def get_Ptolemy_relations(t, N, cohomology_class = None):
if cohomology_class:
cohomology_coefficients = (
cohomology_2_rel_boundary_class_to_coeffs(t, cohomology_class))
eqns = []
for tet in t.tet_list:
i = tet.index
if cohomology_class:
signs = cohomology_coefficients[tet.index]
sign_01 = Z2_to_sign(signs[2] + signs[3])
sign_12 = Z2_to_sign(signs[0] + signs[3])
else:
sign_01 = +1
sign_12 = +1
sign_01 = Polynomial.constantPolynomial(sign_01)
sign_12 = Polynomial.constantPolynomial(sign_12)
for coord in simplex_coords_with_fixed_sum(4, N-2):
eqns.append(
- sign_01 * c_parameter(coord+(1,0,0,1),i)
* c_parameter(coord+(0,1,1,0),i)
- sign_12 * c_parameter(coord+(1,1,0,0),i)
* c_parameter(coord+(0,0,1,1),i)
+ c_parameter(coord+(1,0,1,0),i)
* c_parameter(coord+(0,1,0,1),i))
return eqns
def check_solution_on_gluing_equations(t, N, solution, cohomology_class = None):
maxErr = globalsettings.getSetting("maximalError")
if cohomology_class:
cohomology_coefficients = (
cohomology_2_rel_boundary_class_to_coeffs(t,cohomology_class))
for tet in t.tet_list:
i = tet.index
if cohomology_class:
signs = cohomology_coefficients[tet.index]
sign_01 = Z2_to_sign(signs[2] + signs[3])
sign_12 = Z2_to_sign(signs[0] + signs[3])
else:
sign_01 = +1
sign_12 = +1
for coord in simplex_coords_with_fixed_sum(4, N-2):
err = (
- sign_01 *
solution[c_parameter_var(coord+(1,0,0,1),i)] *
solution[c_parameter_var(coord+(0,1,1,0),i)]
- sign_12 *
solution[c_parameter_var(coord+(1,1,0,0),i)] *
solution[c_parameter_var(coord+(0,0,1,1),i)]
+ solution[c_parameter_var(coord+(1,0,1,0),i)] *
solution[c_parameter_var(coord+(0,1,0,1),i)])
if abs(err) > maxErr:
raise NumericalError(
val = err,
msg = "in verify gluing equations")
