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Journals ACM SIGAPL APL Quote Quad Volume 23 Issue 2

T h e matrix operator is a Sierpinski matrix (geniton Gv, i.e., G mirrored vertically, so that Gv squared modulo 2 is a unit-matrix, then Gu is its o w n modulo-2-matrix-inverse; then, the modulo-2-domino becomes a deprecated facility before being implemented.) The product of such a matrix by the 2nd member produces the solution of all soluble systems in modulo-2 differential algebra. This solution is also the "cognitive" transform of the 2nd member (and, conversely, the 2nd member is the cognitive transform of the solution); the cognitive transformation (and the helix transformation) produce the only-possible equivalents of the Fast Fourier Transform in modulo-2 algebra. More r e c e n t papers have shown t h a t transforms can be obtained in a time which is strictly proportional to the length of the processed information, in all cases, and, of course, with no other function t h a n which always provide exact non-Godelian results. All axiomatics which admit the very axioms t h a t were needed to prove Godells t h e o r e m itself, will be Godelian: namely, with number theory and ordered sets. Here is the reason why ~ \

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On the permutations of a vector obtainable through the restructure and transpose functions of APL

Baker Jr., Henry G.
ACM SIGAPL APL Quote Quad , Volume 23 (2)
Association for Computing Machinery – Dec 1, 1992

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