fix typing issue

examples/kzg.ml

@@ -87,9 +87,7 @@ module KZG :
   let commit c p =
     assert (Polynomial.degree p < Vector.length c.srs_g1);
     let f x p cm =
-      let x = Finite_field. (inj_field x) in
-      let x: (finite_field, ring) typ Polynomial.t = Finite_field.(residue_class x) in
-      let n = Polynomial.(x.%[0]) in
+      let n = Option.get Finite_field.(inj_prime_field (inj_field x)) in
       Elliptic_curve.(add c.curve cm (mul c.curve ~n ~p))
     in
     let acc = Elliptic_curve.zero c.curve in
@@ -113,16 +111,12 @@ module KZG :
       Elliptic_curve.(
         sub c.curve
           Vector.(c.srs_g2.%[2])
-          (mul c.curve
-             ~n:Polynomial.((Finite_field.residue_class x).%[0])
-             ~p:c.g2))
+          (mul c.curve ~n:(Option.get Finite_field.(inj_prime_field x)) ~p:c.g2))
     in
     let numerator =
       Elliptic_curve.(
         sub c.curve cm
-          (mul c.curve
-             ~n:Polynomial.((Finite_field.residue_class y).%[0])
-             ~p:c.g1))
+          (mul c.curve ~n:(Option.get Finite_field.(inj_prime_field y)) ~p:c.g1))
     in
     let lhs =
       Elliptic_curve.weil_pairing c.curve ~l:c.curve_subgroup_order pi
@@ -139,10 +133,9 @@ let c =
   let g = Finite_field.generator ~order:ToyCurve.r in
   let secret = Finite_field.random g in
   let coeff p i =
+    let n = Finite_field.pow secret (Integer.of_int i) in
     Elliptic_curve.mul ToyCurve.curve
-      ~n:
-        Polynomial.(
-          Finite_field.(residue_class (pow secret (Integer.of_int i))).%[0])
+      ~n:(Option.get Finite_field.(inj_prime_field n))
       ~p
   in
   let srs_g1 = Vector.init 100 ~f:(coeff ToyCurve.g1) in
@@ -207,4 +200,3 @@ let rhs =
     r
 
 let () = assert (Finite_field.(equal lhs rhs))
-

examples/number_fields.ml

@@ -23,15 +23,21 @@ let () = Printf.eprintf "%b\n" (Polynomial.is_irreducible q)
 let qmin : Integer.t Polynomial.t = Polynomial.minimal q
 let () = Printf.eprintf "%s\n" (Polynomial.to_string qmin)
 
+let inj_rat =
+  Polynomial.inj_base_ring ~inj:(fun x ->
+      x |> Integer.inj_rat |> Rational.inj_ring)
+
 let () =
-  Printf.eprintf "%b\n" Number_field.(are_isomorphic (create q) (create qmin))
+  Printf.eprintf "%b\n"
+    Number_field.(are_isomorphic (create (inj_rat q)) (create (inj_rat qmin)))
 
 (* Gaussian integers: the ring Z[i] (here we work in the field Q(i)) *)
 let gaussian_integers =
   (* Q(i) = Q[X]/(X^2+1) *)
   Number_field.create
     (Polynomial.create
-       [| Integer.of_int 1; Integer.of_int 0; Integer.of_int 1 |])
+       [| Integer.of_int 1; Integer.of_int 0; Integer.of_int 1 |]
+    |> inj_rat)
 
 (* Euclidean division of 6 + 8i by 1 + 5i. *)
 let a =

src/pari.ml

@@ -4,20 +4,19 @@ type ('kind, 'structure) typ = gen
 
 let t = gen
 
-type group =  Group
-type ring =  Ring
-type field=  Field
-type unique_factorization_domain=  Unique_factorization_domain
-type complex=  Complex
-type real=  Real
-type rational=  Rational
-type integer=  Integer
-type polynomial=  Polynomial
-type integer_mod=  Integer_mod
-type finite_field=  Finite_field
-type number_field=  Number_field
-type elliptic_curve=  Elliptic_curve
-
+type group = Group
+type ring = Ring
+type field = Field
+type unique_factorization_domain = Unique_factorization_domain
+type complex = Complex
+type real = Real
+type rational = Rational
+type integer = Integer
+type 'a polynomial = Polynomial of 'a
+type integer_mod = Integer_mod
+type finite_field = Finite_field
+type number_field = Number_field
+type elliptic_curve = Elliptic_curve
 
 let register_gc v =
   Gc.finalise_last (fun () -> pari_free Ctypes.(coerce gen (ptr void) v)) v
@@ -274,6 +273,8 @@ module Polynomial = struct
       acc := f p.%[i] Vector.(v.%[i + 1]) !acc
     done;
     !acc
+
+  let inj_base_ring ~inj:_ p = p
 end
 
 module Integer_mod = struct
@@ -384,6 +385,16 @@ module Finite_field = struct
 
   let prime_field_element x ~p = ff_z_mul (ff_1 (generator ~order:p)) x
 
+  let inj_prime_field x =
+    let p = ff_to_fpxq_i x in
+
+    if
+      glength p = Signed.Long.one
+      || Polynomial.degree p = 0
+      || Polynomial.degree p = 1
+    then Some Polynomial.(p.%[0])
+    else None
+
   let finite_field_element coeffs a =
     let len = Array.length coeffs in
     fst

src/pari.mli

@@ -97,17 +97,17 @@ type bb_field
 type bb_algebra
 type bb_ring
 type ring = private Ring
-type field= private Field
-type unique_factorization_domain= private Unique_factorization_domain
-type complex= private Complex
-type real= private Real
-type rational= private Rational
-type integer= private Integer
-type polynomial= private Polynomial
-type integer_mod= private Integer_mod
-type finite_field= private Finite_field
-type number_field= private Number_field
-type elliptic_curve= private Elliptic_curve
+type field = private Field
+type unique_factorization_domain = private Unique_factorization_domain
+type complex = private Complex
+type real = private Real
+type rational = private Rational
+type integer = private Integer
+type 'a polynomial = private Polynomial of 'a
+type integer_mod = private Integer_mod
+type finite_field = private Finite_field
+type number_field = private Number_field
+type elliptic_curve = private Elliptic_curve
 
 val factor :
   ('kind, unique_factorization_domain) typ ->
@@ -267,7 +267,7 @@ module Matrix : sig
 end
 
 module rec Polynomial : sig
-  type 'a t = (polynomial, ring) typ constraint 'a = ('b, ring) typ
+  type 'a t = ('a polynomial, ring) typ constraint 'a = ('b, ring) typ
 
   val to_string : 'a t -> string
   val mul : 'a t -> 'a t -> 'a t
@@ -351,6 +351,8 @@ module rec Polynomial : sig
     'a t ->
     ('b, _) Vector.t ->
     ('c, 'd) typ
+
+  val inj_base_ring : inj:('a -> 'b) -> 'a t -> 'b t
 end
 
 and Fp : sig
@@ -367,6 +369,7 @@ and Finite_field : sig
   val inj_field : (finite_field, ring) typ -> t
   val generator : order:Integer.t -> t
   val prime_field_element : Integer.t -> p:Integer.t -> t
+  val inj_prime_field : t -> Fp.t option
   val finite_field_element : Integer.t array -> t -> t
 
   val create : p:int -> degree:int -> (finite_field, ring) typ Polynomial.t