@@ -10,40 +10,6 @@ root-data computations.
1010<p><a href="Semisimple.jl.pdf">Download the PDF manual</a>.</p>
1111```
1212
13- Semisimple.jl is a finite-type root-data and highest-weight package. It does not
14- construct concrete Lie algebra elements, brackets, Chevalley bases, ideals,
15- subalgebras, homomorphisms, arbitrary-field Lie algebras, or module
16- homomorphisms.
17-
18- Semisimple.jl is inspired by (and partially ported) from [ LiE] ( http://wwwmathlabo.univ-poitiers.fr/~maavl/LiE/ ) ,
19- a computer algebra system for Lie group computations written in C.
20- Parts of the Semisimple.jl code have been written with the assistance of Claude Opus 4.6.
21-
22- Similar features are also available in [ SageMath] ( https://sagemath.org ) ,
23- and a similar package is [ LieART] ( https://lieart.hepforge.org/ ) ,
24- which runs on the proprietary [ Mathematica] ( https://www.wolfram.com/mathematica/ ) software.
25-
26- Note that Semisimple.jl is less feature-complete than any of the aforementioned packages.
27- Porting more features is planned.
28-
29- ## Relationship to OSCAR
30-
31- Semisimple.jl overlaps partly with OSCAR's [ stable Lie Theory] ( https://docs.oscar-system.org/stable/LieTheory/intro/ )
32- module, but the emphasis is different. OSCAR stable provides intentionally
33- minimal combinatorial scaffolding: Cartan matrices, root systems, Weyl groups,
34- and weight lattices, represented with OSCAR/AbstractAlgebra parent objects and
35- integer matrices. Semisimple.jl focuses on finite-type complex semisimple root data
36- with type-level Dynkin types, ` StaticArrays ` -based weights and roots, optimized
37- Weyl orbit traversal, and highest-weight representation-ring computations.
38-
39- OSCAR's [ experimental Lie Algebras] ( https://docs.oscar-system.org/stable/Experimental/LieAlgebras/introduction/ )
40- module is broader on the algebraic side: it has concrete finite-dimensional Lie
41- algebra objects, brackets, ideals, subalgebras, homomorphisms, modules, and
42- module homomorphisms. That module is explicitly experimental, so its API carries
43- stability caveats. Use OSCAR when you need integrated algebraic objects; use
44- Semisimple.jl when you need lightweight, optimized highest-weight and character
45- computations.
46-
4713## Features
4814
4915- ** Dynkin types** — Type-level classification (` TypeA{N} ` , ` TypeB{N} ` , …, ` TypeG2 ` , products) with text Dynkin diagrams
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