Implement Tetranacci constant in ca

Note: Represent ca_tetranacci_constant in Q(a) where a^4-a^3-a^2-a-1 = 0.

Author: Raoul Bourquin

doc/source/ca.rst

@@ -349,6 +349,11 @@ Special values
     Sets *res* to Euler's constant `\gamma`. This creates an element
     of the (transcendental?) number field `\mathbb{Q}(\gamma)`.
 
+.. function:: void ca_tetranacci_constant(ca_t res, ca_ctx_t ctx)
+
+    Sets *res* to the Tetranacci constant `T_t`. This creates an element
+    of the algebraic number field `\mathbb{Q}(T_t)`.
+
 .. function:: void ca_unknown(ca_t res, ca_ctx_t ctx)
 
     Sets *res* to the meta-value *Unknown*.

src/ca.h

@@ -314,6 +314,8 @@ void ca_pi(ca_t res, ca_ctx_t ctx);
 void ca_pi_i(ca_t res, ca_ctx_t ctx);
 void ca_euler(ca_t res, ca_ctx_t ctx);
 
+void ca_tetranacci_constant(ca_t res, ca_ctx_t ctx);
+
 void ca_unknown(ca_t x, ca_ctx_t ctx);
 
 void ca_undefined(ca_t x, ca_ctx_t ctx);

src/ca/set_fexpr.c

@@ -79,6 +79,9 @@ _ca_set_fexpr(ca_t res, fexpr_vec_t inputs, ca_vec_t outputs, const fexpr_t expr
                 ca_add_ui(res, res, 1, ctx);
                 ca_div_ui(res, res, 2, ctx);
                 return 1;
+            case FEXPR_TetranacciConstant:
+                ca_tetranacci_constant(res, ctx);
+                return 1;
             case FEXPR_Infinity:
                 ca_pos_inf(res, ctx);
                 return 1;

src/ca/tetranacci.c

@@ -0,0 +1,24 @@
+/*
+    Copyright (C) 2022 Raoul Bourquin
+
+    This file is part of Calcium.
+
+    Calcium is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "ca.h"
+
+void
+ca_tetranacci_constant(ca_t res, ca_ctx_t ctx)
+{
+    qqbar_t tc;
+    qqbar_init(tc);
+    qqbar_tetranacci_constant(tc);
+
+    ca_set_qqbar(res, tc, ctx);
+
+    qqbar_clear(tc);
+}