröbner Bases and Their Applications; Rewriting Systems and Gröbner Bases; Exercises; ; Nonsymmetric Operads ; Introduction; Nonsymmetric Operads; Free Nonsymmetric Operads; Normal Forms; Computing Gröbner Bases; Examples of Gröbner 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 Gröbner 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 Gröbner Bases; Examples of Gröbner Bases for Shuffle Operads; Exercises; ; Operadic Homological Algebra and Gröbner Bases; Introduction; First Instances of Koszul Signs for Graded Operads; Koszul Duality for Operads; Models for Operads from Gröbner Bases; Exercises; ; Commutative Gröbner Bases; Introduction; Commutative Associative Polynomials; Equivalent Definitions of Commutative Gröbner Bases; Classification of Commutative Monomial Orders; Zero-Dimensional Ideals; Complexity of Gröbner 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;
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 512.62; Operads; Algebraic functions; Algebra
• Languages: English
• ISBNs: 9781482248579
• Related ISBNs: 9781482248562
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.