def _element_constructor_(self, x):
"""
Convert ``x`` into ``self``, if coercion failed
INPUT:
- ``self`` -- a basis of the symmetric functions
- ``x`` -- an element of the symmetric functions
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s(2)
2*s[]
sage: s([2,1]) # indirect doctest
s[2, 1]
sage: s([[2,1],[1]])
s[1, 1] + s[2]
sage: s([[],[]])
s[]
sage: McdJ = SymmetricFunctions(QQ['q','t'].base_ring())
sage: s = SymmetricFunctions(McdJ.base_ring()).s()
sage: s._element_constructor_(McdJ(s[2,1]))
s[2, 1]
"""
R = self.base_ring()
eclass = self.element_class
if isinstance(x, int):
x = Integer(x)
##############
# Partitions #
##############
if x in sage.combinat.partition.Partitions():
return eclass(
self, {
sage.combinat.partition.Partition(
filter(lambda x: x != 0, x)):
R.one()
})
# Todo: discard all of this which is taken care by Sage's coercion
# (up to changes of base ring)
##############
# Dual bases #
##############
elif sfa.is_SymmetricFunction(x) and hasattr(x, 'dual'):
#Check to see if it is the dual of some other basis
#If it is, try to coerce its corresponding element
#in the other basis
return self(x.dual())
##################################################################
# Symmetric Functions, same basis, possibly different coeff ring #
##################################################################
# self.Element is used below to test if another symmetric
# function is expressed in the same basis but in another
# ground ring. This idiom is fragile and depends on the
# internal (unstable) specifications of parents and categories
#
# TODO: find the right idiom
#
# One cannot use anymore self.element_class: it is build by
# the category mechanism, and depends on the coeff ring.
elif isinstance(x, self.Element):
P = x.parent()
#same base ring
if P is self:
return x
#different base ring
else:
return eclass(
self,
dict([(e1, R(e2))
for e1, e2 in x._monomial_coefficients.items()]))
##################################################
# Classical Symmetric Functions, different basis #
##################################################
elif isinstance(x, SymmetricFunctionAlgebra_classical.Element):
R = self.base_ring()
xP = x.parent()
xm = x.monomial_coefficients()
#determine the conversion function.
try:
t = conversion_functions[(xP.basis_name(), self.basis_name())]
except AttributeError:
raise TypeError, "do not know how to convert from %s to %s" % (
xP.basis_name(), self.basis_name())
if R == QQ and xP.base_ring() == QQ:
if xm:
return self._from_dict(t(xm)._monomial_coefficients,
coerce=True)
else:
return self.zero()
else:
f = lambda part: self._from_dict(
t({
part: ZZ.one()
})._monomial_coefficients)
return self._apply_module_endomorphism(x, f)
###############################
# Hall-Littlewood Polynomials #
###############################
elif isinstance(x, hall_littlewood.HallLittlewood_generic.Element):
#
#Qp: Convert to Schur basis and then convert to self
#
if isinstance(x, hall_littlewood.HallLittlewood_qp.Element):
Qp = x.parent()
sx = Qp._s._from_cache(x,
Qp._s_cache,
Qp._self_to_s_cache,
t=Qp.t)
return self(sx)
#
#P: Convert to Schur basis and then convert to self
#
elif isinstance(x, hall_littlewood.HallLittlewood_p.Element):
P = x.parent()
sx = P._s._from_cache(x, P._s_cache, P._self_to_s_cache, t=P.t)
return self(sx)
#
#Q: Convert to P basis and then convert to self
#
elif isinstance(x, hall_littlewood.HallLittlewood_q.Element):
return self(x.parent()._P(x))
#######
# LLT #
#######
#Convert to m and then to self.
elif isinstance(x, llt.LLT_generic.Element):
P = x.parent()
BR = self.base_ring()
zero = BR.zero()
PBR = P.base_ring()
if not BR.has_coerce_map_from(PBR):
raise TypeError, "no coerce map from x's parent's base ring (= %s) to self's base ring (= %s)" % (
PBR, self.base_ring())
z_elt = {}
for m, c in x._monomial_coefficients.iteritems():
n = sum(m)
P._m_cache(n)
for part in P._self_to_m_cache[n][m]:
z_elt[part] = z_elt.get(part, zero) + BR(
c * P._self_to_m_cache[n][m][part].subs(t=P.t))
m = P._sym.monomial()
return self(m._from_dict(z_elt))
#########################
# Macdonald Polynomials #
#########################
elif isinstance(x, macdonald.MacdonaldPolynomials_generic.Element):
if isinstance(x, macdonald.MacdonaldPolynomials_j.Element):
J = x.parent()
sx = J._s._from_cache(x,
J._s_cache,
J._self_to_s_cache,
q=J.q,
t=J.t)
return self(sx)
elif isinstance(x, (macdonald.MacdonaldPolynomials_q.Element,
macdonald.MacdonaldPolynomials_p.Element)):
J = x.parent()._J
jx = J(x)
sx = J._s._from_cache(jx,
J._s_cache,
J._self_to_s_cache,
q=J.q,
t=J.t)
return self(sx)
elif isinstance(x, (macdonald.MacdonaldPolynomials_h.Element,
macdonald.MacdonaldPolynomials_ht.Element)):
H = x.parent()
sx = H._s._from_cache(x,
H._s_cache,
H._self_to_s_cache,
q=H.q,
t=H.t)
return self(sx)
elif isinstance(x, macdonald.MacdonaldPolynomials_s.Element):
S = x.parent()
sx = S._s._from_cache(x,
S._s_cache,
S._self_to_s_cache,
q=S.q,
t=S.t)
return self(sx)
else:
raise TypeError
####################
# Jack Polynomials #
####################
elif isinstance(x, jack.JackPolynomials_generic.Element):
if isinstance(x, jack.JackPolynomials_p.Element):
P = x.parent()
mx = P._m._from_cache(x, P._m_cache, P._self_to_m_cache, t=P.t)
return self(mx)
if isinstance(x, (jack.JackPolynomials_j.Element,
jack.JackPolynomials_q.Element)):
return self(x.parent()._P(x))
else:
raise TypeError
#####################
# k-Schur Functions #
#####################
if isinstance(x, kschur.kSchurFunctions_generic.Element):
if isinstance(x, kschur.kSchurFunctions_t.Element):
P = x.parent()
sx = P._s._from_cache(x, P._s_cache, P._self_to_s_cache, t=P.t)
return self(sx)
else:
raise TypeError
####################################################
# Bases defined by orthogonality and triangularity #
####################################################
elif isinstance(
x, orthotriang.SymmetricFunctionAlgebra_orthotriang.Element):
#Convert to its base and then to self
xp = x.parent()
if self is xp._sf_base:
return xp._sf_base._from_cache(x, xp._base_cache,
xp._self_to_base_cache)
else:
return self(xp._sf_base(x))
###################
# Skew Partitions #
###################
elif x in sage.combinat.skew_partition.SkewPartitions():
import sage.libs.lrcalc.lrcalc as lrcalc
skewschur = lrcalc.skew(x[0], x[1])
return self._from_dict(skewschur)
#############################
# Elements of the base ring #
#############################
elif x.parent() is R:
return eclass(self, {sage.combinat.partition.Partition([]): x})
###########################################
# Elements that coerce into the base ring #
###########################################
elif R.has_coerce_map_from(x.parent()):
return eclass(self, {sage.combinat.partition.Partition([]): R(x)})
#################################
# Last shot -- try calling R(x) #
#################################
else:
try:
return eclass(self,
{sage.combinat.partition.Partition([]): R(x)})
except Exception:
raise TypeError, "do not know how to make x (= %s) an element of self" % (
x)
def _element_constructor_(self, x):
"""
Convert ``x`` into ``self``, if coercion failed
INPUT:
- ``self`` -- a basis of the symmetric functions
- ``x`` -- an element of the symmetric functions
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s(2)
2*s[]
sage: s([2,1]) # indirect doctest
s[2, 1]
sage: s([[2,1],[1]])
s[1, 1] + s[2]
sage: s([[],[]])
s[]
sage: McdJ = SymmetricFunctions(QQ['q','t'].base_ring())
sage: s = SymmetricFunctions(McdJ.base_ring()).s()
sage: s._element_constructor_(McdJ(s[2,1]))
s[2, 1]
"""
R = self.base_ring()
eclass = self.element_class
if isinstance(x, int):
x = Integer(x)
##############
# Partitions #
##############
if x in sage.combinat.partition.Partitions():
return eclass(self, {sage.combinat.partition.Partition(filter(lambda x: x!=0, x)):R(1)})
# Todo: discard all of this which is taken care by Sage's coercion
# (up to changes of base ring)
##############
# Dual bases #
##############
elif sfa.is_SymmetricFunction(x) and hasattr(x, 'dual'):
#Check to see if it is the dual of some other basis
#If it is, try to coerce its corresponding element
#in the other basis
return self(x.dual())
##################################################################
# Symmetric Functions, same basis, possibly different coeff ring #
##################################################################
# self.Element is used below to test if another symmetric
# function is expressed in the same basis but in another
# ground ring. This idiom is fragile and depends on the
# internal (unstable) specifications of parents and categories
#
# TODO: find the right idiom
#
# One cannot use anymore self.element_class: it is build by
# the category mechanism, and depends on the coeff ring.
elif isinstance(x, self.Element):
P = x.parent()
#same base ring
if P is self:
return x
#different base ring
else:
return eclass(self, dict([ (e1,R(e2)) for e1,e2 in x._monomial_coefficients.items()]))
##################################################
# Classical Symmetric Functions, different basis #
##################################################
elif isinstance(x, SymmetricFunctionAlgebra_classical.Element):
R = self.base_ring()
xP = x.parent()
xm = x.monomial_coefficients()
#determine the conversion function.
try:
t = conversion_functions[(xP.basis_name(),self.basis_name())]
except AttributeError:
raise TypeError, "do not know how to convert from %s to %s"%(xP.basis_name(), self.basis_name())
if R == QQ and xP.base_ring() == QQ:
if xm:
return self._from_dict(t(xm)._monomial_coefficients, coerce=True)
else:
return self(0)
else:
f = lambda part: self._from_dict(t( {part:Integer(1)} )._monomial_coefficients)
return self._apply_module_endomorphism(x, f)
###############################
# Hall-Littlewood Polynomials #
###############################
elif isinstance(x, hall_littlewood.HallLittlewood_generic.Element):
#
#Qp: Convert to Schur basis and then convert to self
#
if isinstance(x, hall_littlewood.HallLittlewood_qp.Element):
Qp = x.parent()
sx = Qp._s._from_cache(x, Qp._s_cache, Qp._self_to_s_cache, t=Qp.t)
return self(sx)
#
#P: Convert to Schur basis and then convert to self
#
elif isinstance(x, hall_littlewood.HallLittlewood_p.Element):
P = x.parent()
sx = P._s._from_cache(x, P._s_cache, P._self_to_s_cache, t=P.t)
return self(sx)
#
#Q: Convert to P basis and then convert to self
#
elif isinstance(x, hall_littlewood.HallLittlewood_q.Element):
return self( x.parent()._P( x ) )
#######
# LLT #
#######
#Convert to m and then to self.
elif isinstance(x, llt.LLT_generic.Element):
P = x.parent()
BR = self.base_ring()
zero = BR(0)
PBR = P.base_ring()
if not BR.has_coerce_map_from(PBR):
raise TypeError, "no coerce map from x's parent's base ring (= %s) to self's base ring (= %s)"%(PBR, self.base_ring())
z_elt = {}
for m, c in x._monomial_coefficients.iteritems():
n = sum(m)
P._m_cache(n)
for part in P._self_to_m_cache[n][m]:
z_elt[part] = z_elt.get(part, zero) + BR(c*P._self_to_m_cache[n][m][part].subs(t=P.t))
m = P._sym.monomial()
return self( m._from_dict(z_elt) )
#########################
# Macdonald Polynomials #
#########################
elif isinstance(x, macdonald.MacdonaldPolynomials_generic.Element):
if isinstance(x, macdonald.MacdonaldPolynomials_j.Element):
J = x.parent()
sx = J._s._from_cache(x, J._s_cache, J._self_to_s_cache, q=J.q, t=J.t)
return self(sx)
elif isinstance(x, (macdonald.MacdonaldPolynomials_q.Element, macdonald.MacdonaldPolynomials_p.Element)):
J = x.parent()._J
jx = J(x)
sx = J._s._from_cache(jx, J._s_cache, J._self_to_s_cache, q=J.q, t=J.t)
return self(sx)
elif isinstance(x, (macdonald.MacdonaldPolynomials_h.Element,macdonald.MacdonaldPolynomials_ht.Element)):
H = x.parent()
sx = H._s._from_cache(x, H._s_cache, H._self_to_s_cache, q=H.q, t=H.t)
return self(sx)
elif isinstance(x, macdonald.MacdonaldPolynomials_s.Element):
S = x.parent()
sx = S._s._from_cache(x, S._s_cache, S._self_to_s_cache, q=S.q, t=S.t)
return self(sx)
else:
raise TypeError
####################
# Jack Polynomials #
####################
elif isinstance(x, jack.JackPolynomials_generic.Element):
if isinstance(x, jack.JackPolynomials_p.Element):
P = x.parent()
mx = P._m._from_cache(x, P._m_cache, P._self_to_m_cache, t=P.t)
return self(mx)
if isinstance(x, (jack.JackPolynomials_j.Element, jack.JackPolynomials_q.Element)):
return self( x.parent()._P(x) )
else:
raise TypeError
#####################
# k-Schur Functions #
#####################
if isinstance(x, kschur.kSchurFunctions_generic.Element):
if isinstance(x, kschur.kSchurFunctions_t.Element):
P = x.parent()
sx = P._s._from_cache(x, P._s_cache, P._self_to_s_cache, t=P.t)
return self(sx)
else:
raise TypeError
####################################################
# Bases defined by orthogonality and triangularity #
####################################################
elif isinstance(x, orthotriang.SymmetricFunctionAlgebra_orthotriang.Element):
#Convert to its base and then to self
xp = x.parent()
if self is xp._sf_base:
return xp._sf_base._from_cache(x, xp._base_cache, xp._self_to_base_cache)
else:
return self( xp._sf_base(x) )
###################
# Skew Partitions #
###################
elif x in sage.combinat.skew_partition.SkewPartitions():
import sage.libs.lrcalc.lrcalc as lrcalc
skewschur = lrcalc.skew(x[0], x[1])
return self._from_dict(skewschur)
#############################
# Elements of the base ring #
#############################
elif x.parent() is R:
return eclass(self, {sage.combinat.partition.Partition([]):x})
###########################################
# Elements that coerce into the base ring #
###########################################
elif R.has_coerce_map_from(x.parent()):
return eclass(self, {sage.combinat.partition.Partition([]):R(x)})
#################################
# Last shot -- try calling R(x) #
#################################
else:
try:
return eclass(self, {sage.combinat.partition.Partition([]):R(x)})
except StandardError:
raise TypeError, "do not know how to make x (= %s) an element of self"%(x)