move mathematical constants to Base.MathConstants (#23427)

- only export pi, π and ℯ from Base
 - remove eu as alias for ℯ
 - add \euler as tab completion for ℯ

NEWS.md

@@ -378,6 +378,15 @@ Deprecated or removed
 
   * `diagm(A::BitMatrix)` has been deprecated, use `diagm(vec(A))` instead ([#23373]).
 
+  * `ℯ` (written as `\mscre<TAB>` or `\euler<TAB>`) is the new default for Euler's
+    number ([#23427]).
+
+  * The mathematical constants `π`, `pi`, `ℯ`, `e`, `γ`, `eulergamma`, `catalan`, `φ` and
+    `golden` have been have been moved from `Base` to a new module; `Base.MathConstants`.
+    Only `π`, `pi` and `ℯ` are now exported by default from `Base` ([#23427]).
+
+  * `eu` (previously an alias for `ℯ`) has been deprecated in favor of `ℯ` (or `MathConstants.e`) ([#23427]).
+
   * `GMP.gmp_version()`, `GMP.GMP_VERSION`, `GMP.gmp_bits_per_limb()`, and `GMP.GMP_BITS_PER_LIBM`
     have been renamed to `GMP.version()`, `GMP.VERSION`, `GMP.bits_per_libm()`, and `GMP.BITS_PER_LIBM`,
     respectively. Similarly, `MPFR.get_version()`, has been renamed to `MPFR.version()` ([#23323]). Also,

base/deprecated.jl

@@ -1691,6 +1691,15 @@ export hex2num
 @eval MPFR @deprecate get_version() version() false
 @eval LinAlg.LAPACK @deprecate laver() version() false
 
+# PR #23427
+@deprecate_binding e          ℯ
+@deprecate_binding eu         ℯ
+@deprecate_binding γ          MathConstants.γ
+@deprecate_binding eulergamma MathConstants.eulergamma
+@deprecate_binding catalan    MathConstants.catalan
+@deprecate_binding φ          MathConstants.φ
+@deprecate_binding golden     MathConstants.golden
+
 # PR #23271
 function IOContext(io::IO; kws...)
     depwarn("IOContext(io, k=v, ...) is deprecated, use IOContext(io, :k => v, ...) instead.", :IOContext)

base/exports.jl

@@ -186,10 +186,7 @@ export
     NaN64,
     im,
     π, pi,
-    e, eu,
-    γ, eulergamma,
-    catalan,
-    φ, golden,
+    ℯ,
     I,
 
 # Operators

base/irrationals.jl

@@ -141,91 +141,6 @@ end
 big(x::Irrational) = convert(BigFloat,x)
 big(::Type{<:Irrational}) = BigFloat
 
-## specific irrational mathematical constants
-
-@irrational π        3.14159265358979323846  pi
-@irrational e        2.71828182845904523536  exp(big(1))
-@irrational γ        0.57721566490153286061  euler
-@irrational catalan  0.91596559417721901505  catalan
-@irrational φ        1.61803398874989484820  (1+sqrt(big(5)))/2
-
-# aliases
-"""
-    pi
-    π
-
-The constant pi.
-
-```jldoctest
-julia> pi
-π = 3.1415926535897...
-```
-"""
-π, const pi = π
-
-"""
-    e
-    eu
-
-The constant e.
-
-```jldoctest
-julia> e
-e = 2.7182818284590...
-```
-"""
-e, const eu = e
-
-"""
-    γ
-    eulergamma
-
-Euler's constant.
-
-```jldoctest
-julia> eulergamma
-γ = 0.5772156649015...
-```
-"""
-γ, const eulergamma = γ
-
-"""
-    φ
-    golden
-
-The golden ratio.
-
-```jldoctest
-julia> golden
-φ = 1.6180339887498...
-```
-"""
-φ, const golden = φ
-
-"""
-    catalan
-
-Catalan's constant.
-
-```jldoctest
-julia> catalan
-catalan = 0.9159655941772...
-```
-"""
-catalan
-
-# special behaviors
-
-# use exp for e^x or e.^x, as in
-#    ^(::Irrational{:e}, x::Number) = exp(x)
-# but need to loop over types to prevent ambiguity with generic rules for ^(::Number, x) etc.
-for T in (Irrational, Rational, Integer, Number)
-    ^(::Irrational{:e}, x::T) = exp(x)
-end
-
-log(::Irrational{:e}) = 1 # use 1 to correctly promote expressions like log(x)/log(e)
-log(::Irrational{:e}, x::Number) = log(x)
-
 # align along = for nice Array printing
 function alignment(io::IO, x::Irrational)
     m = match(r"^(.*?)(=.*)$", sprint(0, showcompact, x, env=io))

base/linalg/lapack.jl

@@ -5299,7 +5299,7 @@ for (bdsdc, elty) in
                 u, ldu, vt, ldvt,
                 q, iq, work, iwork, info)
             chklapackerror(info[])
-            d, e, u, vt, q, iq
+            d, e_, u, vt, q, iq
         end
     end
 end

base/mathconstants.jl

@@ -0,0 +1,92 @@
+# This file is a part of Julia. License is MIT: https://julialang.org/license
+
+"""
+    Base.MathConstants
+
+Module containing the mathematical constants.
+See [`π`](@ref), [`ℯ`](@ref), [`γ`](@ref), [`φ`](@ref) and [`catalan`](@ref).
+"""
+module MathConstants
+
+export π, pi, ℯ, e, γ, eulergamma, catalan, φ, golden
+
+Base.@irrational π        3.14159265358979323846  pi
+Base.@irrational ℯ        2.71828182845904523536  exp(big(1))
+Base.@irrational γ        0.57721566490153286061  euler
+Base.@irrational φ        1.61803398874989484820  (1+sqrt(big(5)))/2
+Base.@irrational catalan  0.91596559417721901505  catalan
+
+# aliases
+"""
+    π
+    pi
+
+The constant pi.
+
+```jldoctest
+julia> pi
+π = 3.1415926535897...
+```
+"""
+π, const pi = π
+
+"""
+    ℯ
+    e
+
+The constant ℯ.
+
+```jldoctest
+julia> ℯ
+ℯ = 2.7182818284590...
+```
+"""
+ℯ, const e = ℯ
+
+"""
+    γ
+    eulergamma
+
+Euler's constant.
+
+```jldoctest
+julia> MathConstants.eulergamma
+γ = 0.5772156649015...
+```
+"""
+γ, const eulergamma = γ
+
+"""
+    φ
+    golden
+
+The golden ratio.
+
+```jldoctest
+julia> MathConstants.golden
+φ = 1.6180339887498...
+```
+"""
+φ, const golden = φ
+
+"""
+    catalan
+
+Catalan's constant.
+
+```jldoctest
+julia> MathConstants.catalan
+catalan = 0.9159655941772...
+```
+"""
+catalan
+
+# loop over types to prevent ambiguities for ^(::Number, x)
+for T in (Irrational, Rational, Integer, Number)
+    Base.:^(::Irrational{:ℯ}, x::T) = exp(x)
+end
+
+Base.log(::Irrational{:ℯ}) = 1 # use 1 to correctly promote expressions like log(x)/log(ℯ)
+Base.log(::Irrational{:ℯ}, x::Number) = log(x)
+
+end # module

base/repl/latex_symbols.jl

@@ -88,6 +88,7 @@ const latex_symbols = Dict(
     "\\implies" => "⟹",
     "\\impliedby" => "⟸",
     "\\to" => "→",
+    "\\euler" => "ℯ",
 
     # Superscripts
     "\\^0" => "⁰",

base/sysimg.jl

@@ -323,6 +323,8 @@ include("hashing2.jl")
 
 # irrational mathematical constants
 include("irrationals.jl")
+include("mathconstants.jl")
+using .MathConstants: ℯ, π, pi
 
 # random number generation
 include("random/dSFMT.jl")

contrib/julia.xml

@@ -306,8 +306,8 @@
       <item> im </item>
       <item> π </item>
       <item> pi </item>
+      <item> ℯ </item>
       <item> e </item>
-      <item> eu </item>
       <item> γ </item>
       <item> eulergamma </item>
       <item> catalan </item>

doc/src/manual/variables.md

@@ -81,7 +81,7 @@ julia> pi
 π = 3.1415926535897...
 
 julia> pi = 3
-ERROR: cannot assign variable Base.pi from module Main
+ERROR: cannot assign variable MathConstants.pi from module Main
 
 julia> sqrt(100)
 10.0

doc/src/stdlib/numbers.md

@@ -69,12 +69,12 @@ Base.bytes2hex
 Base.one
 Base.oneunit
 Base.zero
-Base.pi
 Base.im
-Base.eu
-Base.catalan
-Base.eulergamma
-Base.golden
+Base.MathConstants.pi
+Base.MathConstants.ℯ
+Base.MathConstants.catalan
+Base.MathConstants.eulergamma
+Base.MathConstants.golden
 Base.Inf
 Base.Inf32
 Base.Inf16

test/bigfloat.jl

@@ -7,7 +7,7 @@ for T in [Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt
     @test big(2.0)^T(3) == 8
 end
 
-for x in (2f0, pi, 7.8, big(e))
+for x in (2f0, pi, 7.8, big(ℯ))
     @test big(typeof(x)) == typeof(big(x))
     @test big(typeof(complex(x, x))) == typeof(big(complex(x, x)))
 end

test/complex.jl

@@ -901,7 +901,7 @@ end
     @test round.([1:5;] + 0.5im) == [1.0:5.0;]
 
     @test float(Complex(1, 2)) == Complex(1.0, 2.0)
-    @test round(float(Complex(π, e)),3) == Complex(3.142, 2.718)
+    @test round(float(Complex(π, ℯ)),3) == Complex(3.142, 2.718)
 end
 
 @testset "Complex32 arithmetic, PR #10003" begin
@@ -947,7 +947,7 @@ end
 @test big(1)/(10+10im) ≈ (5-5im)/big(100) ≈ big"0.05" - big"0.05"*im
 
 @testset "Complex Irrationals, issue #21204" begin
-    for x in (pi, e, catalan) # No need to test all of them
+    for x in (pi, ℯ, Base.MathConstants.catalan) # No need to test all of them
         z = Complex(x, x)
         @test typeof(z) == Complex{typeof(x)}
         @test exp(z) ≈ exp(x) * cis(x)

test/core.jl

@@ -942,7 +942,7 @@ end
 
 @test unsafe_pointer_to_objref(ccall(:jl_call1, Ptr{Void}, (Any,Any),
                                      x -> x+1, 314158)) == 314159
-@test unsafe_pointer_to_objref(pointer_from_objref(e+pi)) == e+pi
+@test unsafe_pointer_to_objref(pointer_from_objref(ℯ+pi)) == ℯ+pi
 
 let
     local a, aa

test/floatfuncs.jl

@@ -68,7 +68,7 @@ for elty in (Float32,Float64)
 end
 
 @testset "Types" begin
-    for x in (Int16(0), 1, 2f0, pi, 3//4, big(5//6), 7.8, big(9), big(e))
+    for x in (Int16(0), 1, 2f0, pi, 3//4, big(5//6), 7.8, big(9), big(ℯ))
         @test float(typeof(x)) == typeof(float(x))
         @test float(typeof(complex(x, x))) == typeof(float(complex(x, x)))
     end