add Exp rules

src/rules.jl

@@ -52,6 +52,7 @@ rules() = [
     rules(:BOOLEAN)
     rules(:CALCULUS)
     rules(:LOGARITHM)
+    rules(:EXP)
     rules(:TRIGONOMETRY)
     rules(:TYPES)
 ]
@@ -219,6 +220,21 @@ function rules(::Val{:LOGARITHM})
     ]
 end
 
+function rules(::Val{:EXP})
+    @vars α β n
+    @term RULES [
+        exp(*(2, π, im)) => 1
+        exp(π * im) => -1
+        exp(π * im * inv(2)) => im
+        exp(π * im * inv(3)) => 1 / 2 + √3 / 2 * im
+        exp(π * im * inv(4)) => √2 / 2 + √2 / 2 * im
+        exp(π * im * inv(6)) => √3 / 2 + 1 / 2 * im
+
+        exp(α) * exp(β) => exp(α + β)
+        exp(α)^n => exp(α * n)
+    ]
+end
+
 function rules(::Val{:TRIGONOMETRY})
     @vars α β θ
 

src/types.jl

@@ -5,7 +5,7 @@ export Variable, @vars
 using MacroTools
 
 macro term(ex)
-    :(convert(Term, $(esc(_term(ex)))))
+     :(convert(Term, $(esc(_term(ex)))))
 end
 function _term(ex::Expr)
     ex.head === :$ && return ex.args[1]
@@ -69,6 +69,8 @@ function _show_term(f::Function)
         return f
     end
 end
+
+_show_term(::Irrational{sym}) where sym = sym
 _show_term(x::Symbolic) = x.name
 _show_term(x::Variable) = x.name
 _show_term(x::Symbol) = Meta.quot(x)

src/utils.jl

@@ -1,5 +1,5 @@
 is_constant(t::Term) = is_constant(get(t))
-is_constant(x) = typeof(x) ∉ [Expr, Symbolic, Variable]
+is_constant(x) = !any(T->typeof(x) <: T, [Expr, Symbolic, Variable, Irrational])
 
 is_ground(t::Term) = is_ground(get(t))
 is_ground(ex::Expr) = all(is_ground, ex.args)

test/rules.jl

@@ -1,3 +1,5 @@
+using Test
+using Simplify
 using Simplify: PatternRule, EvalRule, OrderRule
 using Simplify: diff
 using SpecialSets
@@ -251,6 +253,21 @@ end
         end
     end
 
+    @testset "EXP" begin
+        @vars α β n
+        @test normalize(@term(exp(2π * im))) == @term(1)
+        @test normalize(@term(exp(π * im))) == @term(-1)
+        @test normalize(@term(exp(π * im * inv(2)))) == @term(im)
+
+        # actually broken: the order of imaginary and real is not correct
+        @test normalize(@term(exp(π * im * inv(3)))) == @term(√3 * inv(2) * im + inv(2))
+        @test normalize(@term(exp(π * im * inv(4)))) == @term(√2 * inv(2) + √2 * inv(2) * im)
+        @test normalize(@term(exp(π * im * inv(6)))) == @term(inv(2) * im + √3 * inv(2))
+
+        @test normalize(@term(exp(α) * exp(β))) == @term(exp(α + β))
+        @test normalize(@term(exp(α)^n)) == @term(exp(α * n))
+        @test normalize(@term(exp(π * im))) == @term(-1)
+    end
 
     @testset "custom" begin
         @syms a