Make variables return a sorted list

Author: odow

docs/src/submodules/Nonlinear/SymbolicAD.md

@@ -153,8 +153,8 @@ existing function.
 
 ## `variables`
 
-Use [`Nonlinear.SymbolicAD.variables`](@ref) to return a list of the variables
-that appear in the function:
+Use [`Nonlinear.SymbolicAD.variables`](@ref) to return a sorted list of the
+variables that appear in the function:
 
 ```jldoctest
 julia> x = MOI.VariableIndex.(1:3)
@@ -168,13 +168,10 @@ atan(MOI.VariableIndex(3), 0.0 + 2.0 MOI.VariableIndex(1))
 
 julia> MOI.Nonlinear.SymbolicAD.variables(f)
 2-element Vector{MathOptInterface.VariableIndex}:
- MOI.VariableIndex(3)
  MOI.VariableIndex(1)
+ MOI.VariableIndex(3)
 ```
 
-Note that this list is not sorted, but it is guaranteed to contain only unique
-items.
-
 ## `derivative`
 
 Use [`Nonlinear.SymbolicAD.derivative`](@ref) to compute the symbolic derivative

src/Nonlinear/SymbolicAD/SymbolicAD.jl

@@ -310,12 +310,12 @@ end
 """
     variables(f::Union{Real,MOI.AbstractScalarFunction})
 
-Return a list of the `MOI.VariableIndex` present in the function `f`.
+Return a sorted list of the `MOI.VariableIndex` present in the function `f`.
 """
 function variables(f::MOI.AbstractScalarFunction)
     ret = MOI.VariableIndex[]
     _variables(ret, f)
-    return ret
+    return sort!(ret; by = x -> x.value)
 end
 
 variables(::Real) = MOI.VariableIndex[]

test/Nonlinear/SymbolicAD.jl

@@ -163,9 +163,9 @@ function test_variable()
         )=>[x, y],
         1.0*x*x=>[x],
         1.0*x*x+x=>[x],
-        1.0*x*x+y=>[y, x],
+        1.0*x*x+y=>[x, y],
         1.0*x*y=>[x, y],
-        1.0*y*x=>[y, x],
+        1.0*y*x=>[x, y],
         # ::NonlinearExpr
         MOI.ScalarNonlinearFunction(:sin, Any[x])=>[x],
         MOI.ScalarNonlinearFunction(:sin, Any[1.0*x+y])=>[x, y],
@@ -704,6 +704,7 @@ function test_gradient_and_hessian()
     sin_x = op(:sin, x[1])
     for (f, ret) in Any[
         (2.0*x[1]*x[2])=>(x, Any[2.0*x[2], 2.0*x[1]], [(1, 2)], [2.0]),
+        (2.0*x[2]*x[1])=>(x, Any[2.0*x[2], 2.0*x[1]], [(1, 2)], [2.0]),
         op(:*, x[1], x[2])=>(x, Any[x[2], x[1]], [(1, 2)], [true]),
         sin_x=>([x[1]], Any[op(:cos, x[1])], [(1, 1)], Any[op(:-, sin_x)]),
     ]