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)abbrev package UPCDEN UnivariatePolynomialCommonDenominator
++ Author: Manuel Bronstein
++ Date Created: 2 May 1988
++ Date Last Updated: 22 Feb 1990
++ Description: 
++ UnivariatePolynomialCommonDenominator provides
++ functions to compute the common denominator of the coefficients of
++ univariate polynomials over the quotient field of a gcd domain.
 
UnivariatePolynomialCommonDenominator(R, Q, UP) : SIG == CODE where
  R : IntegralDomain
  Q : QuotientFieldCategory R
  UP : UnivariatePolynomialCategory Q
 
  SIG ==> with

    commonDenominator : UP -> R
      ++ commonDenominator(q) returns a common denominator d for
      ++ the coefficients of q.

    clearDenominator : UP -> UP
      ++ clearDenominator(q) returns p such that \spad{q = p/d} where d is
      ++ a common denominator for the coefficients of q.

    splitDenominator : UP -> Record(num: UP, den: R)
      ++ splitDenominator(q) returns \spad{[p, d]} such that 
      ++ \spad{q = p/d} and d
      ++ is a common denominator for the coefficients of q.
 
  CODE ==> add

    import CommonDenominator(R, Q, List Q)
 
    commonDenominator p == commonDenominator coefficients p
 
    clearDenominator p ==
      d := commonDenominator p
      map(x +-> numer(d*x)::Q, p)
 
    splitDenominator p ==
      d := commonDenominator p
      [map(x +-> numer(d*x)::Q, p), d]