def _element_constructor_(self, x):
"""
Construct an element of ``self``.
EXAMPLES::
sage: C = CombinatorialFreeModule(QQ, ['a','b','c'])
sage: TA = TensorAlgebra(C)
sage: TA(['a','b','c'])
B['a'] # B['b'] # B['c']
sage: TA(['a','b','b'])
B['a'] # B['b'] # B['b']
sage: TA(['a','b','c']) + TA(['a'])
B['a'] + B['a'] # B['b'] # B['c']
sage: TA(['a','b','c']) + TA(['a','b','a'])
B['a'] # B['b'] # B['a'] + B['a'] # B['b'] # B['c']
sage: TA(['a','b','c']) + TA(['a','b','c'])
2*B['a'] # B['b'] # B['c']
sage: TA(C.an_element())
2*B['a'] + 2*B['b'] + 3*B['c']
"""
FM = self._indices
if isinstance(x, (list, tuple)):
x = FM.prod(FM.gen(elt) for elt in x)
return self.monomial(x)
if x in FM._indices:
return self.monomial(FM.gen(x))
if x in self._base_module:
return self.sum_of_terms((FM.gen(k), v) for k,v in x)
return CombinatorialFreeModule._element_constructor_(self, x)
def _element_constructor_(self, x):
"""
Construct an element of ``self``.
EXAMPLES::
sage: C = CombinatorialFreeModule(QQ, ['a','b','c'])
sage: TA = TensorAlgebra(C)
sage: TA(['a','b','c'])
B['a'] # B['b'] # B['c']
sage: TA(['a','b','b'])
B['a'] # B['b'] # B['b']
sage: TA(['a','b','c']) + TA(['a'])
B['a'] + B['a'] # B['b'] # B['c']
sage: TA(['a','b','c']) + TA(['a','b','a'])
B['a'] # B['b'] # B['a'] + B['a'] # B['b'] # B['c']
sage: TA(['a','b','c']) + TA(['a','b','c'])
2*B['a'] # B['b'] # B['c']
sage: TA(C.an_element())
2*B['a'] + 2*B['b'] + 3*B['c']
"""
FM = self._indices
if isinstance(x, (list, tuple)):
x = FM.prod(FM.gen(elt) for elt in x)
return self.monomial(x)
if x in FM._indices:
return self.monomial(FM.gen(x))
if x in self._base_module:
return self.sum_of_terms((FM.gen(k), v) for k, v in x)
return CombinatorialFreeModule._element_constructor_(self, x)
def _element_constructor_(self, x):
r"""
Convert ``x`` into ``self``.
EXAMPLES::
sage: R = algebras.FQSym(QQ).G()
sage: x, y, z = R([1]), R([2,1]), R([3,2,1])
sage: R(x)
G[1]
sage: R(x+4*y)
G[1] + 4*G[2, 1]
sage: R(1)
G[]
sage: D = algebras.FQSym(ZZ).G()
sage: X, Y, Z = D([1]), D([2,1]), D([3,2,1])
sage: R(X-Y).parent()
Free Quasi-symmetric functions over Rational Field in the G basis
sage: R([1, 3, 2])
G[1, 3, 2]
sage: R(Permutation([1, 3, 2]))
G[1, 3, 2]
sage: R(SymmetricGroup(4)(Permutation([1,3,4,2])))
G[1, 3, 4, 2]
sage: RF = algebras.FQSym(QQ).F()
sage: R(RF([2, 3, 4, 1]))
G[4, 1, 2, 3]
sage: R(RF([3, 2, 4, 1]))
G[4, 2, 1, 3]
sage: DF = algebras.FQSym(ZZ).F()
sage: D(DF([2, 3, 4, 1]))
G[4, 1, 2, 3]
sage: R(DF([2, 3, 4, 1]))
G[4, 1, 2, 3]
sage: RF(R[2, 3, 4, 1])
F[4, 1, 2, 3]
"""
if isinstance(x, (list, tuple, PermutationGroupElement)):
x = Permutation(x)
try:
P = x.parent()
if isinstance(P, FreeQuasisymmetricFunctions.G):
if P is self:
return x
return self.element_class(self, x.monomial_coefficients())
except AttributeError:
pass
return CombinatorialFreeModule._element_constructor_(self, x)
def _element_constructor_(self, x):
"""
Construct an element of ``self``.
EXAMPLES::
sage: D = DescentAlgebra(QQ, 4).D()
sage: D([1, 3])
D{1, 3}
"""
if isinstance(x, (list, set)):
x = tuple(x)
if isinstance(x, tuple):
return self.monomial(x)
return CombinatorialFreeModule._element_constructor_(self, x)
def _element_constructor_(self, x):
"""
Construct an element of ``self``.
EXAMPLES::
sage: D = DescentAlgebra(QQ, 4).D()
sage: D([1, 3])
D{1, 3}
"""
if isinstance(x, (list, set)):
x = tuple(x)
if isinstance(x, tuple):
return self.monomial(x)
return CombinatorialFreeModule._element_constructor_(self, x)
def _element_constructor_(self, x):
"""
Convert ``x`` into ``self``.
EXAMPLES::
sage: F.<x,y> = FreeAlgebra(QQ, 2)
sage: R = F.pbw_basis()
sage: R(3)
3*PBW[1]
sage: R(x*y)
PBW[x*y] + PBW[y]*PBW[x]
"""
if isinstance(x, FreeAlgebraElement):
return self._alg.pbw_element(self._alg(x))
return CombinatorialFreeModule._element_constructor_(self, x)
def _element_constructor_(self, x):
"""
Convert ``x`` into ``self``.
EXAMPLES::
sage: F.<x,y> = FreeAlgebra(QQ, 2)
sage: R = F.pbw_basis()
sage: R(3)
3*PBW[1]
sage: R(x*y)
PBW[x*y] + PBW[y]*PBW[x]
"""
if isinstance(x, FreeAlgebraElement):
return self._alg.pbw_element(self._alg(x))
return CombinatorialFreeModule._element_constructor_(self, x)
def _element_constructor_(self, x):
r"""
Convert ``x`` into ``self``.
EXAMPLES::
sage: R = algebras.FQSym(QQ).F()
sage: x, y, z = R([1]), R([2,1]), R([3,2,1])
sage: R(x)
F[1]
sage: R(x+4*y)
F[1] + 4*F[2, 1]
sage: R(1)
F[]
sage: D = algebras.FQSym(ZZ).F()
sage: X, Y, Z = D([1]), D([2,1]), D([3,2,1])
sage: R(X-Y).parent()
Free Quasi-symmetric functions over Rational Field in the F basis
sage: R([1, 3, 2])
F[1, 3, 2]
sage: R(Permutation([1, 3, 2]))
F[1, 3, 2]
sage: R(SymmetricGroup(4)(Permutation([1,3,4,2])))
F[1, 3, 4, 2]
"""
if isinstance(x, (list, tuple, PermutationGroupElement)):
x = Permutation(x)
try:
P = x.parent()
if isinstance(P, FreeQuasisymmetricFunctions.F):
if P is self:
return x
return self.element_class(self, x.monomial_coefficients())
except AttributeError:
pass
return CombinatorialFreeModule._element_constructor_(self, x)
