#17018: Polishing documentation of posets
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Reporter: jmantysalo | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-wishlist
Component: documentation | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by jmantysalo):
Maybe something like this:
== Comparing & intervals ==
compare_elements() Compare x and y in the poset.
closed_interval() Returns a list of the elements z such that x≤z≤y.
interval() Returns a list of the elements z such that
x≤z≤y.
open_interval() Returns a list of the elements z such that
x<z<y. The order is that induced by the ordering in
is_lequal() Returns True if x is less than or equal to
y in the poset, and False otherwise.
is_less_than() Returns True if x is less than but not
equal to y in the poset, and False otherwise.
is_greater_than() Returns True if x is greater than but not
equal to y in the poset, and False otherwise.
is_gequal() Returns True if x is greater than or equal
to y in the poset, and False otherwise.
order_filter() Returns the order filter generated by a
list of elements.
order_ideal() Returns the order ideal generated by a
list of elements.
== Covering & relations ==
cover_relations_iterator() Returns an iterator for the cover
relations of the poset.
cover_relations() Returns the list of pairs [u,v] which are
cover relations
covers() Returns True if y covers x and False
otherwise.
lower_covers_iterator() Returns an iterator for the lower covers
of the element y. An lower cover of y is an element x such that y x is a
cover relation.
lower_covers() Returns a list of lower covers of the
element y. An lower cover of y is an element x such that y x is a cover
relation.
upper_covers_iterator() Returns an iterator for the upper covers
of the element y. An upper cover of y is an element x such that y x is a
cover relation.
upper_covers() Returns a list of upper covers of the
element y. An upper cover of y is an element x such that y x is a cover
relation.
relations_iterator() Returns an iterator for all the relations
of the poset.
relations() Returns a list of all relations of the
poset.
== Properties of the poset ==
cardinality() Returns the number of elements in the poset.
has_top() Returns True if the poset contains a
unique maximal element, and False otherwise.
has_bottom() Returns True if the poset has a unique
minimal element.
is_bounded() Returns True if the poset contains a
unique maximal element and a unique minimal element, and False otherwise.
is_chain() Returns True if the poset is totally
ordered, and False otherwise.
is_connected()
is_graded() Returns whether this poset is graded.
is_ranked() Returns whether this poset is ranked.
is_slender() Returns whether the poset self is slender
or not.
is_join_semilattice() Returns True is the poset has a join
operation, and False otherwise.
is_meet_semilattice() Returns True if self has a meet operation,
and False otherwise.
is_lattice() # XX Toisesta filusta
rank() Returns the rank of an element, or the
rank of the poset if element is None.
rank_function() Returns a rank function of the poset, if
it exists.
?? is_incomparable_chain_free() Returns whether the poset is
(m+n)-free.
height()
width()
== Specific elements ==
bottom() Returns the bottom element of the poset, if it
exists.
top() Returns the top element of the poset, if it
exists.
maximal_elements() Returns a list of the maximal elements of
the poset.
minimal_elements() Returns a list of the minimal elements of
the poset.
== New posets from old ones ==
dual() Returns the dual poset of the given poset.
subposet() Returns the poset containing elements with
partial order induced by that of self.
random_subposet() Returns a random subposet that contains
each element with probability p.
product() Returns the cartesian product of self and
other.
relabel() Returns a copy of this poset with its
elements relabelled
disjoint_union()
ordinal_sum()
== Chains & antichains ==
antichains_iterator() Returns an iterator over the antichains of the
poset.
antichains() Returns the antichains of the poset.
maximal_chains() Returns all maximal chains of this poset.
Each chain is listed in increasing order.
chains() Returns all the chains of self
== Drawing ==
show() Shows the Graphics object corresponding
the Hasse diagram of the poset.
plot() Returns a Graphic object corresponding the
Hasse diagram of the poset.
graphviz_string() Returns a representation in the DOT
language, ready to render in graphviz.
== Comparing posets ==
is_isomorphic() Returns True if both posets are
isomorphic.
== Polytopes ==
chain_polytope() Returns the chain polytope of the poset.
order_polytope() Returns the order polytope of the poset.
== Other & not yet classified ==
chain_polynomial() Returns the chain polynomial of the poset.
comparability_graph() Returns the comparability graph of the poset.
coxeter_transformation() Returns the matrix of the Auslander-Reiten
translation acting on the Grothendieck group of the derived category of
modules
evacuation() Computes evacuation on the linear
extension associated to the poset self.
f_polynomial() Returns the f-polynomial of a bounded
poset.
flag_f_polynomial() Returns the flag f-polynomial of a bounded
and ranked poset.
flag_h_polynomial() Returns the flag h-polynomial of a bounded
and ranked poset.
frank_network() Returns Frank’s network (a DiGraph along
with a cost function on its edges) associated to self.
greene_shape() Computes the Greene-Kleitman partition aka
Greene shape of the poset self.
h_polynomial() Returns the h-polynomial of a bounded
poset.
hasse_diagram() Returns the Hasse diagram of self as a
Sage DiGraph.
incomparability_graph() Returns the incomparability graph of the
poset.
is_EL_labelling() Returns whether f is an EL labelling of
self
is_linear_extension() Returns whether l is a linear extension of
self
lequal_matrix() Computes the matrix whose (i,j) entry is 1
if self.linear_extension()[i] < self.linear_extension()[j] and 0 otherwise
level_sets() Returns a list l such that l[i+1] is the
set of minimal elements of the poset obtained by removing the elements in
l[0], l[1], ..., l[i].
linear_extension() Returns a linear extension of this poset.
linear_extensions() Returns the enumerated set of all the
linear extensions of this poset
list() List the elements of the poset. This just
returns the result of linear_extension().
mobius_function_matrix() Returns a matrix whose (i,j) entry is the
value of the Mobius function evaluated at self.linear_extension()[i] and
self.linear_extension()[j].
mobius_function() Returns the value of the Mobius function
of the poset on the elements x and y.
order_complex() Returns the order complex associated to
this poset.
order_polynomial() Returns the order polynomial of the poset.
p_partition_enumerator() Returns a P-partition enumerator of the
poset.
promotion() Computes the (extended) promotion on the
linear extension of the poset self
unwrap() Unwraps an element of this poset
with_linear_extension() Returns a copy of self with a different
default linear extension
zeta_polynomial() Returns the zeta polynomial of the poset.
completion_by_cuts()
cover_relations_graph()
cuts()
dilworth_decomposition()
intervals()
intervals_iterator()
intervals_number()
is_incomparable_chain_free()
isomorphic_subposets()
isomorphic_subposets_iterator()
relations_number()
--
Ticket URL: <http://trac.sagemath.org/ticket/17018#comment:2>
Sage <http://www.sagemath.org>
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