Books in the Texts & Monographs in Symbolic Computation series

This book demonstrates how to formally model various mathematical domains (including algorithms operating in these domains) in a way that makes them amenable to a fully automatic analysis by computer software.The presented domains are typically investigated in discrete mathematics, logic, algebra, and computer science; they are modeled in a formal language based on first-order logic which is sufficiently rich to express the core entities in whose correctness we are interested: mathematical theorems and algorithmic specifications. This formal language is the language of RISCAL, a ¿mathematical model checker¿ by which the validity of all formulas and the correctness of all algorithms can be automatically decided. The RISCAL software is freely available; all formal contents presented in the book are given in the form of specification files by which the reader may interact with the software while studying the corresponding book material.

This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews.

The book is centered around the research areas of combinatorics, special functions, and computer algebra. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.

In this book, origami is treated as a set of basic geometrical objects that are represented and manipulated symbolically and graphically by computers.

This book is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory.