# IRREDUCIBLE POLYNOMIALS OF DEGREE n OVER GF(p) # Format: Maple Table # For each p, the maximum degree corresponds to the # largest n for which there are less than 1000 polys. # p n #------------ # 2 1-13 # 3 1-8 # 5 1-5 # 7 1-4 # 11 1-3 # 13 1-3 # 17 1-2 # 19 1-2 # 23 1-2 # 29 1-2 # 31 1-2 # 37 1-2 # 41 1-2 # 43 1-2 # USAGE: # read(`irrpoly`): (this file) # IrrPoly[p]: # IrrPoly[p][n]: # List of coefficients of irreducible polynomials over GF(p) # in lexicographycal order: [1,4,7] -> x^2 + 4x + 7 # INPUT: p: a prime # n: a +ve integer in the above range # OUTPUT: a list of lists [[deg 1],[deg 2],...] # a list [deg n]. #---------------------------------- testing function (see end of this file) # TestIrrPoly(p:integer,n:integer) # Test the list of irreducible polynomials of degree # n over Fp,as given by IrrPoly(p)[n]. # The list is tested for correctness,completeness # and lexicographical ordering. # INPUT: p: a prime # n: an integer # OUTPUT: diagnostics (if any). #============================================================ alias(irrpoly=IrrPoly): IrrPoly := table([ (2)=[ [[1,0], [1,1]], [[1,1,1]], [[1,0,1,1], [1,1,0,1]], [[1,0,0,1,1], [1,1,0,0,1], [1,1,1,1,1]], [[1,0,0,1,0,1], [1,0,1,0,0,1], [1,0,1,1,1,1], [1,1,0,1,1,1], [1,1,1,0,1,1], [1,1,1,1,0,1]], [[1,0,0,0,0,1,1], [1,0,0,1,0,0,1], [1,0,1,0,1,1,1], [1,0,1,1,0,1,1], [1,1,0,0,0,0,1], [1,1,0,0,1,1,1], [1,1,0,1,1,0,1], [1,1,1,0,0,1,1], [1,1,1,0,1,0,1]], [[1,0,0,0,0,0,1,1], [1,0,0,0,1,0,0,1], [1,0,0,0,1,1,1,1], [1,0,0,1,0,0,0,1], [1,0,0,1,1,1,0,1], [1,0,1,0,0,1,1,1], [1,0,1,0,1,0,1,1], [1,0,1,1,1,0,0,1], [1,0,1,1,1,1,1,1], [1,1,0,0,0,0,0,1], [1,1,0,0,1,0,1,1], [1,1,0,1,0,0,1,1], [1,1,0,1,0,1,0,1], [1,1,1,0,0,1,0,1], [1,1,1,0,1,1,1,1], [1,1,1,1,0,0,0,1], [1,1,1,1,0,1,1,1], [1,1,1,1,1,1,0,1]], [[1,0,0,0,1,1,0,1,1], [1,0,0,0,1,1,1,0,1], [1,0,0,1,0,1,0,1,1], [1,0,0,1,0,1,1,0,1], [1,0,0,1,1,1,0,0,1], [1,0,0,1,1,1,1,1,1], [1,0,1,0,0,1,1,0,1], [1,0,1,0,1,1,1,1,1], [1,0,1,1,0,0,0,1,1], [1,0,1,1,0,0,1,0,1], [1,0,1,1,0,1,0,0,1], [1,0,1,1,1,0,0,0,1], [1,0,1,1,1,0,1,1,1], [1,0,1,1,1,1,0,1,1], [1,1,0,0,0,0,1,1,1], [1,1,0,0,0,1,0,1,1], [1,1,0,0,0,1,1,0,1], [1,1,0,0,1,1,1,1,1], [1,1,0,1,0,0,0,1,1], [1,1,0,1,0,1,0,0,1], [1,1,0,1,1,0,0,0,1], [1,1,0,1,1,1,1,0,1], [1,1,1,0,0,0,0,1,1], [1,1,1,0,0,1,1,1,1], [1,1,1,0,1,0,1,1,1], [1,1,1,0,1,1,1,0,1], [1,1,1,1,0,0,1,1,1], [1,1,1,1,1,0,0,1,1], [1,1,1,1,1,0,1,0,1], [1,1,1,1,1,1,0,0,1]], [[1,0,0,0,0,0,0,0,1,1], [1,0,0,0,0,1,0,0,0,1], [1,0,0,0,0,1,0,1,1,1], [1,0,0,0,0,1,1,0,1,1], [1,0,0,0,1,0,0,0,0,1], [1,0,0,0,1,0,1,1,0,1], [1,0,0,0,1,1,0,0,1,1], [1,0,0,1,0,0,1,0,1,1], [1,0,0,1,0,1,1,0,0,1], [1,0,0,1,0,1,1,1,1,1], [1,0,0,1,1,0,0,1,0,1], [1,0,0,1,1,0,1,0,0,1], [1,0,0,1,1,0,1,1,1,1], [1,0,0,1,1,1,0,1,1,1], [1,0,0,1,1,1,1,1,0,1], [1,0,1,0,0,0,0,1,1,1], [1,0,1,0,0,1,0,1,0,1], [1,0,1,0,0,1,1,0,0,1], [1,0,1,0,1,0,0,0,1,1], [1,0,1,0,1,0,0,1,0,1], [1,0,1,0,1,0,1,1,1,1], [1,0,1,0,1,1,0,1,1,1], [1,0,1,0,1,1,1,1,0,1], [1,0,1,1,0,0,1,1,1,1], [1,0,1,1,0,1,0,0,0,1], [1,0,1,1,0,1,1,0,1,1], [1,0,1,1,1,1,0,1,0,1], [1,0,1,1,1,1,1,0,0,1], [1,1,0,0,0,0,0,0,0,1], [1,1,0,0,0,1,0,0,1,1], [1,1,0,0,0,1,0,1,0,1], [1,1,0,0,0,1,1,1,1,1], [1,1,0,0,1,0,0,0,1,1], [1,1,0,0,1,1,0,0,0,1], [1,1,0,0,1,1,1,0,1,1], [1,1,0,1,0,0,1,0,0,1], [1,1,0,1,0,0,1,1,1,1], [1,1,0,1,0,1,1,0,1,1], [1,1,0,1,1,0,0,0,0,1], [1,1,0,1,1,0,1,0,1,1], [1,1,0,1,1,0,1,1,0,1], [1,1,0,1,1,1,0,0,1,1], [1,1,0,1,1,1,1,1,1,1], [1,1,1,0,0,0,0,1,0,1], [1,1,1,0,0,0,1,1,1,1], [1,1,1,0,1,0,0,0,0,1], [1,1,1,0,1,1,0,1,0,1], [1,1,1,0,1,1,1,0,0,1], [1,1,1,1,0,0,0,1,1,1], [1,1,1,1,0,0,1,0,1,1], [1,1,1,1,0,0,1,1,0,1], [1,1,1,1,0,1,0,1,0,1], [1,1,1,1,0,1,1,0,0,1], [1,1,1,1,1,0,0,0,1,1], [1,1,1,1,1,0,1,0,0,1], [1,1,1,1,1,1,1,0,1,1]], [[1,0,0,0,0,0,0,1,0,0,1], [1,0,0,0,0,0,0,1,1,1,1], [1,0,0,0,0,0,1,1,0,1,1], [1,0,0,0,0,0,1,1,1,0,1], [1,0,0,0,0,1,0,0,1,1,1], [1,0,0,0,0,1,0,1,1,0,1], [1,0,0,0,0,1,1,0,1,0,1], [1,0,0,0,1,0,0,0,1,1,1], [1,0,0,0,1,0,1,0,0,1,1], [1,0,0,0,1,1,0,0,0,1,1], [1,0,0,0,1,1,0,0,1,0,1], [1,0,0,0,1,1,0,1,1,1,1], [1,0,0,1,0,0,0,0,0,0,1], [1,0,0,1,0,0,0,1,0,1,1], [1,0,0,1,0,0,1,1,0,0,1], [1,0,0,1,0,1,0,1,0,0,1], [1,0,0,1,0,1,0,1,1,1,1], [1,0,0,1,1,0,0,0,1,0,1], [1,0,0,1,1,0,0,1,0,0,1], [1,0,0,1,1,0,1,0,1,1,1], [1,0,0,1,1,1,0,0,1,1,1], [1,0,0,1,1,1,0,1,1,0,1], [1,0,0,1,1,1,1,0,0,1,1], [1,0,0,1,1,1,1,1,1,1,1], [1,0,1,0,0,0,0,1,0,1,1], [1,0,1,0,0,0,0,1,1,0,1], [1,0,1,0,0,0,1,1,0,0,1], [1,0,1,0,0,0,1,1,1,1,1], [1,0,1,0,0,1,0,0,0,1,1], [1,0,1,0,0,1,1,0,0,0,1], [1,0,1,0,0,1,1,1,1,0,1], [1,0,1,0,1,0,0,0,0,1,1], [1,0,1,0,1,0,1,0,1,1,1], [1,0,1,0,1,1,0,0,0,0,1], [1,0,1,0,1,1,0,0,1,1,1], [1,0,1,0,1,1,0,1,0,1,1], [1,0,1,1,0,0,0,0,1,0,1], [1,0,1,1,0,0,0,1,1,1,1], [1,0,1,1,0,0,1,0,1,1,1], [1,0,1,1,0,0,1,1,0,1,1], [1,0,1,1,0,1,0,0,0,0,1], [1,0,1,1,0,1,0,1,0,1,1], [1,0,1,1,0,1,1,1,0,0,1], [1,0,1,1,1,0,0,0,0,0,1], [1,0,1,1,1,0,0,0,1,1,1], [1,0,1,1,1,1,0,0,1,0,1], [1,0,1,1,1,1,1,0,1,1,1], [1,0,1,1,1,1,1,1,0,1,1], [1,1,0,0,0,0,1,0,0,1,1], [1,1,0,0,0,0,1,0,1,0,1], [1,1,0,0,0,1,0,0,0,1,1], [1,1,0,0,0,1,0,0,1,0,1], [1,1,0,0,0,1,1,0,0,0,1], [1,1,0,0,0,1,1,0,1,1,1], [1,1,0,0,1,0,0,0,0,1,1], [1,1,0,0,1,0,0,1,1,1,1], [1,1,0,0,1,0,1,0,0,0,1], [1,1,0,0,1,0,1,1,0,1,1], [1,1,0,0,1,1,1,1,0,0,1], [1,1,0,0,1,1,1,1,1,1,1], [1,1,0,1,0,0,0,0,1,0,1], [1,1,0,1,0,0,0,1,0,0,1], [1,1,0,1,0,1,0,0,1,1,1], [1,1,0,1,0,1,0,1,1,0,1], [1,1,0,1,0,1,1,0,1,0,1], [1,1,0,1,0,1,1,1,1,1,1], [1,1,0,1,1,0,0,0,0,0,1], [1,1,0,1,1,0,0,1,1,0,1], [1,1,0,1,1,0,1,0,0,1,1], [1,1,0,1,1,0,1,1,1,1,1], [1,1,0,1,1,1,1,0,1,1,1], [1,1,0,1,1,1,1,1,1,0,1], [1,1,1,0,0,0,0,1,1,1,1], [1,1,1,0,0,0,1,0,0,0,1], [1,1,1,0,0,0,1,0,1,1,1], [1,1,1,0,0,0,1,1,1,0,1], [1,1,1,0,0,1,0,0,0,0,1], [1,1,1,0,0,1,0,1,0,1,1], [1,1,1,0,0,1,1,0,1,0,1], [1,1,1,0,0,1,1,1,0,0,1], [1,1,1,0,1,0,0,0,1,1,1], [1,1,1,0,1,0,0,1,1,0,1], [1,1,1,0,1,0,1,0,1,0,1], [1,1,1,0,1,0,1,1,0,0,1], [1,1,1,0,1,1,0,0,0,1,1], [1,1,1,0,1,1,1,1,0,1,1], [1,1,1,0,1,1,1,1,1,0,1], [1,1,1,1,0,0,0,0,0,0,1], [1,1,1,1,0,0,0,0,1,1,1], [1,1,1,1,0,0,0,1,1,0,1], [1,1,1,1,0,0,1,0,0,1,1], [1,1,1,1,0,1,0,1,0,0,1], [1,1,1,1,0,1,1,0,0,0,1], [1,1,1,1,1,0,0,0,1,0,1], [1,1,1,1,1,0,1,1,0,1,1], [1,1,1,1,1,1,0,1,0,1,1], [1,1,1,1,1,1,1,0,0,1,1], [1,1,1,1,1,1,1,1,0,0,1], [1,1,1,1,1,1,1,1,1,1,1]], [[1,0,0,0,0,0,0,0,0,1,0,1], [1,0,0,0,0,0,0,1,0,1,1,1], [1,0,0,0,0,0,1,0,1,0,1,1], [1,0,0,0,0,0,1,0,1,1,0,1], [1,0,0,0,0,1,0,0,0,1,1,1], [1,0,0,0,0,1,1,0,0,0,1,1], [1,0,0,0,0,1,1,0,0,1,0,1], [1,0,0,0,0,1,1,1,0,0,0,1], [1,0,0,0,0,1,1,1,1,0,1,1], [1,0,0,0,1,0,0,0,1,1,0,1], [1,0,0,0,1,0,0,1,0,1,0,1], [1,0,0,0,1,0,0,1,1,1,1,1], [1,0,0,0,1,0,1,0,1,0,0,1], [1,0,0,0,1,0,1,1,0,0,0,1], [1,0,0,0,1,1,0,0,0,0,1,1], [1,0,0,0,1,1,0,0,1,1,1,1], [1,0,0,0,1,1,0,1,0,0,0,1], [1,0,0,0,1,1,1,0,0,0,0,1], [1,0,0,0,1,1,1,0,0,1,1,1], [1,0,0,0,1,1,1,0,1,0,1,1], [1,0,0,0,1,1,1,1,0,1,0,1], [1,0,0,1,0,0,0,0,1,1,0,1], [1,0,0,1,0,0,0,1,0,0,1,1], [1,0,0,1,0,0,1,0,0,1,0,1], [1,0,0,1,0,0,1,0,1,0,0,1], [1,0,0,1,0,0,1,1,0,1,1,1], [1,0,0,1,0,0,1,1,1,0,1,1], [1,0,0,1,0,0,1,1,1,1,0,1], 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[1,1,1,1,1,0,1,0,1,1,1,1,0,1], [1,1,1,1,1,0,1,1,0,0,0,1,0,1], [1,1,1,1,1,0,1,1,0,1,0,1,1,1], [1,1,1,1,1,0,1,1,0,1,1,1,0,1], [1,1,1,1,1,0,1,1,1,0,0,0,0,1], [1,1,1,1,1,0,1,1,1,1,1,0,0,1], [1,1,1,1,1,1,0,0,0,0,1,1,0,1], [1,1,1,1,1,1,0,0,0,1,1,0,0,1], [1,1,1,1,1,1,0,0,0,1,1,1,1,1], [1,1,1,1,1,1,0,0,1,0,0,1,0,1], [1,1,1,1,1,1,0,0,1,1,0,1,1,1], [1,1,1,1,1,1,0,0,1,1,1,1,0,1], [1,1,1,1,1,1,0,1,0,0,0,0,1,1], [1,1,1,1,1,1,0,1,0,0,0,1,0,1], [1,1,1,1,1,1,0,1,0,0,1,0,0,1], [1,1,1,1,1,1,0,1,0,1,0,0,0,1], [1,1,1,1,1,1,0,1,0,1,0,1,1,1], [1,1,1,1,1,1,0,1,1,0,0,0,0,1], [1,1,1,1,1,1,1,0,0,0,0,0,1,1], [1,1,1,1,1,1,1,0,0,0,1,0,0,1], [1,1,1,1,1,1,1,0,0,1,0,0,0,1], [1,1,1,1,1,1,1,0,1,0,1,0,1,1], [1,1,1,1,1,1,1,0,1,1,0,1,0,1], [1,1,1,1,1,1,1,1,1,0,0,0,1,1], [1,1,1,1,1,1,1,1,1,1,0,1,1,1], [1,1,1,1,1,1,1,1,1,1,1,1,0,1]] ], (3)=[ [[1,0], [1,1], [1,2]], [[1,0,1], [1,1,2], [1,2,2]], [[1,0,2,1], [1,0,2,2], [1,1,0,2], [1,1,1,2], [1,1,2,1], [1,2,0,1], [1,2,1,1], [1,2,2,2]], [[1,0,0,1,2], [1,0,0,2,2], [1,0,1,0,2], [1,0,1,1,1], [1,0,1,2,1], [1,0,2,0,2], [1,1,0,0,2], [1,1,0,2,1], [1,1,1,0,1], [1,1,1,1,1], [1,1,1,2,2], [1,1,2,2,2], [1,2,0,0,2], [1,2,0,1,1], [1,2,1,0,1], [1,2,1,1,2], [1,2,1,2,1], [1,2,2,1,2]], [[1,0,0,0,2,1], [1,0,0,0,2,2], [1,0,0,1,1,2], [1,0,0,2,1,1], [1,0,1,0,1,1], [1,0,1,0,1,2], [1,0,1,1,0,2], [1,0,1,1,2,2], [1,0,1,2,0,1], [1,0,1,2,2,1], [1,0,2,1,0,1], [1,0,2,1,1,2], [1,0,2,1,2,2], [1,0,2,2,0,2], [1,0,2,2,1,1], [1,0,2,2,2,1], [1,1,0,0,0,2], [1,1,0,0,1,2], [1,1,0,0,2,1], [1,1,0,1,0,1], [1,1,0,1,1,1], [1,1,0,1,2,2], [1,1,1,0,1,1], [1,1,1,1,2,1], [1,1,1,2,1,1], [1,1,1,2,1,2], [1,1,2,0,0,1], [1,1,2,0,2,2], [1,1,2,1,0,2], [1,1,2,1,1,1], [1,1,2,2,0,1], [1,1,2,2,0,2], [1,2,0,0,0,1], [1,2,0,0,1,1], [1,2,0,0,2,2], [1,2,0,2,0,2], [1,2,0,2,1,2], [1,2,0,2,2,1], [1,2,1,0,1,2], [1,2,1,1,1,1], [1,2,1,1,1,2], [1,2,1,2,2,2], [1,2,2,0,0,2], [1,2,2,0,2,1], [1,2,2,1,0,1], [1,2,2,1,0,2], [1,2,2,2,0,1], [1,2,2,2,1,2]], [[1,0,0,0,0,1,2], [1,0,0,0,0,2,2], [1,0,0,0,1,1,1], [1,0,0,0,1,2,1], [1,0,0,0,2,0,1], [1,0,0,1,0,1,2], [1,0,0,1,0,2,1], [1,0,0,1,1,0,1], [1,0,0,1,1,2,2], [1,0,0,1,2,2,1], [1,0,0,2,0,1,1], [1,0,0,2,0,2,2], [1,0,0,2,1,0,1], [1,0,0,2,1,1,2], [1,0,0,2,2,1,1], [1,0,1,0,2,0,1], [1,0,1,0,2,1,2], [1,0,1,0,2,2,2], [1,0,1,1,0,0,1], [1,0,1,1,0,1,1], [1,0,1,1,0,2,2], [1,0,1,1,1,2,2], [1,0,1,2,0,0,1], [1,0,1,2,0,1,2], [1,0,1,2,0,2,1], [1,0,1,2,1,1,2], [1,0,2,0,0,0,1], [1,0,2,0,1,0,1], [1,0,2,0,1,1,2], [1,0,2,0,1,2,2], [1,0,2,1,0,2,1], [1,0,2,1,1,0,2], [1,0,2,1,1,1,2], [1,0,2,1,1,2,1], [1,0,2,2,0,1,1], [1,0,2,2,1,0,2], [1,0,2,2,1,1,1], [1,0,2,2,1,2,2], [1,1,0,0,0,0,2], [1,1,0,0,0,1,2], [1,1,0,0,1,1,1], [1,1,0,1,0,0,2], [1,1,0,1,0,1,1], [1,1,0,1,1,0,1], [1,1,0,1,1,1,2], [1,1,0,1,2,1,2], [1,1,0,2,0,0,1], [1,1,0,2,1,1,1], [1,1,0,2,1,2,1], [1,1,0,2,2,0,1], [1,1,0,2,2,0,2], [1,1,1,0,0,0,1], [1,1,1,0,0,1,1], [1,1,1,0,1,2,2], [1,1,1,0,2,0,2], [1,1,1,0,2,2,1], [1,1,1,1,0,1,2], [1,1,1,1,0,2,1], [1,1,1,1,1,1,1], [1,1,1,1,1,1,2], [1,1,1,1,2,2,2], [1,1,1,2,0,1,1], 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[1,33,31], [1,33,34], [1,33,35], [1,33,36], [1,33,38], [1,33,39], [1,33,40], [1,33,41], [1,33,42], [1,34,1], [1,34,2], [1,34,3], [1,34,4], [1,34,5], [1,34,9], [1,34,11], [1,34,12], [1,34,13], [1,34,19], [1,34,23], [1,34,24], [1,34,26], [1,34,28], [1,34,29], [1,34,32], [1,34,35], [1,34,37], [1,34,40], [1,34,41], [1,34,42], [1,35,4], [1,35,8], [1,35,9], [1,35,11], [1,35,13], [1,35,14], [1,35,17], [1,35,20], [1,35,22], [1,35,25], [1,35,26], [1,35,27], [1,35,29], [1,35,30], [1,35,31], [1,35,32], [1,35,33], [1,35,37], [1,35,39], [1,35,40], [1,35,41], [1,36,1], [1,36,3], [1,36,4], [1,36,5], [1,36,11], [1,36,15], [1,36,16], [1,36,18], [1,36,20], [1,36,21], [1,36,24], [1,36,27], [1,36,29], [1,36,32], [1,36,33], [1,36,34], [1,36,36], [1,36,37], [1,36,38], [1,36,39], [1,36,40], [1,37,1], [1,37,2], [1,37,4], [1,37,6], [1,37,7], [1,37,10], [1,37,13], [1,37,15], [1,37,18], [1,37,19], [1,37,20], [1,37,22], [1,37,23], [1,37,24], [1,37,25], [1,37,26], [1,37,30], [1,37,32], [1,37,33], [1,37,34], [1,37,40], [1,38,5], [1,38,9], [1,38,10], [1,38,12], [1,38,14], [1,38,15], [1,38,18], [1,38,21], [1,38,23], [1,38,26], [1,38,27], [1,38,28], [1,38,30], [1,38,31], [1,38,32], [1,38,33], [1,38,34], [1,38,38], [1,38,40], [1,38,41], [1,38,42], [1,39,1], [1,39,2], [1,39,5], [1,39,8], [1,39,10], [1,39,13], [1,39,14], [1,39,15], [1,39,17], [1,39,18], [1,39,19], [1,39,20], [1,39,21], [1,39,25], [1,39,27], [1,39,28], [1,39,29], [1,39,35], [1,39,39], [1,39,40], [1,39,42], [1,40,1], [1,40,5], [1,40,6], [1,40,8], [1,40,10], [1,40,11], [1,40,14], [1,40,17], [1,40,19], [1,40,22], [1,40,23], [1,40,24], [1,40,26], [1,40,27], [1,40,28], [1,40,29], [1,40,30], [1,40,34], [1,40,36], [1,40,37], [1,40,38], [1,41,2], [1,41,5], [1,41,7], [1,41,10], [1,41,11], [1,41,12], [1,41,14], [1,41,15], [1,41,16], [1,41,17], [1,41,18], [1,41,22], [1,41,24], [1,41,25], [1,41,26], [1,41,32], [1,41,36], [1,41,37], [1,41,39], [1,41,41], [1,41,42], [1,42,3], [1,42,4], [1,42,6], [1,42,8], [1,42,9], [1,42,12], [1,42,15], [1,42,17], [1,42,20], [1,42,21], [1,42,22], [1,42,24], [1,42,25], [1,42,26], [1,42,27], [1,42,28], [1,42,32], [1,42,34], [1,42,35], [1,42,36], [1,42,42]] ] ]): # ======= testing lists of irreducible polynomials of degree n over Fp alias(testirrpoly=TestIrrPoly): TestIrrPoly := proc(p::integer,n::integer) local i,d,data,shouldbe,x,number: data:=IrrPoly[p][n]: number:=nops(data): #----------------------------------------- check repeated entries if(number > nops({op(data)})) then lprint(`there are repeated entries`) fi: #----------------------------------------- check completeness shouldbe:=0: for d in divisors(n) do shouldbe:=shouldbe+mobius(n/d)*p^d od: shouldbe:=shouldbe/n: if(shouldbe<>number) then lprint(`wrong number of polys: n=`,n,shouldbe,number) fi: #----------------------------------------- check irreducibility map(Coeff2Poly,data,x): {op(map(Irreduc,%) mod p)}: if(nops(%)>1) then lprint(`error,some poly is reducible: p,n`,p,n): for i to number do if(not(Irreduc(Coeff2Poly(data[i],x)) mod p)) then lprint(data[i]) fi od fi: #----------------------------------------- check lexicographical ordering map(Digit2Number,data,p): sort(%): if(not %% = %) then lprint(`error,polys are not in lexicographical order`) fi end: # ======================= list of digits -> integer in base p Digit2Number := proc(l::list,p::integer) local i,n,number,powerp: n:=nops(l): number := l[n]: powerp := 1: for i from n-1 to 1 by -1 do powerp := powerp*p: number := number + l[i] * powerp od: number end: