First developed in the early 1980s by Lenstra, Lenstra, and Lovász, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an introduction to the theory and applications of lattice basis reduction and the LLL algorithm. With numerous examples and suggested exercises, the text discusses various applications of lattice basis reduction to cryptography, number theory, polynomial factorization, and matrix canonical forms.

This book presents a systematic treatment of Grobner bases in several contexts. The book builds up to the theory of Grobner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra. Throughout the book, both the mathematical theory and computational methods are emphasized and numerous algorithms, examples, and exercises are provided to clarify and illustrate the concrete meaning of abstract theory.

This flash-submission third issue is launched in honour of The Violet Hour Magazine's first Halloween in print, and is based on the themes of "Gothic" and "Macabre." It contains short fiction by Kevin M. Folliard and Alyson Faye, short non-fiction by Vivian Wagner, and poetry by Doc Wallace, Devon Balwit, Hannah Litvin, and many more.

The fourth poetry collection from R. Bremner, who has published in International Poetry Review, Poets Online, Oleander Review, Yellow Chair Review, Passaic Review, Paterson Literary Review, and sundry elsewheres.

A collection of poems featured in the 2020 series of Parousia Christian Poetry Chapbook. R. Bremner, a former cab driver, truck unloader, computer programmer, and bank vice-president, hails from Glen Ridge by way of Lyndhurst, NJ, USA, with his beautiful sociologist wife, their brilliant son, and their excitable puppy Ariel. A regular contributor to Poets Online and the Poetry Super Highway live radio show, he has appeared in three Holocaust Remembrance (Yom HaShoah) anthologies - two for PSH and one for Lagan Online.