Fix bug in pow! with test (#270)

* Fix bug in pow! with test

* Add  another test

* Bump patch version

Project.toml

@@ -1,7 +1,7 @@
 name = "TaylorSeries"
 uuid = "6aa5eb33-94cf-58f4-a9d0-e4b2c4fc25ea"
 repo = "https://github.com/JuliaDiff/TaylorSeries.jl.git"
-version = "0.10.11"
+version = "0.10.12"
 
 [deps]
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

src/power.jl

@@ -178,7 +178,7 @@ exploits `k_0`, the order of the first non-zero coefficient of `a`.
     end
 
     # Relevant for positive integer r, to avoid round-off errors
-    if isinteger(r) && (k > r*findlast(a))
+    if isinteger(r) && r > 0 && (k > r*findlast(a))
         @inbounds c[k] = zero(a[0])
         return nothing
     end

test/onevariable.jl

@@ -184,6 +184,12 @@ Base.iszero(::SymbNumber) = false
     @test Taylor1(BigFloat,5)/6 == 1im*Taylor1(5)/complex(0,BigInt(6))
     @test Taylor1(BigFloat,5)/(6*Taylor1(3)) == 1/BigInt(6)
     @test Taylor1(BigFloat,5)/(6im*Taylor1(3)) == -1im/BigInt(6)
+    @test isapprox((1+(1.5+t)/4)^(-2), inv(1+(1.5+t)/4)^2, rtol=eps(Float64))
+    @test isapprox((1+(big(1.5)+t)/4)^(-2), inv(1+(big(1.5)+t)/4)^2, rtol=eps(BigFloat))
+    @test isapprox((1+(1.5+t)/4)^(-2), inv(1+(1.5+t)/4)^2, rtol=eps(Float64))
+    @test isapprox((1+(big(1.5)+t)/4)^(-2), inv(1+(big(1.5)+t)/4)^2, rtol=eps(BigFloat))
+    @test isapprox((1+(1.5+t)/5)^(-2.5), inv(1+(1.5+t)/5)^2.5, rtol=eps(Float64))
+    @test isapprox((1+(big(1.5)+t)/5)^(-2.5), inv(1+(big(1.5)+t)/5)^2.5, rtol=2eps(BigFloat))
 
     # These tests involve some sort of factorization
     @test t/(t+t^2) == 1/(1+t)