18 Jan
2002
18 Jan
'02
9:16 p.m.
Dear Richard,
hare is the promised patch for normal.cpp. This adds a note of clarification to the documentation for sqrfree(). Feel free to edit it at will. All the best
Roberto
--
Prof. Roberto Bagnara
Computer Science Group
Department of Mathematics, University of Parma, Italy
http://www.cs.unipr.it/~bagnara/
mailto:bagnara@cs.unipr.it
diff -rcp GiNaC-1.0.3.orig/ginac/normal.cpp GiNaC-1.0.3/ginac/normal.cpp
*** GiNaC-1.0.3.orig/ginac/normal.cpp Thu Dec 20 12:33:43 2001
--- GiNaC-1.0.3/ginac/normal.cpp Fri Jan 18 22:09:25 2002
*************** static exvector sqrfree_yun(const ex &a,
*** 1741,1751 ****
return res;
}
! /** Compute square-free factorization of multivariate polynomial in Q[X].
*
* @param a multivariate polynomial over Q[X]
* @param x lst of variables to factor in, may be left empty for autodetection
! * @return polynomial a in square-free factored form. */
ex sqrfree(const ex &a, const lst &l)
{
if (is_a<numeric>(a) || // algorithm does not trap a==0
--- 1741,1781 ----
return res;
}
! /** Compute a square-free factorization of a multivariate polynomial in Q[X].
*
* @param a multivariate polynomial over Q[X]
* @param x lst of variables to factor in, may be left empty for autodetection
! * @return a square-free factorization of \p a.
! *
! * \note
! * A polynomial \f$p(X) \in C[X]\f$ is said <EM>square-free</EM>
! * if, whenever any two polynomials \f$q(X)\f$ and \f$r(X)\f$
! * are such that
! * \f[
! * p(X) = q(X)^2 r(X),
! * \f]
! * we have \f$q(X) \in C\f$.
! * This means that \f$p(X)\f$ has no repeated factors, apart
! * eventually from constants.
! * Given a polynomial \f$p(X) \in C[X]\f$, we say that the
! * decomposition
! * \f[
! * p(X) = b \cdot p_1(X)^{a_1} \cdot p_2(X)^{a_2} \cdots p_r(X)^{a_r}
! * \f]
! * is a <EM>square-free factorization</EM> of \f$p(X)\f$ if the
! * following conditions hold:
! * -# \f$b \in C\f$ and \f$b \neq 0\f$;
! * -# \f$a_i\f$ is a positive integer for \f$i = 1, \ldots, r\f$;
! * -# the degree of the polynomial \f$p_i\f$ is strictly positive
! * for \f$i = 1, \ldots, r\f$;
! * -# the polynomial \f$\Pi_{i=1}^r p_i(X)\f$ is square-free.
! *
! * Square-free factorizations need not be unique. For example, if
! * \f$a_i\f$ is even, we could change the polynomial \f$p_i(X)\f$
! * into \f$-p_i(X)\f$.
! * Observe also that the factors \f$p_i(X)\f$ need not be irreducible
! * polynomials.
! */
ex sqrfree(const ex &a, const lst &l)
{
if (is_a<numeric>(a) || // algorithm does not trap a==0