From e0433433b658984c3ee62efaf21be8aad7b9d046 Mon Sep 17 00:00:00 2001
From: Srajan Garg <srajan.garg@gmail.com>
Date: Fri, 22 Jan 2016 03:09:01 +0530
Subject: [PATCH] fixed main trigno functions, to simplify if arg is inverse

---
 symengine/functions.cpp                  | 42 +++++++++++++++++-------
 symengine/tests/basic/test_functions.cpp | 24 ++++++++++++++
 2 files changed, 54 insertions(+), 12 deletions(-)

diff --git a/symengine/functions.cpp b/symengine/functions.cpp
index dfb34955d4..1e2f63fa36 100644
--- a/symengine/functions.cpp
+++ b/symengine/functions.cpp
@@ -327,9 +327,12 @@ RCP<const Basic> sin(const RCP<const Basic> &arg)
     if (is_a_Number(*arg) and not static_cast<const Number &>(*arg).is_exact()) {
         return static_cast<const Number &>(*arg).get_eval().sin(*arg);
     }
+    if (is_a<ASin>(*arg)) {
+        return rcp_static_cast<const ASin>(arg)->get_arg();
+    }
+
     RCP<const Basic> ret_arg;
-    int index;
-    int sign;
+    int index, sign;
     bool conjugate = eval(arg, 2, 1, 0, //input
                           outArg(ret_arg), index, sign); //output
 
@@ -406,9 +409,12 @@ RCP<const Basic> cos(const RCP<const Basic> &arg)
     if (is_a_Number(*arg) and not static_cast<const Number &>(*arg).is_exact()) {
         return static_cast<const Number &>(*arg).get_eval().cos(*arg);
     }
+    if (is_a<ACos>(*arg)) {
+        return rcp_static_cast<const ACos>(arg)->get_arg();
+    }
+
     RCP<const Basic> ret_arg;
-    int index;
-    int sign;
+    int index, sign;
     bool conjugate =  eval(arg, 2, 0, 1, //input
                       outArg(ret_arg), index, sign); //output
 
@@ -484,9 +490,12 @@ RCP<const Basic> tan(const RCP<const Basic> &arg)
     if (is_a_Number(*arg) and not static_cast<const Number &>(*arg).is_exact()) {
         return static_cast<const Number &>(*arg).get_eval().tan(*arg);
     }
+    if (is_a<ATan>(*arg)) {
+        return rcp_static_cast<const ATan>(arg)->get_arg();
+    }
+
     RCP<const Basic> ret_arg;
-    int index;
-    int sign;
+    int index, sign;
     bool conjugate =  eval(arg, 1, 1, 1, //input
                       outArg(ret_arg), index, sign); //output
 
@@ -563,9 +572,12 @@ RCP<const Basic> cot(const RCP<const Basic> &arg)
     if (is_a_Number(*arg) and not static_cast<const Number &>(*arg).is_exact()) {
         return static_cast<const Number &>(*arg).get_eval().cot(*arg);
     }
+    if (is_a<ACot>(*arg)) {
+        return rcp_static_cast<const ACot>(arg)->get_arg();
+    }
+
     RCP<const Basic> ret_arg;
-    int index;
-    int sign;
+    int index, sign;
     bool conjugate =  eval(arg, 1, 1, 1, //input
                       outArg(ret_arg), index, sign); //output
 
@@ -643,9 +655,12 @@ RCP<const Basic> csc(const RCP<const Basic> &arg)
     if (is_a_Number(*arg) and not static_cast<const Number &>(*arg).is_exact()) {
         return static_cast<const Number &>(*arg).get_eval().csc(*arg);
     }
+    if (is_a<ACsc>(*arg)) {
+        return rcp_static_cast<const ACsc>(arg)->get_arg();
+    }
+
     RCP<const Basic> ret_arg;
-    int index;
-    int sign;
+    int index, sign;
     bool conjugate =  eval(arg, 2, 1, 0, //input
                       outArg(ret_arg), index, sign); //output
 
@@ -723,9 +738,12 @@ RCP<const Basic> sec(const RCP<const Basic> &arg)
     if (is_a_Number(*arg) and not static_cast<const Number &>(*arg).is_exact()) {
         return static_cast<const Number &>(*arg).get_eval().sec(*arg);
     }
+    if (is_a<ASec>(*arg)) {
+        return rcp_static_cast<const ASec>(arg)->get_arg();
+    }
+
     RCP<const Basic> ret_arg;
-    int index;
-    int sign;
+    int index, sign;
     bool conjugate =  eval(arg, 2, 0, 1, //input
                       outArg(ret_arg), index, sign); //output
 
diff --git a/symengine/tests/basic/test_functions.cpp b/symengine/tests/basic/test_functions.cpp
index e6efdee5e0..ad3faf5e80 100644
--- a/symengine/tests/basic/test_functions.cpp
+++ b/symengine/tests/basic/test_functions.cpp
@@ -170,6 +170,10 @@ TEST_CASE("Sin: functions", "[functions]")
     r2 = sin(y);
     REQUIRE(eq(*r1, *r2));
 
+    // sin(asin(x)) = x
+    r1 = sin(asin(x));
+    REQUIRE(eq(*r1, *x));
+
     // sin(pi + y) = -sin(y)
     r1 = sin(add(pi, y));
     r2 = mul(im1, sin(y));
@@ -263,6 +267,10 @@ TEST_CASE("Cos: functions", "[functions]")
     r2 = cos(y);
     REQUIRE(eq(*r1, *r2));
 
+    // cos(acos(x)) = x
+    r1 = cos(acos(x));
+    REQUIRE(eq(*r1, *x));
+
     // cos(pi - y) = -cos(y)
     r1 = cos(sub(pi, y));
     r2 = mul(im1, cos(y));
@@ -368,6 +376,10 @@ TEST_CASE("Tan: functions", "[functions]")
     r2 = mul(im1, tan(y));
     REQUIRE(eq(*r1, *r2));
 
+    // tan(atan(x)) = x
+    r1 = tan(atan(x));
+    REQUIRE(eq(*r1, *x));
+
     // tan(pi + y) = -tan(y)
     r1 = tan(add(pi, y));
     r2 = tan(y);
@@ -459,6 +471,10 @@ TEST_CASE("Cot: functions", "[functions]")
     r2 = mul(im1, cot(y));
     REQUIRE(eq(*r1, *r2));
 
+    // cot(acot(x)) = x
+    r1 = cot(acot(x));
+    REQUIRE(eq(*r1, *x));
+
     // cot(pi + y) = -cot(y)
     r1 = cot(add(pi, y));
     r2 = cot(y);
@@ -551,6 +567,10 @@ TEST_CASE("Csc: functions", "[functions]")
     r2 = csc(y);
     REQUIRE(eq(*r1, *r2));
 
+    // csc(acsc(x)) = x
+    r1 = csc(acsc(x));
+    REQUIRE(eq(*r1, *x));
+
     // csc(pi + y) = -csc(y)
     r1 = csc(add(pi, y));
     r2 = mul(im1, csc(y));
@@ -642,6 +662,10 @@ TEST_CASE("Sec: functions", "[functions]")
     r2 = mul(im1, sec(y));
     REQUIRE(eq(*r1, *r2));
 
+    // sec(asec(x)) = x
+    r1 = sec(asec(x));
+    REQUIRE(eq(*r1, *x));
+
     // sec(pi + y) = -sec(y)
     r1 = sec(add(pi, y));
     r2 = mul(im1, sec(y));