Merge pull request #469 from pagnani/master

added rule for 1^x == 1 in POW_RULES

Author: shashi

src/simplify_rules.jl

@@ -40,6 +40,7 @@ let
         @rule(^(~x, ~z::_iszero) => 1)
         @rule(^(~x, ~z::_isone) => ~x)
         @rule(inv(~x) => 1/(~x))
+        @rule(^(~x::_isone, ~z) => 1)
     ]
 
     ASSORTED_RULES = [

test/rulesets.jl

@@ -5,7 +5,7 @@ using SymbolicUtils: getdepth, Rewriters, Term
     @syms w z α::Real β::Real
 
     r1 = @rule ~x + ~x => 2 * (~x)
-    r2 = @acrule ~x * +(~~ys) => sum(map(y-> ~x * y,  ~~ys));
+    r2 = @acrule ~x * +(~~ys) => sum(map(y -> ~x * y, ~~ys))
 
     rset = Rewriters.Postwalk(Rewriters.Chain([r2]))
     @test getdepth(rset) == typemax(Int)
@@ -22,36 +22,36 @@ end
     @eqtest simplify(Term{Real}(real, [x])) == x
     @eqtest simplify(Term{Real}(imag, [x])) == 0
     @eqtest simplify(Term{Real}(imag, [y])) == imag(y)
-    @eqtest simplify(x - y) == x + -1*y
-    @eqtest simplify(x - sin(y)) == x + -1*sin(y)
-    @eqtest simplify(-sin(x)) == -1*sin(x)
+    @eqtest simplify(x - y) == x + -1 * y
+    @eqtest simplify(x - sin(y)) == x + -1 * sin(y)
+    @eqtest simplify(-sin(x)) == -1 * sin(x)
     @eqtest simplify(1 * x * 2) == 2 * x
     @eqtest simplify(1 + x + 2) == 3 + x
-    @eqtest simplify(b*b) == b^2 # tests merge_repeats
-    @eqtest simplify((a*b)^2) == a^2 * b^2
-    @eqtest simplify((a*b)^c) == (a*b)^c
+    @eqtest simplify(b * b) == b^2 # tests merge_repeats
+    @eqtest simplify((a * b)^2) == a^2 * b^2
+    @eqtest simplify((a * b)^c) == (a * b)^c
 
     @eqtest simplify(1x + 2x) == 3x
     @eqtest simplify(3x + 2x) == 5x
 
-    @eqtest simplify(a + b + (x * y) + c + 2 * (x * y) + d)     == simplify((3 * x * y) + a + b + c + d)
+    @eqtest simplify(a + b + (x * y) + c + 2 * (x * y) + d) == simplify((3 * x * y) + a + b + c + d)
     @eqtest simplify(a + b + 2 * (x * y) + c + 2 * (x * y) + d) == simplify((4 * x * y) + a + b + c + d)
 
-    @eqtest simplify(a * x^y * b * x^d) == simplify(a * b * (x ^ (d + y)))
+    @eqtest simplify(a * x^y * b * x^d) == simplify(a * b * (x^(d + y)))
 
-    @eqtest simplify(a + b + 0*c + d) == simplify(a + b + d)
+    @eqtest simplify(a + b + 0 * c + d) == simplify(a + b + d)
     @eqtest simplify(a * b * c^0 * d) == simplify(a * b * d)
-    @eqtest simplify(a * b * 1*c * d) == simplify(a * b * c * d)
-    @eqtest simplify_fractions(x^2.0/(x*y)^2.0) == simplify_fractions(1 / (y^2.0))
+    @eqtest simplify(a * b * 1 * c * d) == simplify(a * b * c * d)
+    @eqtest simplify_fractions(x^2.0 / (x * y)^2.0) == simplify_fractions(1 / (y^2.0))
 
     @test simplify(Term(one, [a])) == 1
-    @test simplify(Term(one, [b+1])) == 1
-    @test simplify(Term(one, [x+2])) == 1
+    @test simplify(Term(one, [b + 1])) == 1
+    @test simplify(Term(one, [x + 2])) == 1
 
 
     @test simplify(Term(zero, [a])) == 0
-    @test simplify(Term(zero, [b+1])) == 0
-    @test simplify(Term(zero, [x+2])) == 0
+    @test simplify(Term(zero, [b + 1])) == 0
+    @test simplify(Term(zero, [x + 2])) == 0
 end
 
 @testset "boolean" begin
@@ -67,14 +67,14 @@ end
     @eqtest simplify((0 < a) & false) == false
     @eqtest simplify(Term{Bool}(!, [true])) == false
     @eqtest simplify(Term{Bool}(|, [false, true])) == true
-    @eqtest simplify(ifelse(true, a,b)) == a
-    @eqtest simplify(ifelse(false, a,b)) == b
+    @eqtest simplify(ifelse(true, a, b)) == a
+    @eqtest simplify(ifelse(false, a, b)) == b
 
     # abs
-    @test simplify(substitute(ifelse(!(a < 0), a,-a), Dict(a=>-1))) == 1
-    @test simplify(substitute(ifelse(!(a < 0), a,-a), Dict(a=>1))) == 1
-    @test simplify(substitute(ifelse(a < 0, -a, a), Dict(a=>-1))) == 1
-    @test simplify(substitute(ifelse(a < 0, -a, a), Dict(a=>1))) == 1
+    @test simplify(substitute(ifelse(!(a < 0), a, -a), Dict(a => -1))) == 1
+    @test simplify(substitute(ifelse(!(a < 0), a, -a), Dict(a => 1))) == 1
+    @test simplify(substitute(ifelse(a < 0, -a, a), Dict(a => -1))) == 1
+    @test simplify(substitute(ifelse(a < 0, -a, a), Dict(a => 1))) == 1
 end
 
 @testset "Pythagorean Identities" begin
@@ -92,29 +92,32 @@ end
 
 @testset "Double angle formulas" begin
     @syms r x
-    @eqtest simplify(r*cos(x/2)^2 - r*sin(x/2)^2) == r*cos(x)
-    @eqtest simplify(r*sin(x/2)^2 - r*cos(x/2)^2) == -r*cos(x)
-    @eqtest simplify(2cos(x)*sin(x)) == sin(2x)
+    @eqtest simplify(r * cos(x / 2)^2 - r * sin(x / 2)^2) == r * cos(x)
+    @eqtest simplify(r * sin(x / 2)^2 - r * cos(x / 2)^2) == -r * cos(x)
+    @eqtest simplify(2cos(x) * sin(x)) == sin(2x)
 end
 
 @testset "Exponentials" begin
     @syms a::Real b::Real
-    @eqtest simplify(exp(a)*exp(b)) == simplify(exp(a+b))
-    @eqtest simplify(exp(a)*exp(a)) == simplify(exp(2a))
-    @test simplify(exp(a)*exp(-a)) == 1
+    @eqtest simplify(exp(a) * exp(b)) == simplify(exp(a + b))
+    @eqtest simplify(exp(a) * exp(a)) == simplify(exp(2a))
+    @test simplify(exp(a) * exp(-a)) == 1
     @eqtest simplify(exp(a)^2) == simplify(exp(2a))
-    @eqtest simplify(exp(a) * a * exp(b)) == simplify(a*exp(a+b))
+    @eqtest simplify(exp(a) * a * exp(b)) == simplify(a * exp(a + b))
+    @eqtest simplify(one(Int)^a) == 1
+    @eqtest simplify(one(Complex{Float64})^a) == 1
+    @eqtest simplify(a^b * 1^a) == a^b
 end
 
 @testset "simplify_fractions" begin
     @syms x y z
-    @eqtest simplify(2*((y + z)/x) - 2*y/x - z/x*2) == 0
+    @eqtest simplify(2 * ((y + z) / x) - 2 * y / x - z / x * 2) == 0
 end
 
 @testset "Depth" begin
     @syms x
     R = Rewriters.Postwalk(Rewriters.Chain([@rule(sin(~x) => cos(~x)),
-                                            @rule(1 + ~x => ~x - 1)]))
+        @rule(1 + ~x => ~x - 1)]))
     @eqtest R(sin(sin(sin(x + 1)))) == cos(cos(cos(x - 1)))
     #@eqtest R(sin(sin(sin(x + 1))), depth=2) == cos(cos(sin(x + 1)))
 end
@@ -125,24 +128,28 @@ pred(x) = error("Fail")
     @syms a b
 
     rs = Rewriters.Postwalk(Rewriters.Chain(([@rule ~x + ~y::pred => ~x])))
-    @test_throws Metatheory.Rules.RuleRewriteError rs(a+b)
-    err = try rs(a+b) catch err; err; end
-    @test sprint(io->Base.showerror(io, err)) == "Failed to apply rule ~x + ~(y::pred) => ~x on expression a + b"
+    @test_throws Metatheory.Rules.RuleRewriteError rs(a + b)
+    err = try
+        rs(a + b)
+    catch err
+        err
+    end
+    @test sprint(io -> Base.showerror(io, err)) == "Failed to apply rule ~x + ~(y::pred) => ~x on expression a + b"
 end
 
 @testset "Threading" begin
     @syms a b c d
     ex = (((0.6666666666666666 / (c / 1)) + ((1 * a) / (c / 1))) +
           (1.0 / (((1 * d) / (1 + b)) * (1 / b)))) +
-          ((((1 * a) + (1 * a)) / ((2.0 * (d + 1)) / 1.0)) +
-           ((((d * 1) / (1 + c)) * 2.0) / ((1 / d) + (1 / c))))
+         ((((1 * a) + (1 * a)) / ((2.0 * (d + 1)) / 1.0)) +
+          ((((d * 1) / (1 + c)) * 2.0) / ((1 / d) + (1 / c))))
     @eqtest simplify(ex) == simplify(ex, threaded=true, thread_subtree_cutoff=3)
     @test SymbolicUtils.node_count(a + b * c / d) == 7
 end
 
 @testset "timerwrite" begin
     @syms a b c d
-    expr1 = foldr((x,y)->rand([*, /])(x,y), rand([a,b,c,d], 100))
+    expr1 = foldr((x, y) -> rand([*, /])(x, y), rand([a, b, c, d], 100))
     SymbolicUtils.@timerewrite simplify(expr1)
 end
 
@@ -159,14 +166,14 @@ _f(x) = x === a
 @testset "where" begin
     using Metatheory
     expected = :(_f(~x) ? ~x + ~y : nothing)
-    @test Metatheory.Syntax.rewrite_rhs(:((~x + ~y) where _f(~x))) == expected
+    @test Metatheory.Syntax.rewrite_rhs(:((~x + ~y) where {_f(~x)})) == expected
 
     @syms a b
-    r = @rule ~x => ~x where _f(~x)
+    r = @rule ~x => ~x where {_f(~x)}
     @eqtest r(a) == a
     @test isnothing(r(b))
 
-    r = @acrule ~x => ~x where _f(~x)
+    r = @acrule ~x => ~x where {_f(~x)}
     @eqtest r(a) == a
     @test r(b) === nothing
 end