úÎìŸ      Safe-Inferred Berlekamp'#s Factorization Algorithm over Fp[x]r : computes the factorization of a monic square-free polynomial P into irreducible factor polynomials over F_{p}[x]R , p is a prime number. This method is based on linear algebra over finite field.  | g pivotPos' lswap triangulizedModIntegerMat htriangulizedModIntegerMat p m: gives the gauss triangular decomposition of an integeral matrix m in Fp. e The result is (r, u) where u is a unimodular matrix, r is an upper-triangular matrix , and u.m = r. GnullSpaceModIntegerMat p m : computes the null space of matrix m in Fp mmultZ C mmultZ p a b : compute the product of two integer matrices in Fp.  gcdPolyZ H gcdPolyZ p P1 P2 : gives the polynomial gcd of P1 , P2 modulo over Fp[x]. <Frobenius automorphism : linear map V -> V^p - V , V in Fp[x] P and Fp[x]%P as vector space over the field Fp.  matrixBerl l matrixBerl p f : is the matrix of the Frobenius endomorphism over the canonical base {1,X,X^2..,X^(p-1)} , % matrixBerl(i,j) = X^(pj)-X^j mod P. 0derivPolyZ : derivative of polynmial P over Fp[x] squareFreePolyZ D squareFreePolyZ p f : gives the euclidean quotient of P and gcd(f,f'.). That quotient is a square free polynomial.  berlekamp _ berlekamp p P: gives a complete factorization of a polynom P of irreducible polynoms over Fp[x]. irreducibilityTestPolyZ G irreducibilityTestPolyZ : irreducibility test of polynomials over Fp[x]  multPoly 5 multPoly : product of polynomials P1, .., Pk in Fp[x].               BerlekampAlgorithm-0.1.0.0BerlekampAlgorithmg pivotPos'lswaptriangulizedModIntegerMatnullSpaceModIntegerMatmmultZfrobmatrixBerlTranspose derivPolyZsquareFreePolyZ berlekampirreducibilityTestPolyZmultPolygcdPolyZpivotMinsswaphnf'gaussZ'gaussZmatIff zipgcdPolyzgcdPolyphi multPoly'