(* ---------------------------------------------------------------------------- * $Id: DIPDEC0.md,v 1.2 1992/02/12 17:34:14 pesch Exp $ * ---------------------------------------------------------------------------- * This file is part of MAS. * ---------------------------------------------------------------------------- * Copyright (c) 1989 - 1992 Universitaet Passau * ---------------------------------------------------------------------------- * $Log: DIPDEC0.md,v $ * Revision 1.2 1992/02/12 17:34:14 pesch * Moved CONST definition to the right place * * Revision 1.1 1992/01/22 15:14:30 kredel * Initial revision * * ---------------------------------------------------------------------------- *) DEFINITION MODULE DIPDEC0; (* DIP Ideal Decomposition 0 System Definition Module. *) FROM MASSTOR IMPORT LIST;CONSTrcsid = "$Id: DIPDEC0.md,v 1.2 1992/02/12 17:34:14 pesch Exp $";CONSTcopyright = "Copyright (c) 1989 - 1992 Universitaet Passau";PROCEDURE DIGFET(P,IL,JL: LIST): LIST; (*DIP G base successful extension test. P is a Groebner base of an ideal of dimension 0 in inverse lexicographical term ordering. i and j are indexes of variables where an field extension is required. t=1 if the extension was successful t=0 else. *)PROCEDURE DIGISM(P: LIST): LIST; (*DIP G base index search for extension multiple univariats. P is a Groebner base of dimension 0 in inverse lexicographical term ordering. I is a list of indexes of variables where an field extension is required or I=() if no field extension is neccessary. *)PROCEDURE DIGISR(P: LIST): LIST; (*DIP G base index search for extension reductas. P is a Groebner base of an ideal of dimension 0 in inverse lexicographical term ordering. I is a list of indexes of variables where an field extension is required or I=() if no field extension is neccessary. *)PROCEDURE DINTFE(T,IL,JL: LIST): LIST; (*DIP normalized tupel field extension. T is a normalized tupel of a zero set with a final Groebner base of dimension 0. i and j determine the variable indexes for the field extension. TP is a list of normalized tupels for the field extension for T. Trial values are used for the transcendent parameter. *)PROCEDURE DINTSR(T: LIST): LIST; (*DIP normalized tupel separation refinement. T is a list of normalized tupels with final Groebner base of dimension 0. TP is a list of normalized tupels for some field extensions for T. *)PROCEDURE DINTSS(T: LIST): LIST; (*DIP normalized tupel strong separation. T is a list of normalized tupels with final Groebner base of dimension 0. TP is a list of normalized tupels for some field extensions for T. *)PROCEDURE DINTZS(N: LIST): LIST; (*DIP nomalized tupels from system zero. N is a zero set. T is the list of nomalized tupels of N. *)PROCEDURE DIRGZS(VB,PB,W: LIST): LIST; (*Distributive rational Groebner base zero set. VB is a rest of a variable list. PB is a Groebner base. W is the total variable list. N is the zero set of P. *)PROCEDURE DIRLPD(A,VP: LIST): LIST; (*DIP rational polynomial ideal primary ideal decomposition. A is a non empty list of distributive rational polynomials representing a Groebner base. The polynomials in A have r variables. L=(l1, ...,ln) with li=(pi,ei,vpi,qi) i=1, ...,n where qi = ideal(pi**e,A) with A contained in qi and e maximal. Ideal(pi) is a prime ideal in at most r+1 variables. VPI is the variable list vor pi. *)PROCEDURE DIRLPW(A,V,L: LIST); (*DIP rational polynomial ideal primary ideal decomposition write. A is a non empty list of distributive rational polynomials representing a Groebner base. The polynomials in a have r variables. L=(l1, ...,ln) with li=(pi,eli,vpi,qi) i=1, ...,n where qi = ideal(pi)**e with A contained in qi and e maximal. Ideal(pi) is a prime ideal in at most r+1 variables. VPI is the variable list for pi. *)PROCEDURE DIRPDA(A,VP: LIST): LIST; (*DIP rational polynomial ideal primary ideal decomposition over Q(alpha). A is a non empty list of distributive rational polynomials representing a Groebner base. The polynomials in A have r variables. L=(l1, ...,ln) with li=(pi,ei,vpi,qi) i=1, ...,n where qi = ideal(pi**e,A) with A contained in qi and e maximal. Ideal(pi) is a prime ideal in at most r+1 variables. VPI is the variable list vor pi. *)PROCEDURE DITFZS(N: LIST): LIST; (*DIP tupel from zero set. N is a zero set. T is a list of tupels of the zero set. *)PROCEDURE DITSPL(T: LIST;VART0,T1: LIST); (*DIP zero set tupel split. T is a list of normalized tupels of a zero set. T0 is a list of normalized tupels of a zero set with a final Groebner base of a ideal of dimension 0. T1=T-T0. *)ENDDIPDEC0. (* -EOF- *)