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• Executable file r37/packages/matrix/nestdom.red — part of check-in [f2fda60abd] at 2011-09-02 18:13:33 on branch master — Some historical releases purely for archival purposes

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module nestdom; % nested domain: domain elements are standard quotients
                % coefficients are taken from the integers or another
		% dnest.

% Original version by Herbert Melenk, 1993(?)
 
% Improved version with Rainer mod.

% Changes to nestlevel, nestdmode and nestsq by Winfried Neun, 1998.
 

%%%%%%%%%
% Adaption to allow convertion between arnum and nested.
%%%%%%%%%
symbolic procedure ident(x);x;
put('!:ar!:,'!:nest!:,'ident);
%%%%%%%%%

% data structure:
%  a domain element is a list
%      ('!:nest!: level# dmode* . sq)

smacro procedure nestlevel u; if fixp u then 0 else cadr u;
smacro procedure nestdmode u; if fixp u then nil else caddr u;
smacro procedure nestsq u; if fixp u then simp u else cdddr u;

global '(domainlist!*);

fluid '(alglist!* nestlevel!*);
nestlevel!* := 0;

switch nested;

domainlist!* := union('(!:nest!:),domainlist!*);

put('nested,'tag,'!:nest!:);
put('!:nest!:,'dname,'nested);
flag('(!:nest!:),'field);
flag('(!:nest!:),'convert);
put('!:nest!:,'i2d,'!*i2nest);
%put('!:nest!:,'!:bf!:,'nestcnv);
%put('!:nest!:,'!:ft!:,'nestcnv);
%put('!:nest!:,'!:rn!:,'nestcnv);
put('!:nest!:,'!:bf!:,mkdmoderr('!:nest!:,'!:bf!:));
put('!:nest!:,'!:ft!:,mkdmoderr('!:nest!:,'!:ft!:));
put('!:nest!:,'!:rn!:,mkdmoderr('!:nest!:,'!:rn!:));
put('!:nest!:,'minusp,'nestminusp!:);
put('!:nest!:,'plus,'nestplus!:);
put('!:nest!:,'times,'nesttimes!:);
put('!:nest!:,'difference,'nestdifference!:);
put('!:nest!:,'quotient,'nestquotient!:);
put('!:nest!:,'divide,'nestdivide!:);
% put('!:nest!:,'gcd,'nestgcd!:);
put('!:nest!:,'zerop,'nestzerop!:);
put('!:nest!:,'onep,'nestonep!:);
% put('!:nest!:,'factorfn,'factornest!:);
put('!:nest!:,'prepfn,'nestprep!:);
put('!:nest!:,'prifn,'prin2);
put('!:rn!:,'!:nest!:,'rn2nest);

symbolic procedure !*i2nest u;
   %converts integer u to nested form;
   if domainp u then u else
   '!:nest!: . 0 . dmode!* . (u ./ 1);

symbolic procedure rn2nest u;
   %converts integer u to nested form;
   if domainp u then u else
   '!:nest!: . 0 . dmode!* . (cdr u);


symbolic procedure nestcnv u;
   rederr list("Conversion between `nested' and",
		get(car u,'dname),"not defined");

symbolic procedure nestminusp!: u; 
         nestlevel u = 0 and minusf car nestsq u;

symbolic procedure sq2nestedf sq;
   '!:nest!: . nestlevel!* . dmode!* . sq;

symbolic procedure nest2op!:(u,v,op);
  (begin scalar r,nlu,nlv,nlr,dm,nestlevel!*;
     nlu := if not eqcar (u,'!:nest!:) then 0 else nestlevel u;
     nlv := if not eqcar (v,'!:nest!:) then 0 else nestlevel v;
     if nlu = nlv then goto case1
     else if nlu #> nlv then goto case2
     else goto case3;
   case1:    % same level for u and v
            dm := nestdmode u;
            if dm then setdmode(dm,t);
            nlr := nlu;
            nestlevel!* := nlu - 1;
            r := apply(op,list(nestsq u,nestsq v));
            goto ready;       
   case2:    % v below u 
            dm := nestdmode u;
            if dm then setdmode(dm,t);
            nlr := nlu;
            nestlevel!* := nlv;
            r := apply(op,list (nestsq u, v ./ 1)); 
            goto ready;
   case3:     % u below v
            dm := nestdmode v;
            if dm then setdmode(dm,t); 
            nlr := nlv;
            nestlevel!* := nlu;
            r := apply(op,list (u ./ 1,nestsq v));  
   ready:
	    r := if null numr r then nil
		else if domainp numr r and denr r = 1 then numr r
		else '!:nest!: . nlr . dm . r;
	    if dm then setdmode (dm,nil);
	    return r;
   end )  where dmode!* = nil;

symbolic procedure nestplus!:(u,v); nest2op!:(u,v,'addsq);

symbolic procedure nesttimes!:(u,v); nest2op!:(u,v,'multsq);

symbolic procedure nestdifference!:(u,v);
    nest2op!:(u,v,function (lambda(x,y); addsq(x,negsq y)));

symbolic procedure nestdivide!:(u,v); nest2op!:(u,v,'quotsq) . 1;

% symbolic procedure nestgcd!:(u,v); !*i2nest 1;

symbolic procedure nestquotient!:(u,v); nest2op!:(u,v,'quotsq);

symbolic procedure nestzerop!: u; null numr nestsq u;

symbolic procedure nestonep!: u; 
       (car v = 1 and cdr v = 1) where v = nestsq u;

initdmode 'nested;


% nested routines are defined in the gennest nestule with the exception
% of the following:

symbolic procedure setnest u;
   begin 
      u := reval u;  
      if not fixp u then typerr(u,"nestulus");
      nestlevel!* := u;
   end;

flag('(setnest),'opfn);   %to make it a symbolic operator;

flag('(setnest),'noval);

algebraic operator co;
 
symbolic procedure simpco u;
 % conmvert an expression to a nested coefficient
   begin scalar  sq,lev;
     if not (length u = 2 and fixp car u) then
             typerr(u,"nested coefficient");
     sq := simp cadr u;
     lev := car u;
     return (if null numr sq then nil else ('!:nest!: . lev . dmode!* .
						 sq)) ./ 1;
   end;

put('co,'simpfn,'simpco);

symbolic procedure nestprep!: u; list('co,nestlevel u,prepsq nestsq u);


endmodule;

end;