.. _basic.at_ref: basic.at Function References ======================================================= | .. _\#_int_n->[int]:_for_i1: \# ------------------------------------------------- | ``#:int n->[int]: for i`` Defined in line number 3. | | .. _\#_bool_b->int1: \# ------------------------------------------------- | ``#:bool b->int`` Defined in line number 4. | | .. _assert_bool_b,string_message->void1: assert ------------------------------------------------- | ``assert:bool b,string message->void`` Defined in line number 8. | | .. _assert_bool_b->void1: assert ------------------------------------------------- | ``assert:bool b->void`` Defined in line number 9. | | .. _list_(int->bool)_filter,_int_limit->[int]1: list ------------------------------------------------- | ``list:(int->bool) filter, int limit->[int]`` Defined in line number 13. | | .. _complement_(int->bool)_filter,_int_limit->[int]1: complement ------------------------------------------------- | ``complement:(int->bool) filter, int limit->[int]`` Defined in line number 15. | | .. _count_(int->bool)_filter,_int_limit->int1: count ------------------------------------------------- | ``count:(int->bool) filter, int limit->int`` Defined in line number 18. | | .. _all_[bool]_p->bool1: all ------------------------------------------------- | ``all:[bool] p->bool`` Defined in line number 21. | | .. _none_[bool]_p->bool1: none ------------------------------------------------- | ``none:[bool] p->bool`` Defined in line number 23. | | .. _first_[bool]_p->int1: first ------------------------------------------------- | ``first:[bool] p->int`` Defined in line number 25. | | .. _last_[bool]_p->int1: last ------------------------------------------------- | ``last:[bool] p->int`` Defined in line number 27. | | .. _all_int_limit,(int->bool)_filter->bool1: all ------------------------------------------------- | ``all:int limit,(int->bool) filter->bool`` Defined in line number 30. | | .. _none_int_limit,(int->bool)_filter->bool1: none ------------------------------------------------- | ``none:int limit,(int->bool) filter->bool`` Defined in line number 32. | | .. _first_int_limit,(int->bool)_filter->int1: first ------------------------------------------------- | ``first:int limit,(int->bool) filter->int`` Defined in line number 34. | | .. _last_int_limit,(int->bool)_filter->int1: last ------------------------------------------------- | ``last:int limit,(int->bool) filter->int`` Defined in line number 36. | | .. _all_[(->bool)]_p->bool1: all ------------------------------------------------- | ``all:[(->bool)] p->bool`` Defined in line number 40. | | .. _none_[(->bool)]_p->bool1: none ------------------------------------------------- | ``none:[(->bool)] p->bool`` Defined in line number 42. | | .. _first_[(->bool)]_p->int1: first ------------------------------------------------- | ``first:[(->bool)] p->int`` Defined in line number 44. | | .. _last_[(->bool)]_p->int1: last ------------------------------------------------- | ``last:[(->bool)] p->int`` Defined in line number 46. | | .. _binary_search_first_(int->bool)pred,_int_low,_int_high->int1: binary_search_first ------------------------------------------------- | ``binary_search_first:(int->bool)pred, int low, int high->int`` Defined in line number 51. | | .. _from_stops_[int]_stops->(int->int)1: from_stops ------------------------------------------------- | ``from_stops:[int] stops->(int->int)`` Defined in line number 56. | | .. _abs_int_k->int1: abs ------------------------------------------------- | ``abs:int k->int`` Defined in line number 61. | | .. _sign_int_k->int1: sign ------------------------------------------------- | ``sign:int k->int`` Defined in line number 62. | | .. _is_odd_int_n->bool1: is_odd ------------------------------------------------- | ``is_odd:int n->bool`` Defined in line number 64. | | .. _is_even_int_n->bool1: is_even ------------------------------------------------- | ``is_even:int n->bool`` Defined in line number 65. | | .. _min_int_k,_int_l->int1: min ------------------------------------------------- | ``min:int k, int l->int`` Defined in line number 67. | | .. _max_int_k,_int_l->int1: max ------------------------------------------------- | ``max:int k, int l->int`` Defined in line number 68. | | .. _min_[int]_a->int1: min ------------------------------------------------- | ``min:[int] a->int`` Defined in line number 70. | | .. _max_[int]_a->int1: max ------------------------------------------------- | ``max:[int] a->int`` Defined in line number 72. | | .. _min_loc_[int]_a->int1: min_loc ------------------------------------------------- | ``min_loc:[int] a->int`` Defined in line number 75. | | .. _max_loc_[int]_a->int1: max_loc ------------------------------------------------- | ``max_loc:[int] a->int`` Defined in line number 81. | | .. _min_int_!seed->([int]->int)1: min ------------------------------------------------- | ``min:int !seed->([int]->int)`` Defined in line number 89. | | .. _max_int_!seed->([int]->int)1: max ------------------------------------------------- | ``max:int !seed->([int]->int)`` Defined in line number 91. | | .. _lcm_[int]_list)_=_let_(,d->%(ratvec1: lcm ------------------------------------------------- | ``lcm:[int] list) = let (,d->%(ratvec`` Defined in line number 94. | | .. _\=_(int,int)(x0,y0),(int,int)(x1,y1)->bool1: \= ------------------------------------------------- | ``=:(int,int)(x0,y0),(int,int)(x1,y1)->bool`` Defined in line number 96. | | .. _\!=_(int,int)(x0,y0),(int,int)(x1,y1)->bool1: \!= ------------------------------------------------- | ``!=:(int,int)(x0,y0),(int,int)(x1,y1)->bool`` Defined in line number 97. | | .. _is_integer_rat_r->bool1: is_integer ------------------------------------------------- | ``is_integer:rat r->bool`` Defined in line number 106. | | .. _sign_rat_a->int1: sign ------------------------------------------------- | ``sign:rat a->int`` Defined in line number 107. | | .. _abs_rat_a->rat1: abs ------------------------------------------------- | ``abs:rat a->rat`` Defined in line number 109. | | .. _floor_rat_a->int1: floor ------------------------------------------------- | ``floor:rat a->int`` Defined in line number 111. | | .. _ceil_rat_a->int1: ceil ------------------------------------------------- | ``ceil:rat a->int`` Defined in line number 112. | | .. _\\_(rat,int)p->int1: \\ ------------------------------------------------- | ``\:(rat,int)p->int`` Defined in line number 114. | | .. _\\_(rat,rat)p->int1: \\ ------------------------------------------------- | ``\:(rat,rat)p->int`` Defined in line number 115. | | .. _\%_(rat,int)p->(int,rat)1: \% ------------------------------------------------- | ``\%:(rat,int)p->(int,rat)`` Defined in line number 116. | | .. _\%_(rat,rat)p->(int,rat)1: \% ------------------------------------------------- | ``\%:(rat,rat)p->(int,rat)`` Defined in line number 117. | | .. _floor_[rat]_v->vec1: floor ------------------------------------------------- | ``floor:[rat] v->vec`` Defined in line number 120. | | .. _ceil_[rat]_v->vec1: ceil ------------------------------------------------- | ``ceil:[rat] v->vec`` Defined in line number 121. | | .. _rat_as_int_rat_r->int1: rat_as_int ------------------------------------------------- | ``rat_as_int:rat r->int`` Defined in line number 125. | | .. _\*_int_n,string_s->string1: \* ------------------------------------------------- | ``*:int n,string s->string`` Defined in line number 141. | | .. _\+_string_s,_int_i->string1: \+ ------------------------------------------------- | ``+:string s, int i->string`` Defined in line number 143. | | .. _\+_int_i,_string_s->string1: \+ ------------------------------------------------- | ``+:int i, string s->string`` Defined in line number 144. | | .. _plural_int_n->string1: plural ------------------------------------------------- | ``plural:int n->string`` Defined in line number 148. | | .. _plural_int_n,string_s->string1: plural ------------------------------------------------- | ``plural:int n,string s->string`` Defined in line number 149. | | .. _l_adjust_int_w,_string_s->string1: l_adjust ------------------------------------------------- | ``l_adjust:int w, string s->string`` Defined in line number 153. | | .. _r_adjust_int_w,_string_s->string1: r_adjust ------------------------------------------------- | ``r_adjust:int w, string s->string`` Defined in line number 155. | | .. _c_adjust_int_w,_string_s->string1: c_adjust ------------------------------------------------- | ``c_adjust:int w, string s->string`` Defined in line number 157. | | .. _width_int_n->int1: width ------------------------------------------------- | ``width:int n->int`` Defined in line number 160. | | .. _split_lines_string_text->[string]1: split_lines ------------------------------------------------- | ``split_lines:string text->[string]`` Defined in line number 162. | | .. _is_substring_string_s,_string_text->bool1: is_substring ------------------------------------------------- | ``is_substring:string s, string text->bool`` Defined in line number 168. | | .. _fgrep_string_s,_string_text->[string]1: fgrep ------------------------------------------------- | ``fgrep:string s, string text->[string]`` Defined in line number 172. | | .. _vector_int_n,(int->int)f->vec:_for_i1: vector ------------------------------------------------- | ``vector:int n,(int->int)f->vec: for i`` Defined in line number 180. | | .. _ones_int_n->vec:_for_i1: ones ------------------------------------------------- | ``ones:int n->vec: for i`` Defined in line number 182. | | .. _gcd_[int]_v->int1: gcd ------------------------------------------------- | ``gcd:[int] v->int`` Defined in line number 185. | | .. _\*_int_c,vec_v->vec1: \* ------------------------------------------------- | ``*:int c,vec v->vec`` Defined in line number 189. | | .. _sum_vec_v->int1: sum ------------------------------------------------- | ``sum:vec v->int`` Defined in line number 192. | | .. _product_vec_v->1_in_for_e_in_v_do_s*1: product ------------------------------------------------- | ``product:vec v->1 in for e in v do s*`` Defined in line number 193. | | .. _half_int_n->int1: half ------------------------------------------------- | ``half:int n->int`` Defined in line number 195. | | .. _reverse_vec_v->vec:_v~[1: reverse ------------------------------------------------- | ``reverse:vec v->vec: v~[`` Defined in line number 197. | | .. _lower_int_k,vec_v->vec:_v[1: lower ------------------------------------------------- | ``lower:int k,vec v->vec: v[`` Defined in line number 198. | | .. _upper_int_k,vec_v->vec:_v[k~1: upper ------------------------------------------------- | ``upper:int k,vec v->vec: v[k~`` Defined in line number 199. | | .. _drop_lower_int_k,vec_v->vec:_v[k1: drop_lower ------------------------------------------------- | ``drop_lower:int k,vec v->vec: v[k`` Defined in line number 200. | | .. _drop_upper_int_k,vec_v->vec:_v[1: drop_upper ------------------------------------------------- | ``drop_upper:int k,vec v->vec: v[`` Defined in line number 201. | | .. _<=_vec_v->bool1: <= ------------------------------------------------- | ``<=:vec v->bool`` Defined in line number 203. | | .. _\<_vec_v->bool1: \< ------------------------------------------------- | ``<:vec v->bool`` Defined in line number 204. | | .. _is_member_[int]_v->(int->bool)1: is_member ------------------------------------------------- | ``is_member:[int] v->(int->bool)`` Defined in line number 206. | | .. _contains_int_val->([int]->bool):_([int]_v)bool1: contains ------------------------------------------------- | ``contains:int val->([int]->bool): ([int] v)bool`` Defined in line number 210. | | .. _rec_fun all_0_1_vecs_int_n->[vec]1: rec_fun all_0_1_vecs ------------------------------------------------- | ``rec_fun all_0_1_vecs:int n->[vec]`` Defined in line number 212. | | .. _rec_fun power_set_int_n->[[int]]1: rec_fun power_set ------------------------------------------------- | ``rec_fun power_set:int n->[[int]]`` Defined in line number 218. | | .. _power_set_[int]_s->[[int]]1: power_set ------------------------------------------------- | ``power_set:[int] S->[[int]]`` Defined in line number 220. | | .. _matrix_(int,int)(r,c),(int,int->int)_f->mat1: matrix ------------------------------------------------- | ``matrix:(int,int)(r,c),(int,int->int) f->mat`` Defined in line number 227. | | .. _n_rows_mat_m->int1: n_rows ------------------------------------------------- | ``n_rows:mat m->int`` Defined in line number 230. | | .. _n_columns_mat_m->int1: n_columns ------------------------------------------------- | ``n_columns:mat m->int`` Defined in line number 231. | | .. _column_vec_v->mat1: column ------------------------------------------------- | ``column:vec v->mat`` Defined in line number 233. | | .. _row_vec_v->mat1: row ------------------------------------------------- | ``row:vec v->mat`` Defined in line number 234. | | .. _\=_mat_m,int_k->bool1: \= ------------------------------------------------- | ``=:mat m,int k->bool`` Defined in line number 237. | | .. _\#_mat_m,_vec_v->mat:_n_rows(m)__#_(([vec]1: \# ------------------------------------------------- | ``#:mat m, vec v->mat: n_rows(m) # (([vec]`` Defined in line number 240. | | .. _\#_vec_v,_mat_m->mat:_n_rows(m)__#_(v#([vec]1: \# ------------------------------------------------- | ``#:vec v, mat m->mat: n_rows(m) # (v#([vec]`` Defined in line number 241. | | .. _\^_mat_m,_vec_v->mat:_n_columns(m)_^_(([vec]1: \^ ------------------------------------------------- | ``^:mat m, vec v->mat: n_columns(m) ^ (([vec]`` Defined in line number 244. | | .. _\^_vec_v,_mat_m->mat:_n_columns(m)_^_(v#([vec]1: \^ ------------------------------------------------- | ``^:vec v, mat m->mat: n_columns(m) ^ (v#([vec]`` Defined in line number 245. | | .. _\#\#_mat_A,_mat_B->mat1: \#\# ------------------------------------------------- | ``##:mat A, mat B->mat`` Defined in line number 247. | | .. _\^_mat_A,_mat_B->mat1: \^ ------------------------------------------------- | ``^:mat A, mat B->mat`` Defined in line number 249. | | .. _\#\#_int_n,[mat]_L->mat1: \#\# ------------------------------------------------- | ``##:int n,[mat] L->mat`` Defined in line number 253. | | .. _map_on_mat_m->((int->int)->mat)1: map_on ------------------------------------------------- | ``map_on:mat m->((int->int)->mat)`` Defined in line number 257. | | .. _\*_int_c,mat_m->mat:_map_on(m)((int_e)_int1: \* ------------------------------------------------- | ``*:int c,mat m->mat: map_on(m)((int e) int`` Defined in line number 262. | | .. _\-_mat_m->mat1: \- ------------------------------------------------- | ``-:mat m->mat`` Defined in line number 263. | | .. _\\_mat_m,int_d->mat:_map_on(m)((int_e)_int1: \\ ------------------------------------------------- | ``\:mat m,int d->mat: map_on(m)((int e) int`` Defined in line number 267. | | .. _\%_mat_m,int_d->mat:_map_on(m)((int_e)_int1: \% ------------------------------------------------- | ``%:mat m,int d->mat: map_on(m)((int e) int`` Defined in line number 270. | | .. _inverse_mat_m->mat1: inverse ------------------------------------------------- | ``inverse:mat M->mat`` Defined in line number 293. | | .. _det_mat_m->int1: det ------------------------------------------------- | ``det:mat M->int`` Defined in line number 297. | | .. _saturated_span_mat_m->bool1: saturated_span ------------------------------------------------- | ``saturated_span:mat M->bool`` Defined in line number 305. | | .. _all_mat_m,(vec->bool)_filter->bool1: all ------------------------------------------------- | ``all:mat M,(vec->bool) filter->bool`` Defined in line number 310. | | .. _none_mat_m,(vec->bool)_filter->bool1: none ------------------------------------------------- | ``none:mat M,(vec->bool) filter->bool`` Defined in line number 312. | | .. _first_mat_m,(vec->bool)_filter->int1: first ------------------------------------------------- | ``first:mat M,(vec->bool) filter->int`` Defined in line number 314. | | .. _last_mat_m,(vec->bool)_filter->int1: last ------------------------------------------------- | ``last:mat M,(vec->bool) filter->int`` Defined in line number 317. | | .. _columns_with_(int,vec->bool)_p,mat_m->mat1: columns_with ------------------------------------------------- | ``columns_with:(int,vec->bool) p,mat m->mat`` Defined in line number 320. | | .. _columns_with_(vec->bool)_p,mat_m->mat1: columns_with ------------------------------------------------- | ``columns_with:(vec->bool) p,mat m->mat`` Defined in line number 323. | | .. _columns_with_(int->bool)_p,mat_m->mat1: columns_with ------------------------------------------------- | ``columns_with:(int->bool) p,mat m->mat`` Defined in line number 325. | | .. _rows_with_(int,vec->bool)_p,mat_m->mat1: rows_with ------------------------------------------------- | ``rows_with:(int,vec->bool) p,mat m->mat`` Defined in line number 328. | | .. _rows_with_(vec->bool)_p,mat_m->mat1: rows_with ------------------------------------------------- | ``rows_with:(vec->bool) p,mat m->mat`` Defined in line number 331. | | .. _rows_with_(int->bool)_p,mat_m->mat1: rows_with ------------------------------------------------- | ``rows_with:(int->bool) p,mat m->mat`` Defined in line number 333. | | .. _>=_mat_m->bool1: >= ------------------------------------------------- | ``>=:mat m->bool`` Defined in line number 336. | | .. _\>_mat_m->bool1: \> ------------------------------------------------- | ``>:mat m->bool`` Defined in line number 338. | | .. _<=_mat_m->bool1: <= ------------------------------------------------- | ``<=:mat m->bool`` Defined in line number 340. | | .. _\<_mat_m->bool1: \< ------------------------------------------------- | ``<:mat m->bool`` Defined in line number 341. | | .. _lookup_column_vec_v,mat_m->int1: lookup_column ------------------------------------------------- | ``lookup_column:vec v,mat m->int`` Defined in line number 343. | | .. _lookup_row_vec_v,mat_m->int1: lookup_row ------------------------------------------------- | ``lookup_row:vec v,mat m->int`` Defined in line number 345. | | .. _sum_mat_m->vec1: sum ------------------------------------------------- | ``sum:mat m->vec`` Defined in line number 349. | | .. _order_mat_!m->int1: order ------------------------------------------------- | ``order:mat !M->int`` Defined in line number 374. | | .. _numer_ratvec_a->vec1: numer ------------------------------------------------- | ``numer:ratvec a->vec`` Defined in line number 383. | | .. _denom_ratvec_a->int1: denom ------------------------------------------------- | ``denom:ratvec a->int`` Defined in line number 384. | | .. _\*_int_i,ratvec_v->ratvec1: \* ------------------------------------------------- | ``*:int i,ratvec v->ratvec`` Defined in line number 387. | | .. _\*_rat_r,ratvec_v->ratvec1: \* ------------------------------------------------- | ``*:rat r,ratvec v->ratvec`` Defined in line number 388. | | .. _\#\#_ratvec_a,ratvec_b->ratvec:_##([rat]:a,[rat]1: \#\# ------------------------------------------------- | ``##:ratvec a,ratvec b->ratvec: ##([rat]:a,[rat]`` Defined in line number 391. | | .. _\#\#_[ratvec]_rs->ratvec:_##_for_r_in_rs_do_[rat]1: \#\# ------------------------------------------------- | ``##:[ratvec] rs->ratvec: ## for r in rs do [rat]`` Defined in line number 392. | | .. _sum_[ratvec]_list,_int_l->ratvec1: sum ------------------------------------------------- | ``sum:[ratvec] list, int l->ratvec`` Defined in line number 394. | | .. _\*_[ratvec]_M,ratvec_v->ratvec1: \* ------------------------------------------------- | ``*:[ratvec] M,ratvec v->ratvec`` Defined in line number 402. | | .. _is_integer_ratvec_v->bool1: is_integer ------------------------------------------------- | ``is_integer:ratvec v->bool`` Defined in line number 408. | | .. _\*_ratvec_v,_ratvec_w->rat1: \* ------------------------------------------------- | ``*:ratvec v, ratvec w->rat`` Defined in line number 411. | | .. _\*_vec_v,_ratvec_w->rat1: \* ------------------------------------------------- | ``*:vec v, ratvec w->rat`` Defined in line number 413. | | .. _\\_ratvec_v,_int_k->vec1: \\ ------------------------------------------------- | ``\:ratvec v, int k->vec`` Defined in line number 417. | | .. _ratvec_as_vec_ratvec_v->vec1: ratvec_as_vec ------------------------------------------------- | ``ratvec_as_vec:ratvec v->vec`` Defined in line number 420. | | .. _reverse_ratvec_v->ratvec:_v~[1: reverse ------------------------------------------------- | ``reverse:ratvec v->ratvec: v~[`` Defined in line number 423. | | .. _lower_int_k,ratvec_v->ratvec:_v[1: lower ------------------------------------------------- | ``lower:int k,ratvec v->ratvec: v[`` Defined in line number 424. | | .. _upper_int_k,ratvec_v->ratvec:_v[k~1: upper ------------------------------------------------- | ``upper:int k,ratvec v->ratvec: v[k~`` Defined in line number 425. | | .. _drop_lower_int_k,ratvec_v->ratvec:_v[k1: drop_lower ------------------------------------------------- | ``drop_lower:int k,ratvec v->ratvec: v[k`` Defined in line number 426. | | .. _drop_upper_int_k,ratvec_v->ratvec:_v[1: drop_upper ------------------------------------------------- | ``drop_upper:int k,ratvec v->ratvec: v[`` Defined in line number 427. | | .. _sum_ratvec_v->rat1: sum ------------------------------------------------- | ``sum:ratvec v->rat`` Defined in line number 430. | | .. _<=_ratvec_v->bool1: <= ------------------------------------------------- | ``<=:ratvec v->bool`` Defined in line number 432. | | .. _\<_ratvec_v->bool1: \< ------------------------------------------------- | ``<:ratvec v->bool`` Defined in line number 433. | | .. _solve_mat_a,_ratvec_b->[ratvec]1: solve ------------------------------------------------- | ``solve:mat A, ratvec b->[ratvec]`` Defined in line number 436. | | .. _!one_minus_s = split:_1,-1->split1: !one_minus_s = Split: ------------------------------------------------- | ``!one_minus_s = Split::1,-1->Split`` Defined in line number 447. | | .. _int_part_split_x->int1: int_part ------------------------------------------------- | ``int_part:Split x->int`` Defined in line number 449. | | .. _s_part_split_x->int1: s_part ------------------------------------------------- | ``s_part:Split x->int`` Defined in line number 450. | | .. _s_to_1_split_x->int1: s_to_1 ------------------------------------------------- | ``s_to_1:Split x->int`` Defined in line number 455. | | .. _s_to_minus_1_split_x->int1: s_to_minus_1 ------------------------------------------------- | ``s_to_minus_1:Split x->int`` Defined in line number 456. | | .. _times_s_split_x)_=_let_(a,b->%x_in_split1: times_s ------------------------------------------------- | ``times_s:Split x) = let (a,b->%x in Split`` Defined in line number 457. | | .. _split_as_int_split_x->int1: split_as_int ------------------------------------------------- | ``split_as_int:Split x->int`` Defined in line number 459. | | .. _\%_split_x,_int_n->(split,split)1: \% ------------------------------------------------- | ``\%:Split x, int n->(Split,Split)`` Defined in line number 461. | | .. _half_split_w->split1: half ------------------------------------------------- | ``half:Split w->Split`` Defined in line number 464. | | .. _\/_Split_w,int_n->Split1: \/ ------------------------------------------------- | ``/:Split w,int n->Split`` Defined in line number 465. | | .. _\%_Split_w,int_n->Split1: \% ------------------------------------------------- | ``%:Split w,int n->Split`` Defined in line number 467. | | .. _exp_s_int_n->split1: exp_s ------------------------------------------------- | ``exp_s:int n->Split`` Defined in line number 468. | | .. _is_pure_split_w->bool1: is_pure ------------------------------------------------- | ``is_pure:Split w->bool`` Defined in line number 471. | | .. _split_format_split_w->string1: split_format ------------------------------------------------- | ``split_format:Split w->string`` Defined in line number 474. | | .. _^ =let rec_fun split_power_split_x,int_n->split1: ^ =let rec_fun split_power ------------------------------------------------- | ``^ =let rec_fun split_power:Split x,int n->Split`` Defined in line number 485. | | .. _sum_[split]_list->split1: sum ------------------------------------------------- | ``sum:[Split] list->Split`` Defined in line number 498. | | .. _root_datum_[vec]_simple_roots,_[vec]_simple_coroots,_int_r->rootdatum1: root_datum ------------------------------------------------- | ``root_datum:[vec] simple_roots, [vec] simple_coroots, int r->RootDatum`` Defined in line number 504. | | .. _root_datum_lietype_t,_[ratvec]_gens->rootdatum1: root_datum ------------------------------------------------- | ``root_datum:LieType t, [ratvec] gens->RootDatum`` Defined in line number 507. | | .. _root_datum_lietype_t,_ratvec_gen->rootdatum1: root_datum ------------------------------------------------- | ``root_datum:LieType t, ratvec gen->RootDatum`` Defined in line number 511. | | .. _is_root_(rootdatum,vec)_(rd,):p->bool1: is_root ------------------------------------------------- | ``is_root:(RootDatum,vec) (rd,):p->bool`` Defined in line number 514. | | .. _is_coroot_(rootdatum,vec)_(rd,):p->bool1: is_coroot ------------------------------------------------- | ``is_coroot:(RootDatum,vec) (rd,):p->bool`` Defined in line number 516. | | .. _is_posroot_(rootdatum,vec)(rd,):p->bool1: is_posroot ------------------------------------------------- | ``is_posroot:(RootDatum,vec)(rd,):p->bool`` Defined in line number 518. | | .. _is_poscoroot_(rootdatum,vec)(rd,):p->bool1: is_poscoroot ------------------------------------------------- | ``is_poscoroot:(RootDatum,vec)(rd,):p->bool`` Defined in line number 520. | | .. _posroot_index_(rootdatum,vec)p->int1: posroot_index ------------------------------------------------- | ``posroot_index:(RootDatum,vec)p->int`` Defined in line number 523. | | .. _poscoroot_index_(rootdatum,vec)p->int1: poscoroot_index ------------------------------------------------- | ``poscoroot_index:(RootDatum,vec)p->int`` Defined in line number 525. | | .. _rho_rootdatum_rd->ratvec1: rho ------------------------------------------------- | ``rho:RootDatum rd->ratvec`` Defined in line number 529. | | .. _rho_as_vec_rootdatum_r->vec1: rho_as_vec ------------------------------------------------- | ``rho_as_vec:RootDatum r->vec`` Defined in line number 535. | | .. _rho_check_rootdatum_rd->ratvec1: rho_check ------------------------------------------------- | ``rho_check:RootDatum rd->ratvec`` Defined in line number 537. | | .. _is_positive_root_rootdatum_rd->(vec->bool)1: is_positive_root ------------------------------------------------- | ``is_positive_root:RootDatum rd->(vec->bool)`` Defined in line number 544. | | .. _is_positive_coroot_rootdatum_rd->(vec->bool)1: is_positive_coroot ------------------------------------------------- | ``is_positive_coroot:RootDatum rd->(vec->bool)`` Defined in line number 546. | | .. _is_negative_root_rootdatum_rd->(vec->bool)1: is_negative_root ------------------------------------------------- | ``is_negative_root:RootDatum rd->(vec->bool)`` Defined in line number 548. | | .. _is_negative_coroot_rootdatum_rd->(vec->bool)1: is_negative_coroot ------------------------------------------------- | ``is_negative_coroot:RootDatum rd->(vec->bool)`` Defined in line number 550. | | .. _is_positive_root_rootdatum_rd,vec_alpha->bool1: is_positive_root ------------------------------------------------- | ``is_positive_root:RootDatum rd,vec alpha->bool`` Defined in line number 553. | | .. _is_positive_coroot_rootdatum_rd,vec_alphav->bool1: is_positive_coroot ------------------------------------------------- | ``is_positive_coroot:RootDatum rd,vec alphav->bool`` Defined in line number 555. | | .. _is_negative_root_rootdatum_rd,vec_alpha->bool1: is_negative_root ------------------------------------------------- | ``is_negative_root:RootDatum rd,vec alpha->bool`` Defined in line number 557. | | .. _is_negative_coroot_rootdatum_rd,vec_alphav->bool1: is_negative_coroot ------------------------------------------------- | ``is_negative_coroot:RootDatum rd,vec alphav->bool`` Defined in line number 559. | | .. _roots_all_positive_rootdatum_rd->(mat->bool)1: roots_all_positive ------------------------------------------------- | ``roots_all_positive:RootDatum rd->(mat->bool)`` Defined in line number 563. | | .. _coroots_all_positive_rootdatum_rd->(mat->bool)1: coroots_all_positive ------------------------------------------------- | ``coroots_all_positive:RootDatum rd->(mat->bool)`` Defined in line number 565. | | .. _among_posroots_rootdatum_rd->(mat_m)bool1: among_posroots ------------------------------------------------- | ``among_posroots:RootDatum rd->(mat M)bool`` Defined in line number 568. | | .. _among_poscoroots_rootdatum_rd->(mat_m)bool1: among_poscoroots ------------------------------------------------- | ``among_poscoroots:RootDatum rd->(mat M)bool`` Defined in line number 570. | | .. _roots_rootdatum_rd->mat1: roots ------------------------------------------------- | ``roots:RootDatum rd->mat`` Defined in line number 577. | | .. _coroots_rootdatum_rd->mat1: coroots ------------------------------------------------- | ``coroots:RootDatum rd->mat`` Defined in line number 579. | | .. _root_rootdatum_rd,_vec_alpha_v->vec1: root ------------------------------------------------- | ``root:RootDatum rd, vec alpha_v->vec`` Defined in line number 583. | | .. _coroot_rootdatum_rd,_vec_alpha->vec1: coroot ------------------------------------------------- | ``coroot:RootDatum rd, vec alpha->vec`` Defined in line number 584. | | .. _reflection_rootdatum_rd,_int_i->mat1: reflection ------------------------------------------------- | ``reflection:RootDatum rd, int i->mat`` Defined in line number 587. | | .. _reflection_(rootdatum,vec)(rd,):p->mat1: reflection ------------------------------------------------- | ``reflection:(RootDatum,vec)(rd,):p->mat`` Defined in line number 589. | | .. _coreflection_rootdatum_rd,_int_i->mat1: coreflection ------------------------------------------------- | ``coreflection:RootDatum rd, int i->mat`` Defined in line number 591. | | .. _coreflection_(rootdatum,vec)(rd,):p->mat1: coreflection ------------------------------------------------- | ``coreflection:(RootDatum,vec)(rd,):p->mat`` Defined in line number 593. | | .. _reflect_rootdatum_rd,_int_i,_vec_v->vec1: reflect ------------------------------------------------- | ``reflect:RootDatum rd, int i, vec v->vec`` Defined in line number 595. | | .. _reflect_rootdatum_rd,_vec_alpha,_vec_v->vec1: reflect ------------------------------------------------- | ``reflect:RootDatum rd, vec alpha, vec v->vec`` Defined in line number 597. | | .. _coreflect_rootdatum_rd,_vec_v,_int_i->vec1: coreflect ------------------------------------------------- | ``coreflect:RootDatum rd, vec v, int i->vec`` Defined in line number 599. | | .. _coreflect_rootdatum_rd,_vec_v,_vec_alpha->vec1: coreflect ------------------------------------------------- | ``coreflect:RootDatum rd, vec v, vec alpha->vec`` Defined in line number 601. | | .. _reflect_rootdatum_rd,_int_i,_ratvec_v->ratvec1: reflect ------------------------------------------------- | ``reflect:RootDatum rd, int i, ratvec v->ratvec`` Defined in line number 604. | | .. _reflect_rootdatum_rd,_vec_alpha,_ratvec_v->ratvec1: reflect ------------------------------------------------- | ``reflect:RootDatum rd, vec alpha, ratvec v->ratvec`` Defined in line number 606. | | .. _coreflect_rootdatum_rd,_ratvec_v,_int_i->ratvec1: coreflect ------------------------------------------------- | ``coreflect:RootDatum rd, ratvec v, int i->ratvec`` Defined in line number 608. | | .. _coreflect_rootdatum_rd,_ratvec_v,_vec_alpha->ratvec1: coreflect ------------------------------------------------- | ``coreflect:RootDatum rd, ratvec v, vec alpha->ratvec`` Defined in line number 610. | | .. _left_reflect_rootdatum_rd,_int_i,_mat_m->mat1: left_reflect ------------------------------------------------- | ``left_reflect:RootDatum rd, int i, mat M->mat`` Defined in line number 614. | | .. _left_reflect_rootdatum_rd,_vec_alpha,_mat_m->mat1: left_reflect ------------------------------------------------- | ``left_reflect:RootDatum rd, vec alpha, mat M->mat`` Defined in line number 616. | | .. _right_reflect_rootdatum_rd,_mat_m,_int_i->mat1: right_reflect ------------------------------------------------- | ``right_reflect:RootDatum rd, mat M, int i->mat`` Defined in line number 618. | | .. _right_reflect_rootdatum_rd,_mat_m,_vec_alpha->mat1: right_reflect ------------------------------------------------- | ``right_reflect:RootDatum rd, mat M, vec alpha->mat`` Defined in line number 620. | | .. _conjugate_rootdatum_rd,_int_i,_mat_m->mat1: conjugate ------------------------------------------------- | ``conjugate:RootDatum rd, int i, mat M->mat`` Defined in line number 623. | | .. _conjugate_rootdatum_rd,_vec_alpha,_mat_m->mat1: conjugate ------------------------------------------------- | ``conjugate:RootDatum rd, vec alpha, mat M->mat`` Defined in line number 625. | | .. _singular_simple_indices_rootdatum_rd,ratvec_v->[int]1: singular_simple_indices ------------------------------------------------- | ``singular_simple_indices:RootDatum rd,ratvec v->[int]`` Defined in line number 629. | | .. _is_imaginary_mat_theta->(vec->bool):_(vec_alpha)1: is_imaginary ------------------------------------------------- | ``is_imaginary:mat theta->(vec->bool): (vec alpha)`` Defined in line number 633. | | .. _is_real_mat_theta->(vec->bool):_(vec_alpha)1: is_real ------------------------------------------------- | ``is_real:mat theta->(vec->bool): (vec alpha)`` Defined in line number 634. | | .. _is_complex_mat_theta->(vec->bool):_(vec_alpha)1: is_complex ------------------------------------------------- | ``is_complex:mat theta->(vec->bool): (vec alpha)`` Defined in line number 635. | | .. _imaginary_roots_rootdatum_rd,_mat_theta->mat1: imaginary_roots ------------------------------------------------- | ``imaginary_roots:RootDatum rd, mat theta->mat`` Defined in line number 639. | | .. _real_roots_rootdatum_rd,_mat_theta->mat1: real_roots ------------------------------------------------- | ``real_roots:RootDatum rd, mat theta->mat`` Defined in line number 641. | | .. _imaginary_coroots_rootdatum_rd,_mat_theta->mat1: imaginary_coroots ------------------------------------------------- | ``imaginary_coroots:RootDatum rd, mat theta->mat`` Defined in line number 645. | | .. _real_coroots_rootdatum_rd,_mat_theta->mat1: real_coroots ------------------------------------------------- | ``real_coroots:RootDatum rd, mat theta->mat`` Defined in line number 647. | | .. _imaginary_posroots_rootdatum_rd,mat_theta->mat1: imaginary_posroots ------------------------------------------------- | ``imaginary_posroots:RootDatum rd,mat theta->mat`` Defined in line number 651. | | .. _real_posroots_rootdatum_rd,mat_theta->mat1: real_posroots ------------------------------------------------- | ``real_posroots:RootDatum rd,mat theta->mat`` Defined in line number 653. | | .. _imaginary_poscoroots_rootdatum_rd,mat_theta->mat1: imaginary_poscoroots ------------------------------------------------- | ``imaginary_poscoroots:RootDatum rd,mat theta->mat`` Defined in line number 655. | | .. _real_poscoroots_rootdatum_rd,mat_theta->mat1: real_poscoroots ------------------------------------------------- | ``real_poscoroots:RootDatum rd,mat theta->mat`` Defined in line number 657. | | .. _imaginary_sys_(rootdatum,mat)p->(mat,mat)1: imaginary_sys ------------------------------------------------- | ``imaginary_sys:(RootDatum,mat)p->(mat,mat)`` Defined in line number 659. | | .. _real_sys_(rootdatum,mat)p->(mat,mat)1: real_sys ------------------------------------------------- | ``real_sys:(RootDatum,mat)p->(mat,mat)`` Defined in line number 661. | | .. _is_dominant_rootdatum_rd,_ratvec_v->bool1: is_dominant ------------------------------------------------- | ``is_dominant:RootDatum rd, ratvec v->bool`` Defined in line number 665. | | .. _is_strictly_dominant_rootdatum_rd,_ratvec_v->bool1: is_strictly_dominant ------------------------------------------------- | ``is_strictly_dominant:RootDatum rd, ratvec v->bool`` Defined in line number 667. | | .. _is_regular_rootdatum_rd,ratvec_v->bool1: is_regular ------------------------------------------------- | ``is_regular:RootDatum rd,ratvec v->bool`` Defined in line number 669. | | .. _is_integral_rootdatum_rd,_ratvec_v->bool1: is_integral ------------------------------------------------- | ``is_integral:RootDatum rd, ratvec v->bool`` Defined in line number 671. | | .. _radical_basis_rootdatum_rd->mat1: radical_basis ------------------------------------------------- | ``radical_basis:RootDatum rd->mat`` Defined in line number 675. | | .. _coradical_basis_rootdatum_rd->mat1: coradical_basis ------------------------------------------------- | ``coradical_basis:RootDatum rd->mat`` Defined in line number 677. | | .. _is_semisimple_rootdatum_rd->bool1: is_semisimple ------------------------------------------------- | ``is_semisimple:RootDatum rd->bool`` Defined in line number 680. | | .. _derived_is_simply_connected_rootdatum_rd->bool1: derived_is_simply_connected ------------------------------------------------- | ``derived_is_simply_connected:RootDatum rd->bool`` Defined in line number 682. | | .. _has_connected_center_rootdatum_rd->bool1: has_connected_center ------------------------------------------------- | ``has_connected_center:RootDatum rd->bool`` Defined in line number 684. | | .. _is_simply_connected_rootdatum_rd->bool1: is_simply_connected ------------------------------------------------- | ``is_simply_connected:RootDatum rd->bool`` Defined in line number 686. | | .. _is_adjoint_rootdatum_rd->bool1: is_adjoint ------------------------------------------------- | ``is_adjoint:RootDatum rd->bool`` Defined in line number 688. | | .. _derived_rootdatum_rd->rootdatum1: derived ------------------------------------------------- | ``derived:RootDatum rd->RootDatum`` Defined in line number 694. | | .. _mod_central_torus_rootdatum_rd->rootdatum1: mod_central_torus ------------------------------------------------- | ``mod_central_torus:RootDatum rd->RootDatum`` Defined in line number 695. | | .. _adjoint_rootdatum_rd->rootdatum1: adjoint ------------------------------------------------- | ``adjoint:RootDatum rd->RootDatum`` Defined in line number 697. | | .. _is_simple_for_vec_dual_two_rho->(vec->bool)1: is_simple_for ------------------------------------------------- | ``is_simple_for:vec dual_two_rho->(vec->bool)`` Defined in line number 701. | | .. _simple_from_positive_mat_posroots,mat_poscoroots->(mat,mat)1: simple_from_positive ------------------------------------------------- | ``simple_from_positive:mat posroots,mat poscoroots->(mat,mat)`` Defined in line number 705. | | .. _fundamental_weights_rootdatum_rd->[ratvec]1: fundamental_weights ------------------------------------------------- | ``fundamental_weights:RootDatum rd->[ratvec]`` Defined in line number 710. | | .. _fundamental_coweights_rootdatum_rd->[ratvec]1: fundamental_coweights ------------------------------------------------- | ``fundamental_coweights:RootDatum rd->[ratvec]`` Defined in line number 712. | | .. _dual_integral_innerclass_ic,_ratvec_gamma->innerclass1: dual_integral ------------------------------------------------- | ``dual_integral:InnerClass ic, ratvec gamma->InnerClass`` Defined in line number 720. | | .. _cartan_classes_innerclass_ic->[cartanclass]1: Cartan_classes ------------------------------------------------- | ``Cartan_classes:InnerClass ic->[CartanClass]`` Defined in line number 726. | | .. _print_cartan_info_cartanclass_cc->void1: print_Cartan_info ------------------------------------------------- | ``print_Cartan_info:CartanClass cc->void`` Defined in line number 729. | | .. _fundamental_cartan_innerclass_ic->cartanclass1: fundamental_Cartan ------------------------------------------------- | ``fundamental_Cartan:InnerClass ic->CartanClass`` Defined in line number 749. | | .. _most_split_cartan_innerclass_ic->cartanclass1: most_split_Cartan ------------------------------------------------- | ``most_split_Cartan:InnerClass ic->CartanClass`` Defined in line number 751. | | .. _compact_rank_cartanclass_cc->int1: compact_rank ------------------------------------------------- | ``compact_rank:CartanClass cc->int`` Defined in line number 756. | | .. _split_rank_cartanclass_cc->int1: split_rank ------------------------------------------------- | ``split_rank:CartanClass cc->int`` Defined in line number 758. | | .. _compact_rank_innerclass_ic->int1: compact_rank ------------------------------------------------- | ``compact_rank:InnerClass ic->int`` Defined in line number 761. | | .. _split_rank_realform_g->int1: split_rank ------------------------------------------------- | ``split_rank:RealForm G->int`` Defined in line number 762. | | .. _is_equal_rank_innerclass_ic->bool1: is_equal_rank ------------------------------------------------- | ``is_equal_rank:InnerClass ic->bool`` Defined in line number 764. | | .. _is_split_realform_g->bool1: is_split ------------------------------------------------- | ``is_split:RealForm G->bool`` Defined in line number 768. | | .. _\=_CartanClass_H,CartanClass_J->bool1: \= ------------------------------------------------- | ``=:CartanClass H,CartanClass J->bool`` Defined in line number 772. | | .. _number_cartanclass_h,realform_g->int1: number ------------------------------------------------- | ``number:CartanClass H,RealForm G->int`` Defined in line number 777. | | .. _form_name_realform_f->string1: form_name ------------------------------------------------- | ``form_name:RealForm f->string`` Defined in line number 782. | | .. _real_forms_innerclass_ic->[realform]1: real_forms ------------------------------------------------- | ``real_forms:InnerClass ic->[RealForm]`` Defined in line number 784. | | .. _dual_real_forms_innerclass_ic->[realform]1: dual_real_forms ------------------------------------------------- | ``dual_real_forms:InnerClass ic->[RealForm]`` Defined in line number 786. | | .. _is_quasisplit_realform_g->bool1: is_quasisplit ------------------------------------------------- | ``is_quasisplit:RealForm G->bool`` Defined in line number 789. | | .. _is_quasicompact_realform_g->bool1: is_quasicompact ------------------------------------------------- | ``is_quasicompact:RealForm G->bool`` Defined in line number 790. | | .. _split_form_rootdatum_r->realform1: split_form ------------------------------------------------- | ``split_form:RootDatum r->RealForm`` Defined in line number 792. | | .. _split_form_lietype_t->realform1: split_form ------------------------------------------------- | ``split_form:LieType t->RealForm`` Defined in line number 796. | | .. _quasicompact_form_innerclass_ic->realform1: quasicompact_form ------------------------------------------------- | ``quasicompact_form:InnerClass ic->RealForm`` Defined in line number 798. | | .. _is_compatible_realform_f,_realform_g->bool1: is_compatible ------------------------------------------------- | ``is_compatible:RealForm f, RealForm g->bool`` Defined in line number 801. | | .. _is_compact_realform_g->bool1: is_compact ------------------------------------------------- | ``is_compact:RealForm G->bool`` Defined in line number 806. | | .. _root_datum_kgbelt_x->rootdatum1: root_datum ------------------------------------------------- | ``root_datum:KGBElt x->RootDatum`` Defined in line number 815. | | .. _inner_class_kgbelt_x->innerclass1: inner_class ------------------------------------------------- | ``inner_class:KGBElt x->InnerClass`` Defined in line number 816. | | .. _kgb_realform_rf->[kgbelt]:_for_i1: KGB ------------------------------------------------- | ``KGB:RealForm rf->[KGBElt]: for i`` Defined in line number 818. | | .. _kgb_cartanclass_h,realform_g->[kgbelt]1: KGB ------------------------------------------------- | ``KGB:CartanClass H,RealForm G->[KGBElt]`` Defined in line number 821. | | .. _kgb_elt_(innerclass,_mat,_ratvec)_(,theta,v):all->kgbelt1: KGB_elt ------------------------------------------------- | ``KGB_elt:(InnerClass, mat, ratvec) (,theta,v):all->KGBElt`` Defined in line number 824. | | .. _kgb_elt_rootdatum_rd,_mat_theta,_ratvec_v->kgbelt1: KGB_elt ------------------------------------------------- | ``KGB_elt:RootDatum rd, mat theta, ratvec v->KGBElt`` Defined in line number 829. | | .. _cartan_class_innerclass_ic,_mat_theta->cartanclass1: Cartan_class ------------------------------------------------- | ``Cartan_class:InnerClass ic, mat theta->CartanClass`` Defined in line number 834. | | .. _bruhat_order_realform_g->(kgbelt,kgbelt->bool)1: Bruhat_order ------------------------------------------------- | ``Bruhat_order:RealForm G->(KGBElt,KGBElt->bool)`` Defined in line number 838. | | .. _status_vec_alpha,kgbelt_x->int1: status ------------------------------------------------- | ``status:vec alpha,KGBElt x->int`` Defined in line number 841. | | .. _cross_vec_alpha,kgbelt_x->kgbelt1: cross ------------------------------------------------- | ``cross:vec alpha,KGBElt x->KGBElt`` Defined in line number 843. | | .. _cayley_vec_alpha,kgbelt_x->kgbelt1: Cayley ------------------------------------------------- | ``Cayley:vec alpha,KGBElt x->KGBElt`` Defined in line number 845. | | .. _w_cross_[int]_w,kgbelt_x->kgbelt1: W_cross ------------------------------------------------- | ``W_cross:[int] w,KGBElt x->KGBElt`` Defined in line number 849. | | .. _kgb_status_text_int_i->string1: KGB_status_text ------------------------------------------------- | ``KGB_status_text:int i->string`` Defined in line number 852. | | .. _status_text_(int,kgbelt)p->string1: status_text ------------------------------------------------- | ``status_text:(int,KGBElt)p->string`` Defined in line number 854. | | .. _status_text_(vec,kgbelt)p->string1: status_text ------------------------------------------------- | ``status_text:(vec,KGBElt)p->string`` Defined in line number 855. | | .. _status_texts_kgbelt_x->[string]1: status_texts ------------------------------------------------- | ``status_texts:KGBElt x->[string]`` Defined in line number 856. | | .. _is_imaginary_kgbelt_x->(vec->bool)1: is_imaginary ------------------------------------------------- | ``is_imaginary:KGBElt x->(vec->bool)`` Defined in line number 870. | | .. _is_real_kgbelt_x->(vec->bool)1: is_real ------------------------------------------------- | ``is_real:KGBElt x->(vec->bool)`` Defined in line number 871. | | .. _is_complex_kgbelt_x->(vec->bool)1: is_complex ------------------------------------------------- | ``is_complex:KGBElt x->(vec->bool)`` Defined in line number 872. | | .. _imaginary_posroots_kgbelt_x->mat1: imaginary_posroots ------------------------------------------------- | ``imaginary_posroots:KGBElt x->mat`` Defined in line number 875. | | .. _real_posroots_kgbelt_x->mat1: real_posroots ------------------------------------------------- | ``real_posroots:KGBElt x->mat`` Defined in line number 877. | | .. _imaginary_poscoroots_kgbelt_x->mat1: imaginary_poscoroots ------------------------------------------------- | ``imaginary_poscoroots:KGBElt x->mat`` Defined in line number 879. | | .. _real_poscoroots_kgbelt_x->mat1: real_poscoroots ------------------------------------------------- | ``real_poscoroots:KGBElt x->mat`` Defined in line number 881. | | .. _imaginary_sys_kgbelt_x->(mat,mat)1: imaginary_sys ------------------------------------------------- | ``imaginary_sys:KGBElt x->(mat,mat)`` Defined in line number 883. | | .. _real_sys_kgbelt_x->(mat,mat)1: real_sys ------------------------------------------------- | ``real_sys:KGBElt x->(mat,mat)`` Defined in line number 886. | | .. _rho_i_kgbelt_x->ratvec1: rho_i ------------------------------------------------- | ``rho_i:KGBElt x->ratvec`` Defined in line number 890. | | .. _rho_r_kgbelt_x->ratvec1: rho_r ------------------------------------------------- | ``rho_r:KGBElt x->ratvec`` Defined in line number 891. | | .. _rho_check_i_kgbelt_x->ratvec1: rho_check_i ------------------------------------------------- | ``rho_check_i:KGBElt x->ratvec`` Defined in line number 892. | | .. _rho_check_r_kgbelt_x->ratvec1: rho_check_r ------------------------------------------------- | ``rho_check_r:KGBElt x->ratvec`` Defined in line number 893. | | .. _rho_i_(rootdatum,mat)_rd_theta->ratvec1: rho_i ------------------------------------------------- | ``rho_i:(RootDatum,mat) rd_theta->ratvec`` Defined in line number 895. | | .. _rho_r_(rootdatum,mat)_rd_theta->ratvec1: rho_r ------------------------------------------------- | ``rho_r:(RootDatum,mat) rd_theta->ratvec`` Defined in line number 897. | | .. _rho_check_i_(rootdatum,mat)_rd_theta->ratvec1: rho_check_i ------------------------------------------------- | ``rho_check_i:(RootDatum,mat) rd_theta->ratvec`` Defined in line number 899. | | .. _rho_check_r_(rootdatum,mat)_rd_theta->ratvec1: rho_check_r ------------------------------------------------- | ``rho_check_r:(RootDatum,mat) rd_theta->ratvec`` Defined in line number 901. | | .. _is_compact_kgbelt_x->(vec->bool)1: is_compact ------------------------------------------------- | ``is_compact:KGBElt x->(vec->bool)`` Defined in line number 905. | | .. _is_noncompact_kgbelt_x->(vec->bool)1: is_noncompact ------------------------------------------------- | ``is_noncompact:KGBElt x->(vec->bool)`` Defined in line number 908. | | .. _is_compact_imaginary_kgbelt_x->(vec->bool)1: is_compact_imaginary ------------------------------------------------- | ``is_compact_imaginary:KGBElt x->(vec->bool)`` Defined in line number 913. | | .. _is_noncompact_imaginary_kgbelt_x->(vec->bool)1: is_noncompact_imaginary ------------------------------------------------- | ``is_noncompact_imaginary:KGBElt x->(vec->bool)`` Defined in line number 916. | | .. _compact_posroots_kgbelt_x->mat1: compact_posroots ------------------------------------------------- | ``compact_posroots:KGBElt x->mat`` Defined in line number 920. | | .. _noncompact_posroots_kgbelt_x->mat1: noncompact_posroots ------------------------------------------------- | ``noncompact_posroots:KGBElt x->mat`` Defined in line number 922. | | .. _rho_ci_kgbelt_x->ratvec1: rho_ci ------------------------------------------------- | ``rho_ci:KGBElt x->ratvec`` Defined in line number 925. | | .. _rho_nci_kgbelt_x->ratvec1: rho_nci ------------------------------------------------- | ``rho_nci:KGBElt x->ratvec`` Defined in line number 926. | | .. _is_imaginary_vec_v,kgbelt_x->bool1: is_imaginary ------------------------------------------------- | ``is_imaginary:vec v,KGBElt x->bool`` Defined in line number 928. | | .. _is_real_vec_v,kgbelt_x->bool1: is_real ------------------------------------------------- | ``is_real:vec v,KGBElt x->bool`` Defined in line number 929. | | .. _is_complex_vec_v,kgbelt_x->bool1: is_complex ------------------------------------------------- | ``is_complex:vec v,KGBElt x->bool`` Defined in line number 930. | | .. _is_compact_imaginary_vec_v,kgbelt_x->bool1: is_compact_imaginary ------------------------------------------------- | ``is_compact_imaginary:vec v,KGBElt x->bool`` Defined in line number 931. | | .. _is_noncompact_imaginary_vec_v,kgbelt_x->bool1: is_noncompact_imaginary ------------------------------------------------- | ``is_noncompact_imaginary:vec v,KGBElt x->bool`` Defined in line number 932. | | .. _print_kgb_kgbelt_x->void1: print_KGB ------------------------------------------------- | ``print_KGB:KGBElt x->void`` Defined in line number 935. | | .. _no_cminus_roots_kgbelt_x->bool1: no_Cminus_roots ------------------------------------------------- | ``no_Cminus_roots:KGBElt x->bool`` Defined in line number 939. | | .. _no_cplus_roots_kgbelt_x->bool1: no_Cplus_roots ------------------------------------------------- | ``no_Cplus_roots:KGBElt x->bool`` Defined in line number 941. | | .. _blocks_innerclass_ic->[block]1: blocks ------------------------------------------------- | ``blocks:InnerClass ic->[Block]`` Defined in line number 946. | | .. _raw_kl_(realform,realform)_p->(mat,[vec],vec)1: raw_KL ------------------------------------------------- | ``raw_KL:(RealForm,RealForm) p->(mat,[vec],vec)`` Defined in line number 954. | | .. _dual_kl_(realform,realform)_p->(mat,[vec],vec)1: dual_KL ------------------------------------------------- | ``dual_KL:(RealForm,RealForm) p->(mat,[vec],vec)`` Defined in line number 955. | | .. _print_block_(realform,realform)_p->void1: print_block ------------------------------------------------- | ``print_block:(RealForm,RealForm) p->void`` Defined in line number 957. | | .. _print_blocku_(realform,realform)_p->void1: print_blocku ------------------------------------------------- | ``print_blocku:(RealForm,RealForm) p->void`` Defined in line number 958. | | .. _print_blockd_(realform,realform)_p->void1: print_blockd ------------------------------------------------- | ``print_blockd:(RealForm,RealForm) p->void`` Defined in line number 959. | | .. _print_kl_basis_(realform,realform)_p->void1: print_KL_basis ------------------------------------------------- | ``print_KL_basis:(RealForm,RealForm) p->void`` Defined in line number 960. | | .. _print_prim_kl_(realform,realform)_p->void1: print_prim_KL ------------------------------------------------- | ``print_prim_KL:(RealForm,RealForm) p->void`` Defined in line number 961. | | .. _print_kl_list_(realform,realform)_p->void1: print_KL_list ------------------------------------------------- | ``print_KL_list:(RealForm,RealForm) p->void`` Defined in line number 962. | | .. _print_w_cells_(realform,realform)_p->void1: print_W_cells ------------------------------------------------- | ``print_W_cells:(RealForm,RealForm) p->void`` Defined in line number 963. | | .. _print_w_graph_(realform,realform)_p->void1: print_W_graph ------------------------------------------------- | ``print_W_graph:(RealForm,RealForm) p->void`` Defined in line number 964. | | .. _root_datum_param_p->rootdatum1: root_datum ------------------------------------------------- | ``root_datum:Param p->RootDatum`` Defined in line number 969. | | .. _inner_class_param_p->innerclass1: inner_class ------------------------------------------------- | ``inner_class:Param p->InnerClass`` Defined in line number 970. | | .. _null_module_param_p->parampol1: null_module ------------------------------------------------- | ``null_module:Param p->ParamPol`` Defined in line number 972. | | .. _x_param_p->kgbelt1: x ------------------------------------------------- | ``x:Param p->KGBElt`` Defined in line number 975. | | .. _lambda_minus_rho_param_p->vec1: lambda_minus_rho ------------------------------------------------- | ``lambda_minus_rho:Param p->vec`` Defined in line number 976. | | .. _lambda_param_p->ratvec1: lambda ------------------------------------------------- | ``lambda:Param p->ratvec`` Defined in line number 977. | | .. _infinitesimal_character_param_p->ratvec1: infinitesimal_character ------------------------------------------------- | ``infinitesimal_character:Param p->ratvec`` Defined in line number 978. | | .. _nu_param_p->ratvec1: nu ------------------------------------------------- | ``nu:Param p->ratvec`` Defined in line number 979. | | .. _cartan_class_param_p->cartanclass1: Cartan_class ------------------------------------------------- | ``Cartan_class:Param p->CartanClass`` Defined in line number 980. | | .. _integrality_datum_param_p->rootdatum1: integrality_datum ------------------------------------------------- | ``integrality_datum:Param p->RootDatum`` Defined in line number 984. | | .. _is_regular_param_p->bool1: is_regular ------------------------------------------------- | ``is_regular:Param p->bool`` Defined in line number 987. | | .. _survives_param_p->bool1: survives ------------------------------------------------- | ``survives:Param p->bool`` Defined in line number 991. | | .. _trivial_realform_g->param1: trivial ------------------------------------------------- | ``trivial:RealForm G->Param`` Defined in line number 994. | | .. _w_cross_[int]_w,param_p->param1: W_cross ------------------------------------------------- | ``W_cross:[int] w,Param p->Param`` Defined in line number 998. | | .. _parameter_realform_g,int_x,ratvec_lambda,ratvec_nu->param1: parameter ------------------------------------------------- | ``parameter:RealForm G,int x,ratvec lambda,ratvec nu->Param`` Defined in line number 1004. | | .. _parameter_kgbelt_x,ratvec_lambda,ratvec_nu->param1: parameter ------------------------------------------------- | ``parameter:KGBElt x,ratvec lambda,ratvec nu->Param`` Defined in line number 1006. | | .. _parameter_gamma_kgbelt_x,_ratvec_lambda,_ratvec_gamma->param1: parameter_gamma ------------------------------------------------- | ``parameter_gamma:KGBElt x, ratvec lambda, ratvec gamma->Param`` Defined in line number 1010. | | .. _singular_block_param_p->([param],int)1: singular_block ------------------------------------------------- | ``singular_block:Param p->([Param],int)`` Defined in line number 1016. | | .. _block_of_param_p->[param]1: block_of ------------------------------------------------- | ``block_of:Param p->[Param]`` Defined in line number 1022. | | .. _singular_block_of_param_p->[param]1: singular_block_of ------------------------------------------------- | ``singular_block_of:Param p->[Param]`` Defined in line number 1023. | | .. _imaginary_type_int_s,_param_p->int1: imaginary_type ------------------------------------------------- | ``imaginary_type:int s, Param p->int`` Defined in line number 1028. | | .. _real_type_int_s,param_p->int1: real_type ------------------------------------------------- | ``real_type:int s,Param p->int`` Defined in line number 1029. | | .. _imaginary_type_vec_alpha,_param_p->int1: imaginary_type ------------------------------------------------- | ``imaginary_type:vec alpha, Param p->int`` Defined in line number 1031. | | .. _real_type_vec_alpha,_param_p->int1: real_type ------------------------------------------------- | ``real_type:vec alpha, Param p->int`` Defined in line number 1033. | | .. _is_nonparity_int_s,param_p->bool1: is_nonparity ------------------------------------------------- | ``is_nonparity:int s,Param p->bool`` Defined in line number 1036. | | .. _is_parity_int_s,param_p->bool1: is_parity ------------------------------------------------- | ``is_parity:int s,Param p->bool`` Defined in line number 1037. | | .. _is_nonparity_vec_alpha,param_p->bool1: is_nonparity ------------------------------------------------- | ``is_nonparity:vec alpha,Param p->bool`` Defined in line number 1039. | | .. _is_parity_vec_alpha,param_p->bool1: is_parity ------------------------------------------------- | ``is_parity:vec alpha,Param p->bool`` Defined in line number 1041. | | .. _status_vec_alpha,param_p->int1: status ------------------------------------------------- | ``status:vec alpha,Param p->int`` Defined in line number 1044. | | .. _status_int_s,param_p->int1: status ------------------------------------------------- | ``status:int s,Param p->int`` Defined in line number 1052. | | .. _block_status_text_int_i->string1: block_status_text ------------------------------------------------- | ``block_status_text:int i->string`` Defined in line number 1055. | | .. _status_text_int_s,param_p->string1: status_text ------------------------------------------------- | ``status_text:int s,Param p->string`` Defined in line number 1058. | | .. _status_texts_param_p->[string]1: status_texts ------------------------------------------------- | ``status_texts:Param p->[string]`` Defined in line number 1059. | | .. _status_text_(vec,param)_ap->string1: status_text ------------------------------------------------- | ``status_text:(vec,Param) ap->string`` Defined in line number 1062. | | .. _parity_poscoroots_param_p->mat1: parity_poscoroots ------------------------------------------------- | ``parity_poscoroots:Param p->mat`` Defined in line number 1064. | | .. _nonparity_poscoroots_param_p->mat1: nonparity_poscoroots ------------------------------------------------- | ``nonparity_poscoroots:Param p->mat`` Defined in line number 1067. | | .. _is_descent_int_s,param_p->bool1: is_descent ------------------------------------------------- | ``is_descent:int s,Param p->bool`` Defined in line number 1071. | | .. _tau_bitset_param_p->((int->bool),int)1: tau_bitset ------------------------------------------------- | ``tau_bitset:Param p->((int->bool),int)`` Defined in line number 1072. | | .. _tau_param_p->[int]1: tau ------------------------------------------------- | ``tau:Param p->[int]`` Defined in line number 1075. | | .. _tau_complement_param_p->[int]1: tau_complement ------------------------------------------------- | ``tau_complement:Param p->[int]`` Defined in line number 1076. | | .. _is_descent_(vec,param)_ap->bool1: is_descent ------------------------------------------------- | ``is_descent:(vec,Param) ap->bool`` Defined in line number 1078. | | .. _lookup_param_p,_[param]_block->int1: lookup ------------------------------------------------- | ``lookup:Param p, [Param] block->int`` Defined in line number 1080. | | .. _null_module_parampol_p->parampol1: null_module ------------------------------------------------- | ``null_module:ParamPol P->ParamPol`` Defined in line number 1152. | | .. _\-_ParamPol_P->ParamPol1: \- ------------------------------------------------- | ``-:ParamPol P->ParamPol`` Defined in line number 1153. | | .. _first_param_parampol_p->param1: first_param ------------------------------------------------- | ``first_param:ParamPol P->Param`` Defined in line number 1155. | | .. _last_param_parampol_p->param1: last_param ------------------------------------------------- | ``last_param:ParamPol P->Param`` Defined in line number 1156. | | .. _s_to_1_parampol_p->parampol1: s_to_1 ------------------------------------------------- | ``s_to_1:ParamPol P->ParamPol`` Defined in line number 1158. | | .. _s_to_minus_1_parampol_p->parampol1: s_to_minus_1 ------------------------------------------------- | ``s_to_minus_1:ParamPol P->ParamPol`` Defined in line number 1159. | | .. _\-_ParamPol_a,_(Split,Param)_(c,p)->ParamPol1: \- ------------------------------------------------- | ``-:ParamPol a, (Split,Param) (c,p)->ParamPol`` Defined in line number 1162. | | .. _sum_realform_g,[parampol]_ps->parampol1: sum ------------------------------------------------- | ``sum:RealForm G,[ParamPol] Ps->ParamPol`` Defined in line number 1164. | | .. _map_(param->param)f,_parampol_p->parampol1: map ------------------------------------------------- | ``map:(Param->Param)f, ParamPol P->ParamPol`` Defined in line number 1173. | | .. _map_(param->parampol)f,_parampol_p->parampol1: map ------------------------------------------------- | ``map:(Param->ParamPol)f, ParamPol P->ParamPol`` Defined in line number 1176. | | .. _half_parampol_p->parampol1: half ------------------------------------------------- | ``half:ParamPol P->ParamPol`` Defined in line number 1179. | | .. _divide_by_int_n,_parampol_p->parampol1: divide_by ------------------------------------------------- | ``divide_by:int n, ParamPol P->ParamPol`` Defined in line number 1181. | | .. _root_datum_parampol_p->rootdatum1: root_datum ------------------------------------------------- | ``root_datum:ParamPol P->RootDatum`` Defined in line number 1184. | | .. _virtual_param_p->parampol1: virtual ------------------------------------------------- | ``virtual:Param p->ParamPol`` Defined in line number 1186. | | .. _virtual_realform_g,_[param]_ps->parampol1: virtual ------------------------------------------------- | ``virtual:RealForm G, [Param] ps->ParamPol`` Defined in line number 1187. | | .. _branch_param_std,_param_k_type->int1: branch ------------------------------------------------- | ``branch:Param std, Param K_type->int`` Defined in line number 1192. | | .. _branch_parampol_p,_param_k_type->split1: branch ------------------------------------------------- | ``branch:ParamPol P, Param K_type->Split`` Defined in line number 1195. | | .. _pol_format_parampol_p->string1: pol_format ------------------------------------------------- | ``pol_format:ParamPol P->string`` Defined in line number 1199. | | .. _infinitesimal_character_parampol_p->ratvec1: infinitesimal_character ------------------------------------------------- | ``infinitesimal_character:ParamPol P->ratvec`` Defined in line number 1203. | | .. _height_split_parampol_p,_int_h->(parampol,parampol)1: height_split ------------------------------------------------- | ``height_split:ParamPol P, int h->(ParamPol,ParamPol)`` Defined in line number 1212. | | .. _separate_by_infinitesimal_character_parampol_p->[(ratvec,parampol)]1: separate_by_infinitesimal_character ------------------------------------------------- | ``separate_by_infinitesimal_character:ParamPol P->[(ratvec,ParamPol)]`` Defined in line number 1219. | | .. _is_pure_1_parampol_p->bool1: is_pure_1 ------------------------------------------------- | ``is_pure_1:ParamPol P->bool`` Defined in line number 1230. | | .. _is_pure_s_parampol_p->bool1: is_pure_s ------------------------------------------------- | ``is_pure_s:ParamPol P->bool`` Defined in line number 1231. | | .. _is_pure_parampol_p->bool1: is_pure ------------------------------------------------- | ``is_pure:ParamPol P->bool`` Defined in line number 1235. | | .. _purity_parampol_p->(int,int,int)1: purity ------------------------------------------------- | ``purity:ParamPol P->(int,int,int)`` Defined in line number 1238. | | .. _find_[int]_v,_int_k->int:______first(#v,(int_i)bool1: find ------------------------------------------------- | ``find:[int] v, int k->int: first(#v,(int i)bool`` Defined in line number 1251. | | .. _find_[param]_p,param_p->int:___first(#p,(int_i)bool1: find ------------------------------------------------- | ``find:[Param] P,Param p->int: first(#P,(int i)bool`` Defined in line number 1252. | | .. _find_[kgbelt]_s,kgbelt_x->int:_first(#s,(int_i)bool1: find ------------------------------------------------- | ``find:[KGBElt] S,KGBElt x->int: first(#S,(int i)bool`` Defined in line number 1253. | | .. _find_[vec]_s,vec_v->int:_______first(#s,(int_i)bool1: find ------------------------------------------------- | ``find:[vec] S,vec v->int: first(#S,(int i)bool`` Defined in line number 1254. | | .. _in_string_list_string_s,[string]_s->bool1: in_string_list ------------------------------------------------- | ``in_string_list:string s,[string] S->bool`` Defined in line number 1261. | | .. _delete_[int]_v,_int_k->[int]:_____v[:k]##v[k+11: delete ------------------------------------------------- | ``delete:[int] v, int k->[int]: v[:k]##v[k+1`` Defined in line number 1265. | | .. _delete_[vec]_v,_int_k->[vec]:_____v[:k]##v[k+11: delete ------------------------------------------------- | ``delete:[vec] v, int k->[vec]: v[:k]##v[k+1`` Defined in line number 1266. | | .. _delete_[ratvec]_v,_int_k->[ratvec]:__v[:k]##v[k+11: delete ------------------------------------------------- | ``delete:[ratvec] v, int k->[ratvec]: v[:k]##v[k+1`` Defined in line number 1267. | | .. _delete_[[ratvec]]_v,_int_k->[[ratvec]]:v[:k]##v[k+11: delete ------------------------------------------------- | ``delete:[[ratvec]] v, int k->[[ratvec]]:v[:k]##v[k+1`` Defined in line number 1268. | | .. _delete_[[vec]]_v,_int_k->[[vec]]:___v[:k]##v[k+11: delete ------------------------------------------------- | ``delete:[[vec]] v, int k->[[vec]]: v[:k]##v[k+1`` Defined in line number 1269. | | .. _delete_[parampol]_p,_int_k->[parampol]:p[:k]##p[k+11: delete ------------------------------------------------- | ``delete:[ParamPol] P, int k->[ParamPol]:P[:k]##P[k+1`` Defined in line number 1270. | | .. _imaginary_roots_and_coroots_(rootdatum,_mat)p->(mat,mat)1: imaginary_roots_and_coroots ------------------------------------------------- | ``imaginary_roots_and_coroots:(RootDatum, mat)p->(mat,mat)`` Defined in line number 1275. | | .. _imaginary_roots_and_coroots_kgbelt_x->(mat,mat)1: imaginary_roots_and_coroots ------------------------------------------------- | ``imaginary_roots_and_coroots:KGBElt x->(mat,mat)`` Defined in line number 1277. | | .. _real_roots_and_coroots_(rootdatum,_mat)p->(mat,mat)1: real_roots_and_coroots ------------------------------------------------- | ``real_roots_and_coroots:(RootDatum, mat)p->(mat,mat)`` Defined in line number 1283. | | .. _real_roots_and_coroots_kgbelt_x->(mat,mat)1: real_roots_and_coroots ------------------------------------------------- | ``real_roots_and_coroots:KGBElt x->(mat,mat)`` Defined in line number 1285. | | .. _complex_posroots_rootdatum_rd,mat_theta->mat1: complex_posroots ------------------------------------------------- | ``complex_posroots:RootDatum rd,mat theta->mat`` Defined in line number 1288. | | .. _complex_posroots_kgbelt_x->mat1: complex_posroots ------------------------------------------------- | ``complex_posroots:KGBElt x->mat`` Defined in line number 1290. | | .. _pad_string_s,int_padding->string1: pad ------------------------------------------------- | ``pad:string s,int padding->string`` Defined in line number 1294. | | .. _monomials_parampol_p->[param]1: monomials ------------------------------------------------- | ``monomials:ParamPol P->[Param]`` Defined in line number 1300. | | .. _monomial_parampol_p,int_i->param1: monomial ------------------------------------------------- | ``monomial:ParamPol P,int i->Param`` Defined in line number 1301. | |