Add displayBigO to set/unset printing the bigO notation (#139)

* Add displayBigO to set/unset printing the bigO notation

This commit also addresses some deprecation warnings for Julia 0.7.

* Add docs [ci skip]

docs/src/api.md

@@ -47,6 +47,7 @@ abs
 norm
 isapprox
 isfinite
+displayBigO
 ```
 
 ## Internals
@@ -79,6 +80,7 @@ atan!
 sinhcosh!
 tanh!
 A_mul_B!
+derivative!
 ```
 
 ## Index

docs/src/userguide.md

@@ -47,7 +47,15 @@ t = shift_taylor(0.0) # Independent variable `t`
 ```
 
 Note that the information about the maximum order considered is displayed
-using a big-𝒪 notation.
+using a big-𝒪 notation. In some cases, it is desirable to not display
+the big-𝒪 notation. The function [`displayBigO`](@ref) allows to
+control whether it is displayed or not.
+```@repl userguide
+displayBigO(false) # turn-off displaying big O notation
+t
+displayBigO(true) # turn it on
+t
+```
 
 The definition of `shift_taylor(a)` uses the method
 [`Taylor1([::Type{Float64}], [order::Int64=1])`](@ref), which is a
@@ -170,7 +178,8 @@ equivalent to `evaluate(p)`. For more details about function-like behavior for a
 given type in Julia, see the [Function-like objects](https://docs.julialang.org/en/stable/manual/methods/#Function-like-objects-1)
 section of the Julia manual.
 
-Useful shortcuts are `taylor_expand` are `update!`. The former returns
+Useful shortcuts are [`taylor_expand`](@ref) are [`update!`](@ref).
+The former returns
 the expansion of a function around a given value `t0`. In turn, `update!`
 provides an in-place update of a given Taylor polynomial, that is, it shifts
 it further by the provided amount.

src/TaylorSeries.jl

@@ -34,7 +34,7 @@ export Taylor1, TaylorN, HomogeneousPolynomial, AbstractSeries
 
 export getcoeff, derivative, integrate,
     evaluate, evaluate!, inverse,
-    show_params_TaylorN, show_monomials,
+    show_params_TaylorN, show_monomials, displayBigO,
     get_order, get_numvars,
     set_variables, get_variables,
     ∇, jacobian, jacobian!, hessian, hessian!,

src/parameters.jl

@@ -140,3 +140,16 @@ function show_params_TaylorN()
     """)
     nothing
 end
+
+
+# Control the display of the big 𝒪 notation
+const bigOnotation = Bool[true]
+
+"""
+    displayBigO(d::Bool) --> nothing
+
+Set/unset displaying of the big 𝒪 notation in  the output
+of `Taylor1` and `TaylorN` polynomials. The initial value is
+`true`.
+"""
+displayBigO(d::Bool) = (bigOnotation[end] = d; d)

src/printing.jl

@@ -22,7 +22,10 @@ end
 function pretty_print(a::Taylor1{T}) where {T<:Number}
     z = zero(a[0])
     space = string(" ")
-    bigO = string("+ 𝒪(t", superscriptify(a.order+1), ")")
+    # bigO = string("+ 𝒪(t", superscriptify(a.order+1), ")")
+    bigO = bigOnotation[end] ?
+        string("+ 𝒪(t", superscriptify(a.order+1), ")") :
+        string("")
     a == zero(a) && return string(space, z, space, bigO)
     strout::String = space
     ifirst = true
@@ -42,7 +45,10 @@ end
 function pretty_print(a::Taylor1{HomogeneousPolynomial{T}}) where {T<:Number}
     z = zero(a[0])
     space = string(" ")
-    bigO = string("+ 𝒪(t", superscriptify(a.order+1), ")")
+    # bigO = string("+ 𝒪(t", superscriptify(a.order+1), ")")
+    bigO = bigOnotation[end] ?
+        string("+ 𝒪(t", superscriptify(a.order+1), ")") :
+        string("")
     a == zero(a) && return string(space, z, space, bigO)
     strout::String = space
     ifirst = true
@@ -64,7 +70,11 @@ end
 function pretty_print(a::Taylor1{TaylorN{T}}) where {T<:Number}
     z = zero(a[0])
     space = string(" ")
-    bigO = string("+ 𝒪(t", superscriptify(a.order+1), ")")
+    # bigO = string("+ 𝒪(t", superscriptify(a.order+1), ")")
+    bigO = bigOnotation[end] ?
+        string("+ 𝒪(t", superscriptify(a.order+1), ")") :
+        string("")
+    a == zero(a) && return string(space, z, space, bigO)
     a == zero(a) && return string(space, z, space, bigO)
     strout::String = space
     ifirst = true
@@ -94,7 +104,11 @@ end
 function pretty_print(a::TaylorN{T}) where {T<:Number}
     z = zero(a[0])
     space = string("")
-    bigO::String  = string(" + 𝒪(‖x‖", superscriptify(a.order+1), ")")
+    # bigO::String  = string(" + 𝒪(‖x‖", superscriptify(a.order+1), ")")
+    bigO::String = bigOnotation[end] ?
+        string(" + 𝒪(‖x‖", superscriptify(a.order+1), ")") :
+        string("")
+    a == zero(a) && return string(space, z, space, bigO)
     a == zero(a) && return string(space, z, bigO)
     strout::String = space#string("")
     ifirst = true

test/manyvariables.jl

@@ -415,6 +415,12 @@ end
     hessian!(hes2,g1(xT+1,yT-1)-g2(xT+1,yT-1))
     @test hes1 == hes2
 
+    displayBigO(false)
+    @test string(-xH) == " - 1 x₁"
+    @test string(xT^2) == " 1 x₁²"
+    @test string(1im*yT) == " ( 1 im ) x₂"
+    @test string(xT-im*yT) == "  ( 1 ) x₁ - ( 1 im ) x₂"
+    displayBigO(true)
     @test string(-xH) == " - 1 x₁"
     @test string(xT^2) == " 1 x₁² + 𝒪(‖x‖¹⁸)"
     @test string(1im*yT) == " ( 1 im ) x₂ + 𝒪(‖x‖¹⁸)"

test/onevariable.jl

@@ -4,8 +4,10 @@
 using TaylorSeries
 if VERSION < v"0.7.0-DEV.2004"
     using Base.Test
+    eeuler = Base.e
 else
     using Test
+    eeuler = Base.MathConstants.e
 end
 
 @testset "Tests for Taylor1 expansions" begin
@@ -177,13 +179,13 @@ end
     @test getcoeff(convert(Taylor1{Rational{Int}},cos(t)),8) == 1//factorial(8)
     @test abs((tan(t))[7]- 17/315) < tol1
     @test abs((tan(t))[13]- 21844/6081075) < tol1
-    @test evaluate(exp(Taylor1([0,1],17)),1.0) == 1.0*e
+    @test evaluate(exp(Taylor1([0,1],17)),1.0) == 1.0*eeuler
     @test evaluate(exp(Taylor1([0,1],1))) == 1.0
     @test evaluate(exp(t),t^2) == exp(t^2)
     #Test function-like behavior for Taylor1s
     t17 = Taylor1([0,1],17)
     myexpfun = exp(t17)
-    @test myexpfun(1.0) == 1.0*e
+    @test myexpfun(1.0) == 1.0*eeuler
     @test myexpfun() == 1.0
     @test myexpfun(t17^2) == exp(t17^2)
     @test exp(t17^2)(t17) == exp(t17^2)
@@ -327,7 +329,7 @@ end
 
     @test norm((inverse(exp(t)-1) - log(1+t)).coeffs) < 2tol1
     cfs = [(-n)^(n-1)/gamma(n+1) for n = 1:15]
-    @test norm(inverse(t*exp(t))[1:end]./cfs-1) < 4tol1
+    @test norm(inverse(t*exp(t))[1:end]./cfs .- 1) < 4tol1
 
     @test_throws ArgumentError Taylor1([1,2,3], -2)
     @test_throws ArgumentError abs(ta(big(0)))
@@ -345,12 +347,17 @@ end
     @test_throws AssertionError derivative(30, exp(ta(1.0pi)))
     @test_throws ArgumentError inverse(exp(t))
 
+    displayBigO(false)
+    @test string(ta(-3)) == " - 3 + 1 t "
+    @test string(ta(0)^3-3) == " - 3 + 1 t³ "
+    @test TaylorSeries.pretty_print(ta(3im)) == " ( 3 im )  + ( 1 ) t "
+    @test string(Taylor1([1,2,3,4,5], 2)) == string(Taylor1([1,2,3]))
+    displayBigO(true)
     @test string(ta(-3)) == " - 3 + 1 t + 𝒪(t¹⁶)"
     @test string(ta(0)^3-3) == " - 3 + 1 t³ + 𝒪(t¹⁶)"
     @test TaylorSeries.pretty_print(ta(3im)) == " ( 3 im )  + ( 1 ) t + 𝒪(t¹⁶)"
     @test string(Taylor1([1,2,3,4,5], 2)) == string(Taylor1([1,2,3]))
 
-
     a = collect(1:12)
     t_a = Taylor1(a,15)
     t_C = complex(3.0,4.0) * t_a