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https://github.com/tkluck/landauginzburgcategories.jl
https://github.com/tkluck/landauginzburgcategories.jl
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- Host: GitHub
- URL: https://github.com/tkluck/landauginzburgcategories.jl
- Owner: tkluck
- Created: 2019-03-08T10:54:51.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2022-06-23T21:31:59.000Z (over 2 years ago)
- Last Synced: 2023-03-26T15:19:26.293Z (over 1 year ago)
- Language: Julia
- Size: 176 KB
- Stars: 2
- Watchers: 3
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Landau-Ginzburg categories for Julia
[](https://tkluck.github.io/LandauGinzburgCategories.jl/stable)
[](https://tkluck.github.io/LandauGinzburgCategories.jl/latest)
| **Build Status** | **Test coverage** |
|:------------------------:|:-------------------------------------------------:|
| [![][c-i-img]][c-i-url] | [![Coverage Status][codecov-img]][codecov-url] |
A library for algebra inside the bicategory of Landau-Ginzburg models.
## Usage
Composition and fusion:
```julia
julia> using LandauGinzburgCategories, PolynomialRings
julia> @ring! ℚ[x,y,z]
julia> A = unit_matrix_factorization(x^2, x = y)
2×2 Arrax{ℚ[x,y,z],2}:
0 x^2 + x*y + y^2
-x + y 0
julia> B = unit_matrix_factorization(y^2, y = z)
2×2 Array{ℚ[x,y,z],2}:
0 y^2 + y*z + z^2
-y + z 0
julia> A ⨶ B
4×4 Array{ℚ[x,y,z],2}:
0 0 y^2 + y*z + z^2 x^2 + x*y + y^2
0 0 -x + y y + -z
-y + z x^2 + x*y + y^2 0 0
-x + y -y^2 + -y*z + -z^2 0 0
julia> fuse(A ⨶ B, :y)
2×2 Arrax{ℚ[x,y,z],2}:
0 x^2 + x*z + z^2
-x + z 0
```
Library of named potentials and of known orbifold equivalences between them:
```julia
julia> using LandauGinzburgCategories; LGLib = LandauGinzburgCategories.Library;
```
The `Aₙ`-series of potentials:
```
julia> LGLib.A₅()
x^6 + y^2
julia> LGLib.A₅(x, y)
x^6 + y^2
julia> LGLib.A(5, x, y)
x^6 + y^2
```
Exceptional unimodular singularities:
```
julia> LGLib.E₆(x, y)
x^3 + y^4
```
Et cetera.
Known orbifold equivalences:
```julia
julia> LGLib.orbifold_equivalence(LGLib.A5, LGLib.A2A2)
.....
```
## Status
This library has not been released yet and should therefore be considered alpha-quality software.
## Citation
If this library has been useful for your work, please cite it as https://arxiv.org/abs/1901.09019.
[c-i-img]: https://github.com/tkluck/LandauGinzburgCategories.jl/workflows/CI/badge.svg
[c-i-url]: https://github.com/tkluck/LandauGinzburgCategories.jl/actions?query=workflow%3ACI
[codecov-img]: https://codecov.io/gh/tkluck/LandauGinzburgCategories.jl/branch/master/graph/badge.svg
[codecov-url]: https://codecov.io/gh/tkluck/LandauGinzburgCategories.jl