(* MAS Non-commutative Groebner Bases Definition Module. *)

DEFINITION MODULE MASNCGB;


FROM MASSTOR IMPORT LIST;


PROCEDURE DINLNF(T,P,S: LIST): LIST; 
(*Distributive non-commutative polynomial left normal form.
P is a list of non zero polynomials in distributive rational
representation in r variables. S is a distributive rational
polynomial. R is a polynomial such that S is left reducible to R
modulo P and R is in normalform with respect to P.
T is a table of distributive polynomials specifying the
non-commutative relations. *)


PROCEDURE DINLIS(T,P: LIST): LIST; 
(*Distributive non-commutative polynomial list left irreducible set.
P is a list of distributive rational polynomials, PP is the
result of left reducing each p element of P modulo P-(p)
until no further reductions are possible.
T is a table of distributive polynomials specifying the
non-commutative relations. *)


PROCEDURE DINLSP(T,A,B: LIST): LIST; 
(*Distributive non-commutative polynomial left S-polynomial.
A and B are rational polynomials in distributive representation.
C is the left S-polynomial of A and B.
T is a table of distributive polynomials specifying the
non-commutative relations. *)


PROCEDURE DINLGB(T,P,TF: LIST): LIST; 
(*Distributive non-commutative polynomials left groebner basis.
P is a list of rational polynomials in distributive representation
in r variables. PP is the left groebner basis of P. t is the
trace flag.
T is a table of distributive polynomials specifying the
non-commutative relations. *)


PROCEDURE DINLGM(T,P: LIST): LIST; 
(*Distributive non-commutative minimal ordered left groebner basis.
P is a list of non zero rational polynomials in distributive
representation in r variables, P is a left groebner basis.
PP is the minimal normed and ordered left groebner basis.
T is a table of distributive polynomials specifying the
non-commutative relations. *)


PROCEDURE DIN1GB(T,P,TF: LIST): LIST; 
(*Distributive non-commutative polynomials groebner basis.
P is a list of rational polynomials in distributive representation
in r variables. PP is the groebner basis of P. t is the
trace flag.
T is a table of distributive polynomials specifying the
non-commutative relations. *)


PROCEDURE DINCGB(T,P,TF: LIST): LIST; 
(*Distributive non-commutative polynomials groebner basis.
P is a list of rational polynomials in distributive representation
in r variables. PP is the groebner basis of P. t is the
trace flag.
T is a table of distributive polynomials specifying the
non-commutative relations. *)


END MASNCGB.