More fixes for complex embedding (#1298)

Project.toml

@@ -1,6 +1,6 @@
 name = "Hecke"
 uuid = "3e1990a7-5d81-5526-99ce-9ba3ff248f21"
-version = "0.22.7"
+version = "0.22.8"
 
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"

src/NumField/ComplexEmbeddings/NfAbs.jl

@@ -257,25 +257,26 @@ function _find_nearest_complex_embedding(K::AnticNumberField, x)
   r = complex_embeddings(K)
   diffs = [e(gen(K)) - x for e in r]
   t = [abs(z) for z in diffs]
-  for i in 1:length(t)
-    for j in (i + 1):length(t)
-      if overlaps(t[i], t[j]) 
-        possible = [ (Float64(real(e.r)), Float64(imag(e.r))) for e in r]
-        s = IOBuffer()
-        for i in 1:length(possible)
-          @printf s "%.2f + i * %.2f" possible[i][1] possible[i][2]
-          if i < length(possible)
-            print(s, ", ")
-          end
+  _, i = findmin(t)
+  for j in 1:length(t)
+    if j == i
+      continue
+    end
+    if overlaps(t[i], t[j]) 
+      possible = [ (Float64(real(e.r)), Float64(imag(e.r))) for e in r]
+      s = IOBuffer()
+      for i in 1:length(possible)
+        @printf s "%.2f + i * %.2f" possible[i][1] possible[i][2]
+        if i < length(possible)
+          print(s, ", ")
         end
-        ss = String(take!(s))
-        error("""Given approximation not close enough to a root. Possible roots are:
-                 $ss
-              """)
       end
+      ss = String(take!(s))
+      error("""Given approximation not close enough to a root. Possible roots are:
+            $ss
+            """)
     end
   end
-  _, i = findmin(t)
   return r[i]
 end
 

src/NumField/ComplexEmbeddings/NfAbsNS.jl

@@ -192,43 +192,44 @@ end
 
 function _find_nearest_complex_embedding(K::NfAbsNS, x)
   r = complex_embeddings(K)
-  t = []
+  t = Vector{arb}[]
   for e in r
     embedded_gens = map(e, gens(K))
     gen_diffs = map(abs, embedded_gens - x)
     push!(t, gen_diffs)
   end
 
+  _, i = findmin(map(y -> sum(y), t))
+
   check_overlaps = y -> isempty(filter(x -> !overlaps(x...), y))
-  for i in 1:length(t)
-    for j in (i + 1):length(t)
-      if check_overlaps([(t[i][s], t[j][s]) for s in 1:length(gens(K))])
-        embedded_roots = [e.roots for e in r]
-        roots_to_tuple = x -> (Float64(real(x)), Float64(imag(x)))
-        possible = [map(roots_to_tuple, roots) for roots in embedded_roots]
-        s = IOBuffer()
-        for k in 1:length(possible)
-          for w in 1:length(possible[k])
-            @printf s "%.2f + i * %.2f" possible[k][w][1] possible[k][w][2]
-            if w < length(possible[k])
+  for j in 1:length(t)
+    if j == i
+      continue
+    end
+    if check_overlaps([(t[i][s], t[j][s]) for s in 1:length(gens(K))])
+      embedded_roots = [e.roots for e in r]
+      roots_to_tuple = x -> (Float64(real(x)), Float64(imag(x)))
+      possible = [map(roots_to_tuple, roots) for roots in embedded_roots]
+      s = IOBuffer()
+      for k in 1:length(possible)
+        for w in 1:length(possible[k])
+          @printf s "%.2f + i * %.2f" possible[k][w][1] possible[k][w][2]
+          if w < length(possible[k])
             print(s, ", ")
           end
 
-          end
-          if k < length(possible)
-            print(s, "\n")
-          end
         end
-        ss = String(take!(s))
-        error("""Given approximation not close enough to a vector of roots. \n 
-              Possible vector of roots are:
-              $ss
-              """)
+        if k < length(possible)
+          print(s, "\n")
+        end
       end
+      ss = String(take!(s))
+      error("""Given approximation not close enough to a vector of roots. \n 
+            Possible vector of roots are:
+            $ss
+            """)
     end
   end
-  _, i = findmin(map(y -> +(y...), t))
-
   return r[i]
 end
 

test/NumField/ComplexEmbeddings/NfAbs.jl

@@ -84,4 +84,11 @@
   # This should be fast
   K, a = cyclotomic_field(19^3, cached = false)
   @test length(@inferred complex_embeddings(K)) == degree(K)
+
+  # Some issue
+  Qx, x = QQ["x"]
+  K, a = number_field(x^4 - 8)
+  e = complex_embedding(K, 1.68)
+  @test number_field(e) === K
+  @test is_real(e(a)) && real(e(a)) > 0
 end

test/NumField/ComplexEmbeddings/NfAbsNS.jl

@@ -83,4 +83,11 @@
   @test Set(complex_embeddings(K)) == Set([r1, r2, r3, r4])
   @test_throws ErrorException Hecke.complex_embedding(K, [0.0, 0.0])
 
+  # Some issue
+
+  Qx, x = QQ["x"]
+  K, (a,) = number_field([x^4 - 8])
+  e = complex_embedding(K, [1.68])
+  @test number_field(e) === K
+  @test is_real(e(a)) && real(e(a)) > 0
 end