def _call_(self, x):
r"""
Convert ``x`` to the codomain.
EXAMPLES::
sage: from pyeantic import RealEmbeddedNumberField
sage: K = NumberField(x**2 - 2, 'a', embedding=sqrt(AA(2)))
sage: KK = RealEmbeddedNumberField(K)
sage: a = KK.an_element()
sage: K(a)
a
sage: K = NumberField(x**2 - 2, 'b', embedding=sqrt(AA(2)))
sage: KK = RealEmbeddedNumberField(K)
sage: b = KK.an_element()
sage: K(b)
b
"""
rational_coefficients = [
ZZ(c.get_str()) / ZZ(x.renf_elem.den().get_str())
for c in x.renf_elem.num_vector()
]
while len(rational_coefficients) < self.domain().number_field.degree():
rational_coefficients.append(QQ.zero())
return self.codomain()(rational_coefficients)
def is_contained_in_dual(C, D):
"""
Test if the cone C is contained in the dual of the cone D.
"""
for v, w in itertools.product(C.rays(), D.rays()):
if vector(QQ, v) * vector(QQ, w) < QQ.zero():
return False
return True
def mittag_leffler_e(alpha, beta=1):
alpha = QQ.coerce(alpha)
if alpha <= QQ.zero():
raise ValueError
num, den = alpha.numerator(), alpha.denominator()
dop0 = prod(alpha * x * Dx + beta - num + t for t in range(num)) - x**den
expo = dop0.indicial_polynomial(x).roots(QQ, multiplicities=False)
pre = prod((x * Dx - k) for k in range(den) if QQ(k) not in expo)
dop = pre * dop0 # homogenize
dop = dop.numerator().primitive_part()
expo = sorted(dop.indicial_polynomial(x).roots(QQ, multiplicities=False))
assert len(expo) == dop.order()
ini = [(1 / funs.gamma(alpha * k + beta) if k in ZZ else 0) for k in expo]
return IVP(0, dop, ini)