Update src/NumField/Subfields.jl

Author: thofma

src/NumField/Subfields.jl

@@ -152,7 +152,7 @@ end
 # In this case, we can use a block system to find if an element is
 # primitive (and find a primitive element) Input does not need to be
 # a basis, generators are sufficient
-function _subfield_primitive_element_from_basis(K::AbsSimpleNumField, as::Vector{AbsSimpleNumFieldElem})
+function _subfield_primitive_element_from_basis(K::AbsSimpleNumField, as::Vector{AbsSimpleNumFieldElem}, lincomb = false)
   if isempty(as) || degree(K) == 1
     return gen(K)
   end
@@ -183,8 +183,18 @@ function _subfield_primitive_element_from_basis(K::AbsSimpleNumField, as::Vector
     b = Vector{Int}[intersect(x, y) for x in b for y in _b]
     b = Vector{Int}[x for x in b if length(x) > 0]
   end
-  @vprintln :Subfields 1 "Have block systems, degree of subfield is $(length(b))\n"
+  @vprintln :Subfields 1 "Have block systems, degree of subfield is $(length(b))"
 
+  # b is the block of the subfield (with respect to the embeddings in C)
+
+  if lincomb
+    return _subfield_primitive_element_from_basis_lincomb(K, b, all_b, C, as)
+  else
+    return _subfield_primitive_element_from_block(K, C, b)
+  end
+end
+
+function _subfield_primitive_element_from_basis_lincomb(K::AbsSimpleNumField, b, all_b, C, as::Vector{AbsSimpleNumFieldElem})
   indices = findall(x->length(x) == length(b), all_b)
 
   @vprintln :Subfields 1 "Found $(length(indices)) primitive elements in the basis"
@@ -214,7 +224,7 @@ function _subfield_primitive_element_from_basis(K::AbsSimpleNumField, as::Vector
     cur_b = Vector{Int}[intersect(x, y) for x in cur_b for y in all_b[i]]
     cur_b = Vector{Int}[x for x in cur_b if length(x) > 0]
     j = 1
-    while block_system(pe + j*as[i], C) != c
+    while block_system(pe + j*as[i], C) != cur_b
       j += 1
       if j > 10
         error("dnw")
@@ -229,7 +239,7 @@ function _subfield_primitive_element_from_basis(K::AbsSimpleNumField, as::Vector
   error("should be hard...")
 end
 
-function _subfield_from_block(K::AbsSimpleNumField, C#=::qAdicConj=#, b::Vector{Vector{Int}})
+function _subfield_primitive_element_from_block(K::AbsSimpleNumField, C#=::qAdicConj=#, b::Vector{Vector{Int}})
   @assert C isa qAdicConj
   # Klueners:
   # - try sum of conj. in block

test/NfAbs/Subfields.jl

@@ -453,3 +453,12 @@ let
   LL, b = number_field(x^2 + 1, :b)
   @test_throws ArgumentError Hecke.subfield(L, [b])
 end
+
+let
+  Qx, x = QQ[:x]
+  K, _ = number_field(x^8 - x^4 + 1, :a)
+  b = Hecke._subfield_primitive_element_from_basis(K, [sqrt(K(2)), sqrt(K(3))], true)
+  @test degree(minpoly(b)) == 2
+  b = Hecke._subfield_primitive_element_from_basis(K, [sqrt(K(2)), sqrt(K(3))], false)
+  @test degree(minpoly(b)) == 2
+end