Welcome to liesym’s documentation!#
Liesym is an extension module on SymPy that reimplements the liealgebra module inside sympy with the idea of using a compiled backend to do speedups on some of the slower aspects of SymPy’s pure python implementation. This python module is mostly a reimplementation of a Mathematica module LieART.
SymPy: https://sympy.org
Module contents#
- Algebra
- Lie Algebra Base
LieAlgebraLieAlgebra.adjoint_rep()LieAlgebra.cartan_matrixLieAlgebra.cocartan_matrixLieAlgebra.conjugate()LieAlgebra.dim()LieAlgebra.dim_name()LieAlgebra.dimensionLieAlgebra.dynkin_index()LieAlgebra.fundamental_weights()LieAlgebra.get_irrep_by_dim()LieAlgebra.irrep_lookup()LieAlgebra.max_dynkin_digit()LieAlgebra.metric_tensorLieAlgebra.n_pos_rootsLieAlgebra.n_rootsLieAlgebra.omega_matrixLieAlgebra.orbit()LieAlgebra.positive_roots()LieAlgebra.quadratic_casimir()LieAlgebra.rankLieAlgebra.reflection_matriciesLieAlgebra.root_system()LieAlgebra.seriesLieAlgebra.simple_roots()LieAlgebra.tensor_product_decomposition()LieAlgebra.to_alpha()LieAlgebra.to_omega()LieAlgebra.to_ortho()
- A Series
AA.adjoint_rep()A.cartan_matrixA.cocartan_matrixA.conjugate()A.dim()A.dim_name()A.dimensionA.dynkin_index()A.fundamental_weights()A.get_irrep_by_dim()A.irrep_lookup()A.max_dynkin_digit()A.metric_tensorA.n_pos_rootsA.n_rootsA.omega_matrixA.orbit()A.positive_roots()A.quadratic_casimir()A.rankA.reflection_matriciesA.root_system()A.seriesA.simple_roots()A.tensor_product_decomposition()A.to_alpha()A.to_omega()A.to_ortho()
- B Series
BB.adjoint_rep()B.cartan_matrixB.cocartan_matrixB.conjugate()B.dim()B.dim_name()B.dimensionB.dynkin_index()B.fundamental_weights()B.get_irrep_by_dim()B.irrep_lookup()B.max_dynkin_digit()B.metric_tensorB.n_pos_rootsB.n_rootsB.omega_matrixB.orbit()B.positive_roots()B.quadratic_casimir()B.rankB.reflection_matriciesB.root_system()B.seriesB.simple_roots()B.tensor_product_decomposition()B.to_alpha()B.to_omega()B.to_ortho()
- C Series
CC.adjoint_rep()C.cartan_matrixC.cocartan_matrixC.conjugate()C.dim()C.dim_name()C.dimensionC.dynkin_index()C.fundamental_weights()C.get_irrep_by_dim()C.irrep_lookup()C.max_dynkin_digit()C.metric_tensorC.n_pos_rootsC.n_rootsC.omega_matrixC.orbit()C.positive_roots()C.quadratic_casimir()C.rankC.reflection_matriciesC.root_system()C.seriesC.simple_roots()C.tensor_product_decomposition()C.to_alpha()C.to_omega()C.to_ortho()
- D Series
DD.adjoint_rep()D.cartan_matrixD.cocartan_matrixD.conjugate()D.dim()D.dim_name()D.dimensionD.dynkin_index()D.fundamental_weights()D.get_irrep_by_dim()D.irrep_lookup()D.max_dynkin_digit()D.metric_tensorD.n_pos_rootsD.n_rootsD.omega_matrixD.orbit()D.positive_roots()D.quadratic_casimir()D.rankD.reflection_matriciesD.root_system()D.seriesD.simple_roots()D.tensor_product_decomposition()D.to_alpha()D.to_omega()D.to_ortho()
- E Series
EE.adjoint_rep()E.cartan_matrixE.cocartan_matrixE.conjugate()E.dim()E.dim_name()E.dimensionE.dynkin_index()E.fundamental_weights()E.get_irrep_by_dim()E.irrep_lookup()E.max_dynkin_digit()E.metric_tensorE.n_pos_rootsE.n_rootsE.omega_matrixE.orbit()E.positive_roots()E.quadratic_casimir()E.rankE.reflection_matriciesE.root_system()E.seriesE.simple_roots()E.tensor_product_decomposition()E.to_alpha()E.to_omega()E.to_ortho()
- G2 Series
G2G2.adjoint_rep()G2.cartan_matrixG2.cocartan_matrixG2.conjugate()G2.dim()G2.dim_name()G2.dimensionG2.dynkin_index()G2.fundamental_weights()G2.get_irrep_by_dim()G2.irrep_lookup()G2.max_dynkin_digit()G2.metric_tensorG2.n_pos_rootsG2.n_rootsG2.omega_matrixG2.orbit()G2.positive_roots()G2.quadratic_casimir()G2.rankG2.reflection_matriciesG2.root_system()G2.seriesG2.simple_roots()G2.tensor_product_decomposition()G2.to_alpha()G2.to_omega()G2.to_ortho()
- F4 Series
F4F4.adjoint_rep()F4.cartan_matrixF4.cocartan_matrixF4.conjugate()F4.dim()F4.dim_name()F4.dimensionF4.dynkin_index()F4.fundamental_weights()F4.get_irrep_by_dim()F4.irrep_lookup()F4.max_dynkin_digit()F4.metric_tensorF4.n_pos_rootsF4.n_rootsF4.omega_matrixF4.orbit()F4.positive_roots()F4.quadratic_casimir()F4.rankF4.reflection_matriciesF4.root_system()F4.seriesF4.simple_roots()F4.tensor_product_decomposition()F4.to_alpha()F4.to_omega()F4.to_ortho()
- Lie Algebra Base
- Groups