Reference

Script Files

The Atlas standard library consists of 51 script files loaded in order by all.at. Each builds on the previous, extending Atlas with higher-level mathematical tools.

Loading scripts

Load all scripts at once with <all.at. Load a specific file with <filename.at — its dependencies are loaded automatically. Reload a file you have edited with <<filename.at.

atlas> <all.at { load the full standard library } atlas> <hermitian.at { load only hermitian and its dependencies }

All Files

basic.at796 defs
The foundational library. Loaded automatically at startup. Defines types, utilities, and wrapper functions for all Atlas types.
generics.at~10 defs
Generic higher-order utilities: identity, composition, and type-parametric helpers.
depends on: basic
combinatorics.at~60 defs
Combinatorial functions: binomial coefficients, multinomials, partitions, Young diagrams.
depends on: basic, sort, groups
number_theory.at~15 defs
Number-theoretic utilities: prime tests, factorizations.
depends on: basic, lazy_lists, polynomial
exp-generating-series.at
hermitian.at43 defs
Hermitian forms on standard and irreducible modules. Computes the c-invariant form and tests for unitarity.
depends on: basic, convert_c_form
extParamPol.at~40 defs
Extended parameter polynomials for the delta-extended group.
depends on: basic, polynomial, hermitian
complex.at~25 defs
Functions for complex groups and locally isomorphic groups.
depends on: basic, lietypes, groups
test_unitarity.at~20 defs
High-level unitarity testing functions.
depends on: groups, hermitian, unitary
modules.at45 defs
Module operations: tagged parameters, composition series, character formulas.
depends on: basic, kl, K_types
print_K_types.at~20 defs
Printing functions for K-types and branching formulas.
depends on: basic
galois.at~30 defs
Galois cohomology for strong real forms.
depends on: basic, groups
jantzen.at~30 defs
Jantzen filtration and associated graded computations.
depends on: dual, hodgeParamPol
finite_dimensional_signature.at~25 defs
Signature of the invariant form on finite-dimensional representations.
depends on: finite_dimensional, representations
W_reps.at25 defs
Representations of the Weyl group: W-graph, W-cells, and character tables.
depends on: basic, W_classes, sort
hodge_K_type_formula.at~60 defs
Hodge-theoretic K-type formulas.
depends on: hodge_functions, K_type_formula
all_finite_order.at9 defs
Functions for elements of finite order in a group.
depends on: basic, groups, sort
hodge_test.at~15 defs
Testing hodge-theoretic properties.
depends on: hodge_K_type_formula
hodge_tensor.at~15 defs
Tensor product formulas in the Hodge setting.
depends on: basic, hodge_K_type_formula
K_Nilpotent.at~50 defs
K-equivariant nilpotent orbits.
depends on: basic, nilpotent_orbits, K_norm
exceptionalNilpotentData.at~20 defs
Hard-coded nilpotent orbit data for exceptional simple groups.
depends on: exceptional
good_W_representatives.at~20 defs
Good W-representatives for Weyl group orbits.
depends on: cyclotomic_Gaussian_elim
finite_unipotents.at~15 defs
Finite unipotent representations.
depends on: W_classes, simple_factors
weyltosemisimple.at~10 defs
Weyl-to-semisimple maps.
depends on: basic, sort, parabolics
cyclotomic_field_bracket.at~15 defs
Cyclotomic field bracket operations.
tits_centralizer.at~40 defs
Tits group and centralizer computations.
depends on: tits, structure_constants
bruhat.at~20 defs
Bruhat order on blocks and KGB.
depends on: tabulate, W_orbit
stable.at~30 defs
Stable distributions and stable virtual characters.
depends on: basic, polynomial, dual
GK_dimension.at~8 defs
Gelfand–Kirillov dimension of representations.
depends on: basic, tensor_product
restricted_roots.at~10 defs
Restricted root system for real forms.
depends on: matrix
nilpotent_centralizer.at~25 defs
Centralizer of nilpotent elements.
depends on: basic, nilpotent_orbits, galois
arthur_parameters.at~10 defs
Arthur parameters for representations.
depends on: disconnected, galois
coherent_irreducible.at~40 defs
Coherent continuation for irreducible representations.
depends on: basic, W_reps, coherent
truncated_induction.at~30 defs
Truncated induction (Lusztig–Spaltenstein).
depends on: basic, class_tables
dirac_index.at~10 defs
Dirac index for equal rank groups.
depends on: K_highest_weights
sub_cells.at~30 defs
Subcells and subquotients of W-graphs.
depends on: basic, K, KGB_cells
associated_variety_annihilator.at~35 defs
Associated variety and annihilator ideal.
depends on: truncated_induction, sub_cells
sommers.at~40 defs
Sommers duality for special nilpotent orbits.
depends on: basic, W_reps_type_BC, nilpotent_centralizer
projectors_using_character_tables.at~20 defs
Projectors onto isotypic components using character tables.
depends on: basic, W_orbit, W_classes
new_conjugacy.at~15 defs
New conjugacy class computations.
depends on: cells
certificate.at~5 defs
Certificates of (non)unitarity.
depends on: basic, K_types, hermitian
geck_generic.at~40 defs
Generic Hecke algebra computations (Geck).
depends on: basic, character_tables
lusztig_cells.at~45 defs
Lusztig's map from nilpotent orbits to W-representations.
depends on: geck_generic
four.at~20 defs
Four inner products (BXYI).
depends on: coherent_characters
special_rep.at~25 defs
Special representations of the Weyl group.
depends on: basic, character_tables, springer_tables
families.at~5 defs
Families of representations in the sense of Lusztig.
depends on: character_tables
L_packet.at~25 defs
L-packets for real groups.
depends on: Vogan-dual, KL_polynomial_matrices
G2_unitary_dual.at~15 defs
The full unitary dual of the real group G2.
depends on: basic, groups, K_norm
adams_johnson.at~10 defs
Adams–Johnson modules.
depends on: basic, parabolics, finite_dimensional
speh.at~8 defs
Speh representations for GL(n).
depends on: basic, groups, parabolics
bmsz.at~6 defs
BMSZ (Barbasch–Ma–Sun–Zhu) signatures.
depends on: signed_and_marked_young_diagrams