reduce-historical/r38/packages/xideal/xideal.red

module xideal;
%
%                               XIDEAL V2.4
%
%
% Authors: 	David Hartley		                           
% 		GMD - German National Research Center 
% 	              for Information Technology 
% 		D-53754 St Augustin 
% 		Germany             
% 
% 		email: 	David.Hartley@gmd.de
%
%
%               Philip A Tuckey                                  
% 		Laboratoire de Physique Mol\'eculaire, 
% 	        Universit\'e de Franche-Comt\'e,      
% 		25030 Besan\c{}con,                     
% 		France               
% 
% 		email: 	pat@rs1.univ-fcomte.fr
%
%
% Description:	Tools for calculations with ideals of polynomials in
%               exterior algebra. Uses Groebner basis algorithms
%               described in D Hartley and P A Tuckey, "A direct
%               characterisation of Groebner bases in Clifford and
%               Grassmann algebras", Preprint MPI-Ph/93-96 1993, and J
%               Apel "A relationship between Groebner bases of ideals
%               and vector modules of G-algebras", Contemp
%               Math 131(1992)195.
% 
% Requires:	REDUCE 3.6 patched to 25 Apr 96 or later
%
% Created:   	5/8/92	V0	as ideal.red
%
% Modified:	4/3/94	V1	Renamed xideal.red
%				Compiles independently
%                               Converted right reduction and spolys to
%                               left
%				Added graded lexicographical ordering
%				Enabled non-graded ideals
%				Fixed trivial ideal bug
%				Removed subform
%				Renamed xtrace -> xstats
%		1/12/94	V2	Enable 2-sided ideals
%				Enable p-forms with p >= 0
%		8/12/95 	Added subs2 checking in reduction
%		19/1/96	V2.2	Added subs2 checking in xrepartit
%				Added resimp before subs2
%				Fixed rtypes of operators
%		16/4/96	V2.3	Added exvars and excoeffs
%
%
% Algebraic mode entry points
%
% xorder k;
%  establishes the term order, where k is one of lex, gradlex (graded by
%  number of factors in term) or deglex (graded by exterior degree of
%  term.)
%
% xvars U,V,W,...;
%  declares which degree 0 kernels are to be regarded as polynomial
%  variables (rest are coefficient parameters). U,V,W can be variables
%  or lists of variables. xvars nil, restores the default, in which all
%  declared 0-forms are polynomial variables.
%
% xideal(S) xideal(S,V,r) or xideal(S,r) 
%  calculates an exterior Groebner basis for the list of generator S,
%  with optional 0-form variables V, optionally up to degree r. 
% 
% xmodideal(F,S) or F xmodideal S
%  reduces F with respect to an exterior Groebner basis for the list of
%  generators S. F may be either a single exterior form,
%  or a list of forms.
% 
% xmod(F,S) or F xmod S
%  reduces F with respect to the set of exterior polynomials S, which is
%  not necessarily a Groebner basis. F may be either a single
%  exterior form, or a list of forms. This routine can be used in
%  conjunction with xideal to produce the same effect as xmodideal:
%         F xmodideal S = F xmod xideal(S,exdegree F). 
% 
% xauto(S)
%  autoreduces the polynomials in S.
%
% exvars(F)
%  returns polynomials variables (as defined by xvars) from F
%
% excoeffs(F)
%  returns polynomials coefficients (as defined by xvars) from F
%
% Switches
% 
% xfullreduce   - Allows reduced Groebner bases to be calculated
%                    (default ON)
% trxideal	- Trace spoly and wedge poly production (default OFF)
% trxmod	- Trace reduction to normal form (default OFF)
%
% ======================================================================

% Need EXCALC loaded first.

load_package 'excalc;
 
create!-package('(
 
     xideal	% Header module
     xgroeb	% GB calculation
     xreduct	% Normal form algorithms
     xcrit	% Critical pairs, critical values
     xpowers	% Powers, including div relation and lcm.
     xstorage	% Storage and retrieval of critical pairs and polynomials.
     xaux	% Auxiliary functions for XIDEAL
     xexcalc	% Modifications to Eberhard Schruefer's excalc
 
		),'(contrib xideal));
 
% Switches

fluid '(!*xfullreduce !*trxideal !*twosided !*trxmod);

switch xfullreduce,trxideal,twosided,trxmod;

!*xfullreduce	:= t;	% whether to autoreduce GB
!*trxideal	:= nil;	% display new polynomials added to GB
!*twosided	:= nil;	% construct GB for two-sided ideal
!*trxmod	:= nil;	% display reduction chains


% Global variables

fluid '(xvars!* xtruncate!* xvarlist!* xdegreelist!* zerodivs!*
	xpolylist!*);

xvars!*		:= t;	% list of variables to include in partition
xtruncate!*	:= nil;	% degree at which to truncate GB
xvarlist!*	:= {};	% variables in current problem
xdegreelist!*	:= {};	% a-list of degrees of variables
zerodivs!*	:= {};	% odd degree variables
xpolylist!*	:= {};	% internal list for debugging only
 
% Macros used in other modules

smacro procedure xkey pr;
  car pr;

smacro procedure pr_type pr;
  cadr pr;

smacro procedure pr_lhs pr;
  caddr pr;

smacro procedure pr_rhs pr;
  cadddr pr;

smacro procedure empty_xset;
  '!*xset!* . nil;

smacro procedure empty_xsetp c;
  null cdr c;

smacro procedure xset_item c;
  car c;


% Macros from other packages for compilation

smacro procedure ldpf u;			% from excalc
   %selector for leading standard form in patitioned sf;
   caar u;

smacro procedure !*k2pf u;			% from excalc
   u .* (1 ./ 1) .+ nil;

smacro procedure negpf u;			% from excalc
   multpfsq(u,(-1) ./ 1);

smacro procedure get!*fdeg u;			% from excalc
   (if x then car x else nil) where x = get(u,'fdegree);

smacro procedure get!*ifdeg u;			% from excalc
   (if x then cdr x else nil)
    where x = assoc(length cdr u,get(car u,'ifdegree));
 
endmodule;
end;