Add two missing helper functions (#1574)

- Add lift for fq_default_poly -> ZZPolyRingElem
- Generalize set_coeff! for qadic

Project.toml

@@ -1,6 +1,6 @@
 name = "Nemo"
 uuid = "2edaba10-b0f1-5616-af89-8c11ac63239a"
-version = "0.37.2"
+version = "0.37.3"
 
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"

src/HeckeMoreStuff.jl

@@ -1272,6 +1272,10 @@ function setcoeff!(x::qadic, i::Int, y::padic)
 end
 
 function setcoeff!(x::qadic, i::Int, y::UInt)
+    return setcoeff!(x, i, ZZRingElem(y))
+end
+
+function setcoeff!(x::qadic, i::Int, y::ZZRingElem)
     R = FlintPadicField(prime(parent(x)), parent(x).prec_max)
     Y = R(ZZRingElem(y))
     ccall((:padic_poly_set_coeff_padic, libflint), Nothing,

src/flint/fq_default_poly.jl

@@ -892,3 +892,27 @@ function (R::FqPolyRing)(x::FqPolyRingElem)
   parent(x) != R && error("Unable to coerce to polynomial")
   return x
 end
+
+################################################################################
+#
+#  Lift
+#
+################################################################################
+
+function lift(R::ZZPolyRing, f::FqPolyRingElem)
+  F = coefficient_ring(f)
+  absolute_degree(F) != 1 && error("Must be a prime field.")
+  if _fq_default_ctx_type(F) == _FQ_DEFAULT_NMOD
+    z = R()
+    ccall((:fmpz_poly_set_nmod_poly_unsigned, libflint), Nothing,
+          (Ref{ZZPolyRingElem}, Ref{FqPolyRingElem}), z, f)
+    return z
+  else
+    @assert _fq_default_ctx_type(F) == _FQ_DEFAULT_FMPZ_NMOD
+    z = R()
+    ccall((:fmpz_mod_poly_get_fmpz_poly, libflint), Nothing,
+          (Ref{ZZPolyRingElem}, Ref{FqPolyRingElem}, Ptr{Nothing}),
+          z, f, pointer_from_objref(F) + 2 * sizeof(Cint))
+    return z
+  end
+end

test/flint/fq_default_poly-test.jl

@@ -563,3 +563,28 @@ end
 
    @test !v
 end
+
+@testset "FqPolyRingElem.lift" begin
+   R, x = NGFiniteField(23, 1, "x")
+   S, y = R["y"]
+   ZZy, z = ZZ["z"]
+   f = lift(ZZy, y^2 + 1)
+   @test parent(f) === ZZy
+   @test map_coefficients(R, f, parent = S) == y^2 + 1
+
+   R, x = NGFiniteField(next_prime(ZZ(2)^100), 1, "x")
+   S, y = R["y"]
+   ZZy, z = ZZ["z"]
+   f = lift(ZZy, y^2 + 1)
+   @test parent(f) === ZZy
+   @test map_coefficients(R, f, parent = S) == y^2 + 1
+
+   R, x = NGFiniteField(23, 2, "x")
+   S, y = R["y"]
+   ZZy, z = ZZ["z"]
+   @test_throws ErrorException lift(ZZy, y^2 + 1)
+   R, x = NGFiniteField(next_prime(ZZ(2)^100), 2, "x")
+   S, y = R["y"]
+   ZZy, z = ZZ["z"]
+   @test_throws ErrorException lift(ZZy, y^2 + 1)
+end

test/flint/qadic-test.jl

@@ -306,3 +306,11 @@ end
 
    @test 6 * log(R(2)) == log(R(2)^6)
 end
+
+@testset "qadic.setcoeff!" begin
+  R, _ = QadicField(7, 1, 30)
+  a = 1 + 7 + 2*7^2 + O(R, 7^3)
+  setcoeff!(a, 0, ZZ(2))
+  @test a == 2
+end
+