def wrapper(*args, **kwds):
from sage.misc.superseded import experimental_warning
experimental_warning(
self.trac_number, 'This class/method/function is marked as '
'experimental. It, its functionality or its '
'interface might change without a '
'formal deprecation.', self.stacklevel)
return func(*args, **kwds)
def wrapper(*args, **kwds):
from sage.misc.superseded import experimental_warning
experimental_warning(self.trac_number,
'This class/method/function is marked as '
'experimental. It, its functionality or its '
'interface might change without a '
'formal deprecation.',
self.stacklevel)
return func(*args, **kwds)
def wrapper(*args, **kwds):
from sage.misc.superseded import experimental_warning
if not wrapper._already_issued:
experimental_warning(
self.trac_number,
"This class/method/function is marked as "
"experimental. It, its functionality or its "
"interface might change without a "
"formal deprecation.",
self.stacklevel,
)
wrapper._already_issued = True
return func(*args, **kwds)
def __init__(self, lie):
r"""
EXAMPLES::
sage: L = LieAlgebra(QQ, 3, 'x')
sage: TestSuite(L.Hall()).run()
"""
experimental_warning(16823, "The Hall basis has not been fully proven correct,"
" but currently no bugs are known")
FreeLieBasis_abstract.__init__(self, lie, "Hall")
# Register the coercions
Lyn = lie.Lyndon()
Hom_HL = Hom(self, Lyn)
Hom_LH = Hom(Lyn, self)
LieAlgebraHomomorphism_im_gens(Hom_HL, Lyn.gens()).register_as_coercion()
LieAlgebraHomomorphism_im_gens(Hom_LH, self.gens()).register_as_coercion()
def __init__(self, lie):
r"""
EXAMPLES::
sage: L = LieAlgebra(QQ, 3, 'x')
sage: TestSuite(L.Hall()).run()
"""
experimental_warning(16823, "The Hall basis has not been fully proven correct,"
" but currently no bugs are known")
FreeLieBasis_abstract.__init__(self, lie, "Hall")
# Register the coercions
Lyn = lie.Lyndon()
Hom_HL = Hom(self, Lyn)
Hom_LH = Hom(Lyn, self)
LieAlgebraHomomorphism_im_gens(Hom_HL, Lyn.gens()).register_as_coercion()
LieAlgebraHomomorphism_im_gens(Hom_LH, self.gens()).register_as_coercion()
from sage.structure.sequence import Sequence
from sage.arith.misc import prod, integer_floor
from sage.functions.log import log
from sage.functions.other import sqrt
from sage.rings.finite_rings import finite_field_base
from sage.rings.number_field import number_field_base
from sage.schemes.elliptic_curves.ell_generic import EllipticCurve_generic
from sage.schemes.elliptic_curves.hom import EllipticCurveHom
from sage.schemes.elliptic_curves.ell_curve_isogeny import EllipticCurveIsogeny
from sage.schemes.elliptic_curves.weierstrass_morphism import WeierstrassIsomorphism
from sage.misc.superseded import experimental_warning
experimental_warning(32744, 'EllipticCurveHom_composite is experimental code.')
#TODO: implement sparse strategies? (cf. the SIKE cryptosystem)
def _eval_factored_isogeny(phis, P):
"""
This method pushes a point `P` through a given sequence ``phis``
of compatible isogenies.
EXAMPLES::
sage: from sage.schemes.elliptic_curves import hom_composite
sage: E = EllipticCurve(GF(419), [1,0])
sage: Q = E(21,8)
sage: phis = []