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/*
* current_curve_basis.c
*
* This file provides the functions
*
* void current_curve_basis( Triangulation *manifold,
* int cusp_index,
* MatrixInt22 basis_change);
*
* void install_current_curve_bases( Triangulation *manifold);
*
*
* current_curve_basis() accepts a Triangulation and a cusp index,
* and computes a 2 x 2 integer matrix basis_change with the property that
*
* if the Cusp of index cusp_index is filled, and has
* integer Dehn filling coefficients,
*
* the first row of basis_change is set to the current
* Dehn filling coefficients (divided by their gcd), and
* the second row of basis_change is set to the shortest
* curve which completes a basis.
*
* else
*
* basis_change is set to the identity
*
* Note that for nonorientable cusps, the only possible Dehn
* filling coefficients are +/- (m,0), and +/- the longitude will be the
* shortest curve which completes the basis.
*
* install_current_curve_bases() installs the current curve basis
* on each Cusp of manifold.
*
* 96/9/28 Modified to accept non relatively prime integer coefficients.
* For example, (15, 20) is treated the same as (3,4). Thus in
* the new basis the surgery coefficients will be of the form (m,0),
* where m is the gcd of the original coefficients.
*
* 99/11/05 Added install_current_curve_bases().
*/
#include "kernel.h"
#define EPSILON 1e-5
#define BIG_MODULUS 1e+5
static void current_curve_basis_on_cusp(Cusp *cusp, MatrixInt22 basis_change);
void current_curve_basis(
Triangulation *manifold,
int cusp_index,
MatrixInt22 basis_change)
{
current_curve_basis_on_cusp( find_cusp(manifold, cusp_index),
basis_change);
}
static void current_curve_basis_on_cusp(
Cusp *cusp,
MatrixInt22 basis_change)
{
int m_int,
l_int,
the_gcd;
long a,
b;
Complex new_shape;
int multiple;
int i,
j;
m_int = (int) cusp->m;
l_int = (int) cusp->l;
if (cusp->is_complete == FALSE /* cusp is filled and */
&& m_int == cusp->m /* coefficients are integers */
&& l_int == cusp->l)
{
/*
* Find a and b such that am + bl = gcd(m, l).
*/
the_gcd = euclidean_algorithm(m_int, l_int, &a, &b);
/*
* Divide through by the g.c.d.
*/
m_int /= the_gcd;
l_int /= the_gcd;
/*
* Set basis_change to
*
* m l
* -b a
*/
basis_change[0][0] = m_int;
basis_change[0][1] = l_int;
basis_change[1][0] = -b;
basis_change[1][1] = a;
/*
* Make sure the new longitude is as short as possible.
* The ratio (new longitude)/(new meridian) should have a
* real part in the interval (-1/2, +1/2].
*/
/*
* Compute the new_shape, using the tentative longitude.
*/
new_shape = transformed_cusp_shape( cusp->cusp_shape[initial],
basis_change);
/*
* 96/10/1 There is a danger that for nonhyperbolic solutions
* the cusp shape will be ill-defined (either very large or NaN).
* However for some nonhyperbolic solutions (flat solutions
* for example) it may make good sense. So we attempt to
* make the longitude short iff the new_shape is defined and
* not outrageously large; otherwise we're content with an
* arbitrary longitude.
*/
if (complex_modulus(new_shape) < BIG_MODULUS)
{
/*
* Figure out how many meridians we need to subtract
* from the longitude.
*/
multiple = (int) floor(new_shape.real - (-0.5 + EPSILON));
/*
* longitude -= multiple * meridian
*/
for (j = 0; j < 2; j++)
basis_change[1][j] -= multiple * basis_change[0][j];
}
}
else
{
/*
* Set basis_change to the identity.
*/
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
basis_change[i][j] = (i == j);
}
}
void install_current_curve_bases(
Triangulation *manifold)
{
Cusp *cusp;
MatrixInt22 *change_matrices;
/*
* Allocate an array to store the change of basis matrices.
*/
change_matrices = NEW_ARRAY(manifold->num_cusps, MatrixInt22);
/*
* Compute the change of basis matrices.
*/
for (cusp = manifold->cusp_list_begin.next;
cusp != &manifold->cusp_list_end;
cusp = cusp->next)
{
if (cusp->index < 0
|| cusp->index >= manifold->num_cusps)
uFatalError("install_current_curve_bases", "current_curve_basis");
current_curve_basis_on_cusp(cusp, change_matrices[cusp->index]);
}
/*
* Install the change of basis matrices.
*/
if (change_peripheral_curves(manifold, change_matrices) != func_OK)
uFatalError("install_current_curve_bases", "current_curve_basis");
/*
* Free the array used to store the change of basis matrices.
*/
my_free(change_matrices);
}
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