(* DIP Polynomial Ideal System Definition Module. *)

DEFINITION MODULE DIPIDEAL;

FROM MASSTOR IMPORT LIST;


PROCEDURE DIPLDV(A,V: LIST): LIST; 
(*Distributive polynomial list dependency on variables.
A is a list of distributive polynomials. V is the variable list.
U is the variable list of variables with positive exponents in A. *)


PROCEDURE DIRLCT(A,B: LIST): LIST; 
(*Distributive rational polynomial list ideal containement test.
A and B are lists of distributive rational
polynomials representing groebner basis.
t = 1 if ideal(A) is contained in ideal(B),
t = 0 else. *)


PROCEDURE DIRLIP(PL,A,B: LIST): LIST; 
(*Distributive rational polynomial list ideal product.
A and B are
lists of distributive rational polynomials. C=GBASIS(p,A*B).*)


PROCEDURE DIRLPI(A,P,VP: LIST): LIST; 
(*Distributive rational polynomial list primary ideal.
A and P are non empty lists of distributive rational
polynomials representing groebner basis.
The polynomials in A have r variables.
ideal(P) is a prime ideal in at most r+1 variables.
VP is the variable list for P.
QP=(P,e,VP,Q) where Q = ideal(P**e,A) with A contained in Q
and e maximal. *)


END DIPIDEAL.