add expand_as_exp() for trignometric functions

ranjithkumar007 · Jul 6, 2017 · 9e02473 · 9e02473
1 parent 9e536b6
commit 9e02473
Show file tree

Hide file tree

Showing 3 changed files with 86 additions and 0 deletions.
diff --git a/symengine/functions.cpp b/symengine/functions.cpp
@@ -715,6 +715,14 @@ bool Sin::is_canonical(const RCP<const Basic> &arg) const
     return true;
 }
 
+RCP<const Basic> Sin::expand_as_exp() const
+{
+    auto expo = mul(I, get_arg());
+    RCP<const Basic> a = exp(expo);
+    RCP<const Basic> b = exp(mul(minus_one, expo));
+    return div(sub(a, b), mul(integer(2), I));
+}
+
 RCP<const Basic> sin(const RCP<const Basic> &arg)
 {
     if (eq(*arg, *zero))
@@ -783,6 +791,14 @@ bool Cos::is_canonical(const RCP<const Basic> &arg) const
     return true;
 }
 
+RCP<const Basic> Cos::expand_as_exp() const
+{
+    auto expo = mul(I, get_arg());
+    RCP<const Basic> a = exp(expo);
+    RCP<const Basic> b = exp(mul(minus_one, expo));
+    return div(add(a, b), integer(2));
+}
+
 RCP<const Basic> cos(const RCP<const Basic> &arg)
 {
     if (eq(*arg, *zero))
@@ -848,6 +864,14 @@ bool Tan::is_canonical(const RCP<const Basic> &arg) const
     return true;
 }
 
+RCP<const Basic> Tan::expand_as_exp() const
+{
+    auto expo = mul(I, get_arg());
+    RCP<const Basic> a = exp(expo);
+    RCP<const Basic> b = exp(mul(minus_one, expo));
+    return div(sub(a, b), mul(I, add(a, b)));
+}
+
 RCP<const Basic> tan(const RCP<const Basic> &arg)
 {
     if (eq(*arg, *zero))
@@ -914,6 +938,14 @@ bool Cot::is_canonical(const RCP<const Basic> &arg) const
     return true;
 }
 
+RCP<const Basic> Cot::expand_as_exp() const
+{
+    auto expo = mul(I, get_arg());
+    RCP<const Basic> a = exp(expo);
+    RCP<const Basic> b = exp(mul(minus_one, expo));
+    return div(mul(I, add(a, b)), sub(a, b));
+}
+
 RCP<const Basic> cot(const RCP<const Basic> &arg)
 {
     if (is_a_Number(*arg) and not down_cast<const Number &>(*arg).is_exact()) {
@@ -979,6 +1011,14 @@ bool Csc::is_canonical(const RCP<const Basic> &arg) const
     return true;
 }
 
+RCP<const Basic> Csc::expand_as_exp() const
+{
+    auto expo = mul(I, get_arg());
+    RCP<const Basic> a = exp(expo);
+    RCP<const Basic> b = exp(mul(minus_one, expo));
+    return div(mul(I, integer(2)), sub(a, b));
+}
+
 RCP<const Basic> csc(const RCP<const Basic> &arg)
 {
     if (is_a_Number(*arg) and not down_cast<const Number &>(*arg).is_exact()) {
@@ -1043,6 +1083,14 @@ bool Sec::is_canonical(const RCP<const Basic> &arg) const
     return true;
 }
 
+RCP<const Basic> Sec::expand_as_exp() const
+{
+    auto expo = mul(I, get_arg());
+    RCP<const Basic> a = exp(expo);
+    RCP<const Basic> b = exp(mul(minus_one, expo));
+    return div(integer(2), add(a, b));
+}
+
 RCP<const Basic> sec(const RCP<const Basic> &arg)
 {
     if (is_a_Number(*arg) and not down_cast<const Number &>(*arg).is_exact()) {

diff --git a/symengine/functions.h b/symengine/functions.h
@@ -289,6 +289,8 @@ class Sin : public TrigFunction
     bool is_canonical(const RCP<const Basic> &arg) const;
     //! \return Canonicalized sin
     virtual RCP<const Basic> create(const RCP<const Basic> &arg) const;
+    //! expands sin in terms of exp function
+    virtual RCP<const Basic> expand_as_exp() const;
 };
 
 //! Canonicalize Sin:
@@ -305,6 +307,8 @@ class Cos : public TrigFunction
     bool is_canonical(const RCP<const Basic> &arg) const;
     //! \return Canonicalized cos
     virtual RCP<const Basic> create(const RCP<const Basic> &arg) const;
+    //! expands cos in terms of exp function
+    virtual RCP<const Basic> expand_as_exp() const;
 };
 
 //! Canonicalize Cos:
@@ -321,6 +325,8 @@ class Tan : public TrigFunction
     bool is_canonical(const RCP<const Basic> &arg) const;
     //! \return Canonicalized tan
     virtual RCP<const Basic> create(const RCP<const Basic> &arg) const;
+    //! expands tan in terms of exp function
+    virtual RCP<const Basic> expand_as_exp() const;
 };
 //! Canonicalize Tan:
 RCP<const Basic> tan(const RCP<const Basic> &arg);
@@ -336,6 +342,8 @@ class Cot : public TrigFunction
     bool is_canonical(const RCP<const Basic> &arg) const;
     //! \return Canonicalized cot
     virtual RCP<const Basic> create(const RCP<const Basic> &arg) const;
+    //! expands cot in terms of exp function
+    virtual RCP<const Basic> expand_as_exp() const;
 };
 //! Canonicalize Cot:
 RCP<const Basic> cot(const RCP<const Basic> &arg);
@@ -351,6 +359,8 @@ class Csc : public TrigFunction
     bool is_canonical(const RCP<const Basic> &arg) const;
     //! \return Canonicalized csc
     virtual RCP<const Basic> create(const RCP<const Basic> &arg) const;
+    //! expands csc in terms of exp function
+    virtual RCP<const Basic> expand_as_exp() const;
 };
 //! Canonicalize Csc:
 RCP<const Basic> csc(const RCP<const Basic> &arg);
@@ -366,6 +376,8 @@ class Sec : public TrigFunction
     bool is_canonical(const RCP<const Basic> &arg) const;
     //! \return Canonicalized sec
     virtual RCP<const Basic> create(const RCP<const Basic> &arg) const;
+    //! expands sec in terms of exp function
+    virtual RCP<const Basic> expand_as_exp() const;
 };
 //! Canonicalize Sec:
 RCP<const Basic> sec(const RCP<const Basic> &arg);

diff --git a/symengine/tests/basic/test_functions.cpp b/symengine/tests/basic/test_functions.cpp
@@ -315,6 +315,10 @@ TEST_CASE("Sin: functions", "[functions]")
     REQUIRE(not(r4->is_canonical(mul(pi, i2))));
     REQUIRE(not(r4->is_canonical(add(mul(pi, i2), div(pi, i2)))));
     REQUIRE(not(r4->is_canonical(real_double(2.0))));
+
+    r1 = sin(x)->expand_as_exp();
+    r2 = div(sub(exp(mul(I, x)), exp(mul(neg(I), x))), mul(integer(2), I));
+    REQUIRE(eq(*r1, *r2));
 }
 
 TEST_CASE("Cos: functions", "[functions]")
@@ -436,6 +440,10 @@ TEST_CASE("Cos: functions", "[functions]")
     REQUIRE(not(r4->is_canonical(mul(pi, i2))));
     REQUIRE(not(r4->is_canonical(add(mul(pi, i2), div(pi, i2)))));
     REQUIRE(not(r4->is_canonical(real_double(2.0))));
+
+    r1 = cos(x)->expand_as_exp();
+    r2 = div(add(exp(mul(I, x)), exp(mul(neg(I), x))), integer(2));
+    REQUIRE(eq(*r1, *r2));
 }
 
 TEST_CASE("Tan: functions", "[functions]")
@@ -557,6 +565,11 @@ TEST_CASE("Tan: functions", "[functions]")
     REQUIRE(not(r4->is_canonical(mul(pi, i2))));
     REQUIRE(not(r4->is_canonical(add(mul(pi, i2), div(pi, i2)))));
     REQUIRE(not(r4->is_canonical(real_double(2.0))));
+
+    r1 = tan(x)->expand_as_exp();
+    r2 = div(sub(exp(mul(I, x)), exp(mul(neg(I), x))),
+             mul(add(exp(mul(I, x)), exp(mul(neg(I), x))), I));
+    REQUIRE(eq(*r1, *r2));
 }
 
 TEST_CASE("Cot: functions", "[functions]")
@@ -674,6 +687,11 @@ TEST_CASE("Cot: functions", "[functions]")
     REQUIRE(not(r4->is_canonical(mul(pi, i2))));
     REQUIRE(not(r4->is_canonical(add(mul(pi, i2), div(pi, i2)))));
     REQUIRE(not(r4->is_canonical(real_double(2.0))));
+
+    r1 = cot(x)->expand_as_exp();
+    r2 = div(mul(add(exp(mul(I, x)), exp(mul(neg(I), x))), I),
+             sub(exp(mul(I, x)), exp(mul(neg(I), x))));
+    REQUIRE(eq(*r1, *r2));
 }
 
 TEST_CASE("Csc: functions", "[functions]")
@@ -793,6 +811,10 @@ TEST_CASE("Csc: functions", "[functions]")
     REQUIRE(not(r4->is_canonical(mul(pi, i2))));
     REQUIRE(not(r4->is_canonical(add(mul(pi, i2), div(pi, i2)))));
     REQUIRE(not(r4->is_canonical(real_double(2.0))));
+
+    r1 = csc(x)->expand_as_exp();
+    r2 = div(mul(integer(2), I), sub(exp(mul(I, x)), exp(mul(neg(I), x))));
+    REQUIRE(eq(*r1, *r2));
 }
 
 TEST_CASE("Sec: functions", "[functions]")
@@ -914,6 +936,10 @@ TEST_CASE("Sec: functions", "[functions]")
     REQUIRE(not(r4->is_canonical(mul(pi, i2))));
     REQUIRE(not(r4->is_canonical(add(mul(pi, i2), div(pi, i2)))));
     REQUIRE(not(r4->is_canonical(real_double(2.0))));
+
+    r1 = sec(x)->expand_as_exp();
+    r2 = div(integer(2), add(exp(mul(I, x)), exp(mul(neg(I), x))));
+    REQUIRE(eq(*r1, *r2));
 }
 
 TEST_CASE("TrigFunction: trig_to_sqrt", "[functions]")