def __mul__(self, other):
if is_number(other):
if other == 1:
return self
fcmap = _mul_fourier_by_num(self.fc_dct, other, self.prec,
cuspidal=self._is_cuspidal,
hol=True)
if hasattr(other, "parent"):
bs = _common_base_ring(self.base_ring, other.parent())
else:
bs = self.base_ring
return ModFormQexpLevel1(self.wt, fcmap, self.prec,
base_ring=bs,
is_cuspidal=self._is_cuspidal,
given_reduced_tuples_only=True)
if isinstance(other, ModFormQexpLevel1) and other.wt == 0:
return self.__mul__(other[(0, 0, 0)])
if is_hol_mod_form(other):
prec = common_prec([self, other])
bsring = _common_base_ring(self.base_ring, other.base_ring)
ms = self.fc_dct
mo = other.fc_dct
cuspidal = self._is_cuspidal or other._is_cuspidal
fcmap = _mul_fourier(ms, mo, prec, cuspidal=cuspidal,
hol=True)
return ModFormQexpLevel1(self.wt + other.wt,
fcmap,
prec,
base_ring=bsring,
is_cuspidal=cuspidal,
given_reduced_tuples_only=True)
else:
return QexpLevel1.__mul__(self, other)
def __eq__(self, other):
if is_number(other) and other == 0:
return self.vec == 0
if isinstance(other, SymTensorRepElt):
return self.wt == other.wt and self.vec == other.vec
else:
raise NotImplementedError
def __mul__(self, other):
if is_number(other):
if other == 1:
return self
fcmap = _mul_fourier_by_num(self.fc_dct, other, self.prec,
self._is_cuspidal)
if hasattr(other, "parent"):
bs = _common_base_ring(self.base_ring, other.parent())
else:
bs = self.base_ring
return QexpLevel1(fcmap, self.prec, base_ring=bs,
is_cuspidal=self._is_cuspidal)
elif isinstance(other, QexpLevel1):
prec = common_prec([self, other])
bsring = _common_base_ring(self.base_ring, other.base_ring)
ms = self.fc_dct
mo = other.fc_dct
cuspidal = self._is_cuspidal or other._is_cuspidal
fcmap = _mul_fourier(ms, mo, prec, cuspidal)
res = QexpLevel1(fcmap, prec, base_ring=bsring,
is_cuspidal=cuspidal)
return res
elif isinstance(other, (SymWtGenElt,
QseriesTimesQminushalf)):
return other.__mul__(self)
else:
raise NotImplementedError
def __getitem__(self, t):
if (isinstance(t, tuple) and isinstance(t[0], tuple) and
is_number(t[1])):
tpl, i = t
return self.forms[i][tpl]
else:
vec = vector([f[t] for f in self.forms])
return vec
def __mul__(self, other):
if isinstance(other, QseriesTimesQminushalf):
return _mul_q_half_monom(self.f_part * other.f_part)
elif isinstance(other, QexpLevel1) or is_number(other):
return QseriesTimesQminushalf(self.f_part * other)
elif isinstance(other, SymWtGenElt):
return other.__mul__(self)
else:
raise NotImplementedError
def __rmul__(self, other):
if is_number(other):
return self.__mul__(other)
elif isinstance(other, list) or (hasattr(other, "parent") and
isinstance(
other.parent(),
sage.matrix.matrix_space.MatrixSpace)):
return self.group_action(other)
else:
raise NotImplementedError
def __mul__(self, other):
res = QseriesTimesQminushalf.__mul__(self, other)
if is_number(other):
return ModFormQsrTimesQminushalf(res.f_part, self.wt)
elif isinstance(other, ModFormQexpLevel1):
return ModFormQsrTimesQminushalf(res.f_part, self.wt + other.wt)
elif isinstance(other, ModFormQsrTimesQminushalf):
return ModFormQexpLevel1(self.wt + other.wt,
res.fc_dct, res.prec,
base_ring=res.base_ring)
else:
return res
def __mul__(self, other):
res = SymWtGenElt.__mul__(self, other)
if is_number(other):
return SymWtModFmElt(res.forms, self.wt, res.prec, res.base_ring)
if isinstance(other, (ModFormQexpLevel1,
ModFormQsrTimesQminushalf)):
return SymWtModFmElt(res.forms,
self.wt + other.wt,
res.prec,
res.base_ring)
else:
return res
def _linearly_indep_tuples_of_given_bd(self, bd):
basis = self.basis()
dim = self.dimension()
if is_number(bd):
bd = list(PrecisionDeg2(bd))
tpls = sorted(list(bd), key=lambda x: (x[0] + x[2], max(x[0], x[2])))
tpls_w_idx = reduce(operator.add,
[[(t, i) for i in range(self.sym_wt + 1)]
for t in tpls], [])
ml = [[f.forms[i][t] for f in basis] for t, i in tpls_w_idx]
index_list = linearly_indep_rows_index_list(ml, dim)
res = [tpls_w_idx[i] for i in index_list]
return res
def __pow__(self, other):
if other == 0:
return 1
elif other == 1:
return self
elif is_number(other) and other > 0:
f = (self.f_part) ** other
q, r = divmod(other, 2)
g = _mul_q_half_monom(f, a=q)
if r == 0:
return g
else:
return QseriesTimesQminushalf(g)
else:
raise NotImplementedError
def __add__(self, other):
if is_number(other):
fcmap = self.fc_dct.copy()
fcmap[(0, 0, 0)] = self.fc_dct[(0, 0, 0)] + other
cuspidal = other == 0 and self._is_cuspidal
return QexpLevel1(fcmap, self.prec, self.base_ring,
is_cuspidal=cuspidal)
prec = common_prec([self, other])
bsring = _common_base_ring(self.base_ring, other.base_ring)
cuspidal = self._is_cuspidal and other._is_cuspidal
ms = self.fc_dct
mo = other.fc_dct
fcmap = _add_fourier(ms, mo, prec, cuspidal)
return QexpLevel1(fcmap, prec, base_ring=bsring,
is_cuspidal=cuspidal)
def __mul__(self, other):
if is_number(other):
prec = self.prec
forms = [other * f for f in self.forms]
if hasattr(other, "parent"):
base_ring = _common_base_ring(self.base_ring, other.parent())
else:
base_ring = self.base_ring
return SymWtGenElt(forms, prec, base_ring)
if isinstance(other, (QexpLevel1, QseriesTimesQminushalf)):
forms = [f * other for f in self.forms]
prec = common_prec(forms)
base_ring = _common_base_ring(self.base_ring, other.base_ring)
return SymWtGenElt(forms, prec, base_ring)
else:
raise NotImplementedError
def __add__(self, other):
if is_number(other):
fcmap = self.fc_dct.copy()
fcmap[(0, 0, 0)] = self.fc_dct[(0, 0, 0)] + other
if other == 0:
return ModFormQexpLevel1(self.wt, fcmap, self.prec,
self.base_ring,
is_cuspidal=self._is_cuspidal)
else:
return QexpLevel1(fcmap, self.prec, self.base_ring)
if is_hol_mod_form(other) and self.wt == other.wt:
prec = common_prec([self, other])
bsring = _common_base_ring(self.base_ring, other.base_ring)
ms = self.fc_dct
mo = other.fc_dct
cuspidal = self._is_cuspidal and other._is_cuspidal
fcmap = _add_fourier(ms, mo, prec, cuspidal=cuspidal,
hol=True)
return ModFormQexpLevel1(self.wt, fcmap, prec, bsring,
is_cuspidal=cuspidal,
given_reduced_tuples_only=True)
else:
return QexpLevel1.__add__(self, other)
def __mul__(self, other):
if is_number(other):
return SymTensorRepElt(self.vec * other, self.wt)
else:
raise NotImplementedError
