JuliaAlgebra
Promote Variables
For implemented an operation op on polynomials, we are always tempted to do
op(p::AbstractPolynomialLike, q::AbstractPolynomialLike) = op(promote(p, q)...)
and then only define op for two polynomials p and q of the same concrete type.
However, this is problematic since it promotes the coefficient type to the same type.
Therefore, multiplying a polynomial with Float64 coefficients with a polynomial with JuMP.AffExpr coefficients will give a polynomials with JuMP.QuadExpr while it should be JuMP.AffExpr.
It is however important to promote p and q to a common type without promoting coefficients.
For example, div currently fails if the two polynomials do not have the same variables since it incorrectly infers the return type.
I suggest having something like
promote_variables(p::AbstractPolynomialLike, q::AbstractPolynomialLike)
which returns a tuple (p2, q2) where p == p2 and q == q2 but p2 and q2 both have the same variables.
What do you think ?
