parity

acb_dirichlet.h

@@ -63,8 +63,8 @@ void acb_dirichlet_group_dlog_precompute(acb_dirichlet_group_t G, ulong num);
 
 ulong acb_dirichlet_number_primitive(const acb_dirichlet_group_t G);
 ulong acb_dirichlet_conductor_ui(const acb_dirichlet_group_t G, ulong a);
+int acb_dirichlet_parity_ui(const acb_dirichlet_group_t G, ulong a);
 /*
-ulong acb_dirichlet_parity_ui(const acb_dirichlet_groupt_t G, ulong a);
 ulong acb_dirichlet_order_ui(const acb_dirichlet_groupt_t G, ulong a);
 */
 

acb_dirichlet/eta.c

@@ -34,4 +34,3 @@ acb_dirichlet_eta(acb_t res, const acb_t s, slong prec)
         acb_clear(t);
     }
 }
-

acb_dirichlet/parity_ui.c

@@ -0,0 +1,46 @@
+/*=============================================================================
+
+    This file is part of ARB.
+
+    ARB is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    ARB is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with ARB; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+=============================================================================*/
+/******************************************************************************
+
+    Copyright (C) 2016 Pascal Molin
+
+******************************************************************************/
+
+#include "acb_dirichlet.h"
+
+int
+acb_dirichlet_parity_ui(const acb_dirichlet_group_t G, ulong a)
+{
+    slong k;
+    int par;
+
+    par = 0;
+
+    if (G->neven && a % 4 == 3)
+        par++;
+
+    for (k = G->neven; k < G->num; k++)
+    {
+        if (n_jacobi_unsigned(a, G->primes[k]) == -1)
+            par++;
+    }
+
+    return par % 2;
+}

acb_dirichlet/test/t-chars.c

@@ -77,6 +77,7 @@ int main()
         /* check number char properties */
         for (iter2 = 0; iter2 < 50; iter2++)
         { 
+            int par;
             ulong m, n;
             ulong order, chim1, pairing, cond;
 
@@ -108,14 +109,16 @@ int main()
                 abort();
             }
 
+            par = acb_dirichlet_parity_ui(G, m);
             chim1 = acb_dirichlet_ui_chi(G, chi, q - 1);
-            if (acb_dirichlet_char_parity(chi) != (chim1 != 0))
+            if (acb_dirichlet_char_parity(chi) != par || par != (chim1 != 0))
             {
                 flint_printf("FAIL: parity\n\n");
                 flint_printf("q = %wu\n\n", q);
                 flint_printf("m = %wu\n\n", m);
                 flint_printf("chi(-1) = %wu\n\n", chim1);
                 flint_printf("char_parity = %d", acb_dirichlet_char_parity(chi));
+                flint_printf("parity_ui = %d", par);
                 acb_dirichlet_char_print(G, chi);
                 abort();
             }