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*To*: Guy.Steele @ CMU-CS-A*Subject*: Rational and complex numbers*From*: Richard E. Zippel <RZ @ MIT-MC>*Date*: Wed, 22 Jun 1983 15:28:00 -0000*Cc*: common-lisp @ SU-AI*In-reply-to*: Msg of 12 Jun 83 2346 EDT () from Guy.Steele at CMU-CS-A

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).

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