Add utilities to use Difference operator

Author: sharanry

src/systems/discrete_system/discrete_system.jl

@@ -120,3 +120,47 @@ function DiffEqBase.DiscreteProblem(sys::DiscreteSystem,u0map,tspan,
     f(u,p,t) = f_oop(u,p,t)
     DiscreteProblem(f,u0,tspan,p;kwargs...)
 end
+
+isdifference(expr) = istree(expr) && operation(expr) isa Difference
+isdifferenceeq(eq) = isdifference(eq.lhs)
+
+difference_vars(x::Sym) = Set([x])
+difference_vars(exprs::Symbolic) = difference_vars([exprs])
+difference_vars(exprs) = foldl(difference_vars!, exprs; init = Set())
+difference_vars!(difference_vars, eq::Equation) = (difference_vars!(difference_vars, eq.lhs); difference_vars!(difference_vars, eq.rhs); difference_vars)
+function difference_vars!(difference_vars, O)
+    if isa(O, Sym)
+        return push!(difference_vars, O)
+    end
+    !istree(O) && return difference_vars
+
+    operation(O) isa Difference && return push!(difference_vars, O)
+
+    if operation(O) === (getindex) &&
+        first(arguments(O)) isa Symbolic
+
+        return push!(difference_vars, O)
+    end
+
+    symtype(operation(O)) <: FnType && push!(difference_vars, O)
+    for arg in arguments(O)
+        difference_vars!(difference_vars, arg)
+    end
+
+    return difference_vars
+end
+
+function collect_difference_variables(sys::DiscreteSystem)
+    eqs = equations(sys)
+    vars = Set()
+    difference_vars = Set()
+    for eq in eqs
+        difference_vars!(vars, eq)
+        for v in vars
+            isdifference(v) || continue
+            push!(difference_vars, arguments(v)[1])
+        end
+        empty!(vars)
+    end
+    return difference_vars
+end