y/(x*((y/x)^2)) and y/x/((y/x)^2) are not equal

[acsofie]

code:

julia> using SymbolicUtils

julia> @syms x y
(x, y)

julia> a = y / (x*((y / x)^2))
y / (x*((y / x)^2))

julia> b = y/x/((y/x)^2)
x / y

julia> simplify(a)
y / (x*((y / x)^2))

julia> isequal(a,b)
false

environment:

Julia Version 1.8.0-beta3 (2022-03-29)
[d1185830] SymbolicUtils v0.19.7

[bowenszhu]

isequal in SymbolicUtils.jl intends to only compare the exact expressions instead of their equivalent simplified forms. See https://github.com/JuliaSymbolics/SymbolicUtils.jl/blob/v0.19.7/src/types.jl (find isequal) and in master branch https://github.com/JuliaSymbolics/SymbolicUtils.jl/blob/97a8a86227f5eb824c3c28e5f2094d8168b5fa57/src/types.jl#L190-L219

[acsofie]

yes, I know. But

1. This function is implemented in this way because of assuming all syms has been simplified.
2. For the semantics of isequal, y / (x*((y / x)^2)) and y/x/((y/x)^2) should be true.
3. My issue is just describing the phenomenon and I don't think this implement has any problem. In fact, I think the problem is on

   julia> a = y / (x*((y / x)^2))
   y / (x*((y / x)^2))

   and

   julia> simplify(a)
   y / (x*((y / x)^2))