diff --git a/examples/number_fields.ml b/examples/number_fields.ml
index a418e7c..b2a1698 100644
--- a/examples/number_fields.ml
+++ b/examples/number_fields.ml
@@ -53,3 +53,27 @@ let q, r = Number_field.divrem gaussian_integers a b
 let () =
   Printf.eprintf "%b\n"
     Number_field.(equal a (add gaussian_integers (mul gaussian_integers b q) r))
+
+let _nf2 =
+  Number_field.create (Option.get @@ Polynomial.of_string "x^4-2" |> inj_rat)
+
+let a = Vector.((Number_field.z_basis _nf2).%[2])
+let a2 = Number_field.mul _nf2 a a
+let _ = Printf.eprintf "%s\n" (gentostr a2)
+let a4 = Number_field.mul _nf2 a2 a2
+let _ = Printf.eprintf "a4=%s\n" (gentostr a4)
+
+let mp =
+  nf_to_scalar_or_alg (Obj.magic _nf2)
+    (Number_field.add _nf2 a2
+       (Number_field.elt
+          [|
+            Integer.of_int (-3) |> Integer.inj_rat;
+            Integer.of_int 0 |> Integer.inj_rat;
+            Integer.of_int 0 |> Integer.inj_rat;
+            Integer.of_int 0 |> Integer.inj_rat;
+          |]))
+
+let _ = Printf.eprintf "mp=%s\n" (gentostr mp)
+let _ = Printf.eprintf "mp=%s\n" (gentostr (Number_field.splitting (`F _nf2)))
+let _ = Printf.eprintf "mp=%s\n" (gentostr (polred (Obj.magic mp)))
diff --git a/src/pari.ml b/src/pari.ml
index 9630917..e8d52e4 100644
--- a/src/pari.ml
+++ b/src/pari.ml
@@ -239,6 +239,11 @@ module Polynomial = struct
     register_gc p;
     p
 
+  let of_string s =
+    let g = gp_read_str s in
+    let typ = gentostr (type0 g) in
+    if typ = "\"t_POL\"" then Some g else None
+
   let var t = function Some var -> Signed.Long.(of_int var) | None -> gvar t
   let deriv ?indeterminate t = deriv t (var t indeterminate)
 
@@ -336,6 +341,7 @@ module Number_field = struct
   let discriminant nf = nf_get_disc nf
   let z_basis nf = nf_get_zk nf
   let elt a = Vector.(transpose_row (of_array a))
+  let inj_ring x = x
   let add nf a b = nfadd nf a b
   let mul nf a b = nfmul nf a b
 
diff --git a/src/pari.mli b/src/pari.mli
index b944092..5d946e1 100644
--- a/src/pari.mli
+++ b/src/pari.mli
@@ -303,6 +303,7 @@ module rec Polynomial : sig
       ]}
   *)
 
+  val of_string : string -> 'a t option
   val deriv : ?indeterminate:int -> 'a t -> 'a t
   val derivn : ?indeterminate:int -> 'a t -> int -> 'a t
   val cyclotomic : Signed.long -> Integer.t t
@@ -477,6 +478,7 @@ module Number_field : sig
   val discriminant : t -> Integer.t
   val z_basis : t -> (elt, [ `ROW ]) Vector.t
   val elt : Rational.t array -> elt
+  val inj_ring : elt -> (number_field, ring) typ
   val add : t -> elt -> elt -> elt
   val mul : t -> elt -> elt -> elt
   val equal : elt -> elt -> bool
@@ -16114,6 +16116,7 @@ val gtovecsmall0 :
   ('kind, 'structure) typ -> Signed.long -> ('kind, 'structure) typ
 
 val gtrunc : ('kind, 'structure) typ -> ('kind, 'structure) typ
+val gvar : ('kind, 'structure) typ -> Signed.long
 val gvar2 : ('kind, 'structure) typ -> Signed.long
 
 val hqfeval :