Switch from FiniteField to finite_field

Command used to create this PR:

    git grep -l -w FiniteField | xargs perl -pi -e 's;\bFiniteField\b;finite_field;g'

Project.toml

@@ -30,7 +30,7 @@ PolymakeExt = "Polymake"
 [compat]
 AbstractAlgebra = "^0.32.1"
 GAP = "0.9.6"
-Nemo = "^0.36.0"
+Nemo = "^0.36.1"
 Polymake = "0.10, 0.11"
 RandomExtensions = "0.4.3"
 julia = "1.6"

examples/Plesken.jl

@@ -214,7 +214,7 @@ function plesken_kummer(p::ZZRingElem, r::Int, s::Int)
 
 
   if (p-1) % r == 0
-    R = FiniteField(p)
+    R = finite_field(p)
     descent = false
   else
     f = cyclotomic(r, polynomial_ring(FlintZZ)[2])
@@ -283,7 +283,7 @@ end
 
 function plesken_as(p::ZZRingElem, r::Int, s::Int)
   @assert p==r
-  R = FiniteField(p)
+  R = finite_field(p)
   g = R(-1)
   t = 1
   while s>1
@@ -300,12 +300,12 @@ function plesken_2(p::ZZRingElem, r::Int, s::Int)
   @assert r==2
   #Plesken, 1.27
   if valuation(p-1, 2) >1
-    R = FiniteField(p)
+    R = finite_field(p)
     g = primitive_root_r_div_qm1(p, r)
     t = 1
   else
     @assert valuation(p+1, 2)>1
-    R = FiniteField(p)
+    R = finite_field(p)
     Rx,x = polynomial_ring(R, "t_1")
     R = residue_ring(Rx, x^2+1)
     g = primitive_root_r_div_qm1(R, 2)

src/EllCrv/Finite.jl

@@ -990,7 +990,7 @@ function _embed_into_p2(j, L)
     if degree(p) <= 1
       return L(_to_z(j))
     end
-    F, a = FiniteField(p)
+    F, a = finite_field(p)
     e = embed(F, L)
     return e(gen(F))
   end

src/GenOrd/Ideal.jl

@@ -576,7 +576,7 @@ end
 ################################################################################
 
 function Hecke.residue_field(R::fpPolyRing, p::fpPolyRingElem)
-  K, _ = FiniteField(p,"o")
+  K, _ = finite_field(p,"o")
   return K, MapFromFunc(R, K, x->K(x), y->R(y))
 end
 

src/LocalField/LocalField.jl

@@ -465,7 +465,7 @@ function residue_field(K::LocalField{S, UnramifiedLocalField}) where {S <: Field
    Fpt = polynomial_ring(ks, cached = false)[1]
    g = defining_polynomial(K)
    f = Fpt([ks(mks(coeff(g, i))) for i=0:degree(K)])
-   kk = Native.FiniteField(f)[1]
+   kk = Native.finite_field(f)[1]
    bas = basis(K)
    u = gen(kk)
    function proj(a::Hecke.LocalFieldElem)

src/LocalField/qAdic.jl

@@ -14,7 +14,7 @@ function residue_field(Q::FlintQadicField)
   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)])
-  k = Native.FiniteField(f, "o", cached = false)[1]
+  k = Native.finite_field(f, "o", cached = false)[1]
   pro = function(x::qadic)
     v = valuation(x)
     v < 0 && error("elt non integral")

src/Misc/Plesken.jl

@@ -78,14 +78,14 @@ end
 function _presentation_artin_schreier(F, n)
   p = characteristic(F)
   Fx, x = polynomial_ring(F, "x", cached = false)
-  F1, a = FiniteField(x^p-x-1, "a", cached = false, check = false)
+  F1, a = finite_field(x^p-x-1, "a", cached = false, check = false)
   F1y, y = polynomial_ring(F1, "y1", cached = false)
   el = a
   for i = 2:n
     pol = y^p-y-el^(p-1)
-    Frel = FiniteField(pol, "a$i", cached = false, check = false)[1]
+    Frel = finite_field(pol, "a$i", cached = false, check = false)[1]
     abs_def_pol = norm(pol)
-    F1, gF1 = FiniteField(abs_def_pol, "a", check = false, cached = false)
+    F1, gF1 = finite_field(abs_def_pol, "a", check = false, cached = false)
     mp = hom(F1, Frel, gen(Frel))
     el = mp\(gen(Frel)*el)
     F1y, y = polynomial_ring(F1, "y1", cached = false)
@@ -132,7 +132,7 @@ function _presentation_kummer(F, r::T, n::Int) where T <: Union{ZZRingElem, Int}
   def_pol1 = Fx()
   setcoeff!(def_pol1, 0, -pr_root)
   setcoeff!(def_pol1, r^n, one(F))
-  F1, gF1 = FiniteField(def_pol1, "a1", cached = false, check = false)
+  F1, gF1 = finite_field(def_pol1, "a1", cached = false, check = false)
   return F1
 end
 
@@ -151,7 +151,7 @@ function _presentation_generic(F, r::T, n::Int) where T <: Union{ZZRingElem, Int
       ind = i
     end
   end
-  F0, gF0 = FiniteField(lF[ind], "a0", cached = false)
+  F0, gF0 = finite_field(lF[ind], "a0", cached = false)
   f = degree(F0)
   Fn = _presentation_kummer(F0, r, n)
   #Now, I need to take the trace.
@@ -163,7 +163,7 @@ function _presentation_generic(F, r::T, n::Int) where T <: Union{ZZRingElem, Int
     g = g^e
     t = add!(t, t, g)
   end
-  return FiniteField(_minpoly(t, r^n), "a", cached = false, check = false)[1]
+  return finite_field(_minpoly(t, r^n), "a", cached = false, check = false)[1]
 end
 
 function _find_exponent(f::Int, p::ZZRingElem, r::ZZRingElem, n::Int)

src/Misc/Poly.jl

@@ -882,7 +882,7 @@ specified, return the `n`-th cyclotomic polynomial over the integers.
 # Examples
 
 ```jldoctest
-julia> F, _ = FiniteField(5)
+julia> F, _ = finite_field(5)
 (Finite field of characteristic 5, 1)
 
 julia> Ft, _ = F["t"]

src/Misc/RelFiniteField.jl

@@ -547,7 +547,7 @@ end
 #
 ################################################################################
 
-function Native.FiniteField(f::T, s::String = "a" ; cached::Bool = true, check::Bool = true) where T <: Union{fqPolyRepPolyRingElem, FqPolyRepPolyRingElem}
+function Native.finite_field(f::T, s::String = "a" ; cached::Bool = true, check::Bool = true) where T <: Union{fqPolyRepPolyRingElem, FqPolyRepPolyRingElem}
   if check
     @assert is_irreducible(f)
   end
@@ -556,7 +556,7 @@ function Native.FiniteField(f::T, s::String = "a" ; cached::Bool = true, check::
   return F, gen(F)
 end
 
-function Native.FiniteField(f::PolyElem{T}, s::String = "a" ; cached::Bool = true, check::Bool = true) where T <: RelFinFieldElem
+function Native.finite_field(f::PolyElem{T}, s::String = "a" ; cached::Bool = true, check::Bool = true) where T <: RelFinFieldElem
   if check
     @assert is_irreducible(f)
   end
@@ -666,7 +666,7 @@ function absolute_field(F::RelFinField{T}; cached::Bool = true) where T <: FinFi
   end
   p = _char(F)
   d = absolute_degree(F)
-  K, gK = Native.FiniteField(p, d, "a", cached = cached)
+  K, gK = Native.finite_field(p, d, "a", cached = cached)
   k, mk = absolute_field(base_field(F))
   def_pol_new = map_coefficients(pseudo_inv(mk), defining_polynomial(F))
   img_gen_k = roots(K, defining_polynomial(k))[1]

src/NumField/NfAbs/Simplify.jl

@@ -139,7 +139,7 @@ function _sieve_primitive_elements(B::Vector{NfAbsNSElem})
   Zx = polynomial_ring(FlintZZ, "x", cached = false)[1]
   pols = [Zx(to_univariate(Globals.Qx, x)) for x in K.pol]
   p, d = _find_prime(pols)
-  F = Native.FiniteField(p, d, "w", cached = false)[1]
+  F = Native.finite_field(p, d, "w", cached = false)[1]
   Fp = Native.GF(p, cached = false)
   Fpt = polynomial_ring(Fp, ngens(K))[1]
   Ft = polynomial_ring(F, "t", cached = false)[1]

src/NumFieldOrd/NfOrd/Hensel.jl

@@ -157,7 +157,7 @@ function _roots_hensel(f::Generic.Poly{nf_elem};
     lp = factor(gp).fac
 
     #set up the mod p data:
-    #need FiniteField as I need to factor (roots)
+    #need finite_field as I need to factor (roots)
     # I want to find a residue field with less roots
     for gp_factor in keys(lp)
       deg_p = degree(gp_factor)
@@ -425,7 +425,7 @@ function _hensel(f::Generic.Poly{nf_elem},
   #later we'll get the HNF matrix for selected powers as well
 
   #set up the mod p data:
-  #need FiniteField as I need to factor (roots)
+  #need finite_field as I need to factor (roots)
 
   rt = roots(fp)
 

src/NumFieldOrd/NfOrd/Ideal/Prime.jl

@@ -1395,7 +1395,7 @@ function prime_dec_nonindex(O::NfAbsOrd{NfAbsNS,NfAbsNSElem}, p::IntegerUnion, d
     =#
     for x = Base.Iterators.product(fac...)
       k = lcm([degree(t[1]) for t = x])
-      Fq = Native.FiniteField(p, k, "y", cached = false)[1]
+      Fq = Native.finite_field(p, k, "y", cached = false)[1]
       Fq2 = residue_ring(Rx, lift(Zx, minpoly(gen(Fq))))
       rt = Vector{Vector{elem_type(Fq)}}()
       RT = []

src/NumFieldOrd/NfOrd/MaxOrd/Polygons.jl

@@ -307,7 +307,7 @@ Computes the residual polynomial of the side $L$ of the Newton Polygon $N$.
 function residual_polynomial(N::NewtonPolygon{ZZPolyRingElem}, L::Line)
   F = GF(N.p, cached = false)
   Ft = polynomial_ring(F, "t", cached = false)[1]
-  FF = FiniteField(Ft(N.phi), "a", cached = false)[1]
+  FF = finite_field(Ft(N.phi), "a", cached = false)[1]
   return residual_polynomial(FF, L, N.development, N.p)
 end
 
@@ -407,7 +407,7 @@ function gens_overorder_polygons(O::NfOrd, p::ZZRingElem)
     isone(m) && continue
     fac = factor(gg)
     for (g, m1) in fac
-      F, a = Native.FiniteField(g, "a", cached = false)
+      F, a = Native.finite_field(g, "a", cached = false)
       phi = lift(Zx, g)
       dev, quos = phi_development_with_quos(Zx(f), phi)
       N = _newton_polygon(dev, p)
@@ -929,7 +929,7 @@ function decomposition_type_polygon(O::NfOrd, p::Union{ZZRingElem, Int})
       continue
     end
     Nl = filter(x -> slope(x)<0, N.lines)
-    F, a = Native.FiniteField(g, "a", cached = false)
+    F, a = Native.finite_field(g, "a", cached = false)
     pols = dense_poly_type(elem_type(F))[]
     for ll in Nl
       rp = residual_polynomial(F, ll, dev, p)

src/QuadForm/Quad/NormalForm.jl

@@ -58,7 +58,7 @@ function _ispadic_normal_form_odd(G, p)
 
   o = identity_matrix(QQ, 1)
 
-  F,  = FiniteField(p, 1, cached = false)
+  F,  = finite_field(p, 1, cached = false)
 
   for i in 1:length(blocks)
     if all(==(o), blocks[i])

test/AlgAss/AlgAss.jl

@@ -86,7 +86,7 @@ end
 
     # Restrict from F_q to F_p
     Fp = GF(7)
-    Fq, a = FiniteField(7, 3, "a")
+    Fq, a = finite_field(7, 3, "a")
 
     A = AlgAss(MatrixAlgebra(Fq, 2))
     B, BtoA = Hecke.restrict_scalars(A, Fp)
@@ -168,7 +168,7 @@ end
 
   @testset "Matrix Algebra" begin
     Fp = GF(7)
-    Fq, a = FiniteField(7, 2, "a")
+    Fq, a = finite_field(7, 2, "a")
 
     A = AlgAss(MatrixAlgebra(Fq, 3))
     B, AtoB = Hecke._as_matrix_algebra(A)

test/EllCrv/Finite.jl

@@ -180,7 +180,7 @@
     F = GF(3)
     Fx, x = F["x"]
     f = x^6 + 2*x^4 + x^2 + 2*x + 2
-    F, a = FiniteField(f)
+    F, a = finite_field(f)
     E = EllipticCurve([a^4 + a^3 + 2*a^2 + 2*a, 2*a^5 + 2*a^3 + 2*a^2 + 1])
     A, = abelian_group(E)
     @test elementary_divisors(A) == [26, 26]
@@ -192,7 +192,7 @@
     F = GF(101)
     Fx, x = F["x"]
     f = x^3 + 3*x + 99
-    F, a = FiniteField(f)
+    F, a = finite_field(f)
     E = EllipticCurve([2*a^2 + 48*a + 27, 89*a^2 + 76*a + 24])
     A, = abelian_group(E)
     @test elementary_divisors(A) == [1031352]

test/EllCrv/Isogeny.jl

@@ -121,7 +121,7 @@
   E = EllipticCurve(F, [0, 1, 1, 1, 1])
   @test is_kernel_polynomial(E, x + 1)
 
-  F, o = FiniteField(47, 2, "o")
+  F, o = finite_field(47, 2, "o")
   E = EllipticCurve(F, [0, o])
   Fx, x = F["x"]
   f = x^3 + (7*o + 11)*x^2 + (25*o + 33)*x + 25*o

test/GenOrd/MaximalOrder.jl

@@ -23,7 +23,7 @@ end
 end
 
 @testset "FldFin" begin
-  for q = [GF(17), GF(next_prime(ZZRingElem(10)^30)), FiniteField(5, 2)[1], FiniteField(next_prime(ZZRingElem(10)^25), 2, "a", cached = false)[1]]
+  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)
     qtx, x = polynomial_ring(qt, cached = false)
     f = x^3+(t+1)^5*(x+1)+(t^2+t+1)^7

test/Misc/FiniteField.jl

@@ -85,7 +85,7 @@ end
 @testset "fqPolyRepField" begin
 
   for p in [31, 11, 101]
-    F = FiniteField(p, 2)[1]
+    F = finite_field(p, 2)[1]
     G, mG = unit_group(F)
     #Test generator
     g = mG(G[1])
@@ -127,9 +127,9 @@ end
 @testset "FqPolyRepField" begin
 
   for p in [31, 11, 101]
-    _ = FiniteField(ZZRingElem(p), 2, "a")[1]
-    _ = FiniteField(ZZRingElem(p), 2, 'a')[1]
-    F = FiniteField(ZZRingElem(p), 2, :a)[1]
+    _ = finite_field(ZZRingElem(p), 2, "a")[1]
+    _ = finite_field(ZZRingElem(p), 2, 'a')[1]
+    F = finite_field(ZZRingElem(p), 2, :a)[1]
     G, mG = unit_group(F)
     #Test generator
     g = mG(G[1])

test/Misc/Poly.jl

@@ -130,7 +130,7 @@ end
 @testset "Cyclotomic polynomials" begin
   listp = Hecke.primes_up_to(50)
   for i in 1:20
-    Fp, _ = FiniteField(rand(listp), cached=false)
+    Fp, _ = finite_field(rand(listp), cached=false)
     Fpt, _ = polynomial_ring(Fp, "t", cached=false)
     chi = @inferred cyclotomic_polynomial(rand(1:100), Fpt)
     @test is_cyclotomic_polynomial(chi)