Add tests and renaming

Author: YingboMa

src/systems/diffeqs/first_order_transform.jl

@@ -26,7 +26,7 @@ function ode_order_lowering(eqs, iv, states)
             # only save to the dict when we need to lower the order to save memory
             maxorder > get(var_order, var, 1) && (var_order[var] = maxorder)
             var′ = lower_varname(var, iv, maxorder - 1)
-            rhs′ = diff2symbol(eq.rhs)
+            rhs′ = diff2term(eq.rhs)
             push!(diff_vars, var′)
             push!(diff_eqs, D(var′) ~ rhs′)
         end

src/utils.jl

@@ -176,7 +176,7 @@ function tosymbol(t::Term; states=nothing, escape=true)
         op = nameof(t.op)
         args = t.args
     elseif t.op isa Differential
-        term = diff2symbol(t)
+        term = diff2term(t)
         op = Symbol(operation(term))
         args = arguments(term)
     else
@@ -211,11 +211,16 @@ function flatten_differential(O::Term)
     return (x, t, order + 1)
 end
 
-function diff2symbol(O)
+"""
+    diff2term(x::Symbolic) -> Term
+
+diff2term(D(D(x(t)))) -> xˍtt(t)
+"""
+function diff2term(O::Symbolic)
     isa(O, Term) || return O
     if is_derivative(O)
         (x, t, order) = flatten_differential(O)
         return lower_varname(x, t, order)
     end
-    return Term(O.op, diff2symbol.(O.args))
+    return Term(O.op, diff2term.(O.args))
 end

test/derivatives.jl

@@ -4,8 +4,11 @@ using Test
 # Derivatives
 @parameters t σ ρ β
 @variables x y z
+@variables uu(t)
 @derivatives D'~t D2''~t Dx'~x
 
+@test Symbol(D(D(uu))) === Symbol("uuˍtt⦗t⦘")
+
 test_equal(a, b) = @test isequal(simplify(a), simplify(b))
 
 @test @macroexpand(@derivatives D'~t D2''~t) == @macroexpand(@derivatives (D'~t), (D2''~t))