Tools¶
-
sage.combinat.tools.
transitive_ideal
(f, x)¶ Return a list of all elements reachable from
in the abstract reduction system whose reduction relation is given by the function
.
In more elementary terms: If
is a set, and
is a function sending every element of
to a list of elements of
, then we can define a digraph on the vertex set
by drawing an edge from
to
for every
and every
. If
, then an element
is said to be reachable from
if there is a path
in this graph. Given
and
, this method computes the list of all elements of
reachable from
.
Note that if there are infinitely many such elements, then this method will never halt.
EXAMPLES:
sage: f = lambda x: [x-1] if x > 0 else [] sage: sage.combinat.tools.transitive_ideal(f, 10) [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]