factor expression that contains complex %i

"Burgess, Don" <deburgess at asbury.edu> writes:
> Why does not the factor command work on an expression that contains
> the imaginary %i?
>
> Please refer to the attached image file for example commands and output.
>
> thanks for your work,
> don burgess

For people following along, the transcript is basically:

  (%i1) lp: %i*w-b;
  (%o1)                              %i w - b
  (%i2) lp*lp;
                                              2
  (%o2)                             (%i w - b)
  (%i3) expand(%);
                                  2               2
  (%o3)                        - w  - 2 %i b w + b
  (%i4) factor(%);
                                  2               2
  (%o4)                       - (w  + 2 %i b w - b )


The point is that factor only works over the reals. Indeed, if you
didn't know about complex numbers, you'd say that %o3 can't be factored
further (R isn't algebraically complete...).

To factor over the complex numbers, or at least the Gaussian integers,
use gfactor:

  (%i5) gfactor (%);
                                               2
  (%o5)                            - (w + %i b)


If you want to work in more complicated number fields, it's possible to
give minimal polynomials for your extensions to factor. I haven't used
that personally, so I'm not really qualified to give you a good example.


Rupert


PS: Although it's fine to attach an image, the result isn't possible to
    quote in replies and so it doesn't work that brilliantly on a help
    mailing list. If your problem is with Maxima, rather than the GUI
    around it, it's probably better to send text to the mailing list. I
    don't use wxMaxima myself though, so I'm not sure what's the easiest
    way to do that. Maybe there's a "copy this line" function?

    Incidentally, if the expressions are really hideous (they aren't
    here), then sometimes the resulting text is much easier to read if
    you also switch 2d display off with "display2d: false".
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