Atlas of Lie Groups and Representations

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Script File

hodge_test.at

Source
atlas-scripts/hodge_test.at (115 lines)
Definitions
19
Loads
Loaded by
none of the other all.at files

Definitions in source order

hodge_test_verbose

L5hodge_test_verbose = true

some test functions L6

test: entries of polynomial matrix are non-negative
L8

test_positive

L10test_positive(i_poly_mat M) = bool

test_positive_hodge_K_type_mat 2 overloads

L12test_positive_hodge_K_type_mat(KType mu,int N) = (i_poly_mat,i_poly_mat,bool)
L15test_positive_hodge_K_type_mat([KType] ktypes,int N) = bool

test_elementary_hodge_grading_std_at_1

L21test_elementary_hodge_grading_std_at_1 (Param p) = bool
legacy |hodge_grading_*| return |ParamPol| rather than |KTypePol|; convert
Note: these tests only verify the formulas for hodge gradings in terms
of tempered, see below for tests involving tempered representations

test_elementary_hodge_grading_std_at_s

L23test_elementary_hodge_grading_std_at_s(Param p) = bool

test_elementary_hodge_grading_irr_at_1

L25test_elementary_hodge_grading_irr_at_1(Param p) = bool

test_elementary_hodge_grading_irr_at_s

L28test_elementary_hodge_grading_irr_at_s(Param p) = bool

test_hodge_grading_std_at_1

L32test_hodge_grading_std_at_1(Param p,int N) = bool
tests involving tempered representations: checking on individual K-types up to height N

test_hodge_grading_std_at_s

L34test_hodge_grading_std_at_s(Param p,int N) = bool

hodge_test

L39hodge_test(Param p, int N)
several tests together

also in this file at line 73, line 74

Commented-out code, lines 60–71 (11 lines)
deprecated
set hodgetest(Param p,int N)=bool:
let hodgedef=hodge_recursive_deform(p) then
(rv,)=hodge_branch_std(hodgedef,N) then
positive=all(##for i:#rv do for c@p in rv[i] do split_as_int(c)>0 od od) then
valid_evaluation_at_s=evaluate_at_s(hodgedef)=recursive_deform(p) then
valid_evaluation_at_1=evaluate_at_1(hodgedef)=p*0 in
prints(p.real_form,new_line,"N:",N,new_line,p,new_line,"hodge_deformation to 0: ");print(rv);prints(new_line,
"correct evaluation at v=1:",valid_evaluation_at_1,new_line,
"correct evaluation at v=s:",valid_evaluation_at_s,new_line,
"positive coefficients: ",positive,new_line);valid_evaluation_at_1 and valid_evaluation_at_s and positive

hodge_test 2 overloads

L73hodge_test(RealForm G,int N) = bool
L74hodge_test([Param] params,int N) = (bool,[bool])

also in this file at line 39

run_hodge_tests 2 overloads

L75run_hodge_tests(int k)
L87run_hodge_tests()

test_hodge_K_type_mat 2 overloads

L92test_hodge_K_type_mat(KType mu,int N) = (i_poly_mat,[bool],bool)
test: all entries of B matrix (for K-type mu) are non-negative
L97test_hodge_K_type_mat([KType] mus,int N) = ([([[vec]],bool)],bool)
test: all entries of each B matrix (running over set of Kptypes) are non-negative

also defined in hodge_K_type_formula.at

Generated from atlas-scripts at commit 7e1b958 (2026-09-17).