def check_roots_are_roots(self, rec, verbose=False):
"""
check that embedding_root_real, and embedding_root_image approximate a root of field_poly
"""
poly = PolynomialRing(ZZ, "x")(rec['field_poly'])
dpoly = poly.derivative()
dbroots = db.mf_hecke_cc.search(
{'hecke_orbit_code': rec['hecke_orbit_code']},
["embedding_root_real", "embedding_root_imag"])
dbroots = [
CCC(root["embedding_root_real"], root["embedding_root_imag"])
for root in dbroots
]
if len(dbroots) != poly.degree():
if verbose:
print("Wrong number of roots")
return False
for r in dbroots:
# f is irreducible, so all roots are simple and checking relative error is the way to go
if poly(r) / dpoly(r) > 1e-11:
# It's still possible that the roots are correct; it could just be a problem of numerical instability
print(r, poly(r) / dpoly(r))
break
else:
return True
roots = poly.roots(CCC, multiplicities=False)
# greedily match. The degrees are all at most 20, so it's okay to use a quadratic algorithm
while len(roots) > 0:
best_dist = infinity
r = roots[0]
for i, s in enumerate(dbroots):
dist = abs(r - s)
if dist < best_dist:
best_dist, best_i = dist, i
# The dim 1 case where poly=x is handled correctly in the earlier loop, so r != 0.
if best_dist / abs(r) > 1e-13:
if verbose:
print("Roots mismatch", sorted(roots), sorted(dbroots))
return False
roots.pop(0)
dbroots.pop(best_i)
return True
def check_roots_are_roots(self, rec, verbose=False):
"""
check that embedding_root_real, and embedding_root_image approximate a root of field_poly
"""
poly = PolynomialRing(ZZ, "x")(rec['field_poly'])
dpoly = poly.derivative()
dbroots = db.mf_hecke_cc.search({'hecke_orbit_code': rec['hecke_orbit_code']}, ["embedding_root_real", "embedding_root_imag"])
dbroots = [CCC(root["embedding_root_real"], root["embedding_root_imag"]) for root in dbroots]
if len(dbroots) != poly.degree():
if verbose:
print "Wrong number of roots"
return False
for r in dbroots:
# f is irreducible, so all roots are simple and checking relative error is the way to go
if poly(r)/dpoly(r) > 1e-11:
# It's still possible that the roots are correct; it could just be a problem of numerical instability
print r, poly(r)/dpoly(r)
break
else:
return True
roots = poly.roots(CCC, multiplicities=False)
# greedily match. The degrees are all at most 20, so it's okay to use a quadratic algorithm
while len(roots) > 0:
best_dist = infinity
r = roots[0]
for i, s in enumerate(dbroots):
dist = abs(r-s)
if dist < best_dist:
best_dist, best_i = dist, i
# The dim 1 case where poly=x is handled correctly in the earlier loop, so r != 0.
if best_dist/abs(r) > 1e-13:
if verbose:
print "Roots mismatch", sorted(roots), sorted(dbroots)
return False
roots.pop(0)
dbroots.pop(best_i)
return True
