```(* ----------------------------------------------------------------------------
* \$Id: DIPRNIB.md,v 1.1 1995/10/12 14:44:59 pesch Exp \$
* ----------------------------------------------------------------------------
* This file is part of MAS.
* ----------------------------------------------------------------------------
* Copyright (c) 1995 Universitaet Passau
* ----------------------------------------------------------------------------
* \$Log: DIPRNIB.md,v \$
* Revision 1.1  1995/10/12 14:44:59  pesch
* Diplomarbeit Rainer Grosse-Gehling.
* Involutive Bases.
* Slightly edited.
*
* ----------------------------------------------------------------------------
*)

DEFINITION MODULE DIPRNIB;

(* DIP Rational Numbers Polynomial Definition Module in the sense of Janet. *)

(* Import lists and declarations. *)

FROM MASSTOR IMPORT LIST;

CONST rcsid = "\$Id: DIPRNIB.md,v 1.1 1995/10/12 14:44:59 pesch Exp \$";

PROCEDURE DIRPNFJ(P,S: LIST): LIST;
(*Distributive rational polynomial normal form in the sense of Janet.
P is a list of non zero polynomials in distributive
representation in r variables. S is a distributive
polynomial. The result R is a polynomial such that S is reducible to R
modulo P in the sense of Janet and R is in normalform with respect to P. *)

PROCEDURE DIRLISJ(P: LIST): LIST;
(*Distributive rational polynomial list irreducible set.
P is a list of distributive polynomials,
The result is a set of polynomials, such that each polynomial p is in
Janet-normalform modulo P-(p) *)

PROCEDURE DIRPCOM(F: LIST): LIST;
(* Distributive rational polynom complete system.
Subalgorithm for computing Invbase.
Input: Distributive polynomial list F.
Output: G: complete system, such that Ideal(G) = Ideal(F). *)

PROCEDURE DIRPIB2(F: LIST): LIST;
(* Distributive rational polynom involutive basis.
Mainalgorithm for computing Invbase.
Input: Distributive polynomial list F.
Output: G: involutive system, such that Ideal(G) = Ideal(F). *)

PROCEDURE DIRPIB(F: LIST): LIST;
(* Second Algorithm for computing the involutive Base for a given F.
Input: Distributiv Rational Polynomial List F.
Output: Equivalent involutive system G.*)

END DIPRNIB.

(* -EOF- *)
```