## General questions

Q: How do I install OSCAR?

You can find our installation instructions here.

Q: Why do some of your types have funny names like fmpz or fmpq_mat?

This has historical reasons. We plan to rename these types before OSCAR 1.0 (the old names will still work indefinitely, though).

Q: Can I find all methods that apply to a given object?

Yes, Julia provides the function methodswith for this very purpose.

For your convenience, let us give an example here. To this end, we first create a projective space in OSCAR:

julia> v = projective_space(NormalToricVariety,2)
A normal, non-affine, smooth, projective, gorenstein, fano, 2-dimensional toric variety without torusfactor

julia> typeof(v)
NormalToricVariety

Suppose that we now want to find all methods that accept a NormalToricVariety as one of their arguments. This can be achieved as follows:

julia> methodswith(typeof(v))
[1] intersection_form(v::NormalToricVariety) in Oscar at /datadisk/Computer/Mathematics_software/PackagesForJulia/Oscar.jl/src/ToricVarieties/CohomologyClasses/special_attributes.jl:101
[2] mori_cone(v::NormalToricVariety) in Oscar at /datadisk/Computer/Mathematics_software/PackagesForJulia/Oscar.jl/src/ToricVarieties/NormalToricVarieties/attributes.jl:976
[3] nef_cone(v::NormalToricVariety) in Oscar at /datadisk/Computer/Mathematics_software/PackagesForJulia/Oscar.jl/src/ToricVarieties/NormalToricVarieties/attributes.jl:953
[4] toric_ideal(ntv::NormalToricVariety) in Oscar at /datadisk/Computer/Mathematics_software/PackagesForJulia/Oscar.jl/src/ToricVarieties/NormalToricVarieties/attributes.jl:510
[5] volume_form(v::NormalToricVariety) in Oscar at /datadisk/Computer/Mathematics_software/PackagesForJulia/Oscar.jl/src/ToricVarieties/CohomologyClasses/special_attributes.jl:50

Often it can be beneficial to also include supertypes in the search:

julia> methodswith(typeof(v), supertypes = true)

As of December 2022, this results in a list of 101 functions.

Note that we can also find the constructors, i.e. functions that return an object of type NormalToricVariety. This is possible with the Julia function methods:

julia> methods(typeof(v))
# 5 methods for type constructor:
[1] NormalToricVariety(P::Polyhedron) in Oscar at /datadisk/Computer/Mathematics_software/PackagesForJulia/Oscar.jl/src/ToricVarieties/NormalToricVarieties/constructors.jl:183
[2] NormalToricVariety(PF::PolyhedralFan) in Oscar at /datadisk/Computer/Mathematics_software/PackagesForJulia/Oscar.jl/src/ToricVarieties/NormalToricVarieties/constructors.jl:155
[3] NormalToricVariety(rays::Vector{Vector{Int64}}, max_cones::Vector{Vector{Int64}}; non_redundant) in Oscar at /datadisk/Computer/Mathematics_software/PackagesForJulia/Oscar.jl/src/ToricVarieties/NormalToricVarieties/constructors.jl:131
[4] NormalToricVariety(C::Cone) in Oscar at /datadisk/Computer/Mathematics_software/PackagesForJulia/Oscar.jl/src/ToricVarieties/NormalToricVarieties/constructors.jl:79
[5] NormalToricVariety(polymakeNTV::Polymake.BigObject) in Oscar at /datadisk/Computer/Mathematics_software/PackagesForJulia/Oscar.jl/src/ToricVarieties/NormalToricVarieties/constructors.jl:8

Q: Why do you have your own matrix types, and why do they not support the exact same commands as Julia matrices?

Unfortunately, Julia's matrices and linear algebra cannot be made to work in our context due to two independent problems:

• In empty matrices (0 rows or columns) all that is known is the type of the matrix entries, however for the complex types used in OSCAR, this information is not sufficient to create elements, hence zero(T) or friends cannot work.
• Many functions (e.g. det) assume that all types used embed into the real or complex numbers, in Julia det(ones(Int, (1,1))) == 1.0, so the fact that this is exactly the integer 1 is lost. Furthermore, more general rings cannot be embedded into the reals at all.

Q: Why can zero(T) for a type T not work?

At least two reasons:

• The type depends on data that is not a bit-type.

• Even if it could, it is not desirable. Typical example: computations in $Z/nZ$, so modular arithmetic. If $n$ is small, then it is tempting to define a type T depending on $n$. We actually did this, and tried to use this. It did not work well, for various reasons. E.g.:

A generic algorithmic pattern for problems over the integers is to solve them by solving them modulo $n$ for many $n$, e.g. chosen as prime numbers, and then to combine them. If the type depends on $n$, then for every prime the code gets compiled, thus negating any advantages from the use of modular techniqes.

Of course, one could make the $n$ an additional parameter to all functions needing it, but then e.g. addition of matrices would have to be implemented specifically for this case, negating the advantages of generic implementations.

In OSCAR, the role of the type is split between the actual Julia type and the parent.

Q: What is a parent?

Almost all element-like objects in OSCAR have a parent, i.e., they belong to some larger structure. For example algebraic numbers belong to a number field, modular integers belong to a ring $Z/nZ$, permutations are elements of permutation groups and so on. The data common to all such elements is out-sourced to the parent. For a number field for example, the parent contains the polynomial used to define the field (plus other information).

Given that a type alone is not large enough to contain the data, the parent is used. Roughly, outside a function signature, a parent replaces the role of the type. For example, for a ring element elm in OSCAR zero(parent(elm)) works, even if zero(typeof(elm)) may not.

Q: How can I install or access custom GAP packages (e.g. unpublished ones)?

TODO

Q: Why does my program not terminate?

Many of the algorithms implemented in OSCAR have a very high complexity. Even if not calling one of these algorithms directly, you may be using it in the background. Please read our page on [Complex Algorithms in OSCAR].

## Windows specific

Q: How can I install OSCAR on Windows?

Q: Why does OSCAR require WSL on Windows?

Several of the OSCAR corner stones originate from Unix-like operating systems and have no or only limited native support for Windows.

Q: How can I access Linux files from the Explorer?

Type \\wsl$ into the Explorer address bar, then press the Enter key. ## Linux specific Q: Why can't I install OSCAR using the Julia version installed by my package manager? Some Linux distributions unfortunately ship crippled versions of Julia by default, which prevent OSCAR from working. For example the Debian and Ubuntu Julia packages are missing some files required by OSCAR. In this case, this can be resolved by also installing the libjulia-dev package. For this reason, we recommend always using the official Julia binaries available form the Julia website. Q: What to do if I get an error similar to libstdc++.so.6: version GLIBCXX_3.4.26'? Sometimes installing or updating OSCAR gives the error libstdc++.so.6: version GLIBCXX_3.4.26' or a similar one. This typically happens when manually installing Julia using the official Julia binaries from their website. These bundle their own copy of the C++ standard library, which can lead to trouble if its version differs from the system's C++ library. As a workaround, you can rename the copy of the C++ library bundled with Julia, so that the system copy is used. This can be achieved by executing the following Julia code:  path = Libdl.dlpath("libstdc++") mv(path,"$path.bak")

If for some reason you need to restore the C++ library bundled with Julia, you can simply rename it back.

Q: Why does OSCAR fail to precompile when using it with GNU parallel?

You get errors like the following when trying to run some script using OSCAR with GNU parallel:

  ERROR: LoadError: InitError: ArgumentError: '.../deps/<something>_jll' exists. force=true is required to remove '...' before copying.

There was a bug in julia versions before 1.8 that ignored the parent argument for the tempname function when the TMPDIR environment variable is set and GNU parallel by default sets TMPDIR to /tmp.

Either upgrade to Julia 1.8 or later, or add ENV["TMPDIR"]=nothing; to the beginning of your julia code (before importing / using Oscar).