Adjust to changes in AA and Nemo

Project.toml

@@ -28,9 +28,9 @@ GAPExt = "GAP"
 PolymakeExt = "Polymake"
 
 [compat]
-AbstractAlgebra = "^0.32.1"
+AbstractAlgebra = "^0.33.0"
 GAP = "0.9.6"
-Nemo = "^0.36.1"
+Nemo = "^0.37.0"
 Polymake = "0.10, 0.11"
 RandomExtensions = "0.4.3"
 julia = "1.6"

docs/src/function_fields/degree_localization.md

@@ -36,7 +36,7 @@ localization(K::Generic.RationalFunctionField{T}, ::typeof(degree)) where T <: F
 
 ```@repl
 using Hecke # hide
-K, x = RationalFunctionField(FlintQQ, "x");
+K, x = rational_function_field(FlintQQ, "x");
 R = localization(K, degree)
 ```
 
@@ -51,7 +51,7 @@ the degree localization
 
 ```@repl
 using Hecke # hide
-K, x = RationalFunctionField(FlintQQ, "x");
+K, x = rational_function_field(FlintQQ, "x");
 R = localization(K, degree)
 
 a = R()

examples/Round2.jl

@@ -1057,7 +1057,7 @@ function Nemo.residue_field(a::HessQR, b::HessQRElem)
   @assert parent(b) == a
   @assert is_prime(b.c)
   F = GF(b.c)
-  Ft, t = RationalFunctionField(F, String(var(a.R)), cached = false)
+  Ft, t = rational_function_field(F, String(var(a.R)), cached = false)
   R = parent(numerator(t))
   return Ft, MapFromFunc(a, Ft,
                          x->F(x.c)*Ft(map_coefficients(F, x.f, parent = R))//Ft(map_coefficients(F, x.g, parent = R)),
@@ -1330,9 +1330,9 @@ Hecke.example("Round2.jl")
 
 ?GenericRound2
 
-Qt, t = RationalFunctionField(QQ, "t")
+Qt, t = rational_function_field(QQ, "t")
 Qtx, x = polynomial_ring(Qt, "x")
-F, a = FunctionField(x^6+27*t^2+108*t+108, "a")
+F, a = function_field(x^6+27*t^2+108*t+108, "a")
 integral_closure(parent(denominator(t)), F)
 integral_closure(localization(Qt, degree), F)
 integral_closure(Hecke.Globals.Zx, F)
@@ -1345,7 +1345,7 @@ integral_closure(localization(ZZ, 2), k)
 
 more interesting and MUCH harder:
 
-G, b = FunctionField(x^6 + (140*t - 70)*x^3 + 8788*t^2 - 8788*t + 2197, "b")
+G, b = function_field(x^6 + (140*t - 70)*x^3 + 8788*t^2 - 8788*t + 2197, "b")
 
 =#
 
@@ -1442,7 +1442,7 @@ function Hecke.splitting_field(f::Generic.Poly{<:Generic.RationalFunctionFieldEl
   end
 
   while true
-    G, b = FunctionField(lf[1], "b", cached = false)
+    G, b = function_field(lf[1], "b", cached = false)
     if length(lf) == 1 && degree(G) < 3
       return G
     end

src/FunField/Factor.jl

@@ -54,7 +54,7 @@
     g = gh[1]
     h = gh[2]
     k = base_ring(g)
-    kt, t = RationalFunctionField(k, base_ring(Pf).S, cached = false)
+    kt, t = rational_function_field(k, base_ring(Pf).S, cached = false)
     ktx, x = polynomial_ring(kt, symbols(Pf)[1], cached = false)
     push!(la, [from_mpoly(g, ktx), from_mpoly(h, ktx)]=>v)
   end
@@ -121,7 +121,7 @@
   end
 
   while true
-    G, b = FunctionField(lf[1], "b", cached = false)
+    G, b = function_field(lf[1], "b", cached = false)
     if length(lf) == 1 && degree(G) < 3
       return G
     end

src/FunField/HessQR.jl

@@ -335,7 +335,7 @@ function Nemo.residue_field(a::HessQR, b::HessQRElem)
   @assert parent(b) == a
   @assert is_prime(b.c)
   F = GF(b.c)
-  Ft, t = RationalFunctionField(F, String(var(a.R)), cached = false)
+  Ft, t = rational_function_field(F, String(var(a.R)), cached = false)
   R = parent(numerator(t))
   return Ft, MapFromFunc(a, Ft,
                          x->F(x.c)*Ft(map_coefficients(F, x.f, parent = R))//Ft(map_coefficients(F, x.g, parent = R)),

src/FunField/IntClsZx.jl

@@ -213,9 +213,9 @@ using .HessMain
 #=
   this should work:
 
-Qt, t = RationalFunctionField(QQ, "t")
+Qt, t = rational_function_field(QQ, "t")
 Qtx, x = polynomial_ring(Qt, "x")
-F, a = FunctionField(x^6+27*t^2+108*t+108, "a")
+F, a = function_field(x^6+27*t^2+108*t+108, "a")
 integral_closure(parent(denominator(t)), F)
 integral_closure(localization(Qt, degree), F)
 integral_closure(Hecke.Globals.Zx, F)
@@ -228,6 +228,6 @@ integral_closure(localization(ZZ, 2), k)
 
 more interesting and MUCH harder:
 
-G, b = FunctionField(x^6 + (140*t - 70)*x^3 + 8788*t^2 - 8788*t + 2197, "b")
+G, b = function_field(x^6 + (140*t - 70)*x^3 + 8788*t^2 - 8788*t + 2197, "b")
 
 =#

src/GenOrd/Auxiliary.jl

@@ -72,20 +72,12 @@
   return H[1:ncols(M), :]
 end
 
-function function_field(f::PolyElem{<:Generic.RationalFunctionFieldElem}, s::String = "_a"; check::Bool = true, cached::Bool = false)
-  return FunctionField(f, s, cached = cached)
+function function_field(f::PolyElem{<:Generic.RationalFunctionFieldElem}, s::VarName = :_a; check::Bool = true, cached::Bool = false)
+  return function_field(f, s, cached = cached)
 end
 
-function function_field(f::PolyElem{<:Generic.RationalFunctionFieldElem}, s::Symbol; check::Bool = true, cached::Bool = false)
-  return FunctionField(f, s, cached = cached)
-end
-
-function extension_field(f::PolyElem{<:Generic.RationalFunctionFieldElem}, s::String = "_a"; check::Bool = true, cached::Bool = false)
-  return FunctionField(f, s, cached = cached)
-end
-
-function extension_field(f::PolyElem{<:Generic.RationalFunctionFieldElem}, s::Symbol; check::Bool = true, cached::Bool = false)
-  return FunctionField(f, s, cached = cached)
+function extension_field(f::PolyElem{<:Generic.RationalFunctionFieldElem}, s::VarName = :_a; check::Bool = true, cached::Bool = false)
+  return function_field(f, s, cached = cached)
 end
 
 function Hecke.basis(F::Generic.FunctionField)

src/Misc/Integer.jl

@@ -416,10 +416,6 @@ function _factors_trial_division(n::ZZRingElem, np::Int=10^5)
 end
 
 
-function (::Type{Base.Rational{BigInt}})(x::QQFieldElem)
-  return Rational{BigInt}(BigInt(numerator(x)), BigInt(denominator(x)))
-end
-
 export euler_phi_inv, Divisors, carmichael_lambda
 
 @doc raw"""

src/QuadForm/Types.jl

@@ -360,9 +360,11 @@ Gram matrix quadratic form:
 [   0      0      0   4//3]
 
 julia> abelian_group_homomorphism(f)
-Map: GrpAb: (Z/3)^2 x Z/12 -> (General) abelian group with relation matrix
-[4 0 0 0; 0 3 0 0; 0 0 3 0; 0 0 0 3]
-with structure of GrpAb: (Z/3)^2 x Z/12
+Map
+  from GrpAb: (Z/3)^2 x Z/12
+  to (General) abelian group with relation matrix
+  [4 0 0 0; 0 3 0 0; 0 0 3 0; 0 0 0 3]
+  with structure of GrpAb: (Z/3)^2 x Z/12
 ```
 
 Note that an object of type `TorQuadModuleMor` needs not to be a morphism
@@ -397,7 +399,9 @@ Gram matrix quadratic form:
 [2   4   3//2]
 
 julia> f = hom(T, T6, gens(T6))
-Map: finite quadratic module -> finite quadratic module
+Map
+  from finite quadratic module: (Z/3)^2 x Z/12 -> Q/2Z
+  to finite quadratic module: (Z/3)^2 x Z/12 -> Q/12Z
 
 julia> T[1]*T[1] == f(T[1])*f(T[1])
 false

src/QuadForm/indefiniteLLL.jl

@@ -60,7 +60,7 @@ If `v` is a square matrix, return the identity matrix of size nxn.
 If `redflag` is set to `true`, it LLL-reduces the `m-n` first rows.
 """
 function _complete_to_basis(v::MatElem{ZZRingElem}, redflag::Bool = false)
-  
+
   n = nrows(v)
   m = ncols(v)
 
@@ -131,7 +131,7 @@ function _quadratic_form_solve_triv(G::MatElem{ZZRingElem}; base::Bool = false,
   #Case 2: G has a block +- [1 0 ; 0 -1] on the diagonal
   for i = 2:n
     if G[i-1,i] == 0 && abs(G[i-1,i-1])==1 &&abs(G[i,i])==1 && sign(G[i-1,i-1])*sign(G[i,i]) == -1
-  
+
       H[i,i-1] = -1
       sol = H[i,:]
       if !base
@@ -298,7 +298,7 @@ function lll_gram_indef_with_transform(G::MatElem{ZZRingElem}; check::Bool = fal
   #The first line of the matrix G3 only contains 0, except some 'g' on the right, where g² | det G.
   n = ncols(G)
   U3 = identity_matrix(ZZ,n)
-  U3[n,1] = round(- G3[n,n]//2*1//G3[1,n])
+  U3[n,1] = round(ZZRingElem, - G3[n,n]//2*1//G3[1,n])
   G4 = U3*G3*transpose(U3)
 
   #The coeff G4[n,n] is reduced modulo 2g
@@ -310,7 +310,7 @@ function lll_gram_indef_with_transform(G::MatElem{ZZRingElem}; check::Bool = fal
     V = G4[[1,n], 2:(n-1)]
   end
 
-  B = map_entries(round, -inv(change_base_ring(QQ,U))*V)
+  B = map_entries(x->round(ZZRingElem, x), -inv(change_base_ring(QQ,U))*V)
   U4 = identity_matrix(ZZ,n)
 
   for j = 2:n-1

test/EllCrv/LocalData.jl

@@ -316,7 +316,7 @@
   @test @inferred kodaira_symbol(E, P) == "I0"
 
   # rational function field
-  QQt, t = RationalFunctionField(QQ, "t")
+  QQt, t = rational_function_field(QQ, "t")
   E = elliptic_curve_from_j_invariant(t)
    _, K, f, c, s = tates_algorithm_local(E, 1//t)
   @test K == "I1"
@@ -356,7 +356,7 @@
   @test s == true
 
   k, a = quadratic_field(2)
-  kt, t = RationalFunctionField(k, "t")
+  kt, t = rational_function_field(k, "t")
   E = elliptic_curve_from_j_invariant(1//(t^2 + t + a))
 
    _, K, f, c, s = tates_algorithm_local(E, 1//t)
@@ -377,7 +377,7 @@
   @test c == 1
   @test s == true
 
-  kt, t = RationalFunctionField(GF(2), "t")
+  kt, t = rational_function_field(GF(2), "t")
   E = elliptic_curve_from_j_invariant(t^3/(t^2 + t + 1))
    _, K, f, c, s = tates_algorithm_local(E, t^2 + t + 1)
   @test K == "I1"

test/EllCrv/MinimalModels.jl

@@ -54,7 +54,7 @@
   end
 
   # _minimize and integral model
-  Kt, t = RationalFunctionField(QQ, "t")
+  Kt, t = rational_function_field(QQ, "t")
   E = EllipticCurve(Kt.([0, t^21, 1//216, -7//1296, 1//t]))
   EE, = integral_model(E)
   @test all(p -> is_one(denominator(p)) && is_one(denominator(numerator(p))), a_invars(EE))
@@ -63,7 +63,7 @@
 
   Qx, x = QQ["x"]
   K, z = number_field(x^2 + 1, "z", cached = false)
-  Kt, t = RationalFunctionField(K, "t")
+  Kt, t = rational_function_field(K, "t")
   E = EllipticCurve(Kt.([0, t^21, (z + 1)//216, -7//1296, (z + 3)//t]))
   EE, = integral_model(E)
   EE = Hecke.reduce_model(E)

test/FunField/DegreeLocalization.jl

@@ -1,5 +1,5 @@
 
-R, x = RationalFunctionField(QQ, "x")
+R, x = rational_function_field(QQ, "x")
 L = localization(R, degree)
 
 @testset "DegreeLocalization" begin

test/FunField/Differential.jl

@@ -3,7 +3,7 @@ import Hecke: divisor
 flds = [QQ, rationals_as_number_field()[1]]
 
 @testset "Differentials" for k in flds
-  kx, x = RationalFunctionField(k, "x")
+  kx, x = rational_function_field(k, "x")
   kt = parent(numerator(x))
   ky, y = polynomial_ring(kx, "y")
 

test/FunField/Divisor.jl

@@ -1,5 +1,5 @@
 k = QQ
-kx, x = RationalFunctionField(k, "x")
+kx, x = rational_function_field(k, "x")
 kt = parent(numerator(x))
 ky, y = polynomial_ring(kx, "y")
 

test/GenOrd/GenOrd.jl

@@ -12,7 +12,7 @@ end
   test_Ring_interface(O)
 
   k = GF(5)
-  kx, x = RationalFunctionField(k, "x")
+  kx, x = rational_function_field(k, "x")
   kt = parent(numerator(x))
   ky, y = polynomial_ring(kx, "y")
   F, a = function_field(y^3+(4*x^3 + 4*x^2 + 2*x +2)*y^2 + (3*x+3)*y +2)

test/GenOrd/Ideal.jl

@@ -1,7 +1,7 @@
 @testset "Ideals for orders over function fields" begin
 
   k = GF(7)
-  kx, x = RationalFunctionField(k, "x")
+  kx, x = rational_function_field(k, "x")
   kt = parent(numerator(x))
   ky, y = polynomial_ring(kx, "y")
   F, a = function_field(y^2+x)
@@ -26,7 +26,7 @@
 
 
   k = QQ
-  kx, x = RationalFunctionField(k, "x")
+  kx, x = rational_function_field(k, "x")
   kt = parent(numerator(x))
   ky, y = polynomial_ring(kx, "y")
   F, a = function_field(y^2+x*y+x^3+y^3)

test/GenOrd/MaximalOrder.jl

@@ -1,8 +1,8 @@
 @testset "Qt" begin
-  qt, t = RationalFunctionField(QQ, "t")
+  qt, t = rational_function_field(QQ, "t")
   qtx, x = polynomial_ring(qt, "x")
   f = x^4 + t*x^3 - 6*x^2 - t*x + 1
-  F, a = FunctionField(f, "a")
+  F, a = function_field(f, "a")
   O = integral_closure(Hecke.localization(qt, degree), F)
   b = basis(O, F)
   mp = map(minpoly, b)
@@ -24,16 +24,16 @@ end
 
 @testset "FldFin" begin
   for q = [GF(17), GF(next_prime(ZZRingElem(10)^30)), finite_field(5, 2)[1], finite_field(next_prime(ZZRingElem(10)^25), 2, "a", cached = false)[1]]
-    qt, t = RationalFunctionField(q, "t", cached = false)
+    qt, t = rational_function_field(q, "t", cached = false)
     qtx, x = polynomial_ring(qt, cached = false)
     f = x^3+(t+1)^5*(x+1)+(t^2+t+1)^7
-    F, a = FunctionField(f, "a", cached = false)
+    F, a = function_field(f, "a", cached = false)
     integral_closure(parent(numerator(t)), F)
     integral_closure(localization(qt, degree), F)
   end
 
   k = GF(5)
-  kx, x = RationalFunctionField(k, "x")
+  kx, x = rational_function_field(k, "x")
   kt = parent(numerator(x))
   ky, y = polynomial_ring(kx, "y")
   F, a = function_field(y^3+(4*x^3 + 4*x^2 + 2*x +2)*y^2 + (3*x+3)*y +2)

test/Misc/Poly.jl

@@ -116,7 +116,7 @@ end
   @test @inferred is_squarefree(x * (x + 1))
   @test @inferred !is_squarefree(x * (x + 1)^2)
 
-  F, a = RationalFunctionField(GF(3), "a")
+  F, a = rational_function_field(GF(3), "a")
   Fx, x = F["x"]
   @test @inferred is_squarefree(x)
   @test @inferred is_squarefree(2*x^0)