diff --git a/python/verify/complex_volume/closed.py b/python/verify/complex_volume/closed.py index fd96e8d2..98d1ec2a 100644 --- a/python/verify/complex_volume/closed.py +++ b/python/verify/complex_volume/closed.py @@ -8,7 +8,7 @@ if _within_sage: from sage.symbolic.constants import pi from sage.arith.misc import XGCD as xgcd - import sage.all + from ...sage_helper import I from .. import hyperbolicity @@ -69,8 +69,8 @@ def zero_lifted_holonomy(manifold, m, l, f): # Compute by what multiple of 2 pi i to adjust g, a, b = xgcd(m_fill, l_fill) - m -= p * a * multiple_of_pi * sage.all.I - l -= p * b * multiple_of_pi * sage.all.I + m -= p * a * multiple_of_pi * I + l -= p * b * multiple_of_pi * I # For sanity, double check that we compute it right. p_interval = (m_fill * m + l_fill * l).imag() / multiple_of_pi @@ -166,4 +166,4 @@ def verified_complex_volume_closed_torsion(manifold, bits_prec=None): # I. # Also add multiples of pi^2/2 to try to get the Chern-Simons part # between -pi^2/4 and pi^2/4. - return normalize_by_pi_square_over_two(complex_volume) / sage.all.I + return normalize_by_pi_square_over_two(complex_volume) / I