Move obvious piracy from Hecke/src/misc/FiniteField.jl to Nemo

src/HeckeMiscFiniteField.jl

@@ -0,0 +1,305 @@
+export representation_matrix, frobenius_matrix
+
+# additional constructors
+
+function FlintFiniteField(p::Integer; cached::Bool=true)
+    @assert is_prime(p)
+    k = GF(p, cached=cached)
+    return k, k(1)
+end
+
+function FlintFiniteField(p::ZZRingElem; cached::Bool=true)
+    @assert is_prime(p)
+    k = GF(p, cached=cached)
+    return k, k(1)
+end
+
+GF(p::Integer, k::Int, s::VarName=:o; cached::Bool=true) = FlintFiniteField(p, k, s, cached=cached)[1]
+GF(p::ZZRingElem, k::Int, s::VarName=:o; cached::Bool=true) = FlintFiniteField(p, k, s, cached=cached)[1]
+
+
+##
+## rand for Flint-Finite fields
+##
+## fqPolyRepFieldElem has no base ring
+function rand(R::fqPolyRepField)
+    #gen is not a generator for the group!
+    r = R(0)
+    for i = 0:degree(R)
+        r *= gen(R)
+        r += rand(1:characteristic(R))
+    end
+
+    return r
+end
+
+function rand(R::FqPolyRepField)
+    #gen is not a generator for the group!
+    r = R(0)
+    for i = 0:degree(R)
+        r *= gen(R)
+        r += rand(1:characteristic(R))
+    end
+
+    return r
+end
+
+################################################################################
+#
+#  Iterators for finite fields
+#
+################################################################################
+
+# fqPolyRepField
+
+function Base.iterate(F::fqPolyRepField)
+    return zero(F), zeros(UInt, degree(F))
+end
+
+function Base.iterate(F::fqPolyRepField, st::Vector{UInt})
+    done = true
+    for j in 1:length(st)
+        if st[j] != F.n - 1
+            done = false
+        end
+    end
+
+    if done
+        return nothing
+    end
+
+    st[1] = st[1] + 1
+    for j in 1:(length(st)-1)
+        if st[j] == F.n
+            st[j] = 0
+            st[j+1] = st[j+1] + 1
+        end
+    end
+
+    d = F()
+    ccall((:fq_nmod_init2, libflint), Nothing,
+        (Ref{fqPolyRepFieldElem}, Ref{fqPolyRepField}), d, F)
+    for j in 1:length(st)
+        ccall((:nmod_poly_set_coeff_ui, libflint), Nothing,
+            (Ref{fqPolyRepFieldElem}, Int, UInt), d, j - 1, st[j])
+    end
+
+    return d, st
+end
+
+Base.length(F::fqPolyRepField) = BigInt(F.n)^degree(F)
+
+Base.IteratorSize(::Type{fqPolyRepField}) = Base.HasLength()
+
+Base.eltype(::fqPolyRepField) = fqPolyRepFieldElem
+
+# FqPolyRepField
+
+function Base.iterate(F::FqPolyRepField)
+    return zero(F), zeros(FlintZZ, degree(F))
+end
+
+function Base.iterate(F::FqPolyRepField, st::Vector{ZZRingElem})
+    done = true
+    for j in 1:length(st)
+        if st[j] != characteristic(F) - 1
+            done = false
+        end
+    end
+
+    if done
+        return nothing
+    end
+
+    st[1] = st[1] + 1
+    for j in 1:(length(st)-1)
+        if st[j] == characteristic(F)
+            st[j] = 0
+            st[j+1] = st[j+1] + 1
+        end
+    end
+
+    d = F()
+    ccall((:fq_init2, libflint), Nothing,
+        (Ref{FqPolyRepFieldElem}, Ref{FqPolyRepField}), d, F)
+    for j in 1:length(st)
+        #ccall((:fmpz_poly_set_coeff_fmpz, libflint), (Ref{ZZPolyRingElem}, Int, Ref{ZZRingElem}), g, j - 1, st[j])
+        ccall((:fmpz_poly_set_coeff_fmpz, libflint), Nothing,
+            (Ref{FqPolyRepFieldElem}, Int, Ref{ZZRingElem}), d, j - 1, st[j])
+    end
+
+    return d, st
+end
+
+Base.eltype(::FqPolyRepField) = FqPolyRepFieldElem
+
+Base.length(F::FqPolyRepField) = BigInt(characteristic(F)^degree(F))
+
+Base.IteratorSize(::Type{FqPolyRepField}) = Base.HasLength()
+
+sub!(z::T, x::T, y::T) where {T} = x - y
+
+function (A::fqPolyRepField)(x::fpFieldElem)
+    @assert characteristic(A) == characteristic(parent(x))
+    return A(lift(x))
+end
+
+function (A::FqPolyRepField)(x::Generic.ResidueFieldElem{ZZRingElem})
+    @assert characteristic(A) == characteristic(parent(x))
+    return A(lift(x))
+end
+
+AbstractAlgebra.promote_rule(::Type{fqPolyRepFieldElem}, ::Type{fpFieldElem}) = fqPolyRepFieldElem
+
+AbstractAlgebra.promote_rule(::Type{FqPolyRepFieldElem}, ::Type{FpFieldElem}) = FqPolyRepFieldElem
+
+## Minpoly/ Charpoly
+
+function minpoly(a::fqPolyRepFieldElem)
+    return minpoly(polynomial_ring(Native.GF(Int(characteristic(parent(a))), cached=false), cached=false)[1], a)
+end
+
+function minpoly(Rx::fpPolyRing, a::fqPolyRepFieldElem)
+    c = [a]
+    fa = frobenius(a)
+    while !(fa in c)
+        push!(c, fa)
+        fa = frobenius(fa)
+    end
+    St = polynomial_ring(parent(a), cached=false)[1]
+    f = prod([gen(St) - x for x = c], init=one(St))
+    g = Rx()
+    for i = 0:degree(f)
+        setcoeff!(g, i, coeff(coeff(f, i), 0))
+    end
+    return g
+end
+
+function charpoly(a::fqPolyRepFieldElem)
+    return charpoly(polynomial_ring(Native.GF(Int(characteristic(parent(a))), cached=false), cached=false)[1], a)
+end
+
+function charpoly(Rx::fpPolyRing, a::fqPolyRepFieldElem)
+    g = minpoly(Rx, a)
+    return g^div(degree(parent(a)), degree(g))
+end
+
+
+function minpoly(a::FqPolyRepFieldElem)
+    return minpoly(polynomial_ring(Native.GF(characteristic(parent(a)), cached=false), cached=false)[1], a)
+end
+
+function minpoly(Rx::FpPolyRing, a::FqPolyRepFieldElem)
+    c = [a]
+    fa = frobenius(a)
+    while !(fa in c)
+        push!(c, fa)
+        fa = frobenius(fa)
+    end
+    St = polynomial_ring(parent(a), cached=false)[1]
+    f = prod([gen(St) - x for x = c])
+    g = Rx()
+    for i = 0:degree(f)
+        setcoeff!(g, i, coeff(coeff(f, i), 0))
+    end
+    return g
+end
+
+################################################################################
+#
+#  Missing ad hoc operations
+#
+################################################################################
+
+function (R::FqPolyRepField)(x::FpFieldElem)
+    return R(lift(x))
+end
+
+function *(a::FqPolyRepFieldElem, b::FpFieldElem)
+    return a * parent(a)(b)
+end
+
+function *(a::FpFieldElem, b::FqPolyRepFieldElem)
+    return parent(b)(a) * b
+end
+
+function preimage(phi::FinFieldMorphism, x::FinFieldElem)
+    return preimage_map(phi)(x)
+end
+
+function (R::zzModRing)(a::fpFieldElem)
+    @assert modulus(R) == characteristic(parent(a))
+    return R(data(a))
+end
+
+function (k::fqPolyRepField)(a::QQFieldElem)
+    return k(numerator(a)) // k(denominator(a))
+end
+
+function (k::FpField)(a::QQFieldElem)
+    return k(numerator(a)) // k(denominator(a))
+end
+
+function (k::FqPolyRepField)(a::QQFieldElem)
+    return k(numerator(a)) // k(denominator(a))
+end
+
+
+(F::fqPolyRepField)(a::zzModRingElem) = F(a.data)
+
+#TODO/ think: 
+# - should those be zzModMatrix of fpMatrix
+# - base_ring/ coeff_field needs to be unique?
+function representation_matrix(a::fpFieldElem)
+    return matrix(parent(a), 1, 1, [a])
+end
+
+function representation_matrix(a::fqPolyRepFieldElem)
+    F = parent(a)
+    k = quo(ZZ, Int(characteristic(F)))[1]
+    k = Native.GF(Int(characteristic(F)))
+    m = zero_matrix(k, degree(F), degree(F))
+    ccall((:fq_nmod_embed_mul_matrix, libflint), Nothing, (Ref{fpMatrix}, Ref{fqPolyRepFieldElem}, Ref{fqPolyRepField}), m, a, F)
+    ccall((:nmod_mat_transpose, libflint), Nothing, (Ref{fpMatrix}, Ref{fpMatrix}), m, m)
+    return m
+end
+
+function frobenius_matrix(F::fqPolyRepField, n::Int=1)
+    a = frobenius(gen(F), n)
+    k = quo(ZZ, Int(characteristic(F)))[1]
+    k = Native.GF(Int(characteristic(F)))
+    m = zero_matrix(k, degree(F), degree(F))
+    ccall((:fq_nmod_embed_composition_matrix_sub, libflint), Nothing, (Ref{fpMatrix}, Ref{fqPolyRepFieldElem}, Ref{fqPolyRepField}, Int), m, a, F, degree(F))
+    ccall((:nmod_mat_transpose, libflint), Nothing, (Ref{fpMatrix}, Ref{fpMatrix}), m, m)
+    return m
+end
+
+function frobenius!(a::fqPolyRepFieldElem, b::fqPolyRepFieldElem, i::Int=1)
+    ccall((:fq_nmod_frobenius, libflint), Nothing,
+        (Ref{fqPolyRepFieldElem}, Ref{fqPolyRepFieldElem}, Int, Ref{fqPolyRepField}),
+        a, b, i, a.parent)
+end
+
+################################################################################
+#
+#  Defining polynomial for finite fields
+#
+################################################################################
+
+defining_polynomial(F::FqPolyRepField) = minpoly(gen(F))
+
+function defining_polynomial(Q::fqPolyRepField, P::Ring=Native.GF(Int(characteristic(Q)), cached=false))
+    Pt, t = polynomial_ring(P, cached=false)
+    f = Pt()
+    for i = 0:Q.len-1
+        j = unsafe_load(reinterpret(Ptr{Int}, Q.j), i + 1)
+        a = ZZRingElem()
+        ccall((:fmpz_set, libflint), Nothing, (Ref{ZZRingElem}, Int64), a, Q.a + i * sizeof(Ptr))
+        setcoeff!(f, j, P(a))
+    end
+    return f
+end
+
+lift(::ZZRing, x::fpFieldElem) = lift(x)
+
+lift(::ZZRing, x::FpFieldElem) = lift(x)

src/HeckeMoreStuff.jl

@@ -1,4 +1,4 @@
-function copy(a::ZZRingElem)
+function Base.copy(a::ZZRingElem)
     return deepcopy(a)
 end
 

src/Nemo.jl

@@ -385,6 +385,7 @@ include("embedding/embedding.jl")
 
 include("Rings.jl")
 
+include("HeckeMiscFiniteField.jl")
 include("HeckeMiscInteger.jl")
 include("HeckeMiscMatrix.jl")
 include("HeckeMiscPoly.jl")