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# Find integral points in a fail-safe way uing both Sage and Magma,
# comparing, returning the union in all cases and outputting a warning
# message if they disagree.
from sage.all import Set
from magma import get_magma
def get_integral_points_with_sage(E, gens):
return [P[0] for P in E.integral_points(mw_base=gens)]
def get_integral_points_with_magma(E, gens):
mag = get_magma()
mE = mag(E)
xs = [E(P.Eltseq().sage())[0] for P in mE.IntegralPoints(FBasis=[mE(list(P)) for P in gens])]
return xs
def get_integral_points(E, gens, verbose=True):
x_list_magma = get_integral_points_with_magma(E, gens)
x_list_sage = get_integral_points_with_sage(E, gens)
if x_list_magma != x_list_sage:
if verbose:
print("Curve {}: \n".format(E.ainvs))
print("Integral points via Magma: {}".format(x_list_magma))
print("Integral points via Sage: {}".format(x_list_sage))
x_list = list(Set(x_list_sage)+Set(x_list_magma))
x_list.sort()
return x_list
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