`is_gen` is not supported for various polynomial rings

[HechtiDerLachs]

julia> using Oscar

julia> S, (x, y, z) = graded_polynomial_ring(QQ, ["x", "y", "z"]; weights=[[0, 1], [1, 1], [2, 1]])
(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])

julia> is_gen(S[1])
ERROR: MethodError: no method matching is_gen(::MPolyDecRingElem{QQFieldElem, QQMPolyRingElem})
The function `is_gen` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  is_gen(::MPolyRingElem, ::Int64)
   @ AbstractAlgebra ~/.julia/packages/AbstractAlgebra/EAjNg/src/MPoly.jl:132
  is_gen(::QQPolyRingElem)
   @ Nemo ~/.julia/packages/Nemo/Dukvj/src/flint/fmpq_poly.jl:63
  is_gen(::zzModMPolyRingElem, ::Int64)
   @ Nemo ~/.julia/packages/Nemo/Dukvj/src/flint/nmod_mpoly.jl:63
  ...

Stacktrace:
 [1] top-level scope
   @ REPL[24]:1

Suggestion for a catchall implementation:

 function is_gen(a::MPolyRingElem)
   is_zero(a) && return false
   !is_one(length(a)) && return false
   e = only(AbstractAlgebra.exponent_vectors(a))
   is_one(only(AbstractAlgebra.coefficients(a))) || return false
   i = findfirst(is_one, e)
   isnothing(i) && return false
   return all(k == i || is_zero(n) for (k, n) in enumerate(e))
 end

[fingolfin]

Alternatively the fallback could be based on the internal helper _is_gen_with_index but see also discussion on issue #2064

[lgoettgens]

I would say that is_gen is something that each ring type should implement on its own. For @HechtiDerLachs 's issue, I suggested a very trivial implementation in oscar-system/Oscar.jl#4841 (comment)

[lgoettgens]

I would say that is_gen is something that each ring type should implement on its own. For @HechtiDerLachs 's issue, I suggested a very trivial implementation in oscar-system/Oscar.jl#4841 (comment)

The interface agrees with me: is_gen is included here (https://nemocas.github.io/AbstractAlgebra.jl/stable/mpoly_interface/#Basic-manipulation-of-rings-and-elements) in the list of required functionality of the MPoly subtype