chore: update AA to 0.47, Nemo to 0.52, and Hecke to 0.38

Project.toml

@@ -28,17 +28,17 @@ cohomCalg_jll = "5558cf25-a90e-53b0-b813-cadaa3ae7ade"
 lib4ti2_jll = "1493ae25-0f90-5c0e-a06c-8c5077d6d66f"
 
 [compat]
-AbstractAlgebra = "0.46.2"
+AbstractAlgebra = "0.47.3"
 AlgebraicSolving = "0.9.0"
 Compat = "4.13.0"
 Distributed = "1.6"
 GAP = "0.15.0"
-Hecke = "0.37.2"
+Hecke = "0.38.5"
 JSON = "^0.20, ^0.21"
 JSON3 = "1.13.2"
 LazyArtifacts = "1.6"
 Markdown = "1.6"
-Nemo = "0.51.1"
+Nemo = "0.52.1"
 Pkg = "1.6"
 Polymake = "0.13.1"
 ProgressMeter = "1.10.2"

docs/src/NumberTheory/abelian_closure.md

@@ -51,10 +51,10 @@ julia> x = z(5)
 zeta(5)
 
 julia> y = F(x)
-Root 0.309017 + 0.951057*im of x^4 + x^3 + x^2 + x + 1
+{a4: 0.309017 + 0.951057*im}
 
 julia> y^5
-Root 1.00000 of x - 1
+{a1: 1.00000}
 ```
 
 Real elements of `K` can be compared with `<` and `>`.

docs/src/Rings/integer.md

@@ -566,7 +566,7 @@ factorisation struct which can be manipulated using the functions below.
 
 ```jldoctest; filter = Main.Oscar.doctestfilter_hash_changes_in_1_13()
 julia> factor(ZZ(-6000361807272228723606))
--1 * 2 * 229^3 * 43669^3 * 3
+-1 * 2 * 3 * 229^3 * 43669^3
 
 julia> factor(ZZ(0))
 ERROR: ArgumentError: Argument is not non-zero
@@ -591,12 +591,12 @@ Once created, a factorisation is iterable:
 
 ```jldoctest; filter = Main.Oscar.doctestfilter_hash_changes_in_1_13()
 julia> F = factor(ZZ(-60))
--1 * 5 * 2^2 * 3
+-1 * 2^2 * 3 * 5
 
 julia> for (p, e) in F; println("$p^$e"); end
-5^1
 2^2
 3^1
+5^1
 
 ```
 
@@ -606,13 +606,13 @@ array using `collect`:
 
 ```jldoctest; filter = Main.Oscar.doctestfilter_hash_changes_in_1_13()
 julia> F = factor(ZZ(-60))
--1 * 5 * 2^2 * 3
+-1 * 2^2 * 3 * 5
 
 julia> collect(F)
 3-element Vector{Pair{ZZRingElem, Int64}}:
- 5 => 1
  2 => 2
  3 => 1
+ 5 => 1
 
 ```
 
@@ -627,7 +627,7 @@ functionality.
 
 ```jldoctest; filter = Main.Oscar.doctestfilter_hash_changes_in_1_13()
 julia> F = factor(ZZ(-60))
--1 * 5 * 2^2 * 3
+-1 * 2^2 * 3 * 5
 
 julia> 5 in F
 true
@@ -642,7 +642,7 @@ julia> F[3]
 1
 
 julia> F[ZZ(7)]
-ERROR: 7 is not a factor of -1 * 5 * 2^2 * 3
+ERROR: 7 is not a factor of -1 * 2^2 * 3 * 5
 [...]
 
 ```

experimental/GModule/src/Brueckner.jl

@@ -180,7 +180,7 @@ function find_primes(mp::Map{<:Oscar.GAPGroup, PcGroup})
     #  expensive find minimal field step can be omitted.
     I = [gmodule(ZZ, gmodule(QQ, gmodule(CyclotomicField, x))) for x = I]
   end
-  lp = Set(collect(keys(factor(order(Q)).fac)))
+  lp = Set(prime_divisors(order(Q)))
   for i = I
     ib = gmodule(i.M, G, [action(i, mp(g)) for g = gens(G)])
     ia = gmodule(FinGenAbGroup, ib)
@@ -217,7 +217,7 @@ function find_primes(mp::Map{<:Oscar.GAPGroup, PcGroup})
 #    q = quo(kernel(da)[1], image(db)[1])[1]
     t = torsion_subgroup(q)[1]
     if order(t) > 1
-      push!(lp, collect(keys(factor(order(t)).fac))...)
+      push!(lp, prime_divisors(order(t))...)
     end
   end
   return lp
@@ -400,14 +400,14 @@ end
 function sq(mp::Map, primes::Vector=[]; index::Union{Integer, ZZRingElem, Nothing} = nothing)
   if index !== nothing
     lf = factor(ZZRingElem(index))
-    primes = collect(keys(lf.fac))
+    primes = prime_divisors(ZZ(index))
     while length(primes) > 0
       @time nw = brueckner(mp; limit = 1, primes)
       if length(nw) == 0 
         return mp
       end
       mp = nw[1]
-      for (p, k) = lf.fac
+      for (p, k) = lf
         if p in primes && valuation(order(codomain(mp)), p) >= k
           deleteat!(primes, findfirst(isequal(p), primes))
 #          @show :removing, p

experimental/GModule/src/Cohomology.jl

@@ -1921,7 +1921,7 @@ function pc_group_with_isomorphism(M::FinGenAbGroup; refine::Bool = true)
   if refine
     hm = elem_type(M)[]
     for i=1:nrows(h)
-      lf = collect(factor(h[i,i]).fac)
+      lf = collect(factor(h[i,i]))
       for (p,k) = lf
         v = divexact(h[i,i], p^k)*M[i]
         for j=1:k-1

experimental/GModule/src/GModule.jl

@@ -294,7 +294,7 @@ function invariant_lattice_classes(M::GModule{<:Oscar.GAPGroup, <:AbstractAlgebr
   res = Any[(M, sub(M.M, gens(M.M))[2])]
   sres = 1
   new = true
-  lp = keys(factor(order(M.G)).fac)
+  lp = prime_divisors(order(M.G))
   while new
     new  = false
     lres = length(res)
@@ -2191,7 +2191,7 @@ function split_homogeneous2(M::GModule{<:Any, <:AbstractAlgebra.FPModule{QQField
     i = _i.elem_in_algebra
     f = minpoly(i)
     lf = factor(f)
-    if length(lf) == 1 && degree(f) == s*m*k &&  haskey(lf.fac, f)
+    if length(lf) == 1 && degree(f) == s*m*k && f in lf
       if first
         best_f = f
         best_i = i

experimental/GModule/src/GaloisCohomology.jl

@@ -270,7 +270,7 @@ function is_coboundary(c::CoChain{2,PermGroupElem,MultGrpElem{AbsSimpleNumFieldE
   cp = coprime_base(vcat([numerator(norm(x.data*denominator(x.data))) for x = values(c.d)],
                          map(x->denominator(x.data), values(c.d))))
   @vprint :GaloisCohomology 2 ".. coprime done, now factoring ..\n"
-  s = Set(reduce(vcat, [collect(keys(factor(x).fac)) for x = cp], init = [1]))
+  s = Set(reduce(vcat, [prime_divisors(x) for x = cp], init = [1]))
   while 1 in s
     pop!(s, 1)
   end
@@ -733,7 +733,7 @@ function Hecke.extend_easy(m::Hecke.CompletionMap, L::FacElemMon{AbsSimpleNumFie
 
   #want a map: L-> codomain(m)
   function to(a::FacElem{AbsSimpleNumFieldElem})
-    return prod(m(k)^v for (k,v) = a.fac)
+    return prod(m(k)^v for (k,v) in a)
   end
   function from(a::Hecke.LocalFieldElem)
     return FacElem(preimage(m, a))
@@ -750,7 +750,7 @@ function Hecke.extend_easy(m::Hecke.CompletionMap, mu::Map, L::FacElemMon{AbsSim
   #want a map: L-> codomain(m) -> domain(mu)
   function to(a::FacElem{AbsSimpleNumFieldElem})
     s = domain(mu)[0]
-    for (k,v) = a.fac
+    for (k,v) = a
       if haskey(cache, k)
         s += v*cache[k]
       else
@@ -834,7 +834,7 @@ function idele_class_gmodule(k::AbsSimpleNumField, s::Vector{Int} = Int[]; redo:
   cf = Tuple{FinGenAbGroup, <:Map}[x for x = cf]
 
   @vprint :GaloisCohomology 2 " .. gathering primes ..\n"
-  s = push!(Set{ZZRingElem}(s), Set{ZZRingElem}(keys(factor(discriminant(zk)).fac))...)
+  s = push!(Set{ZZRingElem}(s), Set{ZZRingElem}(prime_divisors(discriminant(zk)))...)
   for i=1:length(sf)
     l = factor(prod(s)*zf[i])
     q, mq = quo(cf[i][1], [preimage(cf[i][2], P) for P = keys(l)])

experimental/GaloisGrp/src/Solve.jl

@@ -507,7 +507,7 @@ function Oscar.solve(f::ZZPolyRingElem; max_prec::Int=typemax(Int), show_radical
   CHECK = get_assertion_level(:SolveRadical) > 0
   @vprint :SolveRadical 1 "computing initial galois group...\n"
   @vtime :SolveRadical 1 G, C = galois_group(f)
-  lp = [p for p = keys(factor(order(G)).fac) if p > 2]
+  lp = [p for (p, _) in factor(order(G)) if p > 2]
   if length(lp) > 0
     @vprint :SolveRadical 1 "need to add roots-of-one: $lp\n"
     @vtime :SolveRadical 1 G, C = galois_group(f*prod(cyclotomic(Int(p), gen(parent(f))) for p = lp))
@@ -599,7 +599,7 @@ function Oscar.solve(f::ZZPolyRingElem; max_prec::Int=typemax(Int), show_radical
         p = parent(s)
         if p == QQ
           lf = factor(s, ZZ)
-          t = prod([p for (p, k) = lf.fac if isodd(k)], init = ZZ(1)) * lf.unit
+          t = prod([p for (p, k) = lf if isodd(k)], init = ZZ(1)) * lf.unit
           r = root(s//t, 2)    
         else
           _, ma = absolute_simple_field(p)

experimental/GaloisGrp/src/Subfields.jl

@@ -339,7 +339,7 @@ function _subfields(K::AbsSimpleNumField; pStart = 2*degree(K)+1, prime = 0)
   f = divexact(f, content(f))
 
   p, ct = find_prime(Hecke.Globals.Qx(f), pStart = pStart, prime = prime,
-                                          filter_pattern = x->any(t->degree(t) == 1, keys(x.fac)))
+                                          filter_pattern = x->any(t->degree(t) == 1, first.(collect(x))))
   n = degree(K)
   if primitive_by_shape(ct, n)
     return nothing

experimental/StandardFiniteFields/src/StandardFiniteFields.jl

@@ -11,9 +11,8 @@ const PrimeFieldMatrix = Union{FpMatrix,fpMatrix}
 
 # NOTE: These give missing features to OSCAR/Nemo that will likely be added in the near future.
 
-function pop_largest_factor!(f::Fac{ZZRingElem})
-  D = f.fac
-  m = maximum(f)
+function pop_largest_factor!(D::Dict{ZZRingElem, Int})
+  m = maximum(D)
   if isone(m[2])
     Base.delete!(D, m[1])
   else
@@ -463,11 +462,11 @@ function standard_finite_field(p::IntegerUnion, n::IntegerUnion)
   F = Native.GF(p)
   set_standard_prime_field!(F)
 
-  function _sff(N::Fac{ZZRingElem})
+  function _sff(N::Dict{ZZRingElem, Int})
     # local m::ZZRingElem, k::IntegerUnion, nK::ZZRingElem, K::FinField, stn::ZZRingElem,
     #         n1::ZZRingElem, q1::ZZRingElem, l::Vector{ZZRingElem}, c::Vector{ZZRingElem}, b::FinFieldElem
     m, k = pop_largest_factor!(N)
-    nK = evaluate(N)
+    nK = prod(p^e for (p, e) in N; init = one(ZZ))
 
     K = get_standard_extension!(F, nK) do
       _sff(N)
@@ -490,7 +489,7 @@ function standard_finite_field(p::IntegerUnion, n::IntegerUnion)
 
   return get_standard_extension!(F, n) do
     N = factor(ZZ(n))
-    return _sff(N)
+    return _sff(Dict(p => e for (p, e) in N))
   end
 end
 

gap/pkg/OscarInterface/gap/QQBar.gi

@@ -165,7 +165,7 @@ BindGlobal( "_DisplayStringQQBarMatrixElement", function( x )
   str:= String( x );
   if ValueOption( "short" ) = true then
     pos:= Position( str, ' ' );
-    str:= str{ [ pos + 1 .. Position( str, ' ', pos ) - 1 ] };
+    str:= str{ [ pos + 1 .. Position( str, '}', pos ) - 1 ] };
   fi;
   return str;
   end );

gap/pkg/OscarInterface/tst/QQBar.tst

@@ -5,13 +5,13 @@ gap> START_TEST( "QQBar.tst" );
 gap> F:= QQBarField;
 QQBarField
 gap> x:= One( F );
-<Root 1.00000 of x - 1>
+<{a1: 1.00000}>
 gap> Print( x, "\n" );
-<Root 1.00000 of x - 1>
+<{a1: 1.00000}>
 gap> String( x );
-"<Root 1.00000 of x - 1>"
+"<{a1: 1.00000}>"
 gap> z:= Zero( F );
-<Root 0 of x>
+<{a1: 0}>
 gap> Zero( x ) = z;
 true
 gap> z < x;
@@ -38,7 +38,7 @@ true
 gap> x * x = x;
 true
 gap> r:= Sqrt( y );
-<Root 1.41421 of x^2 - 2>
+<{a2: 1.41421}>
 gap> r^2 = y;
 true
 gap> r^-1 = 1 / r;
@@ -63,13 +63,13 @@ gap> M:= [ [ z, r ], [ r, z ] ];;
 gap> Determinant( M ) = -2;
 true
 gap> MinimalPolynomial( M );
-x_1^2+(<Root -2.00000 of x + 2>)
+x_1^2+(<{a1: -2.00000}>)
 gap> Eigenvalues( F, M );
-[ <Root 1.41421 of x^2 - 2>, <Root -1.41421 of x^2 - 2> ]
+[ <{a2: 1.41421}>, <{a2: -1.41421}> ]
 gap> Display( M );
 2x2 matrix over QQBarField:
-                         . <Root 1.41421 of x^2 - 2>
- <Root 1.41421 of x^2 - 2>                         .
+               . <{a2: 1.41421}>
+ <{a2: 1.41421}>               .
 gap> Display( M : short );
 2x2 matrix over QQBarField:
        . 1.41421

src/NumberTheory/GaloisGrp/GaloisGrp.jl

@@ -1335,13 +1335,13 @@ function sum_orbits(K, Qt_to_G, r)
   end
   @vprint :GaloisGroup 1 "... factoring...\n"
   @vtime :GaloisGroup 2 fg  = factor(g)
-  @assert all(isone, values(fg.fac))
+  @assert all(isone(e) for (_, e) in fg)
 
   O = []
   if isa(r[1], AcbFieldElem)
     mm = collect(m)
   end
-  for f = keys(fg.fac)
+  for (f, _) in fg
     r = roots(map_coefficients(Qt_to_G, f))
     if isa(r[1], AcbFieldElem)
       push!(O, [mm[argmin(map(x->abs(x[1]-y), mm))][2] for y = r])
@@ -1708,13 +1708,13 @@ function find_prime(f::QQPolyRingElem, extra::Int = 5; prime::Int = 0, pStart::I
   if prime != 0
     p = prime
     lf = factor(GF(p), f)
-    return p, Set([CycleType(map(degree, collect(keys(lf.fac))))])
+    return p, Set([CycleType(map(degree, first.(collect(lf))))])
   end
   if pStart < 0
     error("should no longer happen")
     p = -pStart
     lf = factor(GF(p), f)
-    return p, Set([CycleType(map(degree, collect(keys(lf.fac))))])
+    return p, Set([CycleType(map(degree, first.(collect(lf))))])
   end
 
   d_max = degree(f)^2
@@ -1737,13 +1737,13 @@ function find_prime(f::QQPolyRingElem, extra::Int = 5; prime::Int = 0, pStart::I
       continue
     end
     lf = factor(GF(p), f)
-    if any(>(1), values(lf.fac))
+    if any(>(1), (e for (_, e) in lf))
       continue
     end
     filter_pattern(lf) || continue
     no_p +=1 
-    push!(ct, sort(map(degree, collect(keys(lf.fac))))) # ct = cycle types as vector of cycle lengths
-    d = lcm([degree(x) for x = keys(lf.fac)])
+    push!(ct, sort(map(degree, first.(collect(lf))))) # ct = cycle types as vector of cycle lengths
+    d = lcm([degree(x) for (x, _) in lf])
     if d <= d_max 
       if d >= d_min
         push!(ps, (p, d))
@@ -2850,7 +2850,7 @@ group of permutations of the roots. Furthermore, the `GaloisCtx` is
 returned allowing algorithmic access to the splitting field.
 """
 function galois_group(f::PolyRingElem{<:FieldElem}; prime=0, pStart::Int = 2*degree(f))
-  lf = [(k,v) for  (k,v) = factor(f).fac]
+  lf = [(k,v) for  (k,v) = factor(f)]
 
   if length(lf) == 1
     @vprint :GaloisGroup 1 "poly has only one factor\n"

src/NumberTheory/GaloisGrp/Qt.jl

@@ -140,7 +140,7 @@ function _subfields(FF::Generic.FunctionField, f::ZZMPolyRingElem; tStart::Int =
   @vprint :Subfields 2 "now looking for a nice prime...\n"
   p, _ = find_prime(defining_polynomial(K), pStart = 200)
 
-  d = lcm(map(degree, collect(keys(factor(GF(p), g).fac))))
+  d = lcm(map(degree, first.(collect(factor(GF(p), g)))))
 
   @assert evaluate(evaluate(f, [X, T+t]), [gen(Zx), zero(Zx)]) == g
 

src/NumberTheory/NmbThy.jl

@@ -87,7 +87,7 @@ function norm_equation_fac_elem(R::AbsNumFieldOrder, k::ZZRingElem; abs::Bool =
   end
   lp = factor(k)
   S = Tuple{Vector{Tuple{Hecke.ideal_type(R), Int}}, Vector{ZZMatrix}}[]
-  for (p, k) = lp.fac
+  for (p, k) in lp
     P = prime_decomposition(R, p)
     s = solve_non_negative(matrix(ZZ, 1, length(P), [degree(x[1]) for x = P]), matrix(ZZ, 1, 1, [k]))
     push!(S, (P, ZZMatrix[view(s, i:i, 1:ncols(s)) for i=1:nrows(s)]))

src/NumberTheory/QuadFormAndIsom/lattices_with_isometry.jl

@@ -153,7 +153,7 @@ julia> L = root_lattice(:A, 5);
 julia> Lf = integer_lattice_with_isometry(L; neg=true);
 
 julia> factor(characteristic_polynomial(Lf))
-1 * (x + 1)^5
+(x + 1)^5
 ```
 """
 characteristic_polynomial(Lf::ZZLatWithIsom) = characteristic_polynomial(isometry(Lf))
@@ -1810,7 +1810,7 @@ julia> mf = minimal_polynomial(Lf)
 x^5 - 1
 
 julia> factor(mf)
-1 * (x - 1) * (x^4 + x^3 + x^2 + x + 1)
+(x - 1) * (x^4 + x^3 + x^2 + x + 1)
 
 julia> kernel_lattice(Lf, x-1)
 Integer lattice of rank 1 and degree 5