add Exp rules

Manifest.toml

@@ -1,6 +1,14 @@
+# This file is machine-generated - editing it directly is not advised
+
 [[Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
+[[CSTParser]]
+deps = ["Tokenize"]
+git-tree-sha1 = "c69698c3d4a7255bc1b4bc2afc09f59db910243b"
+uuid = "00ebfdb7-1f24-5e51-bd34-a7502290713f"
+version = "0.6.2"
+
 [[Combinatorics]]
 deps = ["LinearAlgebra", "Polynomials", "Test"]
 git-tree-sha1 = "50b3ae4d643dc27eaff69fb6be06ee094d5500c9"
@@ -9,9 +17,15 @@ version = "0.7.0"
 
 [[Compat]]
 deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
-git-tree-sha1 = "ec61a16eed883ad0cfa002d7489b3ce6d039bb9a"
+git-tree-sha1 = "84aa74986c5b9b898b0d1acaf3258741ee64754f"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "1.4.0"
+version = "2.1.0"
+
+[[DataStructures]]
+deps = ["InteractiveUtils", "OrderedCollections"]
+git-tree-sha1 = "0809951a1774dc724da22d26e4289bbaab77809a"
+uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+version = "0.17.0"
 
 [[Dates]]
 deps = ["Printf"]
@@ -23,12 +37,12 @@ uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 
 [[DiffRules]]
 deps = ["Random", "Test"]
-git-tree-sha1 = "c49ec69428ffea0c1d1bbdc63d1a70f5df5860ad"
+git-tree-sha1 = "dc0869fb2f5b23466b32ea799bd82c76480167f7"
 uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
-version = "0.0.7"
+version = "0.0.10"
 
 [[Distributed]]
-deps = ["LinearAlgebra", "Random", "Serialization", "Sockets"]
+deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
 [[InteractiveUtils]]
@@ -49,10 +63,10 @@ uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
 [[MacroTools]]
-deps = ["Compat"]
-git-tree-sha1 = "c443e1c8d58a4e9f61b708ad0a88286c7042145b"
+deps = ["CSTParser", "Compat", "DataStructures", "Test", "Tokenize"]
+git-tree-sha1 = "d6e9dedb8c92c3465575442da456aec15a89ff76"
 uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
-version = "0.4.4"
+version = "0.5.1"
 
 [[Markdown]]
 deps = ["Base64"]
@@ -61,15 +75,21 @@ uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 [[Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
+[[OrderedCollections]]
+deps = ["Random", "Serialization", "Test"]
+git-tree-sha1 = "c4c13474d23c60d20a67b217f1d7f22a40edf8f1"
+uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
+version = "1.1.0"
+
 [[Pkg]]
 deps = ["Dates", "LibGit2", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 
 [[Polynomials]]
 deps = ["LinearAlgebra", "SparseArrays", "Test"]
-git-tree-sha1 = "1a1eae52956658a6acae6fa1b6d6c3d488192895"
+git-tree-sha1 = "62142bd65d3f8aeb2226ec64dd8493349147df94"
 uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
-version = "0.5.1"
+version = "0.5.2"
 
 [[Printf]]
 deps = ["Unicode"]
@@ -116,6 +136,11 @@ uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
+[[Tokenize]]
+git-tree-sha1 = "dfcdbbfb2d0370716c815cbd6f8a364efb6f42cf"
+uuid = "0796e94c-ce3b-5d07-9a54-7f471281c624"
+version = "0.5.6"
+
 [[UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

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