cache Galois results (in AbsSimpleField) (#4056)

src/NumberTheory/GaloisGrp/GaloisGrp.jl

@@ -1952,10 +1952,18 @@ function galois_group(K::AbsSimpleNumField, extra::Int = 5;
   pStart::Int = 2*degree(K), 
   prime::Int = 0, 
   do_shape::Bool = true,
+  redo::Bool = false,
   algorithm::Symbol=:pAdic, 
   field::Union{Nothing, AbsSimpleNumField} = nothing)
 
   @assert algorithm in [:pAdic, :Complex, :Symbolic]
+
+  X = get_attribute(K, :GaloisCtx)
+  if X !== nothing && !redo && algorithm == :pAdic
+    if prime == 0 || X.prime == prime
+      return X.G, X
+    end
+  end
 
   if do_shape
     p, ct = find_prime(K.pol, pStart)
@@ -2007,6 +2015,9 @@ function galois_group(K::AbsSimpleNumField, extra::Int = 5;
         G = symmetric_group(degree(K))
       end
       GC.G = G
+      if algorithm == :pAdic
+        set_attribute!(K, :GaloisCtx => GC)
+      end
       return G, GC
     end
 
@@ -2028,6 +2039,9 @@ function galois_group(K::AbsSimpleNumField, extra::Int = 5;
     #   some subgroups of the wreath products
     if degree(K) == 1
       GC.G = G
+      if algorithm == :pAdic 
+        set_attribute!(K, :GaloisCtx => GC)
+      end
       return G, GC
     end
 
@@ -2040,6 +2054,9 @@ function galois_group(K::AbsSimpleNumField, extra::Int = 5;
 
     # TODO: here we know if we are primitive; can we detect 2-transitive (inside starting_group)?
 
+    if algorithm == :pAdic
+      set_attribute!(K, :GaloisCtx => GC)
+    end
     return descent(GC, G, F, si, extra = extra)
   end
 end
@@ -2053,7 +2070,7 @@ supergroup of the Galois group, operating on the roots in `GC`, the context obje
 The groups are filtered by `F` and the result needs to contain the permutation `si`.
 For verbose output, the groups are printed through `grp_id`.
 """
-function descent(GC::GaloisCtx, G::PermGroup, F::GroupFilter, si::PermGroupElem; grp_id = transitive_group_identification, extra::Int = 5)
+function descent(GC::GaloisCtx, G::PermGroup, F::GroupFilter, si::PermGroupElem; grp_id = x -> degree(x) >= 32 ? (degree(x), -1) : transitive_group_identification(x), extra::Int = 5)
   @vprint :GaloisGroup 2 "Have starting group with id $(grp_id(G))\n"
 
   n = degree(GC.f)

test/NumberTheory/galthy.jl

@@ -30,6 +30,11 @@
   Gs, Cs = galois_group(K, algorithm = :Symbolic)
   @test is_isomorphic(G, Gc)
   @test is_isomorphic(G, Gs)
+  _G, _C = galois_group(K)
+  # test caching
+  @test C === _C 
+  _G, _C = galois_group(K; redo = true)
+  @test C !== _C
 
   # from the book
   K, a = number_field(x^9 - 3*x^8 + x^6 + 15*x^5 - 13*x^4 -