Add some finite ring/field coercion (#729)

Matches functions currently in Oscar

src/number/n_Zp.jl

@@ -295,6 +295,27 @@ promote_rule(C::Type{n_Zp}, ::Type{n_Z}) = n_Zp
 # take ownership of the pointer - not for general users
 (R::N_ZpField)(n::libSingular.number_ptr) = n_Zp(R, n)
 
+function (F::N_ZpField)(a::Nemo.fpFieldElem)
+ characteristic(F) == characteristic(parent(a)) || error("characteristic does not match")
+ return F(lift(a))
+end
+
+function (F::N_ZpField)(a::Nemo.zzModRingElem)
+ characteristic(F) == characteristic(parent(a)) || error("characteristic does not match")
+ return F(lift(a))
+end
+
+function (F::Nemo.fpField)(a::n_Zp)
+ characteristic(F) == characteristic(parent(a)) || error("characteristic does not match")
+ return F(Int(a))
+end
+
+function (F::Nemo.zzModRing)(a::n_Zp)
+ characteristic(F) == characteristic(parent(a)) || error("characteristic does not match")
+ return F(Int(a))
+end
+
+
 ###############################################################################
 #
 # Fp constructor

test/libsingular/nemo-test.jl

@@ -367,6 +367,30 @@ end
  @test string(p) == "0"
  @test length(p) == 0
  @test is_zero(p)
+
+ R = residue_ring(Nemo.ZZ, 7)
+ F = Fp(7)
+ for i in -10:10
+ @test R(one(F)*i) == one(R)*i
+ @test F(one(R)*i) == one(F)*i
+ end
+
+ S = Nemo.GF(5)
+ @test_throws ErrorException S(one(F))
+ @test_throws ErrorException F(one(S))
+end
+
+@testset "Nemo.fpFieldElem" begin
+ R = Nemo.GF(7)
+ F = Fp(7)
+ for i in -10:10
+ @test R(one(F)*i) == one(R)*i
+ @test F(one(R)*i) == one(F)*i
+ end
+
+ S = Nemo.GF(5)
+ @test_throws ErrorException S(one(F))
+ @test_throws ErrorException F(one(S))
 end
 
 @testset "Nemo.ZZModRingElem" begin