poset.at

Poset type

set_type Poset=[[int]]

Poset P=[[int]]: encodes a partial order
the underlying set is {0,1,...,#P}
relations: P[i]=[a_1,a_2,...] means i<a_j
i<i is assumed (P[i] should not contain i)

transitive_fill_one

add relations implied by reflexivity and transitivity

equal

cannot overload this onto '='

also defined in springer_tables.at

transitive_fill

repeatedly add all relations implied by transitivity; not needed anymore

trans_close

the fastest way to compute this is using bitsets; avoids needing |sort_u|

closure

cut out the middle

also defined in K_Nilpotent.at, exceptional.at

posets_equal

poset_inverse

less

boolean: i<j in poset P

also defined in W_order.at

greater

minimal_nodes

nodes which point to nothing (only themselves)

basic_nodes

nodes i satisfying:
 P[i] is empty (or P[i]=[i])
 i\in P[j] some j (j\ne i)
in terms of orbit closures:
 orbit is closed, and
 orbit is contained in the closure of a strictly bigger orbit

delete_node

delete all edges pointing to node i, but
keep node i itself, so P does not get renumbered
caution: delete@(Poset,int) is defined,
 by overloading from delete@([vec],int) in basic.at
 and this is different

delete_nodes

is_monotone

Poset P, |P|=n
f is a permutation of P
f=[a_1,...,a_n] means f(i)=a_i
f is monotone if less(P,i,j) => less(P,f(i),f(j))

subPoset

graph 4 overloads

return a string which, when output to
a file, can be processed by graphviz to produce a
graph
suggested usage:
set g=graph(P)
>file.dot prints(g)
(command line):
%tred file.dot | dot -Tpdf -o file.pdf
tred: command line tool to reduce the graph
by eliminating redundant edges
default: each node is a black oval, labeled
by an integer

labels: function giving string to use in place of integers
colors:  function giving color of border of node j
for more options edit the .dot file directly

black borders

black borders, give labels as an array of strings instead of a function

also defined in exceptional.at, nilpotent_posets.at

show

simple text output of poset

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, cyclotomic.at, polynomial.at, character_tables.at, springer_tables.at, hodgeParamLaurentPol.at, hodgeParamPol.at, laurentPolynomial.at, weak_packets.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, exceptional.at, nilpotent_posets.at, lazy_lists.at