def __init__(self,
ec,
P=None,
dmap=None,
order=None,
pairing="weil",
k=None,
seed=None):
self.ec = ec
self.P = P
self.distortion = self._deco(dmap)
if dmap == None:
self.distortion = self._ext
if order == None:
self.order = P.order()
else:
self.order = order
self.pairing = pairing
ord = self.ec.base_ring().cardinality()
if k == None:
k = Zmod(self.order)(ord).multiplicative_order()
self.k = k
random.seed(seed)
self.t = random.randint(2, self.order - 1)
base = FiniteField(ord**self.k, 'b')
self.hom = Hom(self.ec.base_ring(),
base)(base.gen()**((ord**self.k - 1) / (ord - 1)))
self.ec2 = EllipticCurve(map(int,
self.ec.a_invariants())).change_ring(base)
def hom_module_induced_morphism(f, N, action, hom_M_prime_N_data,
hom_M_N_data):
M_prime = f.domain()
M = f.codomain()
hom_M_prime_N, M_prime_basis, M_prime_basis_keys, prime_components, prime_from_components, prime_hom_action = hom_M_prime_N_data
hom_M_N, M_basis, M_basis_keys, components, from_components, hom_action = hom_M_N_data
f_values = {}
for i_prime in M_prime_basis_keys:
f_values[i_prime] = f(M_prime_basis[i_prime])
def f_star_components(x):
c_x = components(x)
c = {}
for i_prime in M_prime_basis_keys:
a = f_values[i_prime]
for c in N.coordinates(
sum_in_module(N, [
linearly_extended_action(N, action, a[i], c_x[i])
for i in a.support()
])):
yield c
matrix_representing_f_star = matrix(
[tuple(f_star_components(x)) for x in hom_M_N.basis()],
ncols=hom_M_prime_N.rank())
return FreeModuleMorphism(Hom(hom_M_N, hom_M_prime_N),
matrix_representing_f_star)
def base_change_morphism(f, R):
M = f.domain()
N = f.codomain()
assert R.has_coerce_map_from(f.base_ring())
MM = base_change_module(M, R)
NN = base_change_module(N, R)
return FreeModuleMorphism(Hom(MM, NN), f.matrix().change_ring(R))
def __init__(self, base=None, category=None):
if base is QQ:
self._element_factory = exactreal.Element[type(exactreal.RationalField())]
self._module_factory = lambda gens: QQModule(*gens)
number_field = QQ
else:
base = RealEmbeddedNumberField(base)
ring = exactreal.NumberField(base.renf)
self._element_factory = exactreal.Element[type(ring)]
self._module_factory = lambda gens: NumberFieldModule(ring, *gens)
number_field = base.number_field
CommutativeRing.__init__(self, base, category=category)
H = Hom(number_field, self)
coercion = H.__make_element_class__(CoercionExactRealsNumberField)(H)
self.register_coercion(coercion)
def __init__(self, domain):
Morphism.__init__(
self, Hom(domain, domain.number_field, SetsWithPartialMaps()))
def __init__(self):
Morphism.__init__(self, Hom(mpq, QQ, QQ.category(), check=False))
def __init__(self):
Morphism.__init__(self, Hom(mpz, ZZ, ZZ.category(), check=False))
def __init__(self, domain):
Morphism.__init__(self, Hom(domain, domain._isomorphic_vector_space, SetsWithPartialMaps()))