doctest failure in src/polynomial.md:282-338 ```jldoctest julia> R, x = polynomial_ring(QQ, :x) (Univariate polynomial ring in x over rationals, x) julia> S, = residue_ring(R, x^3 + 3x + 1); julia> T, y = polynomial_ring(S, :y) (Univariate polynomial ring in y over S, y) julia> f = (3*x^2 + x + 2)*y + x^2 + 1 (3*x^2 + x + 2)*y + x^2 + 1 julia> g = (5*x^2 + 2*x + 1)*y^2 + 2x*y + x + 1 (5*x^2 + 2*x + 1)*y^2 + 2*x*y + x + 1 julia> h = (3*x^3 + 2*x^2 + x + 7)*y^5 + 2x*y + 1 (2*x^2 - 8*x + 4)*y^5 + 2*x*y + 1 julia> invmod(f, g) (707//3530*x^2 + 2151//1765*x + 123//3530)*y - 178//1765*x^2 - 551//3530*x + 698//1765 julia> mulmod(f, g, h) (-30*x^2 - 43*x - 9)*y^3 + (-7*x^2 - 23*x - 7)*y^2 + (4*x^2 - 10*x - 3)*y + x^2 - 2*x julia> powermod(f, 3, h) (69*x^2 + 243*x + 79)*y^3 + (78*x^2 + 180*x + 63)*y^2 + (27*x^2 + 42*x + 18)*y + 3*x^2 + 3*x + 2 julia> h = mod(f, g) (3*x^2 + x + 2)*y + x^2 + 1 julia> q, r = divrem(f, g) (0, (3*x^2 + x + 2)*y + x^2 + 1) julia> div(g, f) (-5//11*x^2 + 2//11*x + 6//11)*y - 13//121*x^2 - 3//11*x - 78//121 julia> d = gcd(f*h, g*h) y + 1//11*x^2 + 6//11 julia> k = gcdinv(f, h) (y + 1//11*x^2 + 6//11, 0) julia> m = lcm(f, h) (-14*x^2 - 23*x - 2)*y - 4*x^2 - 5*x + 1 julia> flag, q = divides(g^2, g) (true, (5*x^2 + 2*x + 1)*y^2 + 2*x*y + x + 1) julia> valuation(3g^3, g) == 3 true julia> val, q = remove(5g^3, g) (3, 5) julia> r, s, t = gcdx(g, h) (1, 311//3530*x^2 - 2419//3530*x + 947//1765, (707//3530*x^2 + 2151//1765*x + 123//3530)*y - 178//1765*x^2 - 551//3530*x + 698//1765) ``` Subexpression: valuation(3g^3, g) == 3 Evaluated output: ERROR: function is_nilpotent is not implemented for argument EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}: 2*x Stacktrace: [1] is_nilpotent(a::EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/NCRings.jl:161 [2] is_unit(f::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/NCPoly.jl:804 [3] remove(z::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}, p::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/Poly.jl:1572 [4] valuation(a::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}, b::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/algorithms/GenericFunctions.jl:192 [5] top-level scope @ none:1 Expected output: true diff = Warning: Diff output requires color. trueERROR: function is_nilpotent is not implemented for argument EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}: 2*x Stacktrace: [1] is_nilpotent(a::EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/NCRings.jl:161 [2] is_unit(f::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/NCPoly.jl:804 [3] remove(z::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}, p::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/Poly.jl:1572 [4] valuation(a::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}, b::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}) @ AbstractAlgebra ~/w

doctest failure in src/polynomial.md:282-338 ```jldoctest julia> R, x = polynomial_ring(QQ, :x) (Univariate polynomial ring in x over rationals, x) julia> S, = residue_ring(R, x^3 + 3x + 1); julia> T, y = polynomial_ring(S, :y) (Univariate polynomial ring in y over S, y) julia> f = (3*x^2 + x + 2)*y + x^2 + 1 (3*x^2 + x + 2)*y + x^2 + 1 julia> g = (5*x^2 + 2*x + 1)*y^2 + 2x*y + x + 1 (5*x^2 + 2*x + 1)*y^2 + 2*x*y + x + 1 julia> h = (3*x^3 + 2*x^2 + x + 7)*y^5 + 2x*y + 1 (2*x^2 - 8*x + 4)*y^5 + 2*x*y + 1 julia> invmod(f, g) (707//3530*x^2 + 2151//1765*x + 123//3530)*y - 178//1765*x^2 - 551//3530*x + 698//1765 julia> mulmod(f, g, h) (-30*x^2 - 43*x - 9)*y^3 + (-7*x^2 - 23*x - 7)*y^2 + (4*x^2 - 10*x - 3)*y + x^2 - 2*x julia> powermod(f, 3, h) (69*x^2 + 243*x + 79)*y^3 + (78*x^2 + 180*x + 63)*y^2 + (27*x^2 + 42*x + 18)*y + 3*x^2 + 3*x + 2 julia> h = mod(f, g) (3*x^2 + x + 2)*y + x^2 + 1 julia> q, r = divrem(f, g) (0, (3*x^2 + x + 2)*y + x^2 + 1) julia> div(g, f) (-5//11*x^2 + 2//11*x + 6//11)*y - 13//121*x^2 - 3//11*x - 78//121 julia> d = gcd(f*h, g*h) y + 1//11*x^2 + 6//11 julia> k = gcdinv(f, h) (y + 1//11*x^2 + 6//11, 0) julia> m = lcm(f, h) (-14*x^2 - 23*x - 2)*y - 4*x^2 - 5*x + 1 julia> flag, q = divides(g^2, g) (true, (5*x^2 + 2*x + 1)*y^2 + 2*x*y + x + 1) julia> valuation(3g^3, g) == 3 true julia> val, q = remove(5g^3, g) (3, 5) julia> r, s, t = gcdx(g, h) (1, 311//3530*x^2 - 2419//3530*x + 947//1765, (707//3530*x^2 + 2151//1765*x + 123//3530)*y - 178//1765*x^2 - 551//3530*x + 698//1765) ``` Subexpression: val, q = remove(5g^3, g) Evaluated output: ERROR: function is_nilpotent is not implemented for argument EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}: 2*x Stacktrace: [1] is_nilpotent(a::EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/NCRings.jl:161 [2] is_unit(f::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/NCPoly.jl:804 [3] remove(z::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}, p::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/Poly.jl:1572 [4] top-level scope @ none:1 Expected output: (3, 5) diff = Warning: Diff output requires color. (3, 5)ERROR: function is_nilpotent is not implemented for argument EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}: 2*x Stacktrace: [1] is_nilpotent(a::EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/NCRings.jl:161 [2] is_unit(f::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/NCPoly.jl:804 [3] remove(z::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}, p::AbstractAlgebra.Generic.Poly{EuclideanRingResidueRingElem{AbstractAlgebra.Generic.Poly{Rational{BigInt}}}}) @ AbstractAlgebra ~/work/AbstractAlgebra.jl/AbstractAlgebra.jl/src/Poly.jl:1572 [4] top-level scope @ none:1