reduce-historical/r38/packages/excalc/hodge.red

module hodge;

% Author: Eberhard Schruefer;

global '(dimex!* sgn!* detm!* basisforml!*);

symbolic procedure formhodge(u,vars,mode);
   if mode eq 'symbolic then 'hash . formlis(cdr u,vars,mode)
    else 'list . mkquote 'hodge . formlis(cdr u,vars,mode);

put('hash,'formfn,'formhodge);

put('hodge,'simpfn,'simphodge);

put('hodge,'rtypefn,'getrtypecar);

put('hodge,'partitfn,'partithodge);

symbolic procedure partithodge u;
   hodgepf partitop car u;

symbolic procedure simphodge u;
   !*pf2sq partithodge u;

symbolic procedure mkhodge u;
   begin scalar x,y;
     return if x := opmtch(y := list('hodge,u))
               then partitop x
             else if deg!*form u = dimex!*
                     then 1 .* mksq(y,1) .+ nil
                   else mkupf y
   end;

smacro procedure mkbaseform u;
   mkupf list(caar basisforml!*,u);

symbolic procedure basisformp u;
   null atom u and (u memq basisforml!*);

symbolic procedure hodgepf u;
   if null u then nil
    else addpf(multpfsq(hodgek ldpf u,lc u),hodgepf red u);

symbolic procedure hodgek u;
   if eqcar(u,'hodge)
      then cadr u .* multsq(mksgnsq multf(deg!*form cadr u,
			      addf(dimex!*,negf deg!*form cadr u)),
				   resimp sgn!*) .+ nil
    else if basisformp u then dual list u
    else if eqcar(u,'wedge) and boundindp(cdr u,basisforml!*) then
	    dual cdr u
    else if basisforml!* and null deg!*form u
            then dual0 u
    else mkhodge u;

symbolic procedure dual0 u;
   (multpfsq(mkwedge ('wedge . basisforml!*),
	     simpexpt list(mk!*sq(absf!* numr x ./
				  absf!* denr x),'(quotient 1 2))))
    where x = simp!* detm!*;

symbolic procedure dual u;
   (multpfsq(mkdual xpnddual u,
	     simpexpt list(mk!*sq(absf!* numr x ./
				  absf!* denr x),'(quotient 1 2))))
    where x = simp!* detm!*;

symbolic procedure !*met2pf u;
   metpf1 getupper cadr u;

symbolic procedure xpnddual u;
   if null cdr u
      then mkunarywedge !*met2pf car u
    else wedgepf2(!*met2pf car u,xpnddual cdr u);

symbolic procedure metpf1 u;
   if null u then nil
    else addpf(multpfsq(mkbaseform caar u,simp cdar u),metpf1 cdr u);

symbolic procedure mkdual u;
   if null u then nil
    else addpf(multpfsq(((if null x then nil
                           else if cdr ldpf x
                                   then multpfsq(mkuniquewedge1 ldpf x,
                                                 lc x)
                           else car ldpf x .* lc x .+ nil)
                          where x = dualk ldpf u),
                         lc u),mkdual red u);

symbolic procedure dualk u;
   begin scalar x;
     x := !*k2pf basisforml!*;
     a: x := dualk2(car u,x);
        if null(u := cdr u) then return x;
        go to a
   end;


symbolic procedure dualk2(u,v);
   dualk0(u,v,nil);

symbolic procedure dualk0(u,v,w);
   if u eq car ldpf v
      then if null cdr ldpf v
              then list 1 .* multsq(mksgnsq w,lc v) .+ nil
            else cdr ldpf v .* multsq(mksgnsq w,lc v) .+ nil
    else if null cdr ldpf v then nil
    else wedgepf2(!*k2pf ldpf car v,
                  dualk0(u,cdr ldpf v .* lc v .+ nil,addf(w,1)));

symbolic procedure hodgeprn u;
   <<prin2!* "#"; rembras cadr u>>;

put('hodge,'prifn,'hodgeprn);

endmodule;

end;