def __call__(self, x):
"""
Coerce x into a boundary symbol space.
If x is a modular symbol (with the same group, weight, character,
sign, and base field), this returns the image of that modular
symbol under the boundary map.
EXAMPLES::
sage: M = ModularSymbols(Gamma0(15), 2) ; B = M.boundary_space()
sage: B(M.0)
[Infinity] - [0]
sage: B(Cusp(1))
[0]
sage: B(Cusp(oo))
[Infinity]
sage: B(7)
Traceback (most recent call last):
...
TypeError: Coercion of 7 (of type <type 'sage.rings.integer.Integer'>) into Space of Boundary Modular Symbols for Congruence Subgroup Gamma0(15) of weight 2 and over Rational Field not (yet) defined.
"""
if isinstance(x, int) and x == 0:
return BoundarySpaceElement(self, {})
elif isinstance(x, cusps.Cusp):
return self._coerce_cusp(x)
elif manin_symbols.is_ManinSymbol(x):
return self._coerce_in_manin_symbol(x)
elif element.is_ModularSymbolsElement(x):
M = x.parent()
if not isinstance(M, ambient.ModularSymbolsAmbient):
raise TypeError(
"x (=%s) must be an element of a space of modular symbols of type ModularSymbolsAmbient"
% x)
if M.level() != self.level():
raise TypeError("x (=%s) must have level %s but has level %s" %
(x, self.level(), M.level()))
S = x.manin_symbol_rep()
if len(S) == 0:
return self(0)
return sum([c * self._coerce_in_manin_symbol(v) for c, v in S])
elif is_FreeModuleElement(x):
y = dict([(i, x[i]) for i in xrange(len(x))])
return BoundarySpaceElement(self, y)
raise TypeError(
"Coercion of %s (of type %s) into %s not (yet) defined." %
(x, type(x), self))
def __call__(self, x):
"""
Coerce x into a boundary symbol space.
If x is a modular symbol (with the same group, weight, character,
sign, and base field), this returns the image of that modular
symbol under the boundary map.
EXAMPLES::
sage: M = ModularSymbols(Gamma0(15), 2) ; B = M.boundary_space()
sage: B(M.0)
[Infinity] - [0]
sage: B(Cusp(1))
[0]
sage: B(Cusp(oo))
[Infinity]
sage: B(7)
Traceback (most recent call last):
...
TypeError: Coercion of 7 (of type <type 'sage.rings.integer.Integer'>) into Space of Boundary Modular Symbols for Congruence Subgroup Gamma0(15) of weight 2 and over Rational Field not (yet) defined.
"""
if isinstance(x, int) and x == 0:
return BoundarySpaceElement(self, {})
elif isinstance(x, cusps.Cusp):
return self._coerce_cusp(x)
elif manin_symbols.is_ManinSymbol(x):
return self._coerce_in_manin_symbol(x)
elif element.is_ModularSymbolsElement(x):
M = x.parent()
if not isinstance(M, ambient.ModularSymbolsAmbient):
raise TypeError, "x (=%s) must be an element of a space of modular symbols of type ModularSymbolsAmbient"%x
if M.level() != self.level():
raise TypeError, "x (=%s) must have level %s but has level %s"%(
x, self.level(), M.level())
S = x.manin_symbol_rep()
if len(S) == 0:
return self(0)
return sum([c*self._coerce_in_manin_symbol(v) for c, v in S])
elif is_FreeModuleElement(x):
y = dict([(i,x[i]) for i in xrange(len(x))])
return BoundarySpaceElement(self, y)
raise TypeError, "Coercion of %s (of type %s) into %s not (yet) defined."%(x, type(x), self)