getting axis equal?

--- On Fri, 3/4/11, Mario Rodriguez <biomates at telefonica.net> wrote:

> From: Mario Rodriguez <biomates at telefonica.net>
> Subject: Re: [Maxima] getting axis equal?
> To: "James Redford" <jrredford at yahoo.com>
> Cc: maxima at math.utexas.edu, Bart.Vandewoestyne at telenet.be
> Date: Friday, March 4, 2011, 8:29 AM
> El vie, 04-03-2011 a las 06:01 -0800,
> James Redford escribi?:
> > (%i8) nxE: express(n~E);? Exn:
> express(E~n);? Exnxn: express((E~n)~n);
> > 
> 
> Try 
> 
> Exnxn: express(express(E~n)~n);
> 
> 
> > (%o8) [-2,1,0]
> > (%i9)
> > (%o9) [2,-1,0]
> > (%i10)
> > (%o10) [-1,-2,0]
> > (%i11) nxH: express(n~H);? Hxn: express(H~n);
> nxnxH: express(n~(n~H));
> 
> and
> 
> nxnxH: express(n~express(n~H));
> 
> I also had to fix this in order to reproduce Bart's
> example.
> 
> Bart:
> 
> I have checked your example under Gnuplot 4.4.0 and you are
> right: the z
> intervals don't seem to be of equal length compared to the
> x and y
> intervals.
> 
> This is a bug in 4.4.0, which was fixed in 4.4 patchlevel
> 2.
> 
> --
> Mario

I get the below error with your modified example.

(%i1) restart; load(vect); load(draw);

(%o1) restart
(%i2)
(%o2) "C:/program1/maxima/share/maxima/5.23.2/share/vector/vect.mac"
(%i3)
(%o3) "C:/program1/maxima/share/maxima/5.23.2/share/draw/draw.lisp"
(%i4) mymax: 8;

(%o4) 8
(%i5) n: [0, 0, 1];

(%o5) [0,0,1]
(%i6) E: [1, 2, -2]; H: [2, 1, 2];

(%o6) [1,2,-2]
(%i7)
(%o7) [2,1,2]
(%i8) Exnxn: express(express(E~n)~n);

(%o8) [-1,-2,0]
(%i9) nxnxH: express(n~express(n~H));

(%o9) [-2,-1,0]
(%i10) sum1: Exnxn+Hxn;  sum2: nxE+nxnxH;

(%o10) [Hxn-1,Hxn-2,Hxn]
(%i11)
(%o11) [nxE-2,nxE-1,nxE]
(%i12) draw3d(proportional_axes=xyz,
       axis_3d=true,
       xtics = 1, ytics = 1, ztics = 1,
       /* xrange=[-mymax, mymax],
       yrange=[-mymax, mymax],
       zrange=[-mymax, mymax], */
       color=black,
       vector([0,0,0], n),
       label(["n", n[1], n[2], n[3]]),
       color=blue,
       vector([0,0,0], E),
       label(["E", E[1], E[2], E[3]]),
       vector([0,0,0], H),
       label(["H", H[1], H[2], H[3]]),
       color=red,
       vector([0, 0, 0], nxE),
       label(["nxE", nxE[1], nxE[2], nxE[3]]),
       vector([0, 0, 0], Exn),
       label(["Exn", Exn[1], Exn[2], Exn[3]]),
       vector([0, 0, 0], Exnxn),
       label(["Exnxn", Exnxn[1], Exnxn[2], Exnxn[3]]),
       vector([0, 0, 0], nxH),
       label(["nxH", nxH[1], nxH[2], nxH[3]]),
       vector([0, 0, 0], nxnxH),
       label(["nxnxH", nxnxH[1], nxnxH[2], nxnxH[3]]),
       vector([0, 0, 0], Hxn),
       label(["Hxn", Hxn[1], Hxn[2], Hxn[3]]),
       color=green,
       vector([0,0,0], sum1),
       label(["sum1", sum1[1], sum1[2], sum1[3]]),
       vector([0,0,0], sum2),
       label(["sum2", sum2[1], sum2[2], sum2[3]]));

draw (vector): coordinates are not correct
 -- an error. To debug this try: debugmode(true);
(%i13)