Represent ca_tribonacci_constant in Q(a) where a^3-a^2-a-1 = 0

Author: Raoul Bourquin

doc/source/ca.rst

@@ -351,7 +351,8 @@ Special values
 
 .. function:: void ca_tribonacci_constant(ca_t res, ca_ctx_t ctx)
 
-    Sets *res* to the Tribonacci constant `T_c`.
+    Sets *res* to the Tribonacci constant `T_c`. This creates an element
+    of the algebraic number field `\mathbb{Q}(T_c)`.
 
 .. function:: void ca_unknown(ca_t res, ca_ctx_t ctx)
 

src/ca/tribonacci.c

@@ -14,48 +14,11 @@
 void
 ca_tribonacci_constant(ca_t res, ca_ctx_t ctx)
 {
-    /* Subexpressions */
-    ca_t third, r33, r33p, r33m;
+    qqbar_t tc;
+    qqbar_init(tc);
+    qqbar_tribonacci_constant(tc);
 
-    /* Init */
-    ca_init(third, ctx);
-    ca_init(r33, ctx);
-    ca_init(r33p, ctx);
-    ca_init(r33m, ctx);
+    ca_set_qqbar(res, tc, ctx);
 
-    /* third := 1/3 */
-    ca_one(third, ctx);
-    ca_div_ui(third, third, 3, ctx);
-
-    /* r33 := 3*sqrt(33) */
-    ca_sqrt_ui(r33, 33, ctx);
-    ca_mul_ui(r33, r33, 3, ctx);
-
-    /* r33p := cbrt(19 + r33) */
-    ca_add_ui(r33p, r33, 19, ctx);
-    /* Todo: now suitable root function in calcium yet */
-    /* ca_root_ui(r33p, r33p, 3, ctx); */
-    ca_pow(r33p, r33p, third, ctx);
-
-    /* r33m := cbrt(19 - r33) */
-    ca_sub_si(r33m, r33, 19, ctx);
-    ca_neg(r33m, r33m, ctx);
-    /* Todo: now suitable root function in calcium yet */
-    /* ca_root_ui(r33m, r33m, 3, ctx); */
-    ca_pow(r33m, r33m, third, ctx);
-
-    /* res := 1 */
-    ca_one(res, ctx);
-    /* res += r33p */
-    ca_add(res, res, r33p, ctx);
-    /* res += r33m */
-    ca_add(res, res, r33m, ctx);
-    /* res /= 3 */
-    ca_div_ui(res, res, 3, ctx);
-
-    /* Free */
-    ca_clear(third, ctx);
-    ca_clear(r33, ctx);
-    ca_clear(r33p, ctx);
-    ca_clear(r33m, ctx);
+    qqbar_clear(tc);
 }