Use siegel_kappa in siegel_kappa2

src/acb_theta/siegel_kappa2.c

@@ -9,146 +9,25 @@
     (at your option) any later version.  See <https://www.gnu.org/licenses/>.
 */
 
-#include "fmpz_mat.h"
-#include "acb_modular.h"
+#include "acb.h"
+#include "acb_mat.h"
 #include "acb_theta.h"
 
-static slong
-acb_siegel_kappa2_g1(const fmpz_mat_t mat, const fmpz_mat_t x)
-{
-    slong g = sp2gz_dim(mat);
-    psl2z_t y;
-    int R[4];
-    int S[4];
-    int C;
-    ulong ab;
-    slong e, res;
-
-    psl2z_init(y);
-
-    /* set y to corresponding psl2z_t and use acb_modular_theta_transform */
-    fmpz_set(&y->a, fmpz_mat_entry(x, 0, 0));
-    fmpz_set(&y->b, fmpz_mat_entry(x, 0, 1));
-    fmpz_set(&y->c, fmpz_mat_entry(x, 1, 0));
-    fmpz_set(&y->d, fmpz_mat_entry(x, 1, 1));
-
-    acb_modular_theta_transform(R, S, &C, y);
-
-    /* find out where theta_00 is going */
-    if (S[2] == 1) /* theta_2 */
-    {
-        ab = 1 << (2 * g - 1);
-    }
-    else if (S[2] == 2) /* theta_0 */
-    {
-        ab = 0;
-    }
-    else /* theta_1, since -theta_3 cannot happen (odd) */
-    {
-        ab = 1 << (g - 1);
-    }
-    acb_theta_char_table(&ab, &e, mat, ab);
-
-    /* adjust root of unity based on R */
-    if (fmpz_is_zero(&y->c))
-    {
-        res = -R[2] - e;
-    }
-    else
-    {
-        res = -R[2] - 1 - e;
-    }
-
-    psl2z_clear(y);
-    return res;
-}
-
-static slong
-acb_siegel_kappa2_j(const fmpz_mat_t mat)
-{
-    slong g = sp2gz_dim(mat);
-    fmpz_mat_t gamma;
-    slong r, res;
-
-    fmpz_mat_window_init(gamma, mat, g, 0, 2 * g, g);
-    r = fmpz_mat_rank(gamma);
-    fmpz_mat_window_clear(gamma);
-
-    res = -r;
-    if (r % 2 == 1)
-    {
-        res -= 2;
-    }
-    return res;
-}
-
 slong
 acb_siegel_kappa2(const fmpz_mat_t mat)
 {
     slong g = sp2gz_dim(mat);
-    fmpz_mat_struct * dec;
-    fmpz_mat_t delta;
-    fmpz_t det;
-    slong nb_dec;
-    fmpz_mat_t x;
-    slong k, res, e;
-    ulong ab;
-
-    fmpz_mat_init(x, 2, 2);
-    fmpz_init(det);
-    dec = sp2gz_decompose(&nb_dec, mat);
+    slong prec = 2;
+    acb_mat_t tau;
+    acb_t s;
+    slong res;
 
-    res = 0;
-    for (k = nb_dec - 1; k >= 0; k--)
-    {
-        if (sp2gz_is_trig(&dec[k]) || sp2gz_is_block_diag(&dec[k]))
-        {
-            /* theta_00(mtau) = theta_ab(tau) */
-            fmpz_mat_window_init(delta, &dec[k], g, g, 2 * g, 2 * g);
-            fmpz_mat_det(det, delta);
-            fmpz_mat_window_clear(delta);
+    acb_mat_init(tau, g, g);
+    acb_init(s);
 
-            if (!fmpz_is_one(det))
-            {
-                res += 2;
-            }
-        }
-        else if (sp2gz_is_embedded(x, &dec[k]))
-        {
-            if (fmpz_cmp_si(fmpz_mat_entry(x, 1, 0), 0) < 0
-                || (fmpz_is_zero(fmpz_mat_entry(x, 1, 0))
-                    && fmpz_cmp_si(fmpz_mat_entry(x, 1, 1), 0) < 0))
-            {
-                fmpz_mat_neg(x, x);
-                res += acb_siegel_kappa2_g1(&dec[k], x);
-                res += 2;
-            }
-            else
-            {
-                res += acb_siegel_kappa2_g1(&dec[k], x);
-            }
-        }
-        else /* embedded j */
-        {
-            res += acb_siegel_kappa2_j(&dec[k]);
-        }
-    }
+    res = acb_siegel_kappa(s, mat, tau, 1, prec);
 
-    /* Adjust final sign based on transformation of coordinates */
-    acb_theta_char_table(&ab, &e, mat, 0);
-    res -= e;
-    ab = 0;
-    for (k = 0; k < nb_dec; k++)
-    {
-        acb_theta_char_table(&ab, &e, &dec[k], ab);
-        res += e;
-    }
-
-    fmpz_mat_clear(x);
-    for (k = 0; k < nb_dec; k++)
-    {
-        fmpz_mat_clear(&dec[k]);
-    }
-    flint_free(dec);
-    return res & 3;
+    acb_mat_clear(tau);
+    acb_clear(s);
+    return res;
 }