Add implicit canonical promotions for finite field arithmetic (#1491)

Nemocas · Jun 11, 2023 · 529c330 · 529c330
1 parent 95c1424
commit 529c330
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Showing 3 changed files with 118 additions and 29 deletions.
diff --git a/src/flint/fq_default.jl b/src/flint/fq_default.jl
@@ -387,27 +387,33 @@ end
 ###############################################################################
 
 function +(x::FqFieldElem, y::FqFieldElem)
-   check_parent(x, y)
-   z = parent(y)()
-   ccall((:fq_default_add, libflint), Nothing,
-        (Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqField}), z, x, y, y.parent)
-   return z
+   if parent(x) === parent(y)
+     z = parent(y)()
+     ccall((:fq_default_add, libflint), Nothing,
+          (Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqField}), z, x, y, y.parent)
+     return z
+   end
+   return +(_promote(x, y)...)
 end
 
 function -(x::FqFieldElem, y::FqFieldElem)
-   check_parent(x, y)
-   z = parent(y)()
-   ccall((:fq_default_sub, libflint), Nothing,
-        (Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqField}), z, x, y, y.parent)
-   return z
+   if parent(x) === parent(y)
+     z = parent(y)()
+     ccall((:fq_default_sub, libflint), Nothing,
+          (Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqField}), z, x, y, y.parent)
+     return z
+   end
+   return -(_promote(x, y)...)
 end
 
 function *(x::FqFieldElem, y::FqFieldElem)
-   check_parent(x, y)
-   z = parent(y)()
-   ccall((:fq_default_mul, libflint), Nothing,
-        (Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqField}), z, x, y, y.parent)
-   return z
+   if parent(x) === parent(y)
+     z = parent(y)()
+     ccall((:fq_default_mul, libflint), Nothing,
+          (Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqField}), z, x, y, y.parent)
+     return z
+   end
+   return *(_promote(x, y)...)
 end
 
 ###############################################################################
@@ -515,22 +521,27 @@ end
 ###############################################################################
 
 function divexact(x::FqFieldElem, y::FqFieldElem; check::Bool=true)
-   check_parent(x, y)
-   iszero(y) && throw(DivideError())
-   z = parent(y)()
-   ccall((:fq_default_div, libflint), Nothing,
-        (Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqField}), z, x, y, y.parent)
-   return z
+   if parent(x) === parent(y)
+     iszero(y) && throw(DivideError())
+     z = parent(y)()
+     ccall((:fq_default_div, libflint), Nothing,
+          (Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqFieldElem}, Ref{FqField}), z, x, y, y.parent)
+     return z
+   end
+   return divexact(_promote(x, y)...)
 end
 
 function divides(a::FqFieldElem, b::FqFieldElem)
-   if iszero(a)
-      return true, zero(parent(a))
-   end
-   if iszero(b)
-      return false, zero(parent(a))
+   if parent(a) === parent(b)
+     if iszero(a)
+        return true, zero(parent(a))
+     end
+     if iszero(b)
+        return false, zero(parent(a))
+     end
+     return true, divexact(a, b)
    end
-   return true, divexact(a, b)
+   return divides(_promote(a, b)...)
 end
 
 ###############################################################################

diff --git a/src/flint/fq_default_extended.jl b/src/flint/fq_default_extended.jl
@@ -709,11 +709,11 @@ function (a::FqField)(b::FqFieldElem)
   end
 
   if k === base_field(a)
-    return (a.image_basefield)(b)
+    return (a.image_basefield)(b)::FqFieldElem
   end
 
   # To make it work in towers
-  return a(base_field(a)(b))
+  return a(base_field(a)(b))::FqFieldElem
 end
 
 ################################################################################
@@ -826,3 +826,47 @@ function lift(R::FqPolyRing, a::FqFieldElem)
     return _lift_standard(R, a)
   end
 end
+
+################################################################################
+#
+#  Promotion
+#
+################################################################################
+
+function _try_promote(K::FqField, a::FqFieldElem)
+  L = parent(a)
+  if degree(K) == 1 && K !== L
+    return false, a
+  end
+
+  if K === L
+    return true, a
+  end
+
+  fl, b = _try_promote(base_field(K), a)
+  if fl
+    return fl, K(a)::FqFieldElem
+  else
+    return false, a
+  end
+end
+
+function _try_promote(a::FqFieldElem, b::FqFieldElem)
+  fl, c = _try_promote(parent(a), b)
+  if fl
+    return true, a, c
+  end
+  fl, c = _try_promote(parent(b), a)
+  if fl
+    return true, c, b
+  end
+  return false, a, b
+end
+
+function _promote(a::FqFieldElem, b::FqFieldElem)
+  fl, aa, bb = _try_promote(a, b)
+  if fl
+    return aa, bb
+  end
+  error("Cannot promote to common finite field")
+end
diff --git a/test/flint/fq_default_extended-test.jl b/test/flint/fq_default_extended-test.jl
@@ -254,3 +254,37 @@ end
   FF, = Nemo._FiniteField(x)
   @test iszero(FF(x))
 end
+
+@testset "Implicit promotions" begin
+  F = Nemo._GF(2, 2)
+  FF = Nemo._GF(2, 3)
+  fl, = Nemo._try_promote(F, one(FF))
+  @test !fl
+  fl, = Nemo._try_promote(FF, one(F))
+  @test !fl
+  fl, = Nemo._try_promote(one(F), one(FF))
+  @test !fl
+
+  Fx, x = F["x"]
+  f = x^2 + gen(F)*x + 1
+  FF, = Nemo._FiniteField(f)
+  for i in 1:10
+    a, b = rand(F), rand(FF)
+    @test a * b == FF(a) * b
+    @test b * a == FF(a) * b
+    @test a + b == FF(a) + b
+    @test b + a == FF(a) + b
+    @test a - b == FF(a) - b
+    @test b - a == -(FF(a) - b)
+    @test divides(a, b) == divides(FF(a), b)
+    @test divides(b, a) == divides(b, FF(a))
+    if !iszero(a)
+      @test divexact(b, a) == divexact(b, FF(a))
+    end
+    @test divexact(b, one(F)) == divexact(b, one(FF))
+    if !iszero(b)
+      @test divexact(a, b) == divexact(FF(a), b)
+    end
+    @test divexact(a, one(FF)) == divexact(FF(a), one(FF))
+  end
+end