Installation

julia> using Pkgjulia> Pkg.add("Oscar")julia> using Oscar

Contributing to OSCAR

Examples of usage

julia> using Oscar  ___   ____   ____    _    ____ / _ \ / ___| / ___|  / \  |  _ \   |  Combining ANTIC, GAP, Polymake, Singular| | | |\___ \| |     / _ \ | |_) |  |  Type "?Oscar" for more information| |_| | ___) | |___ / ___ \|  _ <   |  Manual: https://docs.oscar-system.org \___/ |____/ \____/_/   \_\_| \_\  |  Version 1.4.0-DEVjulia> k, a = quadratic_field(-5)(Imaginary quadratic field defined by x^2 + 5, sqrt(-5))julia> zk = maximal_order(k)Maximal order of Imaginary quadratic field defined by x^2 + 5with basis AbsSimpleNumFieldElem[1, sqrt(-5)]julia> factorizations(zk(6))2-element Vector{Fac{AbsSimpleNumFieldOrderElem}}: -1 * -3 * 2 -1 * (-sqrt(-5) - 1) * (-sqrt(-5) + 1)julia> Qx, x = polynomial_ring(QQ, [:x1,:x2])(Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[x1, x2])julia> R = grade(Qx, [1,2])[1]Multivariate polynomial ring in 2 variables over QQ graded by  x1 -> [1]  x2 -> [2]julia> f = R(x[1]^2+x[2])x1^2 + x2julia> degree(f)[2]julia> F = free_module(R, 1)Free module of rank 1 over Rjulia> s = sub(F, [f*F[1]])[1]Submodule with 1 generator  1: (x1^2 + x2)*e[1]represented as subquotient with no relationsjulia> H, mH = hom(s, quo(F, s)[1])(hom of (s, Subquotient of submodule with 1 generator  1: e[1]by submodule with 1 generator  1: (x1^2 + x2)*e[1]), Map: H -> set of all homomorphisms from s to subquotient of submodule with 1 generator  1: e[1]by submodule with 1 generator  1: (x1^2 + x2)*e[1])julia> mH(H[1])Module homomorphism  from s  to subquotient of submodule with 1 generator    1: e[1]  by submodule with 1 generator    1: (x1^2 + x2)*e[1]

julia> C = Polymake.polytope.cube(3);julia> C.F_VECTORpm::Vector<pm::Integer>8 12 6julia> RP2 = Polymake.topaz.real_projective_plane();julia> RP2.HOMOLOGYpm::Array<topaz::HomologyGroup<pm::Integer> >({} 0)({(2 1)} 0)({} 0)

Citing OSCAR

[OSCAR]    OSCAR -- Open Source Computer Algebra Research system, Version 1.4.0-DEV,    The OSCAR Team, 2025. (https://www.oscar-system.org)[OSCAR-book]    Wolfram Decker, Christian Eder, Claus Fieker, Max Horn, Michael Joswig, eds.    The Computer Algebra System OSCAR: Algorithms and Examples,    Algorithms and Computation in Mathematics, Springer, 2025.

@misc{OSCAR,  key          = {OSCAR},  organization = {The OSCAR Team},  title        = {OSCAR -- Open Source Computer Algebra Research system,                  Version 1.4.0-DEV},  year         = {2025},  url          = {https://www.oscar-system.org},  }@book{OSCAR-book,  editor = {Decker, Wolfram and Eder, Christian and Fieker, Claus and Horn, Max and Joswig, Michael},  title = {The {C}omputer {A}lgebra {S}ystem {OSCAR}: {A}lgorithms and {E}xamples},  year = {2025},  publisher = {Springer},  series = {Algorithms and {C}omputation in {M}athematics},  volume = {32},  edition = {1},  url = {https://link.springer.com/book/9783031621260},  issn = {1431-1550},  doi = {10.1007/978-3-031-62127-7},}

Funding