Atlas of Lie Groups and Representations

Documentation contents

atlas Library · Script File

hodgeParamLaurentPol.at

see hodgeParamPol.at and hodgeParamLaurentPol.pdf

recall: set_type hodgeParamPol=[ParamPol]
[P_0,...,P_m] -> (P_0+P_1*v+...+P_m*v^m)

Generalize this

(data type:
([P_0,...,P_m],int n)->  (P_0+P_1*v+...+P_m*v^m)*v^n
Source
atlas-scripts/hodgeParamLaurentPol.at (291 lines)
Definitions
39
Loads
Loaded by
coherent_irreducible.at

Definitions in source order

hodgeParamLaurentPol type

L16
set_type hodgeParamLaurentPol=(hodgeParamPol hpp,int shift)

Fields: hpp, shift

hodge_param_pol

L19hodge_param_pol(hodgeParamLaurentPol (hpp,)) = hodgeParamPol
ignore Laurent part

also defined in hodgeParamPol.at

monomials 2 overloads

L21monomials(hodgeParamLaurentPol hplp) = [Param]
L22monomials([hodgeParamLaurentPol] list) = [Param]

also defined in basic.at, is_normal.at

hodgeParamLaurentPol versions L25

nullHodgeParamLaurentPol

L27nullHodgeParamLaurentPol(RealForm G) = hodgeParamLaurentPol

hodge_param_laurent_pol 3 overloads

L29hodge_param_laurent_pol(ParamPol P) = hodgeParamLaurentPol
L30hodge_param_laurent_pol(Param p) = hodgeParamLaurentPol
L31hodge_param_laurent_pol(hodgeParamPol P) = hodgeParamLaurentPol

* 2 overloads

L33*(Split c,hodgeParamLaurentPol hplp) = hodgeParamLaurentPol
L34*(hodgeParamLaurentPol hplp,Split c)

also in this file at line 106, line 108, line 110, line 111, line 154, line 158, line 160, line 163; 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, hodgeParamPol.at, laurentPolynomial.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, hodge_functions.at, sparse.at, lazy_lists.at

-

L35-(hodgeParamLaurentPol hplp) = hodgeParamLaurentPol

also in this file at line 148; also defined in basic.at, extParamPol.at, modules.at, ratmat.at, cyclotomic.at, polynomial.at, hodgeParamPol.at, laurentPolynomial.at, cyclotomicMat.at, hodge_functions.at, lazy_lists.at

real_form

L37real_form(hodgeParamLaurentPol hplp) = RealForm

also defined in basic.at, weak_packets_precomputed_cell_traces.at, parabolics.at, K.at, nilpotent_orbits.at, hodgeParamPol.at

coefficient

L39coefficient(hodgeParamLaurentPol hplp,Param p) = i_laurent_poly

also in this file at line 78; also defined in hodgeParamPol.at, hodge_functions.at, lazy_lists.at

= 2 overloads

L45=(hodgeParamLaurentPol hplp_1,hodgeParamLaurentPol hplp_2) = bool
L55=(hodgeParamLaurentPol hplp) = bool

also defined in basic.at, combinatorics.at, modules.at, parabolics.at, synthetic.at, hash.at, tits.at, K_highest_weights.at, nilpotent_orbits.at, cyclotomic.at, polynomial.at, W_reps_type_BC.at, hodgeParamPol.at, laurentPolynomial.at, extended.at, disconnected.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at

rearrange and dearrange
 should be used only for input/output
 all computations internally are in terms of hodgeParamLaurentPols
rearrange takes hodgeParamLaurentPol:([P_0,P_1,..,P_m],n) ->
(P_0+P_1*v+...P_m*v^m)*v^n
\sum a_{i,0}v^i)^{n}p_0 +
\sum a_{i,1}v^i)v^{n}p_1 +
...
\sum a_{i,r}v^i)v^{n}p_r
represented by
[
( ([a_{0,0},a_{1,0},...,a_{m,0}],c_0),n),
( ([a_{0,1},a_{1,1},...,a_{m,1}],c_1),n),
...
( ([a_{0,r},a_{1,r},...,a_{m,r}],c_r),n)]
L57

rearrange

L74rearrange(hodgeParamLaurentPol (hpp,shift)) = [(i_laurent_poly,Param)]

also defined in hodgeParamPol.at

coefficient

L78coefficient(hodgeParamLaurentPol hplp, Param p) = i_laurent_poly

also in this file at line 39; also defined in hodgeParamPol.at, hodge_functions.at, lazy_lists.at

dearrange

L87dearrange([(i_laurent_poly,Param)] pairs,RealForm G) = hodgeParamLaurentPol
go other way:
given f_0(v)p_0 + ... + f_r(v) p_r, take it to ([P_0,...,P_m],n)

also defined in hodgeParamPol.at

* 4 overloads

L106*(i_laurent_poly (f,n),Param p) = hodgeParamLaurentPol
set *(i_laurent_poly f,Param p)=hodgeParamLaurentPol: dearrange([(f,p)],p.real_form)
same, but don't use dearrange:
L108*(i_poly f,Param p) = hodgeParamLaurentPol
L110*(Param p,i_laurent_poly f) = hodgeParamLaurentPol
L111*(Param p,i_poly f) = hodgeParamLaurentPol

also in this file at line 33, line 34, line 154, line 158, line 160, line 163; 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, hodgeParamPol.at, laurentPolynomial.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, hodge_functions.at, sparse.at, lazy_lists.at

+

L114+(hodgeParamLaurentPol P,hodgeParamLaurentPol Q)
old version, used rearrange/dearrange

also in this file at line 136; also defined in basic.at, extParamPol.at, modules.at, ratmat.at, cyclotomic.at, polynomial.at, hodgeParamPol.at, laurentPolynomial.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, hodge_functions.at, lazy_lists.at

pad

L132pad(int k,hodgeParamPol P) = hodgeParamPol
add k copies of nullHodgeParamPol at beginning

also defined in basic.at, tabulate.at

+

L136+(hodgeParamLaurentPol P,hodgeParamLaurentPol Q)

also in this file at line 114; also defined in basic.at, extParamPol.at, modules.at, ratmat.at, cyclotomic.at, polynomial.at, hodgeParamPol.at, laurentPolynomial.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, hodge_functions.at, lazy_lists.at

-

L148-(hodgeParamLaurentPol P,hodgeParamLaurentPol Q)

also in this file at line 35; also defined in basic.at, extParamPol.at, modules.at, ratmat.at, cyclotomic.at, polynomial.at, hodgeParamPol.at, laurentPolynomial.at, cyclotomicMat.at, hodge_functions.at, lazy_lists.at

v_to_1

L149v_to_1(hodgeParamLaurentPol hplp) = ParamPol

also defined in hodgeParamPol.at

* 4 overloads

L154*(i_poly f,hodgeParamLaurentPol (hpp,n)) = hodgeParamLaurentPol
polynomial  in v, or constant, times hodgeParamPol
L158*(hodgeParamLaurentPol hplp,i_poly f) = hodgeParamLaurentPol
L160*(i_laurent_poly f,hodgeParamLaurentPol (hpp,m)) = hodgeParamLaurentPol
L163*(hodgeParamLaurentPol hplp,i_laurent_poly f) = hodgeParamLaurentPol

also in this file at line 33, line 34, line 106, line 108, line 110, line 111; 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, hodgeParamPol.at, laurentPolynomial.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, hodge_functions.at, sparse.at, lazy_lists.at

power_times

L166power_times(Param p,int n) = hodgeParamLaurentPol
v^k*p for k\in Z

sub

L168sub(hodgeParamLaurentPol hpp) = ParamPol

quotient

L172quotient(hodgeParamLaurentPol hpp) = ParamPol

show

L177show(hodgeParamLaurentPol hplp) = void
nice output

also defined in modules.at, K_Nilpotent.at, good_W_representatives.at, arthur_parameters.at, sub_cells.at, associated_variety_annihilator.at, geck_generic.at, L_packet.at, ratmat.at, Levi_subgroups.at, nilpotent_orbits.at, subgroups.at, poset.at, cyclotomic.at, polynomial.at, character_tables.at, springer_tables.at, hodgeParamPol.at, laurentPolynomial.at, weak_packets.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, exceptional.at, nilpotent_posets.at, lazy_lists.at

show_long

L203show_long(hodgeParamLaurentPol hplp) = void
set G=SL(2,R)
set block=block_of(G.trivial)
set a=block[0]
set b=block[1]
set c=block[2]

set f=hodgeParamLaurentPol:
([a+b,b,b,c],-5)
set f=i_laurent_poly:([1],-3)
set g=hodgeParamLaurentPol:([a],-1)
set h=hodgeParamLaurentPol:([b,2*b],0)
set l=hodgeParamLaurentPol:([b],-3)

also in this file at line 258; also defined in character_tables.at, springer_tables.at, hodgeParamPol.at, weak_packets.at, cyclotomic_Lie_algebra.at, bracket.at, exceptional.at

find

L247find(hodgeParamLaurentPol f,[Param] b) = int
f.v_to_1 is a linear combination of irreducible modules J(gamma),
look up to see if this is the composition series of a standard
module in the given list b

also defined in basic.at, tits_centralizer.at, nilpotent_orbits.at, cells.at, K_types.at, extended.at, disconnected.at, nilpotent_posets.at, K_types_plus.at

T_irr_dominant

L253T_irr_dominant(hodgeParamLaurentPol hpp,ratvec lambda) = hodgeParamLaurentPol
this should only be used in the dominant chamber,
so irreducibles -> irreducibles or 0

show_long

L258show_long([Param] b,hodgeParamLaurentPol hplp) = void
also identify hplp.v_to_1 as a standard module if possible

also in this file at line 203; also defined in character_tables.at, springer_tables.at, hodgeParamPol.at, weak_packets.at, cyclotomic_Lie_algebra.at, bracket.at, exceptional.at

Generated from atlas-scripts at commit 648506c (2026-10-13).