Rational and complex numbers

[Richard E. Zippel <RZ @ MIT-MC>]

    Date: 12 Jun 83 2346 EDT (Sunday)
    From: Guy.Steele at CMU-CS-A
    To:   Richard E. Zippel <RZ>
    cc:   common-lisp at SU-AI
    Re:   Rational and complex numbers


    I do foresee one entirely plausible application for Gaussian integers,
    which is graphics applications.  For discrete bit-map representations,
    Gaussian integers may be a very convenient representation.  Some interesting
    work has been done at Yale on picture languages that use complex numbers.

    I also admit once again to harboring the secret ambition for some form
    of LISP to supplant FORTRAN...
    --Guy
Another version of this would use an arbitrary two dimensional module
instead of the complex numbers.  For instance  I suspect that if you
associate the point (a, b) into a + sqrt(-163)*b, and then plot the powers
of (1+ sqrt(-163)) you will get some interesting results.  Similarly, taking
a some image and then multiplying it by a complex number can lead to
interesting versions of scaling.  Finally, the wrap around types of windows
we used in Space War might be best represented as GF(1031)[x]/(x^2+1) or
something (actually GF(1024)xGF(1024) would be more natural).