This book presents version 1.0 of the new Computer Algebra System OSCAR.

Written in Julia, OSCAR builds on and vastly extends four cornerstone systems:

ANTIC for number theory, GAP for group and representation theory, polymake for polyhedral and tropical geometry, and Singular for commutative algebra and algebraic geometry.

It offers powerful computational tools that transcend the boundaries of the individual disciplines involved.

It is freely available, open source software.

The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts.

A unique resource on the new computer algebra system OSCAR Discusses the interaction of computational tools from different disciplines in algebra, geometry, and number theory Presents explicit OSCAR code written by experts

Klappentext

This book presents version 1.0 of the new Computer Algebra System OSCAR. Written in Julia, OSCAR builds on and vastly extends four cornerstone systems: ANTIC for number theory, GAP for group and representation theory, polymake for polyhedral and tropical geometry, and Singular for commutative algebra and algebraic geometry. It offers powerful computational tools that transcend the boundaries of the individual disciplines involved. It is freely available, open source software. The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts.

Inhalt

Commutative Algebra and Algebraic Geometry.- Number Theory.- Group theory.- Polyhedral Geometry.- Toric Geometry.