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)abbrev package NSUP2 NewSparseUnivariatePolynomialFunctions2
++ Description:
++ This package lifts a mapping from coefficient rings R to S to
++ a mapping from sparse univariate polynomial over R to
++ a sparse univariate polynomial over S.
++ Note that the mapping is assumed
++ to send zero to zero, since it will only be applied to the non-zero
++ coefficients of the polynomial.

NewSparseUnivariatePolynomialFunctions2(R,S) : SIG == CODE where
  R : Ring
  S : Ring

  SIG ==> with

    map : (R->S,NewSparseUnivariatePolynomial R) -> NewSparseUnivariatePolynomial S
      ++ \axiom{map(func, poly)} creates a new polynomial by applying func to
      ++ every non-zero coefficient of the polynomial poly.

  CODE ==> add

    map(f, p) == map(f, p)$UnivariatePolynomialCategoryFunctions2(R,
             NewSparseUnivariatePolynomial R, S, NewSparseUnivariatePolynomial S)