void free_symmetry_group(
SymmetryGroup *symmetry_group)
{
if (symmetry_group != NULL)
{
int i;
free_isometry_list(symmetry_group->symmetry_list);
for (i = 0; i < symmetry_group->order; i++)
my_free(symmetry_group->product[i]);
my_free(symmetry_group->product);
my_free(symmetry_group->order_of_element);
my_free(symmetry_group->inverse);
if (symmetry_group->abelian_description != NULL)
free_abelian_group(symmetry_group->abelian_description);
if (symmetry_group->is_direct_product == TRUE)
for (i = 0; i < 2; i++)
free_symmetry_group(symmetry_group->factor[i]);
my_free(symmetry_group);
}
}
FuncResult compute_isometries(
Triangulation *manifold0,
Triangulation *manifold1,
Boolean *are_isometric,
IsometryList **isometry_list,
IsometryList **isometry_list_of_links)
{
Triangulation *simplified_manifold0,
*simplified_manifold1;
IsometryList *the_isometry_list,
*the_isometry_list_of_links;
FuncResult result;
/*
* Make sure the variables used to pass back our results
* are initially empty.
*/
if ((isometry_list != NULL && *isometry_list != NULL)
|| (isometry_list_of_links != NULL && *isometry_list_of_links != NULL))
uFatalError("compute_isometries", "isometry");
/*
* If one of the spaces isn't a manifold, return func_bad_input.
*/
if (all_Dehn_coefficients_are_relatively_prime_integers(manifold0) == FALSE
|| all_Dehn_coefficients_are_relatively_prime_integers(manifold1) == FALSE)
return func_bad_input;
/*
* Check whether the manifolds are obviously nonhomeomorphic.
*
* (In the interest of a robust, beyond-a-shadow-of-a-doubt algorithm,
* stick to discrete invariants like the number of cusps and the
* first homology group, and avoid real-valued invariants like
* the volume which require judging when two floating point numbers
* are equal.) [96/12/6 Comparing canonical triangulations
* relies on having at least a vaguely correct hyperbolic structure,
* so it should be safe to reject manifolds whose volumes differ
* by more than, say, 0.01.]
*/
if (count_unfilled_cusps(manifold0) != count_unfilled_cusps(manifold1)
|| same_homology(manifold0, manifold1) == FALSE
|| ( manifold0->solution_type[filled] == geometric_solution
&& manifold1->solution_type[filled] == geometric_solution
&& fabs(volume(manifold0, NULL) - volume(manifold1, NULL)) > CRUDE_VOLUME_EPSILON))
{
*are_isometric = FALSE;
return func_OK;
}
/*
* Whether the actual manifolds (after taking into account Dehn
* fillings) have cusps or not, we want to begin by getting rid
* of "unnecessary" cusps.
*/
simplified_manifold0 = fill_reasonable_cusps(manifold0);
if (simplified_manifold0 == NULL)
return func_failed;
simplified_manifold1 = fill_reasonable_cusps(manifold1);
if (simplified_manifold1 == NULL)
return func_failed;
/*
* Split into cases according to whether the manifolds are
* closed or cusped (i.e. whether all cusps are filled or not).
* The above tests insure that either both are closed or both
* are cusped.
*/
if (all_cusps_are_filled(simplified_manifold0) == TRUE)
result = compute_closed_isometry( simplified_manifold0,
simplified_manifold1,
are_isometric);
else
{
result = compute_cusped_isometries( simplified_manifold0,
simplified_manifold1,
&the_isometry_list,
&the_isometry_list_of_links);
if (result == func_OK)
{
*are_isometric = the_isometry_list->num_isometries > 0;
if (isometry_list != NULL)
*isometry_list = the_isometry_list;
else
free_isometry_list(the_isometry_list);
if (isometry_list_of_links != NULL)
*isometry_list_of_links = the_isometry_list_of_links;
else
free_isometry_list(the_isometry_list_of_links);
}
}
/*
* We no longer need the simplified manifolds.
*/
free_triangulation(simplified_manifold0);
free_triangulation(simplified_manifold1);
return result;
}
