Error when creating an array with Monomial and other objects

[shashi]

using SymbolicUtils

julia> @syms(a); b = SymbolicUtils.to_mpoly(a^2)
(a², OrderedCollections.OrderedDict{Sym, Any}(a => a))

julia> c = b[1]
a²

julia> typeof(c)
DynamicPolynomials.Monomial{true}

julia> [c, a]
ERROR: MethodError: no method matching one(::Type{Any})
Closest candidates are:
  one(::Type{Union{Missing, T}}) where T at missing.jl:105
  one(::Union{Type{T}, T}) where T<:AbstractString at strings/basic.jl:262
  one(::Union{Type{P}, P}) where P<:Dates.Period at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/Dates/src/periods.jl:54
  ...
Stacktrace:
 [1] one(#unused#::Type{Any})
   @ Base ./missing.jl:106
 [2] convert(#unused#::Type{DynamicPolynomials.Term{true, Any}}, x::DynamicPolynomials.Monomial{true})
   @ DynamicPolynomials ~/.julia/packages/DynamicPolynomials/5p8Ga/src/term.jl:18
 [3] setindex!(A::Vector{DynamicPolynomials.Term{true, Any}}, x::DynamicPolynomials.Monomial{true}, i1::Int64)
   @ Base ./array.jl:839
 [4] copyto!(dest::Vector{DynamicPolynomials.Term{true, Any}}, src::Tuple{DynamicPolynomials.Monomial{true}, Sym{Number, Nothing}})
   @ Base ./abstractarray.jl:840
 [5] vect(::DynamicPolynomials.Monomial{true}, ::Vararg{Any, N} where N)
   @ Base ./array.jl:129
 [6] top-level scope
   @ REPL[193]:1

[blegat]

In MultivariatePolynomials, everything that is not a AbstractPolynomialLike is considered a constant/coefficient.
So here, MultivariatePolynomials tries to create a vector with terms for which the coefficients are symbolic expressions.
The issue is that:

julia> typeof(a)
SymbolicUtils.Sym{Number, Nothing}

julia> promote_type(Int, typeof(a))
Any

So we try instead to create an array of terms with coefficients Any.
Would it make sense for promote_type(Int, typeof(a)) to be a symbolic expression instead ?

[shashi]

Would it make sense for promote_type(Int, typeof(a)) to be a symbolic expression instead ?

No I don't think so, the correct answer is Any here imo because 1 and Sym are different types with only Any as a common ancestor.

In MultivariatePolynomials, everything that is not a AbstractPolynomialLike is considered a constant/coefficient.

I think this is a completely fine behavior when it's actually dealing with these terms, but here we are trying to build a plain julia vector of objects, so I feel the reasoning that anything else should be treated as a coefficient should not be leaking outside the package. Not surprisingly it creates surprising problems. It could even happen in packages like Folds or something, which just deal with collections of objects and expect things like vect to just work.

[shashi]

The problem boils down to:

p = some polynomial
@syms a b
julia> Base.promote_typeof(p, a*b)
DynamicPolynomials.Polynomial{true, Any}

It should not give a type for which convert is not defined. It should just go Any.