Braid Orbit#
Cython function to compute the orbit of the braid moves on a reduced word.
- sage.combinat.root_system.braid_orbit.BraidOrbit(word, rels)#
Return the orbit of
word
by all replacements given byrels
.INPUT:
word
– list of integersrels
– list of pairs(A, B)
, whereA
andB
are lists of integers the same length
EXAMPLES:
sage: from sage.combinat.root_system.braid_orbit import BraidOrbit sage: word = [1,2,1,3,2,1] sage: rels = [[[2, 1, 2], [1, 2, 1]], [[3, 1], [1, 3]], [[3, 2, 3], [2, 3, 2]]] sage: sorted(BraidOrbit(word, rels)) [(1, 2, 1, 3, 2, 1), (1, 2, 3, 1, 2, 1), (1, 2, 3, 2, 1, 2), (1, 3, 2, 1, 3, 2), (1, 3, 2, 3, 1, 2), (2, 1, 2, 3, 2, 1), (2, 1, 3, 2, 1, 3), (2, 1, 3, 2, 3, 1), (2, 3, 1, 2, 1, 3), (2, 3, 1, 2, 3, 1), (2, 3, 2, 1, 2, 3), (3, 1, 2, 1, 3, 2), (3, 1, 2, 3, 1, 2), (3, 2, 1, 2, 3, 2), (3, 2, 1, 3, 2, 3), (3, 2, 3, 1, 2, 3)] sage: len(_) 16