basic.at Function Index¶
Functions
Function | Argument(s) -> Results |
---|---|
# | int n->[int]: for i |
# | bool b->int |
assert | bool b,string message->void |
assert | bool b->void |
list | (int->bool) filter, int limit->[int] |
complement | (int->bool) filter, int limit->[int] |
count | (int->bool) filter, int limit->int |
all | [bool] p->bool |
none | [bool] p->bool |
first | [bool] p->int |
last | [bool] p->int |
all | int limit,(int->bool) filter->bool |
none | int limit,(int->bool) filter->bool |
first | int limit,(int->bool) filter->int |
last | int limit,(int->bool) filter->int |
all | [(->bool)] p->bool |
none | [(->bool)] p->bool |
first | [(->bool)] p->int |
last | [(->bool)] p->int |
binary_search_first | (int->bool)pred, int low, int high->int |
from_stops | [int] stops->(int->int) |
abs | int k->int |
sign | int k->int |
is_odd | int n->bool |
is_even | int n->bool |
min | int k, int l->int |
max | int k, int l->int |
min | [int] a->int |
max | [int] a->int |
min_loc | [int] a->int |
max_loc | [int] a->int |
min | int !seed->([int]->int) |
max | int !seed->([int]->int) |
lcm | [int] list) = let (,d->%(ratvec |
= | (int,int)(x0,y0),(int,int)(x1,y1)->bool |
!= | (int,int)(x0,y0),(int,int)(x1,y1)->bool |
is_integer | rat r->bool |
sign | rat a->int |
abs | rat a->rat |
floor | rat a->int |
ceil | rat a->int |
\_(rat,int)p->int1 | (rat,int)p->int |
\_(rat,rat)p->int1 | (rat,rat)p->int |
% | (rat,int)p->(int,rat) |
% | (rat,rat)p->(int,rat) |
floor | [rat] v->vec |
ceil | [rat] v->vec |
rat_as_int | rat r->int |
* | int n,string s->string |
+ | string s, int i->string |
+ | int i, string s->string |
plural | int n->string |
plural | int n,string s->string |
l_adjust | int w, string s->string |
r_adjust | int w, string s->string |
c_adjust | int w, string s->string |
width | int n->int |
split_lines | string text->[string] |
is_substring | string s, string text->bool |
fgrep | string s, string text->[string] |
vector | int n,(int->int)f->vec: for i |
ones | int n->vec: for i |
gcd | [int] v->int |
* | int c,vec v->vec |
sum | vec v->int |
product | vec v->1 in for e in v do s* |
half | int n->int |
reverse | vec v->vec: v~[ |
lower | int k,vec v->vec: v[ |
upper | int k,vec v->vec: v[k~ |
drop_lower | int k,vec v->vec: v[k |
drop_upper | int k,vec v->vec: v[ |
<= | vec v->bool |
< | vec v->bool |
is_member | [int] v->(int->bool) |
contains | int val->([int]->bool): ([int] v)bool |
rec_fun all_0_1_vecs | int n->[vec] |
rec_fun power_set | int n->[[int]] |
power_set | [int] S->[[int]] |
matrix | (int,int)(r,c),(int,int->int) f->mat |
n_rows | mat m->int |
n_columns | mat m->int |
column | vec v->mat |
row | vec v->mat |
= | mat m,int k->bool |
# | mat m, vec v->mat: n_rows(m) # (([vec] |
# | vec v, mat m->mat: n_rows(m) # (v#([vec] |
^ | mat m, vec v->mat: n_columns(m) ^ (([vec] |
^ | vec v, mat m->mat: n_columns(m) ^ (v#([vec] |
## | mat A, mat B->mat |
^ | mat A, mat B->mat |
## | int n,[mat] L->mat |
map_on | mat m->((int->int)->mat) |
* | int c,mat m->mat: map_on(m)((int e) int |
- | mat m->mat |
\_mat_m,int_d->mat:_map_on(m)((int_e)_int1 | mat m,int d->mat: map_on(m)((int e) int |
% | mat m,int d->mat: map_on(m)((int e) int |
inverse | mat M->mat |
det | mat M->int |
saturated_span | mat M->bool |
all | mat M,(vec->bool) filter->bool |
none | mat M,(vec->bool) filter->bool |
first | mat M,(vec->bool) filter->int |
last | mat M,(vec->bool) filter->int |
columns_with | (int,vec->bool) p,mat m->mat |
columns_with | (vec->bool) p,mat m->mat |
columns_with | (int->bool) p,mat m->mat |
rows_with | (int,vec->bool) p,mat m->mat |
rows_with | (vec->bool) p,mat m->mat |
rows_with | (int->bool) p,mat m->mat |
>= | mat m->bool |
> | mat m->bool |
<= | mat m->bool |
< | mat m->bool |
lookup_column | vec v,mat m->int |
lookup_row | vec v,mat m->int |
sum | mat m->vec |
order | mat !M->int |
numer | ratvec a->vec |
denom | ratvec a->int |
* | int i,ratvec v->ratvec |
* | rat r,ratvec v->ratvec |
## | ratvec a,ratvec b->ratvec: ##([rat]:a,[rat] |
## | [ratvec] rs->ratvec: ## for r in rs do [rat] |
sum | [ratvec] list, int l->ratvec |
* | [ratvec] M,ratvec v->ratvec |
is_integer | ratvec v->bool |
* | ratvec v, ratvec w->rat |
* | vec v, ratvec w->rat |
\_ratvec_v,_int_k->vec1 | ratvec v, int k->vec |
ratvec_as_vec | ratvec v->vec |
reverse | ratvec v->ratvec: v~[ |
lower | int k,ratvec v->ratvec: v[ |
upper | int k,ratvec v->ratvec: v[k~ |
drop_lower | int k,ratvec v->ratvec: v[k |
drop_upper | int k,ratvec v->ratvec: v[ |
sum | ratvec v->rat |
<= | ratvec v->bool |
< | ratvec v->bool |
solve | mat A, ratvec b->[ratvec] |
one_minus_s = split:_1,-1->split1 | 1,-1->Split |
int_part | Split x->int |
s_part | Split x->int |
s_to_1 | Split x->int |
s_to_minus_1 | Split x->int |
times_s | Split x) = let (a,b->%x in Split |
split_as_int | Split x->int |
% | Split x, int n->(Split,Split) |
half | Split w->Split |
/ | Split w,int n->Split |
% | Split w,int n->Split |
exp_s | int n->Split |
is_pure | Split w->bool |
split_format | Split w->string |
^ =let rec_fun split_power | Split x,int n->Split |
sum | [Split] list->Split |
root_datum | [vec] simple_roots, [vec] simple_coroots, int r->RootDatum |
root_datum | LieType t, [ratvec] gens->RootDatum |
root_datum | LieType t, ratvec gen->RootDatum |
is_root | (RootDatum,vec) (rd,):p->bool |
is_coroot | (RootDatum,vec) (rd,):p->bool |
is_posroot | (RootDatum,vec)(rd,):p->bool |
is_poscoroot | (RootDatum,vec)(rd,):p->bool |
posroot_index | (RootDatum,vec)p->int |
poscoroot_index | (RootDatum,vec)p->int |
rho | RootDatum rd->ratvec |
rho_as_vec | RootDatum r->vec |
rho_check | RootDatum rd->ratvec |
is_positive_root | RootDatum rd->(vec->bool) |
is_positive_coroot | RootDatum rd->(vec->bool) |
is_negative_root | RootDatum rd->(vec->bool) |
is_negative_coroot | RootDatum rd->(vec->bool) |
is_positive_root | RootDatum rd,vec alpha->bool |
is_positive_coroot | RootDatum rd,vec alphav->bool |
is_negative_root | RootDatum rd,vec alpha->bool |
is_negative_coroot | RootDatum rd,vec alphav->bool |
roots_all_positive | RootDatum rd->(mat->bool) |
coroots_all_positive | RootDatum rd->(mat->bool) |
among_posroots | RootDatum rd->(mat M)bool |
among_poscoroots | RootDatum rd->(mat M)bool |
roots | RootDatum rd->mat |
coroots | RootDatum rd->mat |
root | RootDatum rd, vec alpha_v->vec |
coroot | RootDatum rd, vec alpha->vec |
reflection | RootDatum rd, int i->mat |
reflection | (RootDatum,vec)(rd,):p->mat |
coreflection | RootDatum rd, int i->mat |
coreflection | (RootDatum,vec)(rd,):p->mat |
reflect | RootDatum rd, int i, vec v->vec |
reflect | RootDatum rd, vec alpha, vec v->vec |
coreflect | RootDatum rd, vec v, int i->vec |
coreflect | RootDatum rd, vec v, vec alpha->vec |
reflect | RootDatum rd, int i, ratvec v->ratvec |
reflect | RootDatum rd, vec alpha, ratvec v->ratvec |
coreflect | RootDatum rd, ratvec v, int i->ratvec |
coreflect | RootDatum rd, ratvec v, vec alpha->ratvec |
left_reflect | RootDatum rd, int i, mat M->mat |
left_reflect | RootDatum rd, vec alpha, mat M->mat |
right_reflect | RootDatum rd, mat M, int i->mat |
right_reflect | RootDatum rd, mat M, vec alpha->mat |
conjugate | RootDatum rd, int i, mat M->mat |
conjugate | RootDatum rd, vec alpha, mat M->mat |
singular_simple_indices | RootDatum rd,ratvec v->[int] |
is_imaginary | mat theta->(vec->bool): (vec alpha) |
is_real | mat theta->(vec->bool): (vec alpha) |
is_complex | mat theta->(vec->bool): (vec alpha) |
imaginary_roots | RootDatum rd, mat theta->mat |
real_roots | RootDatum rd, mat theta->mat |
imaginary_coroots | RootDatum rd, mat theta->mat |
real_coroots | RootDatum rd, mat theta->mat |
imaginary_posroots | RootDatum rd,mat theta->mat |
real_posroots | RootDatum rd,mat theta->mat |
imaginary_poscoroots | RootDatum rd,mat theta->mat |
real_poscoroots | RootDatum rd,mat theta->mat |
imaginary_sys | (RootDatum,mat)p->(mat,mat) |
real_sys | (RootDatum,mat)p->(mat,mat) |
is_dominant | RootDatum rd, ratvec v->bool |
is_strictly_dominant | RootDatum rd, ratvec v->bool |
is_regular | RootDatum rd,ratvec v->bool |
is_integral | RootDatum rd, ratvec v->bool |
radical_basis | RootDatum rd->mat |
coradical_basis | RootDatum rd->mat |
is_semisimple | RootDatum rd->bool |
derived_is_simply_connected | RootDatum rd->bool |
has_connected_center | RootDatum rd->bool |
is_simply_connected | RootDatum rd->bool |
is_adjoint | RootDatum rd->bool |
derived | RootDatum rd->RootDatum |
mod_central_torus | RootDatum rd->RootDatum |
adjoint | RootDatum rd->RootDatum |
is_simple_for | vec dual_two_rho->(vec->bool) |
simple_from_positive | mat posroots,mat poscoroots->(mat,mat) |
fundamental_weights | RootDatum rd->[ratvec] |
fundamental_coweights | RootDatum rd->[ratvec] |
dual_integral | InnerClass ic, ratvec gamma->InnerClass |
Cartan_classes | InnerClass ic->[CartanClass] |
print_Cartan_info | CartanClass cc->void |
fundamental_Cartan | InnerClass ic->CartanClass |
most_split_Cartan | InnerClass ic->CartanClass |
compact_rank | CartanClass cc->int |
split_rank | CartanClass cc->int |
compact_rank | InnerClass ic->int |
split_rank | RealForm G->int |
is_equal_rank | InnerClass ic->bool |
is_split | RealForm G->bool |
= | CartanClass H,CartanClass J->bool |
number | CartanClass H,RealForm G->int |
form_name | RealForm f->string |
real_forms | InnerClass ic->[RealForm] |
dual_real_forms | InnerClass ic->[RealForm] |
is_quasisplit | RealForm G->bool |
is_quasicompact | RealForm G->bool |
split_form | RootDatum r->RealForm |
split_form | LieType t->RealForm |
quasicompact_form | InnerClass ic->RealForm |
is_compatible | RealForm f, RealForm g->bool |
is_compact | RealForm G->bool |
root_datum | KGBElt x->RootDatum |
inner_class | KGBElt x->InnerClass |
KGB | RealForm rf->[KGBElt]: for i |
KGB | CartanClass H,RealForm G->[KGBElt] |
KGB_elt | (InnerClass, mat, ratvec) (,theta,v):all->KGBElt |
KGB_elt | RootDatum rd, mat theta, ratvec v->KGBElt |
Cartan_class | InnerClass ic, mat theta->CartanClass |
Bruhat_order | RealForm G->(KGBElt,KGBElt->bool) |
status | vec alpha,KGBElt x->int |
cross | vec alpha,KGBElt x->KGBElt |
Cayley | vec alpha,KGBElt x->KGBElt |
W_cross | [int] w,KGBElt x->KGBElt |
KGB_status_text | int i->string |
status_text | (int,KGBElt)p->string |
status_text | (vec,KGBElt)p->string |
status_texts | KGBElt x->[string] |
is_imaginary | KGBElt x->(vec->bool) |
is_real | KGBElt x->(vec->bool) |
is_complex | KGBElt x->(vec->bool) |
imaginary_posroots | KGBElt x->mat |
real_posroots | KGBElt x->mat |
imaginary_poscoroots | KGBElt x->mat |
real_poscoroots | KGBElt x->mat |
imaginary_sys | KGBElt x->(mat,mat) |
real_sys | KGBElt x->(mat,mat) |
rho_i | KGBElt x->ratvec |
rho_r | KGBElt x->ratvec |
rho_check_i | KGBElt x->ratvec |
rho_check_r | KGBElt x->ratvec |
rho_i | (RootDatum,mat) rd_theta->ratvec |
rho_r | (RootDatum,mat) rd_theta->ratvec |
rho_check_i | (RootDatum,mat) rd_theta->ratvec |
rho_check_r | (RootDatum,mat) rd_theta->ratvec |
is_compact | KGBElt x->(vec->bool) |
is_noncompact | KGBElt x->(vec->bool) |
is_compact_imaginary | KGBElt x->(vec->bool) |
is_noncompact_imaginary | KGBElt x->(vec->bool) |
compact_posroots | KGBElt x->mat |
noncompact_posroots | KGBElt x->mat |
rho_ci | KGBElt x->ratvec |
rho_nci | KGBElt x->ratvec |
is_imaginary | vec v,KGBElt x->bool |
is_real | vec v,KGBElt x->bool |
is_complex | vec v,KGBElt x->bool |
is_compact_imaginary | vec v,KGBElt x->bool |
is_noncompact_imaginary | vec v,KGBElt x->bool |
print_KGB | KGBElt x->void |
no_Cminus_roots | KGBElt x->bool |
no_Cplus_roots | KGBElt x->bool |
blocks | InnerClass ic->[Block] |
raw_KL | (RealForm,RealForm) p->(mat,[vec],vec) |
dual_KL | (RealForm,RealForm) p->(mat,[vec],vec) |
print_block | (RealForm,RealForm) p->void |
print_blocku | (RealForm,RealForm) p->void |
print_blockd | (RealForm,RealForm) p->void |
print_KL_basis | (RealForm,RealForm) p->void |
print_prim_KL | (RealForm,RealForm) p->void |
print_KL_list | (RealForm,RealForm) p->void |
print_W_cells | (RealForm,RealForm) p->void |
print_W_graph | (RealForm,RealForm) p->void |
root_datum | Param p->RootDatum |
inner_class | Param p->InnerClass |
null_module | Param p->ParamPol |
x | Param p->KGBElt |
lambda_minus_rho | Param p->vec |
lambda | Param p->ratvec |
infinitesimal_character | Param p->ratvec |
nu | Param p->ratvec |
Cartan_class | Param p->CartanClass |
integrality_datum | Param p->RootDatum |
is_regular | Param p->bool |
survives | Param p->bool |
trivial | RealForm G->Param |
W_cross | [int] w,Param p->Param |
parameter | RealForm G,int x,ratvec lambda,ratvec nu->Param |
parameter | KGBElt x,ratvec lambda,ratvec nu->Param |
parameter_gamma | KGBElt x, ratvec lambda, ratvec gamma->Param |
singular_block | Param p->([Param],int) |
block_of | Param p->[Param] |
singular_block_of | Param p->[Param] |
imaginary_type | int s, Param p->int |
real_type | int s,Param p->int |
imaginary_type | vec alpha, Param p->int |
real_type | vec alpha, Param p->int |
is_nonparity | int s,Param p->bool |
is_parity | int s,Param p->bool |
is_nonparity | vec alpha,Param p->bool |
is_parity | vec alpha,Param p->bool |
status | vec alpha,Param p->int |
status | int s,Param p->int |
block_status_text | int i->string |
status_text | int s,Param p->string |
status_texts | Param p->[string] |
status_text | (vec,Param) ap->string |
parity_poscoroots | Param p->mat |
nonparity_poscoroots | Param p->mat |
is_descent | int s,Param p->bool |
tau_bitset | Param p->((int->bool),int) |
tau | Param p->[int] |
tau_complement | Param p->[int] |
is_descent | (vec,Param) ap->bool |
lookup | Param p, [Param] block->int |
null_module | ParamPol P->ParamPol |
- | ParamPol P->ParamPol |
first_param | ParamPol P->Param |
last_param | ParamPol P->Param |
s_to_1 | ParamPol P->ParamPol |
s_to_minus_1 | ParamPol P->ParamPol |
- | ParamPol a, (Split,Param) (c,p)->ParamPol |
sum | RealForm G,[ParamPol] Ps->ParamPol |
map | (Param->Param)f, ParamPol P->ParamPol |
map | (Param->ParamPol)f, ParamPol P->ParamPol |
half | ParamPol P->ParamPol |
divide_by | int n, ParamPol P->ParamPol |
root_datum | ParamPol P->RootDatum |
virtual | Param p->ParamPol |
virtual | RealForm G, [Param] ps->ParamPol |
branch | Param std, Param K_type->int |
branch | ParamPol P, Param K_type->Split |
pol_format | ParamPol P->string |
infinitesimal_character | ParamPol P->ratvec |
height_split | ParamPol P, int h->(ParamPol,ParamPol) |
separate_by_infinitesimal_character | ParamPol P->[(ratvec,ParamPol)] |
is_pure_1 | ParamPol P->bool |
is_pure_s | ParamPol P->bool |
is_pure | ParamPol P->bool |
purity | ParamPol P->(int,int,int) |
find | [int] v, int k->int: first(#v,(int i)bool |
find | [Param] P,Param p->int: first(#P,(int i)bool |
find | [KGBElt] S,KGBElt x->int: first(#S,(int i)bool |
find | [vec] S,vec v->int: first(#S,(int i)bool |
in_string_list | string s,[string] S->bool |
delete | [int] v, int k->[int]: v[:k]##v[k+1 |
delete | [vec] v, int k->[vec]: v[:k]##v[k+1 |
delete | [ratvec] v, int k->[ratvec]: v[:k]##v[k+1 |
delete | [[ratvec]] v, int k->[[ratvec]]:v[:k]##v[k+1 |
delete | [[vec]] v, int k->[[vec]]: v[:k]##v[k+1 |
delete | [ParamPol] P, int k->[ParamPol]:P[:k]##P[k+1 |
imaginary_roots_and_coroots | (RootDatum, mat)p->(mat,mat) |
imaginary_roots_and_coroots | KGBElt x->(mat,mat) |
real_roots_and_coroots | (RootDatum, mat)p->(mat,mat) |
real_roots_and_coroots | KGBElt x->(mat,mat) |
complex_posroots | RootDatum rd,mat theta->mat |
complex_posroots | KGBElt x->mat |
pad | string s,int padding->string |
monomials | ParamPol P->[Param] |
monomial | ParamPol P,int i->Param |