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 1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465 ``````n := 4; on rational, rat; off allfac; array p(n/2+2); harmonic u,v,w,x,y,z; weight e=1, b=1, d=1, a=1; %% Step1: Solve Kepler equation bige := fourier 0; for k:=1:n do << wtlevel k; bige:=fourier e * hsub(fourier(sin u), u, u, bige, k); >>; write "Kepler Eqn solution:", bige\$ %% Ensure we do not calculate things of too high an order wtlevel n; %% Step 2: Calculate r/a in terms of e and l dd:=-e*e; hh:=3/2; j:=1; cc := 1; for i:=1:n/2 do << j:=i*j; hh:=hh-1; cc:=cc+hh*(dd^i)/j >>; bb:=hsub(fourier(1-e*cos u), u, u, bige, n); aa:=fourier 1+hdiff(bige,u); ff:=hint(aa*aa*fourier cc,u); %% Step 3: a/r and f uu := hsub(bb,u,v); uu:=hsub(uu,e,b); vv := hsub(aa,u,v); vv:=hsub(vv,e,b); ww := hsub(ff,u,v); ww:=hsub(ww,e,b); %% Step 4: Substitute f and f' into S yy:=ff-ww; zz:=ff+ww; xx:=hsub(fourier((1-d*d)*cos(u)),u,u-v+w-x-y+z,yy,n)+ hsub(fourier(d*d*cos(v)),v,u+v+w+x+y-z,zz,n); %% Step 5: Calculate R zz:=bb*vv; yy:=zz*zz*vv; on fourier; p(0):= fourier 1; p(1) := xx; for i := 2:n/2+2 do << wtlevel n+4-2i; p(i) := fourier ((2*i-1)/i)*xx*p(i-1) - fourier ((i-1)/i)*p(i-2); >>; wtlevel n; for i:=n/2+2 step -1 until 3 do p(n/2+2):=fourier(a*a)*zz*p(n/2+2)+p(i-1); yy*p(n/2+2); showtime; end; ==John ``````