Merge branch 'master' into mutate

Author: jverzani

src/calculus.jl

@@ -5,30 +5,64 @@ import Base: diff
 ## what is the rest of the interface. This does:
 ## diff(ex, x, n)      f^(n)
 ## diff(ex, x, y, ...) f_{xy...}  # also diff(ex, (x,y))
-## no support for diff(ex, x,n1, y,n2, ...), but can do diff(ex, (x,y), (n1, n2))
+## Support for diff(ex, x,n1, y,n2, ...),
+## but can also do diff(ex, (x,y), (n1, n2))
 
-function diff(b1::SymbolicType, b2::BasicType{Val{:Symbol}})
-    a = Basic()
+
+function diff!(a::Basic, b1::SymbolicType, b2::Basic)
+    is_symbol(b2) || throw(ArgumentError("Must differentiate with respect to a symbol"))
     ret = ccall((:basic_diff, libsymengine), Int, (Ref{Basic}, Ref{Basic}, Ref{Basic}), a, b1, b2)
     return a
 end
 
-diff(b1::SymbolicType, b2::BasicType) =
-    throw(ArgumentError("Second argument must be of Symbol type"))
+function diff(b1::SymbolicType, b2::Basic)
+    a = Basic()
+    diff!(a, b1, b2)
+    a
+end
 
-function diff(b1::SymbolicType, b2::SymbolicType, n::Integer=1)
+function diff(b1::SymbolicType, b2::SymbolicType, n::Integer)
     n < 0 && throw(DomainError("n must be non-negative integer"))
-    n==0 && return b1
-    n==1 && return diff(b1, BasicType(b2))
-    n > 1 && return diff(diff(b1, BasicType(b2)), BasicType(b2), n-1)
+    n == 0 && return b1
+    x = Basic(b2)
+    out = Basic()
+    diff!(out, b1, x)
+    for _ in (n-1):-1:1
+        diff!(out, out, x)
+    end
+    out
+end
+
+function diff(b1::SymbolicType, b2::SymbolicType, n::Integer, xs...)
+    diff(diff(b1,b2,n), xs...)
 end
 
 function diff(b1::SymbolicType, b2::SymbolicType, b3::SymbolicType)
-    isa(BasicType(b3), BasicType{Val{:Integer}}) ? diff(b1, b2, N(b3)) : diff(b1, (b2, b3))
+    if isinteger(b3)
+        n = N(b3)::Int
+        diff(b1, b2, n)
+    else
+        ex = diff(b1, b2)
+        diff(ex, b3)
+    end
+end
+
+function diff(b1::SymbolicType, b2::SymbolicType, b3::SymbolicType, bs...)
+    diff(diff(b1,b2,b3), bs...)
 end
 
-diff(b1::SymbolicType, b2::SymbolicType, b3::SymbolicType, b4::SymbolicType, b5...) =
-    diff(b1, (b2,b3,b4,b5...))
+function diff(b1::SymbolicType)
+    xs = free_symbols(b1)
+    n = length(xs)
+    n == 0 && return zero(b1)
+    n > 1 && throw(ArgumentError("More than one variable; one must be specified"))
+    diff(b1, only(xs))
+end
+
+## deprecate
+diff(b1::SymbolicType, b2::BasicType{Val{:Symbol}}) = diff(b1, Basic(b2))
+diff(b1::SymbolicType, b2::BasicType) =
+    throw(ArgumentError("Second argument must be of Symbol type"))
 
 ## mixed partials
 diff(ex::SymbolicType, bs::Tuple) = reduce((ex, x) -> diff(ex, x), bs, init=ex)

src/mathops.jl

@@ -95,7 +95,7 @@ Base.one(::Type{T}) where {T<:BasicType} = BasicType(Basic(1))
 ## Math constants
 ## no oo!
 
-for op in [:IM, :PI, :E, :EulerGamma, :Catalan, :oo, :zoo, :NAN]
+for op in [:IM, :PI, :E, :EulerGamma, :Catalan, :GoldenRatio, :oo, :zoo, :NAN]
     @eval begin
         const $op = Basic(C_NULL)
     end
@@ -120,6 +120,7 @@ function init_constants()
     @init_constant E E
     @init_constant EulerGamma EulerGamma
     @init_constant Catalan Catalan
+    @init_constant GoldenRatio GoldenRatio
     @init_constant oo infinity
     @init_constant zoo complex_infinity
     @init_constant NAN nan