From f44c6843fd689cb469287e454bac3d9075c96e33 Mon Sep 17 00:00:00 2001
From: Fredrik Johansson <fredrik.johansson@gmail.com>
Date: Thu, 1 Dec 2016 22:33:15 +0100
Subject: [PATCH] use acb_dirichlet_roots_t in l_hurwitz and l_jet; rename
 dirichlet_number_primitive -> dirichlet_group_num_primitive

---
 acb_dirichlet/l_hurwitz.c                         | 15 ++++++++-------
 acb_dirichlet/l_jet.c                             | 15 +++++++++------
 acb_dirichlet/test/t-l_hurwitz.c                  |  2 +-
 dirichlet.h                                       |  3 ++-
 .../{number_primitive.c => group_num_primitive.c} |  2 +-
 dirichlet/test/t-chars.c                          |  2 +-
 doc/source/dirichlet.rst                          | 12 ++++++++----
 7 files changed, 30 insertions(+), 21 deletions(-)
 rename dirichlet/{number_primitive.c => group_num_primitive.c} (93%)

diff --git a/acb_dirichlet/l_hurwitz.c b/acb_dirichlet/l_hurwitz.c
index 1120a8ba..39a41ce8 100644
--- a/acb_dirichlet/l_hurwitz.c
+++ b/acb_dirichlet/l_hurwitz.c
@@ -19,9 +19,9 @@ acb_dirichlet_l_hurwitz(acb_t res, const acb_t s,
     const dirichlet_group_t G, const dirichlet_char_t chi, slong prec)
 {
     ulong order, chin, mult;
-    acb_t t, u, a;
-    acb_ptr z;
+    acb_t t, u, a, w;
     dirichlet_char_t cn;
+    acb_dirichlet_roots_t roots;
     int deflate;
 
     /* remove pole in Hurwitz zeta at s = 1 */
@@ -40,6 +40,7 @@ acb_dirichlet_l_hurwitz(acb_t res, const acb_t s,
     acb_init(t);
     acb_init(u);
     acb_init(a);
+    acb_init(w);
 
     dirichlet_char_one(cn, G);
     acb_zero(t);
@@ -48,9 +49,7 @@ acb_dirichlet_l_hurwitz(acb_t res, const acb_t s,
 
     order = dirichlet_order_char(G, chi);
     mult = G->expo / order;
-    z = _acb_vec_init(order);
-    /* todo: use roots object */
-    _acb_vec_unit_roots(z, order, prec);
+    acb_dirichlet_roots_init(roots, order, dirichlet_group_size(G), prec);
 
     do {
         chin = dirichlet_pairing_char(G, chi, cn) / mult;
@@ -70,7 +69,8 @@ acb_dirichlet_l_hurwitz(acb_t res, const acb_t s,
             acb_dirichlet_hurwitz_precomp_eval(u, precomp, cn->n, G->q, prec);
         }
 
-        acb_addmul(t, z + chin, u, prec);
+        acb_dirichlet_root(w, roots, chin, prec);
+        acb_addmul(t, u, w, prec);
 
     } while (dirichlet_char_next(cn, G) >= 0);
 
@@ -81,9 +81,10 @@ acb_dirichlet_l_hurwitz(acb_t res, const acb_t s,
 
     dirichlet_char_clear(cn);
 
-    _acb_vec_clear(z, order);
+    acb_dirichlet_roots_clear(roots);
     acb_clear(t);
     acb_clear(u);
     acb_clear(a);
+    acb_clear(w);
 }
 
diff --git a/acb_dirichlet/l_jet.c b/acb_dirichlet/l_jet.c
index 819f5870..119092cc 100644
--- a/acb_dirichlet/l_jet.c
+++ b/acb_dirichlet/l_jet.c
@@ -19,9 +19,10 @@ acb_dirichlet_l_jet(acb_ptr res, const acb_t s,
     int deflate, slong len, slong prec)
 {
     ulong order, chin, mult, phi;
-    acb_t a;
-    acb_ptr t, u, z;
+    acb_t a, w;
+    acb_ptr t, u;
     dirichlet_char_t cn;
+    acb_dirichlet_roots_t roots;
     int deflate_hurwitz;
 
     if (len <= 0)
@@ -52,6 +53,7 @@ acb_dirichlet_l_jet(acb_ptr res, const acb_t s,
     t = _acb_vec_init(len);
     u = _acb_vec_init(len + 2);
     acb_init(a);
+    acb_init(w);
 
     dirichlet_char_one(cn, G);
 
@@ -59,8 +61,7 @@ acb_dirichlet_l_jet(acb_ptr res, const acb_t s,
 
     order = dirichlet_order_char(G, chi);
     mult = G->expo / order;
-    z = _acb_vec_init(order);
-    _acb_vec_unit_roots(z, order, prec);
+    acb_dirichlet_roots_init(roots, order, dirichlet_group_size(G), prec);
 
     phi = 0;
     do
@@ -69,7 +70,8 @@ acb_dirichlet_l_jet(acb_ptr res, const acb_t s,
         acb_set_ui(a, cn->n);
         acb_div_ui(a, a, G->q, prec);
         _acb_poly_zeta_cpx_series(u, s, a, deflate_hurwitz, len, prec);
-        _acb_vec_scalar_addmul(t, u, len, z + chin, prec);
+        acb_dirichlet_root(w, roots, chin, prec);
+        _acb_vec_scalar_addmul(t, u, len, w, prec);
         phi++;
     }
     while (dirichlet_char_next(cn, G) >= 0);
@@ -112,9 +114,10 @@ acb_dirichlet_l_jet(acb_ptr res, const acb_t s,
 
     dirichlet_char_clear(cn);
 
-    _acb_vec_clear(z, order);
+    acb_dirichlet_roots_clear(roots);
     _acb_vec_clear(t, len);
     _acb_vec_clear(u, len + 2);
     acb_clear(a);
+    acb_clear(w);
 }
 
diff --git a/acb_dirichlet/test/t-l_hurwitz.c b/acb_dirichlet/test/t-l_hurwitz.c
index fe52f139..db0b630d 100644
--- a/acb_dirichlet/test/t-l_hurwitz.c
+++ b/acb_dirichlet/test/t-l_hurwitz.c
@@ -71,7 +71,7 @@ int main()
         "-1.43652482351673593824956935036654893593947145947637807"
     };
 
-    flint_printf("l....");
+    flint_printf("l_hurwitz....");
     fflush(stdout);
 
     x = _acb_vec_init(nx);
diff --git a/dirichlet.h b/dirichlet.h
index cdd8713a..4b6e7176 100644
--- a/dirichlet.h
+++ b/dirichlet.h
@@ -62,6 +62,8 @@ dirichlet_group_size(const dirichlet_group_t G)
     return G->phi_q;
 }
 
+ulong dirichlet_group_num_primitive(const dirichlet_group_t G);
+
 void dirichlet_group_init(dirichlet_group_t G, ulong q);
 void dirichlet_subgroup_init(dirichlet_group_t H, const dirichlet_group_t G, ulong h);
 void dirichlet_group_clear(dirichlet_group_t G);
@@ -70,7 +72,6 @@ void dirichlet_group_dlog_clear(dirichlet_group_t G);
 
 /* properties of elements without log */
 
-ulong dirichlet_number_primitive(const dirichlet_group_t G);
 ulong dirichlet_conductor_ui(const dirichlet_group_t G, ulong a);
 int dirichlet_parity_ui(const dirichlet_group_t G, ulong a);
 ulong dirichlet_order_ui(const dirichlet_group_t G, ulong a);
diff --git a/dirichlet/number_primitive.c b/dirichlet/group_num_primitive.c
similarity index 93%
rename from dirichlet/number_primitive.c
rename to dirichlet/group_num_primitive.c
index 202e5114..f1c344c2 100644
--- a/dirichlet/number_primitive.c
+++ b/dirichlet/group_num_primitive.c
@@ -12,7 +12,7 @@
 #include "dirichlet.h"
 
 ulong
-dirichlet_number_primitive(const dirichlet_group_t G)
+dirichlet_group_num_primitive(const dirichlet_group_t G)
 {
     if (G->q % 4 == 2)
         return 0;
diff --git a/dirichlet/test/t-chars.c b/dirichlet/test/t-chars.c
index 5cffdce0..11e0c953 100644
--- a/dirichlet/test/t-chars.c
+++ b/dirichlet/test/t-chars.c
@@ -74,7 +74,7 @@ int main()
             dirichlet_char_first_primitive(x, G);
             for (n = 1; dirichlet_char_next_primitive(x, G) >= 0; n++);
 
-            ref = dirichlet_number_primitive(G);
+            ref = dirichlet_group_num_primitive(G);
             if (n != ref)
             {
                 flint_printf("FAIL: number of primitive elements\n\n");
diff --git a/doc/source/dirichlet.rst b/doc/source/dirichlet.rst
index 09818810..00520f67 100644
--- a/doc/source/dirichlet.rst
+++ b/doc/source/dirichlet.rst
@@ -82,6 +82,14 @@ Multiplicative group modulo *q*
     Clears *G*. Remark this function does *not* clear the discrete logarithm
     tables stored in *G* (which may be shared with another group).
 
+.. function:: ulong dirichlet_group_size(const dirichlet_group_t G)
+
+   Returns the number of elements in *G*, i.e. `\varphi(q)`.
+
+.. function:: ulong dirichlet_group_num_primitive(const dirichlet_group_t G)
+
+   Returns the number of primitive elements in *G*.
+
 .. function:: void dirichlet_group_dlog_precompute(dirichlet_group_t G, ulong num)
 
     Precompute decomposition and tables for discrete log computations in *G*,
@@ -194,10 +202,6 @@ Character properties
 As a consequence of the Conrey numbering, all these numbers are available at the
 level of *number* and *char* object. Both case require no discrete log computation.
 
-.. function:: ulong dirichlet_number_primitive(const dirichlet_group_t G)
-
-   Returns the number of primitive elements in *G*.
-
 .. function:: int dirichlet_char_is_principal(const dirichlet_group_t G, const dirichlet_char_t chi)
 
    Returns 1 if *chi* is the principal character mod *q*.