OSCAR – comprehensive computer algebra research system

OSCAR, short for Open Source Computer Algebra Research, is a comprehensive computer algebra system assembled through Julia.

It presents a common programmable environment for four established mathematical systems: GAP, Polymake, Antic and Singular. Users can combine capabilities that would otherwise live in separate applications, move mathematical objects between supported domains and build reproducible research calculations in ordinary Julia sessions.

This is free and open source software.

Key Features

• Unified environment combining and extending GAP, Polymake, Antic and Singular.
• Group theory covering finite and infinite groups, homomorphisms, actions, characters and related structural calculations.
• Rings and fields, including polynomial rings, finite fields, number fields and associated arithmetic.
• Linear algebra over numerous coefficient domains, together with matrices, modules, maps and canonical forms.
• Commutative algebra functionality for ideals, Gröbner bases, modules, resolutions and homological calculations.
• Number-theoretic tools for orders, ideals, units, class groups, factorisation and arithmetic in number fields.
• Algebraic geometry functionality spanning affine, projective and toric constructions, schemes, varieties and divisors.
• Polyhedral geometry tools for polytopes, cones, fans, subdivisions and computations with their combinatorial properties.
• Combinatorial facilities for graphs, matroids, simplicial complexes and related discrete structures.
• Support for Lie algebras, root systems, representation-theoretic objects and selected applications in mathematical physics.
• Exact symbolic arithmetic backed by mature specialist packages, avoiding premature conversion to floating-point approximations.
• Julia programming interface lets researchers compose calculations, define functions and integrate OSCAR with other Julia packages.
• Interactive documentation, searchable manuals, tutorials and examples covering both introductory and specialist workflows.

Website: github.com/oscar-system/Oscar.jl
Support:
Developer: The OSCAR Development Team
License: GNU General Public License v3.0

OSCAR is written in Julia. Learn Julia with our recommended free books and free tutorials.

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