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)abbrev package CYCLOTOM CyclotomicPolynomialPackage
++ This package \undocumented{} 
CyclotomicPolynomialPackage: public == private where
  SUP  ==> SparseUnivariatePolynomial(Integer)
  LSUP ==> List(SUP)
  NNI  ==> NonNegativeInteger
  FR   ==> Factored SUP
  IFP  ==> IntegerFactorizationPackage Integer
 
  public == with
    cyclotomicDecomposition: Integer -> LSUP
	++ cyclotomicDecomposition(n) \undocumented{}
    cyclotomic:              Integer -> SUP
	++ cyclotomic(n) \undocumented{}
    cyclotomicFactorization: Integer -> FR
	++ cyclotomicFactorization(n) \undocumented{}
 
  private == add
    cyclotomic(n:Integer): SUP ==
      x,y,z,l: SUP
      g := factors factor(n)$IFP
      --Now, for each prime in the factorization apply recursion
      l := monomial(1,1) - monomial(1,0)
      for u in g repeat
         l := (monicDivide(multiplyExponents(l,u.factor::NNI),l)).quotient
         if u.exponent>1 then
            l := multiplyExponents(l,((u.factor)**((u.exponent-1)::NNI))::NNI)
      l
 
    cyclotomicDecomposition(n:Integer):LSUP ==
      x,y,z: SUP
      l,ll,m: LSUP
      g := factors factor(n)$IFP
      l := [monomial(1,1) - monomial(1,0)]
      --Now, for each prime in the factorization apply recursion
      for u in g repeat
         m := [(monicDivide(
            multiplyExponents(z,u.factor::NNI),z)).quotient for z in l]
         for rr in 1..(u.exponent-1) repeat
            l := append(l,m)
            m := [multiplyExponents(z,u.factor::NNI) for z in m]
         l := append(l,m)
      l
 
    cyclotomicFactorization(n:Integer):FR ==
      fr : FR := 1$FR
      for f in cyclotomicDecomposition(n) repeat
        fr := fr * primeFactor(f,1$Integer)
      fr

