refactor order

acb_dirichlet.h

@@ -27,6 +27,11 @@
 extern "C" {
 #endif
 
+void _acb_dirichlet_euler_product_real_ui(arb_t res, ulong s,
+    const signed char * chi, int mod, int reciprocal, slong prec);
+
+void acb_dirichlet_eta(acb_t res, const acb_t s, slong prec);
+
 typedef struct
 {
     ulong q;                /* modulus */
@@ -62,11 +67,9 @@ void acb_dirichlet_group_dlog_precompute(acb_dirichlet_group_t G, ulong num);
 /* properties of elements without log */
 
 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_order_ui(const acb_dirichlet_groupt_t G, ulong a);
-*/
+ulong acb_dirichlet_ui_conductor(const acb_dirichlet_group_t G, ulong a);
+int acb_dirichlet_ui_parity(const acb_dirichlet_group_t G, ulong a);
+ulong acb_dirichlet_ui_order(const acb_dirichlet_group_t G, ulong a);
 
 /* elements of the group, keep both number and log */
 typedef struct
@@ -78,11 +81,6 @@ acb_dirichlet_conrey_struct;
 
 typedef acb_dirichlet_conrey_struct acb_dirichlet_conrey_t[1];
 
-void _acb_dirichlet_euler_product_real_ui(arb_t res, ulong s,
-    const signed char * chi, int mod, int reciprocal, slong prec);
-
-void acb_dirichlet_eta(acb_t res, const acb_t s, slong prec);
-
 void acb_dirichlet_conrey_init(acb_dirichlet_conrey_t x, const acb_dirichlet_group_t G);
 void acb_dirichlet_conrey_clear(acb_dirichlet_conrey_t x);
 void acb_dirichlet_conrey_print(const acb_dirichlet_group_t G, const acb_dirichlet_conrey_t x);

acb_dirichlet/char_next.c

@@ -42,8 +42,8 @@ acb_dirichlet_char_next(acb_dirichlet_char_t chi, const acb_dirichlet_group_t G)
         chi->expo[k] = 0;  
     }
 
-    /* should do it with log, but not kept yet */
-    chi->conductor = acb_dirichlet_conductor_ui(G, chi->n);
+    /* should do it with log, but log is not kept yet in the struct */
+    chi->conductor = acb_dirichlet_ui_conductor(G, chi->n);
     acb_dirichlet_char_normalize(chi, G);
 
     /* return last index modified */

acb_dirichlet/conrey_order.c

@@ -0,0 +1,38 @@
+/*=============================================================================
+
+    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"
+
+ulong
+acb_dirichlet_conrey_order(const acb_dirichlet_group_t G, const acb_dirichlet_conrey_t x)
+{
+    ulong k, g;
+    g = G->expo;
+
+    for (k = 0; k < G->num; k++)
+        g = n_gcd(g, G->PHI[k] * x->log[k]);
+
+    return G->expo / g;
+}

acb_dirichlet/test/t-chars.c

@@ -26,25 +26,6 @@
 #include "acb_dirichlet.h"
 
 
-/* order of an element knowing the factorization of a multiple */
-static ulong
-nmod_order_precomp(ulong a, nmod_t mod, ulong expo, n_factor_t fac)
-{
-    int k;
-    ulong pe, ap, order = 1;
-    for (k = 0; k < fac.num; k++)
-    {
-        pe = n_pow(fac.p[k], fac.exp[k]);
-        ap = nmod_pow_ui(a, expo / pe, mod);
-        while ( ap != 1)
-        {
-            ap = nmod_pow_ui(ap, fac.p[k], mod);
-            order *= fac.p[k];
-        }
-    }
-    return order;
-}
-
 int main()
 {
     slong iter, bits;
@@ -61,7 +42,6 @@ int main()
         acb_dirichlet_group_t G;
         acb_dirichlet_char_t chi, chi2;
         ulong q, iter2;
-        n_factor_t fac;
 
         q = 2 + n_randint(state, 1 << bits);
 
@@ -69,9 +49,6 @@ int main()
         acb_dirichlet_char_init(chi, G);
         acb_dirichlet_char_init(chi2, G);
 
-        n_factor_init(&fac);
-        n_factor(&fac, G->expo, 1);
-
         acb_dirichlet_group_dlog_precompute(G, 50);
 
         /* check number char properties */
@@ -87,7 +64,7 @@ int main()
 
             acb_dirichlet_char(chi, G, m);
 
-            order = nmod_order_precomp(m, G->mod, G->expo, fac);
+            order = acb_dirichlet_ui_order(G, m);
             if (order != chi->order)
             {
                 flint_printf("FAIL: order\n\n");
@@ -98,7 +75,7 @@ int main()
                 abort();
             }
 
-            cond = acb_dirichlet_conductor_ui(G, m);
+            cond = acb_dirichlet_ui_conductor(G, m);
             if (cond != acb_dirichlet_char_conductor(G, chi))
             {
                 flint_printf("FAIL: conductor\n\n");
@@ -109,7 +86,7 @@ int main()
                 abort();
             }
 
-            par = acb_dirichlet_parity_ui(G, m);
+            par = acb_dirichlet_ui_parity(G, m);
             chim1 = acb_dirichlet_ui_chi(G, chi, q - 1);
             if (acb_dirichlet_char_parity(chi) != par || par != (chim1 != 0))
             {

acb_dirichlet/theta_length.c

@@ -33,7 +33,7 @@ acb_dirichlet_theta_length_d(ulong q, double x, slong prec)
 {
     double a, la;
     a = PI / (double)q * x * x;
-    la = (a>.3) ? -log(2*a*(1-a)) : .8;
+    la = (a < .3) ? -log(2*a*(1-a)) : .8;
     la = ((double)prec * LOG2 + la) / a;
     return ceil(sqrt(la)+.5);
 }

acb_dirichlet/ui_conductor.c

@@ -26,7 +26,7 @@
 #include "acb_dirichlet.h"
 
 ulong
-acb_dirichlet_conductor_ui(const acb_dirichlet_group_t G, ulong a)
+acb_dirichlet_ui_conductor(const acb_dirichlet_group_t G, ulong a)
 {
     slong k;
     ulong ap, cond;

acb_dirichlet/ui_order.c

@@ -0,0 +1,55 @@
+/*=============================================================================
+
+    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"
+
+/* order of an element knowing the factorization of a multiple */
+ulong
+nmod_order_precomp(ulong a, nmod_t mod, ulong expo, n_factor_t fac)
+{
+    int k;
+    ulong pe, ap, order = 1;
+    for (k = 0; k < fac.num; k++)
+    {
+        pe = n_pow(fac.p[k], fac.exp[k]);
+        ap = nmod_pow_ui(a, expo / pe, mod);
+        while ( ap != 1)
+        {
+            ap = nmod_pow_ui(ap, fac.p[k], mod);
+            order *= fac.p[k];
+        }
+    }
+    return order;
+}
+
+ulong
+acb_dirichlet_ui_order(const acb_dirichlet_group_t G, ulong a)
+{
+    n_factor_t fac;
+
+    n_factor_init(&fac);
+    n_factor(&fac, G->expo, 1);
+    return nmod_order_precomp(a, G->mod, G->expo, fac);
+}

acb_dirichlet/ui_parity.c

@@ -26,7 +26,7 @@
 #include "acb_dirichlet.h"
 
 int
-acb_dirichlet_parity_ui(const acb_dirichlet_group_t G, ulong a)
+acb_dirichlet_ui_parity(const acb_dirichlet_group_t G, ulong a)
 {
     slong k;
     int par;

doc/source/acb_dirichlet.rst

@@ -29,9 +29,10 @@ Working with Dirichlet characters mod *q* consists mainly
 in going from residue classes mod *q* to exponents on a set
 of generators of the group.
 
-This implementation relies on the Conrey generators introduced
-in the LMFDB. We call *number* a residue class, and *index* the
-corresponding vector of exponents.
+This implementation relies on the Conrey numbering scheme
+introduced in the LMFDB.
+We call *number* a residue class modulo *q*, and *index* the
+corresponding vector of exponents of Conrey generators.
 
 Going from an *index* to the corresponding *number* is a cheap
 operation while the converse requires computing discrete
@@ -79,6 +80,9 @@ logarithms.
 
     If *num* gets very large, the entire group may be indexed.
 
+Conrey index
+...............................................................................
+
 .. type:: acb_dirichlet_conrey_struct
 
 .. type:: acb_dirichlet_conrey_t
@@ -130,12 +134,43 @@ the group *G* is isomorphic to its dual.
 
     The returned value is the numerator of the actual value exponent mod the group exponent *G->expo*.
 
+Character properties
+...............................................................................
+
+As a consequence of the Conrey numbering, properties of
+characters such that the order, the parity or the conductor are available
+at the level of their number, whithout any discrete log computation,
+or at the Conrey index level.
+
+.. function:: ulong acb_dirichlet_ui_order(const acb_dirichlet_group_t G, ulong a)
+
+.. function:: ulong acb_dirichlet_conrey_order(const acb_dirichlet_group_t G, const acb_dirichlet_conrey_t x)
+
+   Compute the order of a mod q.
+
+.. function:: ulong acb_dirichlet_ui_conductor(const acb_dirichlet_group_t G, ulong a)
+
+.. function:: ulong acb_dirichlet_conrey_conductor(const acb_dirichlet_group_t G, const acb_dirichlet_conrey_t x)
+
+   Compute the conductor of a mod q, that is the smallest r dividing q such
+   that a corresponds to an element defined modulo r.
+
+.. function:: ulong acb_dirichlet_ui_parity(const acb_dirichlet_group_t G, ulong a)
+
+.. function:: int acb_dirichlet_conrey_parity(const acb_dirichlet_group_t G, const acb_dirichlet_conrey_t x)
+
+   Compute the parity of a mod q, which is the parity of the corresponding
+   Dirichlet character.
+
+Character type
+-------------------------------------------------------------------------------
+
 .. type:: acb_dirichlet_char_struct
 
 .. type:: acb_dirichlet_char_t
 
     Represents a Dirichlet character. This structure contains various
-    useful invariants such as the order of the character.
+    useful invariants such as the order, the parity and the conductor of the character.
 
     An *acb_dirichlet_char_t* is defined as an array of *acb_dirichlet_char_struct*
     of length 1, permitting it to be passed by reference.
@@ -156,13 +191,13 @@ the group *G* is isomorphic to its dual.
     Sets *chi* to the Dirichlet character of Conrey index *x*.
 
 Character properties
--------------------------------------------------------------------------------
+...............................................................................
 
 .. function:: ulong acb_dirichlet_char_order(const acb_dirichlet_char_t chi)
 
 .. function:: int acb_dirichlet_char_parity(const acb_dirichlet_char_t chi)
 
-.. function:: ulong acb_dirichlet_char_conductor(const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi)
+.. function:: ulong acb_dirichlet_char_conductor(const acb_dirichlet_char_t chi)
 
 Character evaluation
 -------------------------------------------------------------------------------