def _mul_(self, other):
r"""
Return the product of self and other.
EXAMPLES::
sage: eta1, eta2 = EtaGroup(4).basis() # indirect doctest
sage: eta1 * eta2
Eta product of level 4 : (eta_1)^8 (eta_4)^-8
"""
newdict = {}
for d in union(self._keys, other._keys):
newdict[d] = self.r(d) + other.r(d)
return EtaProduct(self.level(), newdict)
def _mul_(self, other):
r"""
Return the product of self and other.
EXAMPLES::
sage: eta1, eta2 = EtaGroup(4).basis() # indirect doctest
sage: eta1 * eta2
Eta product of level 4 : (eta_1)^8 (eta_4)^-8
"""
newdict = {}
for d in union(self._keys, other._keys):
newdict[d] = self.r(d) + other.r(d)
return EtaProduct(self.level(), newdict)
def _div_(self, other):
r"""
Return `self * other^{-1}`.
EXAMPLES::
sage: eta1, eta2 = EtaGroup(4).basis()
sage: eta1 / eta2 # indirect doctest
Eta product of level 4 : (eta_1)^-24 (eta_2)^48 (eta_4)^-24
sage: (eta1 / eta2) * eta2 == eta1
True
"""
newdict = {}
for d in union(self._keys, other._keys):
newdict[d] = self.r(d) - other.r(d)
return EtaProduct(self.level(), newdict)
def _div_(self, other):
r"""
Return `self * other^{-1}`.
EXAMPLES::
sage: eta1, eta2 = EtaGroup(4).basis()
sage: eta1 / eta2 # indirect doctest
Eta product of level 4 : (eta_1)^-24 (eta_2)^48 (eta_4)^-24
sage: (eta1 / eta2) * eta2 == eta1
True
"""
newdict = {}
for d in union(self._keys, other._keys):
newdict[d] = self.r(d) - other.r(d)
return EtaProduct(self.level(), newdict)
def _mul_(self, other):
r"""
Return the product of ``self`` and ``other``.
EXAMPLES::
sage: eta1, eta2 = EtaGroup(4).basis() # indirect doctest
sage: eta1 * eta2
Eta product of level 4 : (eta_1)^8 (eta_4)^-8
"""
newdict = {
d: self._rdict.get(d, 0) + other._rdict.get(d, 0)
for d in union(self._rdict, other._rdict)
}
P = self.parent()
return P.element_class(P, newdict)
def _div_(self, other):
r"""
Return `self * other^{-1}`.
EXAMPLES::
sage: eta1, eta2 = EtaGroup(4).basis()
sage: eta1 / eta2 # indirect doctest
Eta product of level 4 : (eta_1)^-24 (eta_2)^48 (eta_4)^-24
sage: (eta1 / eta2) * eta2 == eta1
True
"""
newdict = {
d: self._rdict.get(d, 0) - other._rdict.get(d, 0)
for d in union(self._rdict, other._rdict)
}
P = self.parent()
return P.element_class(P, newdict)
