helm/software/matita/library/Q/inv.ma

   1 (**************************************************************************)
   2 (*       ___                                                                *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
   8 (*      ||A||       E.Tassi, S.Zacchiroli                                 *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU Lesser General Public License Version 2.1         *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "Q/q.ma".
  16
  17 let rec finv f \def
  18   match f with
  19   [ (pp n) \Rightarrow (nn n)
  20   | (nn n) \Rightarrow (pp n)
  21   | (cons x g) \Rightarrow (cons (Zopp x) (finv g))].
  22
  23 definition rinv : ratio \to ratio \def
  24 \lambda r:ratio.
  25   match r with
  26   [one \Rightarrow one
  27   | (frac f) \Rightarrow frac (finv f)].
  28
  29 definition Qinv : Q → Q ≝
  30  λp.
  31   match p with
  32    [ OQ ⇒ OQ  (* arbitrary value *)
  33    | Qpos r ⇒ Qpos (rinv r)
  34    | Qneg r ⇒ Qneg (rinv r)
  35    ].