API overview

All the names below are imported by import h4lat (they are listed in h4lat.__all__). Every function and class has a detailed docstring: use help(h4lat.cg_calc), or h4lat.cg_calc? in Jupyter.

Modules

Module	Contents
h4lat.cg_calculator	cg_calc, get_multiplicities, the ${H(4)}$ group constants and generator matrices
h4lat.moments_operator	Operator, the operator database, kinematic factors, C-parity and symmetry analysis, HDF5 I/O, the PDF catalogue
h4lat.kinematic_data	Euclidean gamma matrices, symbolic momenta, polarisation projectors
h4lat.utilities	Permutation parity, perfect-square test, all-equal check
h4lat.cli	catalogue_main, the entry point of the h4lat-catalogue command

Group theory and Clebsch-Gordan coefficients

Name	Description
cg_calc	Clebsch-Gordan coefficients of a tensor product of irreps, loaded or computed (guide)
get_multiplicities	Multiplicity of each irrep in a tensor product
latex_print_multiplicities	The decomposition of a tensor product as a LaTeX string
CGmat_from_block	Fixes the free parameters of a symbolic Clebsch-Gordan block (theory)
print_CGmat	Pretty-prints a Clebsch-Gordan matrix in Jupyter
rep_label_list, rep_dim_list, n_rep	The 20 irrep labels (k, l), their dimensions, and their number
irrep_index, irrep_dim, irrep_texname	Position in rep_label_list, dimension and LaTeX name of an irrep label
char_table, class_orders	The character table (irreps × classes) and the number of elements of each class
n_ele_h4, n_ele_s4	The orders of ${H(4)}$ (384) and ${S_4}$ (24)

Operators

Name	Description
Operator	One irreducible lattice operator (guide)
get_OperatorList, get_OperatorDict	The bundled operator database as a list or a nested dict (guide)
Operator_from_database	One operator of a database, by ID
OperatorList_from_database, OperatorDict_from_database	The same as the getters, for any database folder
Operator_from_file	One operator from its .npy file
make_operator_database	Builds an operator database with up to a given number of derivatives
OPERATOR_DATABASE	The path of the bundled operator database
operator_show	Writes a PDF catalogue of the operators (guide)
get_paper_operators, AVAILABLE_PAPERS	Operators used in published works (guide)
get_op_selection	A curated selection of operators free of mixing, for one to three derivatives
decomposition_analysis	Irrep content of an operator product, with multiplicities and mixing with fewer derivatives
operator_list_to_h5, h5_to_operator_list	Save and load a list of operators in an HDF5 file (guide)
write_operator, read_operator	Save and load one operator in an HDF5 group

Building blocks of an operator

Name	Description
cg_remapping, cg_remapping_T	Reshape a Clebsch-Gordan column into the cgmat tensor of an operator (_T for the tensor structure)
symO_from_Cgmat	Symbolic expression of an operator
diracO_from_cgmat	Dirac matrix ${M(p)}$ of an operator (theory)
Kfactor_from_diracO	Kinematic factor from the Dirac matrix
latexO_from_diracO	LaTeX string of an operator
C_parity	C-parity of an operator
trace_symm	Whether the traces of an operator vanish
index_symm, index_symm_2exchange, index_symm_index_fixed	Symmetry under permutations of all, two, or the non-fixed indices
Gamma_pol_list, Gamma_pol_s_list, den_K_list	The six polarisation projectors, their symbols, and the denominators of K
Gamma_pol, Gamma_pol_s, den_K	The same for the default projector (index 0)

Command line

Command	Description
h4lat-catalogue	Writes a PDF catalogue of the operators; see h4lat-catalogue --help and Operator catalogue
python scripts/regenerate_data.py	Regenerates the bundled data (in a clone of the repository; see CONTRIBUTING.md)