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Project: cocalc-sagemath-dev-slelievre
Views: 418346############################################################################# ## #A imf31.grp GAP group library Volkmar Felsch ## ## #Y Copyright (C) 1995, Lehrstuhl D für Mathematik, RWTH Aachen, Germany ## ## This file contains, for each Q-class representative of the irreducible ## maximal finite integral matrix groups of dimension 31, ## ## [1] a quadratic form (as lower triangle of the Gram matrix), ## [2] a list of matrix generators. ## ############################################################################# ## ## Quadratic form and matrix generators for the Q-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 31. ## IMFList[31].matrices := [ [ # Q-class [31][01] [[1], [0,1], [0,0,1], [0,0,0,1], [0,0,0,0,1], [0,0,0,0,0,1], [0,0,0,0,0,0,1], [0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]], [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]], [[0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]]], [ # Q-class [31][02] [[4], [1,4], [0,1,4], [1,1,0,4], [1,1,1,1,4], [1,1,1,1,1,4], [1,1,1,1,1,0,4], [1,0,1,0,1,1,1,4], [1,1,1,1,0,1,1,1,4], [1,1,1,1,0,1,1,1,1,4], [1,1,1,1,1,1,1,1,1,1,4], [0,0,1,1,1,1,1,1,1,1,1,4], [1,1,1,1,1,1,0,1,1,0,1,1,4], [0,1,1,1,1,1,1,0,0,0,1,0,0,4], [1,1,1,1,1,1,1,1,0,1,0,1,1,1,4], [1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,4], [0,1,0,1,0,0,1,1,1,1,-1,0,1,0,1,1,4], [1,0,0,1,1,0,1,1,0,1,0,1,0,-1,0,1,1,4], [0,0,1,1,0,1,1,0,1,1,1,1,1,1,0,1,1,0,4], [1,1,1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,4], [1,1,-1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,4], [0,1,1,1,1,1,1,0,-1,0,1,1,1,1,0,0,0,0,1,0,1,4], [0,1,1,0,1,1,0,0,1,0,1,1,1,0,-1,1,0,1,1,1,0,0,4], [1,1,-1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,-1,0,1,0,0,4], [0,1,0,1,1,1,1,0,0,0,-1,1,1,1,1,1,1,1,0,1,0,1,1,1,4], [1,1,0,0,1,0,1,1,1,-1,1,1,1,0,-1,1,0,0,0,1,1,1,1,1,1,4], [0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,0,4], [1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,1,-1,0,1,1,4], [0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,1,0,1,1,1,1,0,0,0,1,0,1,4], [1,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,1,-1,0,0,1,1,0,4], [1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,1,0,0,1,4]], [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [10,2,11,-2,8,-16,-14,5,9,-14,15,7,-14,-18,-10,10,5,-15,12,6,-3,7,-11,18,19,-25,3,4,-2,6,-9], [3,2,5,-1,4,-4,-4,1,2,-7,5,4,-6,-8,-3,5,3,-5,5,3,0,2,-5,5,5,-8,0,1,-4,2,-4], [2,0,0,-1,0,-2,-2,1,2,0,1,0,-1,0,-1,-1,0,-1,1,0,-1,2,0,2,2,-2,1,0,1,0,-1], [-1,0,-2,0,-1,3,2,-1,-1,2,-2,-1,1,2,2,-2,0,2,-2,-1,0,0,2,-3,-3,4,0,-1,0,-1,1], [-3,-1,-4,1,-2,4,4,-1,-2,5,-5,-3,4,5,4,-3,-2,4,-4,-2,0,-1,4,-5,-6,8,0,-2,1,-1,3], [3,0,3,-1,1,-4,-4,1,2,-2,3,1,-3,-3,-2,1,1,-3,3,1,0,2,-2,4,5,-5,1,1,0,0,-2], [0,-1,0,0,0,-1,-1,0,1,1,0,-1,0,0,0,0,-1,0,0,0,0,1,0,1,1,0,1,0,1,0,0], [2,-1,1,-1,1,-5,-4,1,4,0,2,-1,-2,-2,-1,0,-1,-2,3,1,-1,3,-1,5,4,-4,2,1,2,1,-2], [-2,-1,-4,1,-2,4,4,-1,-2,4,-5,-2,4,5,3,-3,-1,3,-4,-1,0,-1,4,-5,-6,7,0,-2,1,-2,3], [2,-1,-1,-1,0,-3,-2,1,3,1,0,-1,-1,0,0,-1,-1,-1,1,0,-1,3,1,2,2,-2,2,0,2,0,-1], 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