Adjust to introduction of Nemo 0.10

REQUIRE

@@ -1,3 +1,3 @@
 julia 1.0
-Nemo 0.9.1 0.10.0
-AbstractAlgebra 0.1.1
+Nemo 0.10.1
+AbstractAlgebra 0.1.3

src/AlgAss/AlgAss.jl

@@ -126,7 +126,7 @@ function AlgAss(O::NfOrd, I::NfOrdIdl, p::Union{Integer, fmpz})
   n = degree(O)
   BO = basis(O)
 
-  Fp = ResidueRing(FlintZZ, p, cached=false)
+  Fp = GF(p, cached=false)
   BOmod = [ mod(O(v), I) for v in BO ]
   B = zero_matrix(Fp, n, n)
   for i = 1:n
@@ -141,7 +141,7 @@ function AlgAss(O::NfOrd, I::NfOrdIdl, p::Union{Integer, fmpz})
   bbasis = Vector{NfOrdElem}(undef, r)
   for i = 1:r
     for j = 1:n
-      b[j] = fmpz(B[i, j])
+      b[j] = lift(B[i, j])
     end
     bbasis[i] = O(b)
   end
@@ -191,7 +191,7 @@ function AlgAss(O::NfOrd, I::NfOrdIdl, p::Union{Integer, fmpz})
   end
 
   function _preimage(a::AlgAssElem)
-    return sum(fmpz(a.coeffs[i])*bbasis[i] for i = 1:r)
+    return sum(lift(a.coeffs[i])*bbasis[i] for i = 1:r)
   end
 
   OtoA = NfOrdToAlgAssMor{elem_type(Fp)}(O, A, _image, _preimage)
@@ -644,7 +644,7 @@ function _primitive_element(A::AlgAss)
   return nothing
 end
 
-function _primitive_element(A::AlgAss{T}) where T <: Union{nmod, fq, fq_nmod, Generic.Res{fmpz}, fmpq}
+function _primitive_element(A::AlgAss{T}) where T <: Union{nmod, fq, fq_nmod, Generic.Res{fmpz}, fmpq, Generic.ResF{fmpz}, gfp_elem}
   d = dim(A)
   a = rand(A)
   f = minpoly(a)
@@ -665,12 +665,7 @@ function _as_field(A::AlgAss{T}) where T
     b = mul!(b, b, a)
     elem_to_mat_row!(M, i + 1, b)
   end
-  if T == Generic.Res{fmpz}
-    A, c = inv(M)
-    B = divexact(A, c)
-  elseif T == nmod
-    B = inv(M)
-  end
+  B = inv(M)
   N = zero_matrix(base_ring(A), 1, d)
   local f
   let N = N, B = B

src/AlgAss/AlgAssOrd.jl

@@ -448,24 +448,24 @@ end
 ###############################################################################
 
 function quo(O::AlgAssAbsOrd, p::Int)
-
-  R=ResidueRing(FlintZZ, p, cached=false)
-  M=Array{nmod, 3}(undef, O.dim, O.dim, O.dim)
-  x=fmpz[0 for i=1:O.dim]
-  for i=1:O.dim
-    x[i]=1
-    N=representation_matrix(O(x))
-    for j=1:O.dim
-      for k=1:O.dim
-        M[i,j,k]=R(N[j,k])
+  # p must be prime
+
+  R = GF(p, cached = false)
+  M = Array{gfp_elem, 3}(undef, O.dim, O.dim, O.dim)
+  x = fmpz[0 for i=1:O.dim]
+  for i = 1:O.dim
+    x[i] = 1
+    N = representation_matrix(O(x))
+    for j = 1:O.dim
+      for k = 1:O.dim
+        M[i, j, k] = R(N[j, k])
       end
     end
-    x[i]=0
+    x[i] = 0
   end
-  oneO=elem_in_basis(O(one(O.algebra)))
-  oneQ=nmod[R(s) for s in oneO]
+  oneO = elem_in_basis(O(one(O.algebra)))
+  oneQ = gfp_elem[R(s) for s in oneO]
   return AlgAss(R, M, oneQ)
-
 end
 
 function _mod(x::fmpz_mat, y::fmpz_mat, pivots::Array{Int,1})
@@ -493,8 +493,8 @@ function quo(O::AlgAssAbsOrd, I::AlgAssAbsOrdIdl, p::Int)
     end
   end
   @hassert :AlgAssOrd 1 check_ideal(I)
-  F= ResidueRing(FlintZZ, p, cached = false)
-  M=Array{nmod, 3}(undef, length(pivots), length(pivots), length(pivots))
+  F= GF(p, cached = false)
+  M=Array{gfp_elem, 3}(undef, length(pivots), length(pivots), length(pivots))
   x=fmpz[0 for s=1:O.dim]
   for i=1:length(pivots)
     x[pivots[i]]=1
@@ -520,7 +520,7 @@ function quo(O::AlgAssAbsOrd, I::AlgAssAbsOrdIdl, p::Int)
       end
     end
   end
-  oneA = Array{nmod, 1}(undef, length(pivots))
+  oneA = Array{gfp_elem, 1}(undef, length(pivots))
   for i=1:length(pivots)
     oneA[i] = F(oneO[pivots[i]])
   end
@@ -789,7 +789,7 @@ function pradical(O::AlgAssAbsOrd, p::Int)
     return pradical_meataxe(O,p)
   end
   n = root(O.dim,2)
-  F = ResidueRing(FlintZZ, p, cached=false)
+  F = GF(p, cached=false)
 
   #First step: kernel of the trace matrix mod p 
   W = MatrixSpace(F,O.dim, O.dim, false)
@@ -1027,8 +1027,8 @@ function _maximal_ideals(O::AlgAssAbsOrd, p::Int)
   #@show dim(A1)
   @vtime :AlgAssOrd 1 lg = gens(A1)
   #@show length(lg)
-  lM = nmod_mat[representation_matrix(lg[i]) for i=1:length(lg)]
-  append!(lM, nmod_mat[representation_matrix(lg[i], :right) for i=1:length(lg)])  
+  lM = gfp_mat[representation_matrix(lg[i]) for i=1:length(lg)]
+  append!(lM, gfp_mat[representation_matrix(lg[i], :right) for i=1:length(lg)])  
   #lM = nmod_mat[representation_matrix(A1[i]) for i=1:dim(A1)]
   #append!(lM, nmod_mat[representation_matrix(A1[i], :right) for i=1:dim(A1)])
   M = ModAlgAss(lM)
@@ -1045,8 +1045,8 @@ function _maximal_ideals(O::AlgAssAbsOrd, I::AlgAssAbsOrdIdl, p::Int)
   #@show dim(A1)
   @vtime :AlgAssOrd 1 lg = gens(A1)
   #@show length(lg)
-  lM = nmod_mat[representation_matrix(lg[i]) for i=1:length(lg)]
-  append!(lM, nmod_mat[representation_matrix(lg[i], :right) for i=1:length(lg)])
+  lM = gfp_mat[representation_matrix(lg[i]) for i=1:length(lg)]
+  append!(lM, gfp_mat[representation_matrix(lg[i], :right) for i=1:length(lg)])
   #lM = nmod_mat[representation_matrix(A1[i]) for i=1:dim(A1)]
   #append!(lM, nmod_mat[representation_matrix(A1[i], :right) for i=1:dim(A1)])
   M = ModAlgAss(lM)
@@ -1057,7 +1057,7 @@ function _maximal_ideals(O::AlgAssAbsOrd, I::AlgAssAbsOrdIdl, p::Int)
 
 end
 
-function _from_submodules_to_ideals(M::ModAlgAss, O::AlgAssAbsOrd, I::AlgAssAbsOrdIdl, x::nmod_mat, p::fmpz, poneO::AlgAssAbsOrdElem, A1::AlgAss, A1toO::Function)
+function _from_submodules_to_ideals(M::ModAlgAss, O::AlgAssAbsOrd, I::AlgAssAbsOrdIdl, x::Zmodn_mat, p::fmpz, poneO::AlgAssAbsOrdElem, A1::AlgAss, A1toO::Function)
   @hassert :AlgAssOrd 1 begin r = rref(x)[1]; closure(x, M.action) == sub(rref(x)[2], 1:r, 1:cols(x)) end
   m = zero_matrix(FlintZZ, rows(x)+O.dim , O.dim)
   gens = Vector{AlgAssAbsOrdElem}(undef, rows(x))
@@ -1085,7 +1085,7 @@ function _from_submodules_to_ideals(M::ModAlgAss, O::AlgAssAbsOrd, I::AlgAssAbsO
 
 end
 
-function _from_submodules_to_ideals(M::ModAlgAss, O::AlgAssAbsOrd, x::nmod_mat, p::fmpz, poneO::AlgAssAbsOrdElem)
+function _from_submodules_to_ideals(M::ModAlgAss, O::AlgAssAbsOrd, x::Zmodn_mat, p::fmpz, poneO::AlgAssAbsOrdElem)
 
   @hassert :AlgAssOrd 1 begin r = rref(x)[1]; closure(x, M.action) == sub(rref(x)[2], 1:r, 1:cols(x)) end
   m = zero_matrix(FlintZZ, O.dim, O.dim)

src/EllCrv/Cleanup.jl

@@ -495,7 +495,7 @@ function mod_red(E, B)
 
     for i in 1:length(P)
         p = P[i]
-        R = ResidueRing(FlintZZ, p)
+        R = GF(p, cached = false)
         Ep = EllipticCurve([R(numerator(minmodel.coeff[1])), R(numerator(minmodel.coeff[2])), R(numerator(minmodel.coeff[3])), R(numerator(minmodel.coeff[4])), R(numerator(minmodel.coeff[5]))],  false) # reduction of E mod p 
 
         if  disc(Ep) != 0 # can only determine group order if curve is non-singular

src/EllCrv/Finite.jl

@@ -408,7 +408,7 @@ function order_via_schoof(E::EllCrv)
   t = 0
   for i = 1:L
     n_i = div(product, S[i])
-    B = ResidueRing(FlintZZ, S[i])
+    B = ResidueRing(FlintZZ, S[i], cached = false)
     M_i = inv(B(n_i))
     M_i = M_i.data
     t = t + (M_i * n_i * t_mod_l[i])
@@ -454,7 +454,7 @@ function t_mod_prime(l, E)
 
   S, x = PolynomialRing(R, "x")
   T, y = PolynomialRing(S, "y")
-  Z = ResidueRing(FlintZZ, l)
+  Z = GF(l, cached = false)
 
   f = x^3 + E.coeff[1]*x + E.coeff[2]
   fl = fn_from_schoof(E, l, x)

src/EllCrv/Misc.jl

@@ -158,7 +158,8 @@ function issquare(x::ResElem{fmpz})
         return false, zero(R)
     end
 end
-function issquare(x::Nemo.nmod)
+
+function issquare(x::Union{nmod, gfp_elem})
     R = parent(x)
     p = modulus(R)
     xnew = x.data
@@ -184,7 +185,7 @@ end
 """
 function issquare(x::FinFieldElem)
     R = parent(x)
-    S, t = PolynomialRing(R, "t")
+    S, t = PolynomialRing(R, "t", cached = false)
 
     # check if x is a square by considering the polynomial f = t^2 - x
     # x is a square in F_q iff f has a root in F_q
@@ -212,8 +213,8 @@ end
 > $ax^2 + bx + c = 0$ has a root modulo $p$.
 """
 function quadroots(a, b, c, p)
-  F_p = ResidueRing(FlintZZ, p)
-  R, x = PolynomialRing(F_p, "x")
+  F_p = GF(p, cached = false)
+  R, x = PolynomialRing(F_p, "x", cached = false)
   f = F_p(a)*x^2 + F_p(b)*x + F_p(c)
 
   if degree(f) == -1
@@ -244,7 +245,7 @@ end
 > modulo $p$.
 """
 function nrootscubic(b, c, d, p)
-  F_p = ResidueRing(FlintZZ, p)
+  F_p = GF(p, cached = false)
   R, x = PolynomialRing(F_p, "x")
   f = x^3 + F_p(b)*x^2 + F_p(c)*x + F_p(d)
 

src/Hecke.jl

@@ -75,7 +75,7 @@ for i in names(Nemo)
 end
 
 import Nemo: acb_struct, Ring, Group, Field, NmodRing, nmod, arf_struct,
-       elem_to_mat_row!, elem_from_mat_row,
+       elem_to_mat_row!, elem_from_mat_row, gfp_elem, gfp_mat, Zmodn_poly, Zmodn_mat, GaloisField,
        acb_vec, array, acb_vec_clear
 
 export @vprint, @hassert, @vtime, add_verbose_scope, get_verbose_level,

src/LargeField/FB.jl

@@ -62,7 +62,7 @@ function induce(FB::Hecke.NfFactorBase, A::Map)
         push!(prm, (i, FP.lp[id][1]))
       end
     else
-      px = PolynomialRing(ResidueRing(FlintZZ, Int(p), cached=false), "x", cached=false)[1]
+      px = PolynomialRing(GF(Int(p), cached=false), "x", cached=false)[1]
       fpx = px(f)
       gpx = px(K.pol)
       #idea/ reason

src/LargeField/misc2.jl

@@ -296,9 +296,9 @@ function basis_rels_5(b::Array{nf_elem, 1}, no_b::Int = 250, no_rel::Int = 10000
 
 
   lpx = [modular_init(K, p) for p=lp]
-  bp = Array{nmod_mat}(length(lpx))
+  bp = Array{gfp_mat}(length(lpx))
   for i=1:length(lpx)
-    bp[i] = zero_matrix(ResidueRing(FlintZZ, lpx[i].p, cached=false), n, n)
+    bp[i] = zero_matrix(GF(lpx[i].p, cached=false), n, n)
     for k=1:n
       ap = modular_proj(b[k], lpx[i])
       for l=1:n
@@ -308,11 +308,11 @@ function basis_rels_5(b::Array{nf_elem, 1}, no_b::Int = 250, no_rel::Int = 10000
   end
 #  bp = [[deepcopy(modular_proj(x, me)) for x = b] for me = lpx]
 
-  tmp = Array{nmod_mat}(length(lpx))
-  lcp = Array{nmod_mat}(length(lpx))
+  tmp = Array{gfp_mat}(length(lpx))
+  lcp = Array{gfp_mat}(length(lpx))
   for i=1:length(lpx)
-    tmp[i] = zero_matrix(ResidueRing(FlintZZ, lpx[i].p, cached=false), n, 1)
-    lcp[i] = zero_matrix(ResidueRing(FlintZZ, lpx[i].p, cached=false), n, 1)
+    tmp[i] = zero_matrix(GF(lpx[i].p, cached=false), n, 1)
+    lcp[i] = zero_matrix(GF(lpx[i].p, cached=false), n, 1)
   end
 
   lc = Array{Int, 1}()