Warning: new definition for norm Warning: new definition for trace Version of June 24, 1997 written by Doron Zeilberger(zeilberg@math.temple.edu). HORTON: A Maple package accompanying the paper "Proof of Conway's "Lost" Cosmological Theorem" by Shalosh B. Ekhad and Doron Zeilberger. (ERA-AMS, v.3) It proves the Cosmological Theorem and also investigates John HORTON Conway's brilliant analysis of his brilliant Audioacive decay, as it is explained in his paper "The weird and wonderful chemistry of audioactive decay" that appeared in "Open problems in communication and computation", edited by Thomas M. Cover and B. Gopinath, Springer, 1987. The most current version of the program is available from http://www.math.temple.edu/~zeilberg For a list of the procedures type ezra(), for help with a specific procedure, type ezra(procedure_name) The set of elements is [[3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 2, 2, 2], [3, 1, 1, 3, 1, 1, 2, 2, 2], [3], [1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2], [1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2], [3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2], [3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2], [3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2], [1, 3], [1, 1, 1, 3], [3, 1, 1, 3], [1, 3, 2, 1, 1, 3], [1, 3, 2], [ 3, 1, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2 ], [1, 3, 2, 1, 1], [1, 1, 1, 3, 1, 2], [1, 1, 1, 3, 1, 2, 2, 1], [1, 1, 1, 3, 1, 2, 2, 1, 1, 3], [1, 1, 1, 3, 1], [3, 1, 1, 3, 1, 1], [2, 2], [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3], [1, 3, 2, 1, 1, 3, 2, 1], [1, 3, 2, 1, 1, 3, 2], [1, 3, 2, 2, 1, 1, 3], [1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2], [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2], [3, 1, 2], [1, 2], [1, 1, 1, 3, 2, 2, 2, 1, 1, 3], [1, 1, 1, 3, 2, 2, 2], [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2], [1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 3, 2], [1, 3, 1, 1, 1, 2], [1, 1, 1, 2], [3, 1, 1, 3, 3, 2], [3, 1, 1, 3, 3, 2, 2, 1, 1, 3], [1, 3, 2, 2, 1, 1, 3, 3, 1, 1, 2], [3, 1, 1, 2], [1, 2, 3, 2, 2, 2, 1, 1, 3], [3, 1, 1, 3, 1, 1, 1, 2], [1, 1, 1, 3, 2], [3, 2, 1, 1, 2], [1, 1, 1, 3, 3, 1, 1, 2], [1, 3, 2, 1, 1, 2], [3, 1, 1, 2, 1, 1, 2], [1, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3], [1, 3, 2, 1, 1, 3, 3, 1, 1, 2], [1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2], [1, 3, 1, 2, 2, 1, 1, 2], [1, 1, 1, 3, 1, 2, 2, 1, 1, 2], [3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3], [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2], [3, 1, 1, 3, 1, 2], [1, 3, 2, 1, 1, 3, 1, 1, 1, 2], [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1], [1, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2], [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2], [1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1], [1, 3, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3], [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1], [3, 1, 1, 3, 2], [1, 3, 2, 2, 1, 1, 2], [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1], [1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3], [1, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2], [1, 3, 2, 1, 1, 3, 2, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1], [1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 1, 1], [1, 3, 2, 1, 1, 3, 1, 2], [1, 1, 1, 3, 2, 2, 2, 1, 1, 2], [3, 1, 1, 3, 1, 1, 2, 2, 1, 1], [3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3], [1, 3, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2], [1, 3, 2, 1, 1, 2, 2, 1, 1, 2], [3, 1, 1, 3, 2, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1], [3, 1, 1, 2, 2, 2, 1], [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2], [1, 2, 3, 2, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1], [3, 1, 1, 3, 3, 2, 2, 1, 1, 2], [1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1], [1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3], [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1], [1, 1, 1, 2, 1, 3, 3], [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2], [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2], [1, 2, 3, 2, 2, 2, 1, 1, 2], [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1], [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3], [1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 1, 2], [ 3, 1, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3 ], [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 2] , [1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3] ] The Splitting table atom->Splitting(JHC(atom)) is table([ %5 = [[1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2]] (1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1) = [[3, 1, 1, 3, 1, 1, 2, 2, 2], [1, 2, 3, 2, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1]] (1, 1, 1, 2, 1, 3, 3) = [[3, 1, 1, 2, 1, 1, 2], [3]] %4 = [[1, 3, 2, 1, 1, 3, 2, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1]] (1, 1, 1, 3, 2, 2, 2, 1, 1, 3) = [[3, 1, 1, 3, 3, 2, 2, 1, 1, 3]] (3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2) = [[%2], [1, 3], [2, 2], [1, 2], [3, 2, 1, 1, 2]] (3, 1, 1, 3, 1, 1, 2, 2, 2) = [[%2], [1, 3, 2]] (1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2) = [[3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2]] (3, 1, 1, 2, 2, 2, 1) = [[1, 3, 2], [1, 3, 2, 1, 1]] (3, 1, 1, 2, 1, 1, 2) = [[1, 3, 2, 1, 1, 2, 2, 1, 1, 2]] (1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1) = [[3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1]] (3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2) = [[%2], [1, 3, 2, 2, 1, 1, 3, 3, 1, 1, 2]] (3, 1, 1, 3) = [[1, 3, 2, 1, 1, 3]] %2 = [[1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2]] (1, 3, 1, 2, 2, 1, 1, 2) = [[1, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2]] (1, 3, 2, 1, 1, 3, 2, 1) = [[1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1]] (1, 3, 2, 2, 1, 1, 3) = [[1, 1, 1, 3, 2, 2, 2, 1, 1, 3]] (1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2) = [[3, 1, 1, 3, 1, 1, 2, 2, 2], [1, 2], [3, 2, 1, 1, 2]] (1, 3, 1, 1, 1, 2) = [[1, 1, 1, 3, 3, 1, 1, 2]] (1, 2, 3, 2, 2, 2, 1, 1, 2) = [[1, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2]] (1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2) = [[%6], [1, 2], [%5]] (3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3) = [[1, 3, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3]] %6 = [[%2], [1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 3, 2]] %3 = [[3, 1, 1, 3, 3, 2]] (1, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2) = [[3, 1, 1, 3, 2], [1, 3, 2, 2, 1, 1, 2]] (1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 1, 2) = [[1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 2]] (1, 3, 2, 1, 1, 3, 3, 1, 1, 2) = [[1, 1, 1, 3, 1], [2, 2], [1, 2], [3, 2, 1, 1, 2]] (1, 3, 2, 1, 1) = [[1, 1, 1, 3, 1, 2, 2, 1]] (1, 3, 2, 1, 1, 3, 1, 2) = [[1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2]] (3, 1, 1, 3, 1, 1) = [[1, 3, 2, 1, 1, 3, 2, 1]] (1, 3, 2, 2, 1, 1, 3, 3, 1, 1, 2) = [[%3], [1, 2], [3, 2, 1, 1, 2]] (1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 2) = [[%6], [1, 2, 3, 2, 2, 2, 1, 1, 2]] %1 = [[1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3]] (1, 1, 1, 3, 1, 2, 2, 1) = [[3, 1, 1, 3, 1, 1, 2, 2, 1, 1]] (1, 3, 2) = [[1, 1, 1, 3, 1, 2]] (1, 1, 1, 3, 2) = [[3, 1, 1, 3, 1, 2]] (1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2) = [[3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2]] (1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3) = [[%6], [1, 2], [%1]] (1, 1, 1, 2) = [[3, 1, 1, 2]] (1, 1, 1, 3, 2, 2, 2, 1, 1, 2) = [[3, 1, 1, 3, 3, 2, 2, 1, 1, 2]] (1, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3) = [[3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3]] (3, 1, 1, 3, 2) = [[1, 3, 2, 1, 1, 3, 1, 2]] (1, 1, 1, 3, 1, 2, 2, 1, 1, 3) = [[3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3]] (3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2) = [[1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2]] (1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2) = [[3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2]] (3, 1, 1, 2) = [[1, 3, 2, 1, 1, 2]] 3 = [[1, 3]] (3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1) = [[%2], [1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 1, 1]] (3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3) = [[1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3]] (1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2) = [[1, 1, 1, 3, 2], [1, 3], [2, 2], [1, 2], [%5]] (1, 3, 2, 2, 1, 1, 2) = [[1, 1, 1, 3, 2, 2, 2, 1, 1, 2]] (1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 1, 1) = [[%3], [1, 2], [3, 1, 1, 2, 2, 2, 1]] (3, 1, 1, 3, 3, 2, 2, 1, 1, 3) = [[1, 3, 2], [1, 2, 3, 2, 2, 2, 1, 1, 3]] (1, 3, 2, 1, 1, 3, 2, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1) = [[1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1]] (3, 1, 1, 3, 1, 2) = [[1, 3, 2, 1, 1, 3, 1, 1, 1, 2]] (1, 2, 3, 2, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1) = [[1, 1, 1, 2, 1, 3, 3], [2, 2], [1, 2], [%4]] (1, 3, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3) = [[1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3]] (1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2) = [[1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2]] (1, 1, 1, 3, 3, 1, 1, 2) = [[3, 1, 2], [3, 2, 1, 1, 2]] (1, 3) = [[1, 1, 1, 3]] (1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1) = [[1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1]] (1, 3, 2, 1, 1, 3) = [[1, 1, 1, 3, 1, 2, 2, 1, 1, 3]] (3, 1, 2) = [[1, 3, 1, 1, 1, 2]] (1, 1, 1, 3, 1, 2, 2, 1, 1, 2) = [[3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2]] (1, 3, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2) = [[1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2]] (1, 2) = [[1, 1, 1, 2]] (3, 1, 1, 3, 1, 1, 1, 2) = [[1, 3, 2, 1, 1, 3, 3, 1, 1, 2]] (1, 3, 2, 1, 1, 2, 2, 1, 1, 2) = [[1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2]] (1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1) = [[3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1]] (3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2) = [[1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 1, 2]] (1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1) = [[%3], [1, 2], [%4]] (1, 1, 1, 3, 1) = [[3, 1, 1, 3, 1, 1]] (3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2) = [[%2], [1, 3, 2, 2, 1, 1, 2]] (1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3) = [[1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3]] (3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1) = [[%2], [1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1]] (3, 1, 1, 3, 3, 2) = [[1, 3, 2], [1, 2], [3, 1, 2]] (2, 2) = [[2, 2]] (1, 1, 1, 3, 1, 2) = [[3, 1, 1, 3, 1, 1, 1, 2]] (3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2) = [[1, 3, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2]] (1, 1, 1, 3) = [[3, 1, 1, 3]] (1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 3, 2) = [[%3], [1, 2], [3, 1, 1, 3], [2, 2], [1, 2], [3, 1, 2]] (1, 3, 2, 1, 1, 2) = [[1, 1, 1, 3, 1, 2, 2, 1, 1, 2]] (3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3) = [[%2], [1, 3, 2, 2, 1, 1, 3]] (1, 2, 3, 2, 2, 2, 1, 1, 3) = [[1, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3]] (1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2) = [[3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2]] (1, 3, 2, 1, 1, 3, 1, 1, 1, 2) = [[1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2]] (1, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2) = [[3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2]] (3, 1, 1, 3, 1, 1, 2, 2, 1, 1) = [[1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1]] (1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3) = [[3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3]] (3, 1, 1, 3, 3, 2, 2, 1, 1, 2) = [[1, 3, 2], [1, 2, 3, 2, 2, 2, 1, 1, 2]] (1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3) = [[1, 1, 1, 3, 2], [1, 3], [2, 2], [1, 2], [%1]] (3, 2, 1, 1, 2) = [[1, 3, 1, 2, 2, 1, 1, 2]] ]) %1 := 3, 1, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3 %2 := 1, 3, 2, 1, 1, 3, 2 %3 := 1, 1, 1, 3, 2, 2, 2 %4 := 3, 1, 1, 3, 2, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1 %5 := 3, 1, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2 %6 := 3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 2, 2, 2 The Abundance table is table([ [1, 3, 2, 2, 1, 1, 2] = .032032812959971354362123150684716869917127793360480 [1, 2, 3, 2, 2, 2, 1, 1, 2] = .014481448773301683884803685435730365739117964597861 [3, 1, 1, 3, 2, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1] = .00038607704942869787861710220296887369555881845642258 [1, 3, 2] = .029820456167398478714149678011934906548865126331831 [3, 1, 1, 3, 3, 2, 2, 1, 1, 3] = .0014116286100067878671079841443493164287710351007179 [1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2] = .0050149302464005035746600700591912153343759003056539 [1, 3, 2, 1, 1, 2] = .025312784217426199613817448515098772558234366443851 [1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1] = .00032899480575929406277985779027123303879183334267838 [3, 1, 1, 3, 1, 1] = .0079219188283763493473298067921913038932391687450539 [3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2] = .0085219396539127219870236583663922925303444765663563 [2, 2] = .091790383215976643913773736384350234890339760510539 [3, 1, 1, 2] = .032997170121806884652956376503869499351885357235618 [1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1] = .00072878492055824105141247310998407606538854430233282 [1, 3, 2, 1, 1] = .0016143946686552738527495534651561928751928602182219 [3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2] = .0038470525418992739090915176779309067062528554908099 [1, 1, 1, 3, 2] = .0026690970363259511282334601584713809977729103922223 [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1] = .00042887015041816936030635563997474105261710158499845 [1, 3, 2, 1, 1, 3, 1, 1, 1, 2] = .0015706911808397138806026682648060152938403889741227 [1, 1, 1, 3, 3, 1, 1, 2] = .013871124199736550565784473266652134202794424355490 [3, 1, 1, 3, 3, 2, 2, 1, 1, 2] = .018850441227484385262597579964139027026873488384407 [3, 1, 1, 3] = .0069269352045137379003562252714843768152199530525032 [1, 3, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2] = .0065373490750002595399377238581591400455829873278127 [1, 3] = .0098835986391304503579687803925163084257293184053410 [3, 1, 1, 2, 1, 1, 2] = .00010256285248972459490050563413096002374936353938957 [1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2] = .000060355455682167257044781279342776099924239936639009 [1, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3] = .00037500456738529797891541719506567280051454819379115 [1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3] = .00024207736665589105328532406681015468361827346060047 [1, 1, 1, 3, 1, 2] = .022875863882997732093834358848343933175609711272115 [3, 1, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2] = .0042200665981766694539331422838650979266049623673943 [1, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2] = .011109006820922623068840532523630512548203756088438 [1, 1, 1, 3, 1, 2, 2, 1] = .0012384341971928017939199411583854377858070297990889 [3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2] = .000046299868151950215274496238820608946002705185227211 [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3] = .0031270209328296497148503440780683838323702537322030 [1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2] = .0029511503715841949843704529163309065275324303803838 [1, 3, 1, 2, 2, 1, 1, 2] = .035015858545548347900726914414831447923950823988812 [1, 1, 1, 3, 1, 2, 2, 1, 1, 3] = .0040763134078311527508927049855252000430476617888606 [1, 1, 1, 3, 1, 2, 2, 1, 1, 2] = .019417939249721785668772971348619517508244829539739 [1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 1, 2] = .000035517547944242414949403144829168965082479317510388 [3, 1, 1, 3, 1, 1, 2, 2, 1, 1] = .00095002745645468851802169961864616362703174155861210 [1, 3, 2, 1, 1, 3, 2, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1] = .00029616736851717871330023290250110038668429022971003 [1, 2, 3, 2, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1] = .00017428645997178697759651081186533281747747001573188 [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2] = .012126002782780671127905243214982827406800603387692 [1, 3, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3] = .00022068001228516175936219607839522188873456614943971 [3, 1, 1, 3, 1, 1, 1, 2] = .017548529286602558016401231953243486348717556970660 [1, 1, 1, 3, 2, 2, 2, 1, 1, 3] = .0018401669683233283663854686706524612437425092542804 [1, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3] = .00083070513292792713054771414889789411535075083696526 [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2] = .0093020974443377186216052184682521679871034062882836 [3, 1, 1, 2, 2, 2, 1] = .0021044881933091697026139471993188557781452252053753 [3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3] = .00063725039754898621324811714298619165693642535520854 [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 2] = .000027246216076285362154911431075588943416610495283201 [1, 3, 2, 1, 1, 3, 2] = .047987529438391840356310728500691942553093963144664 [1, 1, 1, 3, 1] = .010326833311806214414027097450151151828881468412872 [1, 3, 2, 2, 1, 1, 3] = .0023987998311340449871670074288175239686531737198865 [3, 1, 2] = .023571391336285967550014024595055192515100834050306 [3, 1, 2, 2, 1, 1, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3] = .00031556655252030050208453490284868765205056634222330 [1, 1, 1, 2, 1, 3, 3] = .00013369860315292257369996419776351574297275016596239 [1, 3, 2, 1, 1, 3, 2, 1] = .0060770611888967573575433921647054902468814443888761 [3, 1, 1, 3, 1, 1, 2, 2, 2] = .0010985955997262605447156412070848522822896322538930 [1, 2] = .056072543128543630604447830480356945277048819924615 [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1] = .00022719586751967728192703089733169923101350055275881 [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2] = .028239358949242623446822043470555044768980531787523 [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2] = .0012049083841445764510573763268975984380696281237447 [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2] = .036812186418332916794576534437550902845863803532031 [1, 1, 1, 3, 2, 2, 2, 1, 1, 2] = .024573006695415604788467557262292250961353261804206 [1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 1, 3, 3, 2] = .0014478905642301389037359007537935163973494195487351 [1, 3, 2, 2, 1, 1, 3, 3, 1, 1, 2] = .021662972821060798702189580911304510203818195860176 [1, 3, 2, 1, 1, 3, 1, 2] = .015807181591879505630724785154625427354374058590341 [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3] = .00016928801807709013623425289091551630545450111497956 [3, 2, 1, 1, 2] = .045645877255697145048772837800009898646040311313949 [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1] = .0046618342719328847589604818208424574648070333121860 [1, 1, 1, 3, 2, 2, 2] = .020085668709301691252530857139776663120228060975069 [1, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2] = .026861360179660435749978866814468199115312032419616 [1, 3, 2, 1, 1, 3, 3, 1, 1, 2] = .013461825166376743558774429507650986145947954217699 [3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3] = .00028767344774514614353656009214261637191789117059102 [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 2, 2, 2] = .0018874372275796509809109982382696574270843772585073 [1, 3, 2, 1, 1, 3] = .0053137894999084201556520859117878991477924022215509 [1, 3, 1, 1, 1, 2] = .018082082202728112608755709055051357401618895871684 [3] = .00010256285248972459490050563413096002374936353938957 [1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2] = .0032372968587454265085457172226194708380543477213967 [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2] = .014895886658185438573969519686550822309926409858832 [1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 1, 1] = .0027433629717488878640647083654397898555897208601544 [3, 1, 1, 3, 1, 2] = .0020475173200152883864995722143858044203979235755976 [3, 1, 1, 3, 3, 2] = .015408115181527646372092988888543297156629318084672 [1, 2, 3, 2, 2, 2, 1, 1, 3] = .0010828883285549594109285724002380862832793173689299 [3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 2, 1] = .0035761856106822268454640537666513986964251514981990 [1, 1, 1, 3] = .0075819047124474049013788385236777447171967999755875 [1, 3, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 3] = .00048884742982751451347202449760365485701425693978047 [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1] = .00055906537945244512116486857328754954669104013846490 [1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 2, 1, 1, 2] = .0022638860324485696929102520226555254914380524538544 [1, 1, 1, 2] = .043014360913245099898173435743462923662653703246422 [1, 3, 2, 1, 1, 2, 2, 1, 1, 2] = .000078678000089480099262233104872435401385448623801439 [3, 1, 1, 3, 2] = .020605882610671487811717452225382778901249976213400 ]) The characteristic polynomial is 71 69 68 67 66 65 64 63 62 61 60 (x + 1) (x - x - 2 x - x + 2 x + 2 x + x - x - x - x - x 59 58 57 56 55 54 53 52 51 - x + 2 x + 5 x + 3 x - 2 x - 10 x - 3 x - 2 x + 6 x 50 49 48 47 46 45 44 43 42 + 6 x + x + 9 x - 3 x - 7 x - 8 x - 8 x + 10 x + 6 x 41 40 39 38 37 36 35 34 33 + 8 x - 5 x - 12 x + 7 x - 7 x + 7 x + x - 3 x + 10 x 32 31 30 29 28 27 26 25 24 + x - 6 x - 2 x - 10 x - 3 x + 2 x + 9 x - 3 x + 14 x 23 21 20 19 18 17 16 15 14 - 8 x - 7 x + 9 x + 3 x - 4 x - 10 x - 7 x + 12 x + 7 x 13 12 11 10 9 7 6 5 4 3 + 2 x - 12 x - 4 x - 2 x + 5 x + x - 7 x + 7 x - 4 x + 12 x 2 2 18 - 6 x + 3 x - 6) (x - 1) x Conway's Constant, lambda is, 1.3035772690342963912570991121525518907307025046594