Use rational representation if possible

[YingboMa]

using Symbolics, RootedTrees
using Symbolics: variables
p = 5
s = 7
A = variables(:A, 1:s, 1:s)
b = variables(:b, 1:s)
c = variables(:c, 1:s)

# Explicit condition
for i in 1:s, j in 1:s
    if i <= j
        A[i, j] = 0
    end
end
c[1] = 0
c[end-1] = 1
c[end] = 1
b[end] = 0
A[end, :] = b

constraints = map(Iterators.flatten(RootedTreeIterator(i) for i in 1:p)) do t
    residual_order_condition(t, A, b, c)
end

Master:

julia> constraints[10]
(1//2)*(-0.016666666666666666 + (A₂ˏ₁^2)*A₃ˏ₂*A₄ˏ₃*b₄ + ((A₂ˏ₁^2)*A₃ˏ₂*A₅ˏ₃ + ((A₂ˏ₁^2)*A₄ˏ₂ + ((A₃ˏ₁ + A₃ˏ₂)^2)*A₄ˏ₃)*A₅ˏ₄)*b₅ + ((A₂ˏ₁^2)*A₃ˏ₂*A₆ˏ₃ + ((A₂ˏ₁^2)*A₄ˏ₂ + ((A₃ˏ₁ + A₃ˏ₂)^2)*A₄ˏ₃)*A₆ˏ₄ + ((A₂ˏ₁^2)*A₅ˏ₂ + ((A₃ˏ₁ + A₃ˏ₂)^2)*A₅ˏ₃ + ((A₄ˏ₁ + A₄ˏ₂ + A₄ˏ₃)^2)*A₅ˏ₄)*A₆ˏ₅)*b₆)

PR:

julia> constraints[10]
(1//2)*(-(1//60) + (A₂ˏ₁^2)*A₃ˏ₂*A₄ˏ₃*b₄ + ((A₂ˏ₁^2)*A₃ˏ₂*A₅ˏ₃ + ((A₂ˏ₁^2)*A₄ˏ₂ + ((A₃ˏ₁ + A₃ˏ₂)^2)*A₄ˏ₃)*A₅ˏ₄)*b₅ + ((A₂ˏ₁^2)*A₃ˏ₂*A₆ˏ₃ + ((A₂ˏ₁^2)*A₄ˏ₂ + ((A₃ˏ₁ + A₃ˏ₂)^2)*A₄ˏ₃)*A₆ˏ₄ + ((A₂ˏ₁^2)*A₅ˏ₂ + ((A₃ˏ₁ + A₃ˏ₂)^2)*A₅ˏ₃ + ((A₄ˏ₁ + A₄ˏ₂ + A₄ˏ₃)^2)*A₅ˏ₄)*A₆ˏ₅)*b₆)