hodge_functions.at

hodge_functions_verbose

multiplicity_function type

set_type multiplicity_function=(KType -> int)

signature_function type

set_type signature_function=(KType -> Split)

hodge_function type

set_type hodge_function= ((KType->i_poly) f,RealForm real_form)

Fields: f, real_form

minus_vee_to_the_k

coefficient

also defined in hodgeParamLaurentPol.at, hodgeParamPol.at, lazy_lists.at

branch_function_std

the multiplicity function of I(p)

also defined in hodge_tensor.at

branch_function_std_as_hodge_function

Psi_S

convert function f to \sum_mu f(mu)*mu

this function is slow and should be used sparingly

was called hodge_polynomial, renamed to Psi_S
see hodgeTempered.pdf (towards the end) and hodge_tensor.at

hodgePrint

warning: this is slow

print

nullHodgeFunction

sort 2 overloads

also defined in sommers.at, sort.at, nilpotent_posets.at

* 2 overloads

multiply function by polynomial: f_new(mu)=f(mu)*poly\in Z[v]

also defined in basic.at, extParamPol.at, complex.at, modules.at, hodge_tensor.at, tits_centralizer.at, stable.at, synthetic.at, Weylgroup.at, group_operations.at, ratmat.at, tits.at, twisted_root_datum.at, cyclotomic.at, polynomial.at, hodgeParamLaurentPol.at, hodgeParamPol.at, laurentPolynomial.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, sparse.at, lazy_lists.at

+

also defined in basic.at, extParamPol.at, modules.at, ratmat.at, cyclotomic.at, polynomial.at, hodgeParamLaurentPol.at, hodgeParamPol.at, laurentPolynomial.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, lazy_lists.at

-

also defined in basic.at, extParamPol.at, modules.at, ratmat.at, cyclotomic.at, polynomial.at, hodgeParamLaurentPol.at, hodgeParamPol.at, laurentPolynomial.at, cyclotomicMat.at, lazy_lists.at

is_zero

also defined in polynomial.at

hodge_theta_induce_standard 2 overloads

Note: algorithm is, formally induce the parameter (which may be non-standard),
and then apply hodge_normalize. Recall hodge_normalize uses imaginary
wall-crossings, based on an SL(2,R) calculation, and always preserves nu=0.
The first step of standardize is a Cayley transform introduces non-zero nu,
but this is a red herring. See hodge_normalization.pdf in Dropbox