def __init__(self, R, names=None):
"""
Initialize ``self``.
TESTS::
sage: A = algebras.FreePreLie(QQ, '@'); A
Free PreLie algebra on one generator ['@'] over Rational Field
sage: TestSuite(A).run()
sage: A = algebras.FreePreLie(QQ, None); A
Free PreLie algebra on one generator ['o'] over Rational Field
sage: F = algebras.FreePreLie(QQ, 'xy')
sage: TestSuite(F).run() # long time
"""
if names is None:
Trees = RootedTrees()
key = RootedTree.sort_key
self._alphabet = Alphabet(['o'])
else:
Trees = LabelledRootedTrees()
key = LabelledRootedTree.sort_key
self._alphabet = names
# Here one would need LabelledRootedTrees(names)
# so that one can restrict the labels to some fixed set
cat = MagmaticAlgebras(R).WithBasis().Graded() & LieAlgebras(
R).WithBasis().Graded()
CombinatorialFreeModule.__init__(self,
R,
Trees,
latex_prefix="",
sorting_key=key,
category=cat)
def __init__(self, R, names=None):
"""
Initialize ``self``.
TESTS::
sage: A = algebras.FreePreLie(QQ, '@'); A
Free PreLie algebra on one generator ['@'] over Rational Field
sage: TestSuite(A).run()
sage: F = algebras.FreePreLie(QQ, 'xy')
sage: TestSuite(F).run() # long time
sage: F = algebras.FreePreLie(QQ, ZZ)
sage: elts = F.some_elements()[:-1] # Skip the last element
sage: TestSuite(F).run(some_elements=elts) # long time
"""
if names.cardinality() == 1:
Trees = RootedTrees()
else:
Trees = LabelledRootedTrees()
# Here one would need LabelledRootedTrees(names)
# so that one can restrict the labels to some fixed set
self._alphabet = names
cat = MagmaticAlgebras(R).WithBasis().Graded()
CombinatorialFreeModule.__init__(self,
R,
Trees,
latex_prefix="",
category=cat)