feat: adjust to finite field changes in Nemo (#1338)

Project.toml

@@ -28,7 +28,7 @@ GAPExt = "GAP"
 PolymakeExt = "Polymake"
 
 [compat]
-AbstractAlgebra = "^0.34.4"
+AbstractAlgebra = "^0.35.2"
 Dates = "1.6"
 Distributed = "1.6"
 GAP = "0.9.6, 0.10"
@@ -37,7 +37,7 @@ LazyArtifacts = "1.6"
 Libdl = "1.6"
 LinearAlgebra = "1.6"
 Markdown = "1.6"
-Nemo = "^0.38.2"
+Nemo = "^0.39.1"
 Pkg = "1.6"
 Polymake = "0.10, 0.11"
 Printf = "1.6"

examples/Plesken.jl

@@ -234,7 +234,7 @@ function plesken_kummer(p::ZZRingElem, r::Int, s::Int)
     end
     descent = true
     ord = degree(opt)
-    R = FlintFiniteField(opt, "a")[1]
+    R = Native.finite_field(opt, "a")[1]
     T = residue_ring(FlintZZ, p)
     J = CoerceMap(T, R)
   end

ext/GAPExt/brauer.jl

@@ -662,12 +662,12 @@ function _obstruction_prime_no_extend(x::FieldsTower, cocycles, p::Int)
   GC = automorphism_list(K, copy = false)
   D = x.isomorphism
   Pcomp = 2
-  R = GF(Pcomp, cached = false)
+  R = Native.GF(Pcomp, cached = false)
   Rx = polynomial_ring(R, "x", cached = false)[1]
   ff = Rx(K.pol)
   while iszero(mod(p, Pcomp)) || iszero(discriminant(ff))
     Pcomp = next_prime(Pcomp)
-    R = GF(Pcomp, cached = false)
+    R = Native.GF(Pcomp, cached = false)
     Rx = polynomial_ring(R, "x", cached = false)[1]
     ff = Rx(K.pol)
   end
@@ -738,13 +738,13 @@ function _obstruction_prime(x::FieldsTower, cocycles::Vector{cocycle_ctx}, p)
   permGC = _from_autos_to_perm(autsK)
   Gperm = _perm_to_gap_grp(permGC)
   Pcomp = 2
-  R = GF(Pcomp, cached = false)
+  R = Native.GF(Pcomp, cached = false)
   Rx = polynomial_ring(R, "x", cached = false)[1]
   ff1 = Rx(K.pol)
   ff2 = Rx(K1.pol)
   while iszero(mod(p, Pcomp)) || iszero(discriminant(ff1)) || iszero(discriminant(ff2))
     Pcomp = next_prime(Pcomp)
-    R = GF(Pcomp, cached = false)
+    R = Native.GF(Pcomp, cached = false)
     Rx = polynomial_ring(R, "x", cached = false)[1]
     ff1 = Rx(K.pol)
     ff2 = Rx(K1.pol)
@@ -801,12 +801,12 @@ function action_on_roots(G::Vector{NfToNfMor}, zeta::nf_elem, pv::Int)
   p = 11
   K = domain(G[1])
   Qx = parent(K.pol)
-  R = GF(p, cached = false)
+  R = Native.GF(p, cached = false)
   Rx, x = polynomial_ring(R, "x", cached = false)
   fmod = Rx(K.pol)
   while iszero(discriminant(fmod)) || iszero(mod(pv, p))
     p = next_prime(p)
-    R = GF(p, cached = false)
+    R = Native.GF(p, cached = false)
     Rx, x = polynomial_ring(R, "x", cached = false)
     fmod = Rx(K.pol)
   end
@@ -833,13 +833,13 @@ function restriction(autsK1::Vector{NfToNfMor}, autsK::Vector{NfToNfMor}, mp::Nf
   K = domain(mp)
   K1 = codomain(mp)
   p = 11
-  R = GF(p, cached = false)
+  R = Native.GF(p, cached = false)
   Rx, x = polynomial_ring(R, "x", cached = false)
   ff1 = Rx(K.pol)
   fmod = Rx(K1.pol)
   while iszero(discriminant(ff1)) || iszero(discriminant(fmod))
     p = next_prime(p)
-    R = GF(p, cached = false)
+    R = Native.GF(p, cached = false)
     Rx, x = polynomial_ring(R, "x", cached = false)
     ff1 = Rx(K.pol)
     fmod = Rx(K1.pol)
@@ -914,13 +914,13 @@ function _obstruction_pp(F::FieldsTower, cocycles::Vector{cocycle_ctx}, pv::Int)
   permGC = _from_autos_to_perm(autsK)
   Gperm = _perm_to_gap_grp(permGC)
   Pcomp = 7
-  R = GF(Pcomp, cached = false)
+  R = Native.GF(Pcomp, cached = false)
   Rx, x = polynomial_ring(R, "x", cached = false)
   ff1 = Rx(K.pol)
   ff2 = Rx(K1.pol)
   while iszero(discriminant(ff1)) || iszero(discriminant(ff2))
     Pcomp = next_prime(Pcomp)
-    R = GF(Pcomp, cached = false)
+    R = Native.GF(Pcomp, cached = false)
     Rx, x = polynomial_ring(R, "x", cached = false)
     ff1 = Rx(K.pol)
     ff2 = Rx(K1.pol)
@@ -1006,12 +1006,12 @@ function _obstruction_pp_no_extend(F::FieldsTower, cocycles::Vector{cocycle_ctx}
   permGC = _from_autos_to_perm(autsK)
   Gperm = _perm_to_gap_grp(permGC)
   Pcomp = 7
-  R = GF(Pcomp, cached = false)
+  R = Native.GF(Pcomp, cached = false)
   Rx, x = polynomial_ring(R, "x", cached = false)
   ff1 = Rx(K.pol)
   while iszero(discriminant(ff1))
     Pcomp = next_prime(Pcomp)
-    R = GF(Pcomp, cached = false)
+    R = Native.GF(Pcomp, cached = false)
     Rx, x = polynomial_ring(R, "x", cached = false)
     ff1 = Rx(K.pol)
   end

ext/GAPExt/fields.jl

@@ -173,12 +173,12 @@ function permutations(G::Vector{Hecke.NfToNfMor})
   dK = degree(K)
   d = numerator(discriminant(K.pol))
   p = 11
-  R = GF(p, cached = false)
+  R = Native.GF(p, cached = false)
   Rx, x = polynomial_ring(R, "x", cached = false)
   fmod = Rx(K.pol)
   while iszero(discriminant(fmod))
     p = next_prime(p)
-    R = GF(p, cached = false)
+    R = Native.GF(p, cached = false)
     Rx, x = polynomial_ring(R, "x", cached = false)
     fmod = Rx(K.pol)
   end
@@ -264,12 +264,12 @@ function _from_autos_to_perm(G::Vector{Hecke.NfToNfMor})
   n = length(G)
   #First, find a good prime
   p = 3
-  R = GF(p, cached = false)
+  R = Native.GF(p, cached = false)
   Rx, x = polynomial_ring(R, "x", cached = false)
   fmod = Rx(K.pol)
   while iszero(discriminant(fmod))
     p = next_prime(p)
-    R = GF(p, cached = false)
+    R = Native.GF(p, cached = false)
     Rx, x = polynomial_ring(R, "x", cached = false)
     fmod = Rx(K.pol)
   end

ext/GAPExt/maximal_abelian_subextension.jl

@@ -58,7 +58,7 @@ function check_abelian_extensions(class_fields::Vector{Tuple{ClassField{MapRayCl
   while iszero(mod(d1, p)) || iszero(mod(d2, p))
     p = next_prime(p)
   end
-  R = GF(p, cached = false)
+  R = Native.GF(p, cached = false)
   Rx, x = polynomial_ring(R, "x", cached = false)
   fmod = Rx(K.pol)
   mp_pol = Rx(image_primitive_element(emb_sub))

src/AlgAss/AbsAlgAss.jl

@@ -1281,7 +1281,7 @@ function _radical(A::AbsAlgAss{T}) where { T <: Union{ fqPolyRepFieldElem, FqPol
   if T <: fqPolyRepFieldElem
     Fp = Native.GF(Int(p))
   elseif T === FqFieldElem
-    Fp = Nemo._GF(p)
+    Fp = GF(p)
   else
     Fp = Native.GF(p)
   end

src/AlgAss/AlgAss.jl

@@ -295,7 +295,7 @@ function AlgAss(O::Union{NfAbsOrd, AlgAssAbsOrd}, I::Union{NfAbsOrdIdl, AlgAssAb
   end
 
   r = length(basis_elts)
-  Fp = Nemo._GF(p, cached = false)
+  Fp = GF(p, cached = false)
 
   if r == 0
     A = _zero_algebra(Fp)

src/EllCrv/EllCrv.jl

@@ -319,7 +319,7 @@ Return an elliptic curve with the given $j$-invariant.
 
 ```jldoctest
 julia> K = GF(3)
-Finite field of characteristic 3
+Finite field of degree 1 over GF(3)
 
 julia> elliptic_curve_from_j_invariant(K(2))
 Elliptic curve with equation

src/EllCrv/Finite.jl

@@ -1050,16 +1050,16 @@ Return the polynomial whose roots correspond to j-invariants
 of supersingular elliptic curves of characteristic p.
 """
 function supersingular_polynomial(p::IntegerUnion)
-  p = ZZRingElem(p)
-  K = GF(p)
-  KJ, J = polynomial_ring(GF(p), "J")
-  if p < 3
+  _p = ZZRingElem(p)
+  K = GF(_p)
+  KJ, J = polynomial_ring(K, "J")
+  if _p < 3
     return J
   end
 
-  m = divexact((p-1), 2)
-  KXT, (X, T) = polynomial_ring(K, ["X", "T"])
-  H = sum([binomial(m, i)^2 *T^i for i in (0:m)])
+  m = divexact((_p -1 ), 2)
+  KXT, (X, T) = polynomial_ring(K, ["X", "T"], cached = false)
+  H = sum(elem_type(KXT)[binomial(m, i)^2 *T^i for i in 0:m])
   F = T^2 * (T - 1)^2 * X - 256 * (T^2 - T + 1)^3
   R = resultant(F, H, 2)
   factors = factor(evaluate(R, [J, zero(KJ)]))
@@ -1144,17 +1144,17 @@ Return a list of generators of the group of rational points on $E$.
 julia> E = elliptic_curve(GF(101, 2), [1, 2]);
 
 julia> gens(E)
-2-element Vector{EllCrvPt{fqPolyRepFieldElem}}:
- Point  (93*o + 10 : 22*o + 69 : 1)  of Elliptic curve with equation
+2-element Vector{EllCrvPt{FqFieldElem}}:
+ Point  (16*o + 42 : 88*o + 97 : 1)  of Elliptic curve with equation
 y^2 = x^3 + x + 2
- Point  (89*o + 62 : 14*o + 26 : 1)  of Elliptic curve with equation
+ Point  (88*o + 23 : 94*o + 22 : 1)  of Elliptic curve with equation
 y^2 = x^3 + x + 2
 
 julia> E = elliptic_curve(GF(101), [1, 2]);
 
 julia> gens(E)
-1-element Vector{EllCrvPt{fpFieldElem}}:
- Point  (50 : 69 : 1)  of Elliptic curve with equation
+1-element Vector{EllCrvPt{FqFieldElem}}:
+ Point  (85 : 58 : 1)  of Elliptic curve with equation
 y^2 = x^3 + x + 2
 ```
 """

src/EllCrv/LocalData.jl

@@ -116,7 +116,7 @@ end
 function _tates_algorithm(E::EllCrv{QQFieldElem}, _p::IntegerUnion)
   p = ZZ(_p)
   F = GF(p, cached = false)
-  _invmod = x -> QQ(lift(inv(F(x))))
+  _invmod = x -> QQ(lift(ZZ, inv(F(x))))
   _uni = p
   return __tates_algorithm_generic(E, ZZ, x -> is_zero(x) ? inf : valuation(x, p), x -> smod(x, p), x -> F(x), x -> QQ(lift(x)), _invmod, p)
 end

src/LocalField/Conjugates.jl

@@ -556,8 +556,8 @@ function completion(K::AnticNumberField, ca::qadic)
   while length(pa) < d
     push!(pa, pa[end]*pa[2])
   end
-  m = matrix(Nemo._GF(p), d, d, [lift(ZZ, coeff(pa[i], j-1)) for j=1:d for i=1:d])
-  o = matrix(Nemo._GF(p), d, 1, [lift(ZZ, coeff(gen(R), j-1)) for j=1:d])
+  m = matrix(GF(p), d, d, [lift(ZZ, coeff(pa[i], j-1)) for j=1:d for i=1:d])
+  o = matrix(GF(p), d, 1, [lift(ZZ, coeff(gen(R), j-1)) for j=1:d])
   s = solve(m, o)
   @hassert :qAdic 1 m*s == o
   a = K()
@@ -566,7 +566,7 @@ function completion(K::AnticNumberField, ca::qadic)
   end
   f = defining_polynomial(parent(ca), FlintZZ)
   fso = inv(derivative(f)(gen(R)))
-  o = matrix(Nemo._GF(p), d, 1, [lift(ZZ, coeff(fso, j-1)) for j=1:d])
+  o = matrix(GF(p), d, 1, [lift(ZZ, coeff(fso, j-1)) for j=1:d])
   s = solve(m, o)
   b = K()
   for i=1:d

src/LocalField/Poly.jl

@@ -170,8 +170,9 @@ function fun_factor(g::Generic.Poly{padic})
   Rt = polynomial_ring(R, "t", cached = false)[1]
   fR = Rt([R(Hecke.lift(coeff(g, i))) for i = 0:degree(g)])
   u, g1 = Hecke.fun_factor(fR)
-  fun = x -> lift(x, K)
-  return map_coefficients(fun, u, parent = Kt), map_coefficients(fun, g1, parent = Kt)
+  liftu = Kt(elem_type(K)[lift(coeff(u, i), K) for i in 0:degree(u)])
+  liftg1 = Kt(elem_type(K)[lift(coeff(g1, i), K) for i in 0:degree(g1)])
+  return (liftu, liftg1)::Tuple{typeof(g), typeof(g)}
 end
 
 function fun_factor(f::Generic.Poly{S}) where S <: Union{qadic, LocalFieldElem}

src/LocalField/qAdic.jl

@@ -8,7 +8,7 @@ function residue_field(Q::FlintQadicField)
   if z !== nothing
     return codomain(z), z
   end
-  Fp = Nemo._GF(prime(Q))
+  Fp = GF(prime(Q))
   Fpt = polynomial_ring(Fp, cached = false)[1]
   g = defining_polynomial(Q) #no Conway if parameters are too large!
   f = Fpt([Fp(lift(coeff(g, i))) for i=0:degree(Q)])
@@ -36,7 +36,7 @@ function residue_field(Q::FlintQadicField)
 end
 
 function residue_field(Q::FlintPadicField)
-  k = Nemo._GF(prime(Q))
+  k = GF(prime(Q))
   pro = function(x::padic)
     v = valuation(x)
     v < 0 && error("elt non integral")

src/Map/MapType.jl

@@ -148,18 +148,18 @@ julia> F = GF(2);
 julia> f = MapFromFunc(QQ, F, x -> F(numerator(x)) * inv(F(denominator(x))))
 Map defined by a julia-function
   from rational field
-  to finite field of characteristic 2
+  to finite field of degree 1 over GF(2)
 
 julia> f(QQ(1//3))
 1
 
 julia> println(f)
 Map: QQ -> GF(2)
 
-julia> f = MapFromFunc(QQ, F, x -> F(numerator(x)) * inv(F(denominator(x))), y -> QQ(lift(y)),)
+julia> f = MapFromFunc(QQ, F, x -> F(numerator(x)) * inv(F(denominator(x))), y -> QQ(lift(ZZ, y)),)
 Map defined by a julia-function with inverse
   from rational field
-  to finite field of characteristic 2
+  to finite field of degree 1 over GF(2)
 
 julia> preimage(f, F(1))
 1

src/Map/NfOrd.jl

@@ -557,7 +557,7 @@ function NfOrdToFqFieldMor(O::NfOrd, P::NfOrdIdl)
   z.P = P
   a, g, b = get_residue_field_data(P)
   p = minimum(P)
-  R = Nemo._GF(p, cached = false)
+  R = GF(p, cached = false)
   Rx, x = polynomial_ring(R, "_\$", cached = false)
   F, = Nemo._residue_field(Rx(g), "_\$", check = false)
   d = degree(g)

src/Misc/Poly.jl

@@ -877,7 +877,7 @@ specified, return the `n`-th cyclotomic polynomial over the integers.
 
 ```jldoctest
 julia> F, _ = finite_field(5)
-(Finite field of characteristic 5, 1)
+(Finite field of degree 1 over GF(5), 0)
 
 julia> Ft, _ = F["t"]
 (Univariate polynomial ring in t over GF(5), t)

src/Misc/RatRecon.jl

@@ -297,7 +297,7 @@ function _modp_results(g::QQPolyRingElem,f::QQPolyRingElem, p::ZZRingElem, M::In
    l1 = fpPolyRingElem[]; l2 = fpPolyRingElem[];l3 = ZZRingElem[]
    L = listprimes([f,g], p, M)
    for j in 1:length(L)
-     Rp, t = polynomial_ring(GF(Int(L[j]), cached=false), cached=false)
+     Rp, t = polynomial_ring(Native.GF(Int(L[j]), cached=false), cached=false)
      gp = Rp(g)
      fp = Rp(f)
      fl, nu_p, de_p = rational_reconstruction_subres(gp, fp, -1, ErrorTolerant = ErrorTolerant)
@@ -424,13 +424,13 @@ function _modpResults(f, p::ZZRingElem, M::Int)
    Np = listprimes([f], p, M)
    Zx, Y = polynomial_ring(FlintZZ, "Y", cached=false)
    for j in 1:length(Np)
-     RNp = GF(Int(Np[j]), cached=false)
+     RNp = Native.GF(Int(Np[j]), cached=false)
      Rp, t = polynomial_ring(RNp, "t", cached=false)
      fp = Rp(f)
      if degree(fp) != degree(f)
        continue #bad prime...
      end
-     L1 = Nemo.fpFieldElem[]
+     L1 = fpFieldElem[]
      for i in 0:degree(fp)
         push!(L1, coeff(fp, i))
      end

src/Misc/nmod_poly.jl

@@ -1265,20 +1265,6 @@ function unit_group_1_part(f::fqPolyRepPolyRingElem, k::Int)
   return gens, rels
 end
 
-#=
-function FlintFiniteField(f::fqPolyRepPolyRingElem, s::AbstractString = "o"; cached::Bool = true, check::Bool = true)
-  if check && !is_irreducible(f)
-    error("poly not irreducible")
-  end
-  k = base_ring(f)
-  p = characteristic(k)
-  K, o = FlintFiniteField(p, degree(k)*degree(f), s, cached = cached)
-  r = roots(K, f)[1]  # not working, embeddings are missing
-  fl || error("s.th. went wrong")
-  return K, r
-end
-=#
-
 function euler_phi(f::T) where {T <: Union{fpPolyRingElem, fqPolyRepPolyRingElem, FpPolyRingElem}}
   lf = factor(f)
   q = size(base_ring(f))

src/NumField/NfAbs/Simplify.jl

@@ -213,7 +213,7 @@ function _sieve_primitive_elements(B::Vector{nf_elem})
 
   p, d = _find_prime(ZZPolyRingElem[f])
 
-  F = FlintFiniteField(p, d, "w", cached = false)[1]
+  F = Nemo.Native.finite_field(p, d, "w", cached = false)[1]
   Ft = polynomial_ring(F, "t", cached = false)[1]
   ap = zero(Ft)
   fit!(ap, degree(K)+1)
@@ -352,7 +352,7 @@ function polredabs(K::AnticNumberField)
   f = Zx(K.pol)
   p, d = _find_prime(ZZPolyRingElem[f])
 
-  F = FlintFiniteField(p, d, "w", cached = false)[1]
+  F = Native.finite_field(p, d, "w", cached = false)[1]
   Ft = polynomial_ring(F, "t", cached = false)[1]
   ap = zero(Ft)
   fit!(ap, degree(K)+1)