User:Nukeh

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John Mark Deutch

Mathematical_elegance T-symmetry Amish Policy Nude Wave Power Energy_crisis John Calvin

Thomas_Jukes Paul_Davies John_Deutch Joshua_Jortner Kairos Scientific Versus Fish & Richardson

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(* complete dictionary of words, one per row, number of rows is (alpha^word), using words of length "word" and an alphabet of "alpha" number of characters *)

alpha=4;word=3;dict=.;

dict=Partition[Flatten[Tuples[Reverse[IdentityMatrix[alpha]],word]],(alpha*word)]

PseudoInverse[dict]==((Transpose[dict])*((alpha)^-(word -1)))-((word - 1)/(alpha^word)/word)

True

(* There is nothing special for alpha=4;word=3 - The method works for all cases where word < alpha, but that is a more verbose loop, and the Mathematica PseudoInverse function takes too long to calculate for values of alpha and word that are large, whereas the transpose side of the equation is fast. The genetic code is structured as alpha=4;word=3 *)

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