Mult dep2 (#1673)

* add test

* include

* move into 'proper' position

* fix index problem, returned too many elementary divisors

Try
  elementary_divisors(sparse_matrix(identity_matrix(ZZ, 2)))
without will give 3 EDs, the last one being 0

* update MultDep - it seems to be working "fine" now.

Needs further work on the Ge stuff and some of the internal
interface are bad.
Example
  k, a = wildanger_field(5,13);
  zk = lll(maximal_order(k))
  class_group(zk)
  h = zk.__attrs[:ClassGrpCtx]
  r = vcat(h.R_gen, h.R_rel);
  r = [x for x = r if isa(x, AbsSimpleNumFieldElem)]

  q = Main.MultDep.syzygies(r)

Then the rows of q are the relations

* reduce exponents

* I hate lin. alg.

* deal with 0 properly in lift

* add mult. group

* add stub to multiplicative group

src/Hecke.jl

@@ -579,6 +579,7 @@ Base.showerror(io::IO, ::NotImplemented) =
 # - The Hecke.MPolyFactor submodule wants to extend it, but is loaded earlier
 # - Introduce the function here, to make everyone happy
 function is_absolutely_irreducible end
+function multiplicative_group end
 
 ################################################################################
 #

src/LocalField/Conjugates.jl

@@ -269,6 +269,9 @@ end
 function conjugates_log(a::FacElem{AbsSimpleNumFieldElem, AbsSimpleNumField}, C::qAdicConj, n::Int = 10; all::Bool = false, flat::Bool = true)
   first = true
   local res::Vector{QadicFieldElem}
+  if length(a.fac) == 0
+    res = conjugates_log(one(base_ring(parent(a))), C, n, flat = false, all = false)
+  end
   for (k, v) = a.fac
     try
       y = conjugates_log(k, C, n, flat = false, all = false)

src/Map/NfOrd.jl

@@ -1087,6 +1087,7 @@ function image(mF::NfToGFMor_easy, a::FacElem{AbsSimpleNumFieldElem, AbsSimpleNu
   p = mF.defining_pol
   q = one(Fq)
   t = mF.t
+  quo = gcd(quo, order(Fq)-1)
   for (k, v) = a.fac
     vv = v
     if quo != 0