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Add more tests to ring interface conformance tests #2213

@YueRen

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@YueRen

@thofma made me aware of the ring interface conformance tests in ollieclarke8787/OscarPuiseuxPolynomials#13 (comment), which proved itself to be super useful. However, here some thing they did not check and maybe should (including errors to show how the missing function errors arose):

  1. characteristic:
ERROR: Characteristic not known
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:44
  [2] characteristic(R::OscarPuiseuxPolynomial.MPuiseuxPolyRing{QQBarFieldElem})    @ AbstractAlgebra ~/.julia/packages/AbstractAlgebra/L8iQ0/src/NCRings.jl:186  [3] characteristic(R::AbstractAlgebra.Generic.MPolyRing{OscarPuiseuxPolynomial.MPuiseuxPolyRingElem{QQBarFieldElem}})
    @ AbstractAlgebra ~/.julia/packages/AbstractAlgebra/L8iQ0/src/MPoly.jl:137
  [4] ^(a::AbstractAlgebra.Generic.MPoly{AbstractAlgebra.Generic.MPoly{…}}, b::Int64)
    @ AbstractAlgebra.Generic ~/.julia/packages/AbstractAlgebra/L8iQ0/src/generic/MPoly.jl:2279
  [5] #evaluate##4
    @ ~/.julia/packages/AbstractAlgebra/L8iQ0/src/MPoly.jl:904 [inlined]
  [6] get!(default::AbstractAlgebra.var"#evaluate##4#evaluate##5"{…}, h::Dict{…}, key::Int64)
    @ Base ./dict.jl:458
  [7] evaluate(a::AbstractAlgebra.Generic.MPoly{…}, vals::Vector{…})
    @ AbstractAlgebra ~/.julia/packages/AbstractAlgebra/L8iQ0/src/MPoly.jl:903
  [8] puiseux_expansion(fiTilde::AbstractAlgebra.Generic.MPoly{…}, w::QQFieldElem, precMax::QQFieldElem)
    @ OscarZerodimensionalTropicalization ~/projects/MartiShahandehSchleis/github/src/puiseux_expansion.jl:182
  [9] improve_root!(Gamma::OscarZerodimensionalTropicalization.RootTree, vertex::Int64)
    @ OscarZerodimensionalTropicalization ~/projects/MartiShahandehSchleis/github/src/root_tree.jl:565
 [10] top-level scope
    @ REPL[33]:1
Some type information was truncated. Use `show(err)` to see complete types.
  1. divrem:
ERROR: function divrem is not implemented for arguments
OscarPuiseuxPolynomial.MPuiseuxPolyRingElem{QQBarFieldElem}: {a1: 768.000}
OscarPuiseuxPolynomial.MPuiseuxPolyRingElem{QQBarFieldElem}: {a1: 256.000}

Stacktrace:
  [1] divrem(a::OscarPuiseuxPolynomial.MPuiseuxPolyRingElem{…}, b::OscarPuiseuxPolynomial.MPuiseuxPolyRingElem{…})
    @ AbstractAlgebra ~/.julia/packages/AbstractAlgebra/L8iQ0/src/algorithms/GenericFunctions.jl:50
  [2] divrem(a::OscarPuiseuxPolynomial.MPuiseuxPolyRingElem{…}, b::OscarPuiseuxPolynomial.MPuiseuxPolyRingElem{…})
    @ AbstractAlgebra ~/.julia/packages/AbstractAlgebra/L8iQ0/src/AbstractAlgebra.jl:67
  [3] divides(a::OscarPuiseuxPolynomial.MPuiseuxPolyRingElem{…}, b::OscarPuiseuxPolynomial.MPuiseuxPolyRingElem{…})
    @ AbstractAlgebra ~/.julia/packages/AbstractAlgebra/L8iQ0/src/algorithms/GenericFunctions.jl:156
  [4] divides_monagan_pearce(a::AbstractAlgebra.Generic.MPoly{…}, b::AbstractAlgebra.Generic.MPoly{…}, bits::Int64)
    @ AbstractAlgebra.Generic ~/.julia/packages/AbstractAlgebra/L8iQ0/src/generic/MPoly.jl:2491
  [5] divides(a::AbstractAlgebra.Generic.MPoly{…}, b::AbstractAlgebra.Generic.MPoly{…})
    @ AbstractAlgebra.Generic ~/.julia/packages/AbstractAlgebra/L8iQ0/src/generic/MPoly.jl:2550
  [6] #divexact#135
    @ ~/.julia/packages/AbstractAlgebra/L8iQ0/src/generic/MPoly.jl:2561 [inlined]
  [7] divexact
    @ ~/.julia/packages/AbstractAlgebra/L8iQ0/src/generic/MPoly.jl:2560 [inlined]
  [8] pow_fps(f::AbstractAlgebra.Generic.MPoly{AbstractAlgebra.Generic.MPoly{…}}, k::Int64, bits::Int64)
    @ AbstractAlgebra.Generic ~/.julia/packages/AbstractAlgebra/L8iQ0/src/generic/MPoly.jl:2208
  [9] ^(a::AbstractAlgebra.Generic.MPoly{AbstractAlgebra.Generic.MPoly{…}}, b::Int64)
    @ AbstractAlgebra.Generic ~/.julia/packages/AbstractAlgebra/L8iQ0/src/generic/MPoly.jl:2307
 [10] #evaluate##4
    @ ~/.julia/packages/AbstractAlgebra/L8iQ0/src/MPoly.jl:904 [inlined]
 [11] get!(default::AbstractAlgebra.var"#evaluate##4#evaluate##5"{…}, h::Dict{…}, key::Int64)
    @ Base ./dict.jl:458
 [12] evaluate(a::AbstractAlgebra.Generic.MPoly{…}, vals::Vector{…})
    @ AbstractAlgebra ~/.julia/packages/AbstractAlgebra/L8iQ0/src/MPoly.jl:903
 [13] puiseux_expansion(fiTilde::AbstractAlgebra.Generic.MPoly{…}, w::QQFieldElem, precMax::QQFieldElem)
    @ OscarZerodimensionalTropicalization ~/projects/MartiShahandehSchleis/github/src/puiseux_expansion.jl:182
 [14] improve_root!(Gamma::OscarZerodimensionalTropicalization.RootTree, vertex::Int64)
    @ OscarZerodimensionalTropicalization ~/projects/MartiShahandehSchleis/github/src/root_tree.jl:565
 [15] top-level scope
    @ REPL[18]:1
Some type information was truncated. Use `show(err)` to see complete types.

A separate question is whether there should be some generic implementation for the functions above in case of (multivariate) polynomial rings.

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