Mathematica

    Chapter 9






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Important: The procedure names polynomialDivision and quotient begin with lower case letters to avoid conflict with Mathematica's pre-defined procedures PolynomialDivision and Quotient .

Section 9.1

SquareFreeFactor, Figure 9.1 page 356 (Squarefreefactor.txt,
    requires the procedures
       quotient, Figure 4.1 page 116
       PolynomialGcd, Figure 4.3 page 130, requires additional procedures (see file))

Section 9.2

Kronecker, KroneckerFactors, Figures 9.2 and 9.3 pages 364-365 (Kronecker.txt,
    requires the procedures
       FindIntegerFactors (Exercise 3, page 369),
       FindxuValues (Exercise 4, page 369),
       FindSsets (Exercise 5, page 369),
       LagrangePolynomial.txt (Exercise 6, page 369),
       polynomialDivision, Figure 4.1 page 116)

Section 9.3

BerlekampFactor, Figure 9.4 page 384 (BerlekampFactor.txt,
    requires the procedures
       Rmatrix (Exercise 5, page 399),
       AuxiliaryBasis, Figure 9.5 pages 393-394, requires additional procedures (see below),
       FindFactors, Figure 9.7 page 396, requires additional procedures (see below))
AuxiliaryBasis, Figures 9.5 and 9.6, pages 393-394, (AuxiliaryBasis.txt,
    requires the procedures
       MultiplicativeInverseP (Exercise 11, page 60))
FindFactors, Figure 9.7 page 396 (FindFactors.txt,
    requires the procedures
       PolyDivP (Exercise 9, page 125),
       PolyGcdP (Exercise 4, page 142))

Section 9.4

IrreducibleFactor, Figure 9.8 page 423 (IrreducibleFactor.txt,
    requires the procedures
       FindPrime (Exercise 13, page 428),
       Mathematica's Prime operator (Prime.nb, see Exercise 13, page 428)
       BerlekampFactor, Figure 9.4 page 384, requires additional procedures (see above),
       FindK (Exercise 17, page 429),
       HenselLift, Figure 9.9 page 424, requires additional procedures (see below),
       Tnn (Exercise 2(a), page 427)
       Ts (Exercise 2(b), page 427)
       PolynomialContent (Exercise 7(a), page 260))
HenselLift, Figure 9.9 page 424 (HenselLift.txt,
    requires the procedures
       TrueFactors, Figure 9.10 page 426, requires additional procedures (see below),
       GenExtSigmaP, GenExtRP (Exercise 11, page 427),
       Ts (Exercise 2(b), page 427)
TrueFactors, Figure 9.10 page 426 (TrueFactors.txt,
    requires the procedures
       CleanUp (Exercise 14, page 428),
       Comb (Exercise 15, page 428),
       polynomialDivision, Figure 4.1 page 116)
       Ts (Exercise 2(b), page 427)