Please include. This works with any polynomial. Best, ralf diff -u --recursive GiNaC-1.2.1-orig/doc/tutorial/ginac.texi GiNaC-1.2.1/doc/tutorial/ginac.texi --- GiNaC-1.2.1-orig/doc/tutorial/ginac.texi Mon Mar 15 18:47:17 2004 +++ GiNaC-1.2.1/doc/tutorial/ginac.texi Sun Jun 20 15:45:19 2004 @@ -4371,7 +4399,7 @@ original polynomial. -@subsection GCD and LCM +@subsection GCD, LCM, resultant @cindex GCD @cindex LCM @cindex @code{gcd()} @@ -4408,7 +4436,37 @@ @} @end example +@cindex resultant +@cindex @code{resultant()} + +The resultant of two expressions only makes sense with polynomials. +It is always computed with respect to a specific symbol within the +expressions. The function has the interface + +@example +ex resultant(const ex & a, const ex & b, const symbol & s); +@end example +Resultants are commutative. The following example computes the resultant +of two expressions with respect to both @code{x} and @code{y}: + +@example +#include <ginac/ginac.h> +using namespace GiNaC; + +int main() +@{ + symbol x("x"), y("y"); + + ex e1 = x+pow(y,2), e2 = 2*pow(x,3)-1; // x+y^2, 2*x^3-1 + ex r; + + r = resultant (e1, e2, x); + // -> 1+2*y^6 + r = resultant (e1, e2, y); + // -> 1-4*x^3+4*x^6 +@} +@end example @subsection Square-free decomposition @cindex square-free decomposition @cindex factorization diff -u --recursive GiNaC-1.2.1-orig/ginac/normal.cpp GiNaC-1.2.1/ginac/normal.cpp --- GiNaC-1.2.1-orig/ginac/normal.cpp Thu Jan 8 16:06:50 2004 +++ GiNaC-1.2.1/ginac/normal.cpp Sun Jun 20 11:58:11 2004 @@ -2374,5 +2374,33 @@ return e; } +/** Resultant of two expressions e1,e2 with respect to symbol s. + * Method: Compute determinant of Sylvester matrix of e1,e2,s. */ +ex resultant (const ex &e1, const ex &e2, const symbol &s) +{ + const int h1 = e1.degree (s); + const int l1 = e1.ldegree (s); + const int h2 = e2.degree (s); + const int l2 = e2.ldegree (s); + + const int msize = h1 + h2; + matrix m (msize, msize); + + for (int l = h1; l >= l1; --l) + { + const ex e = e1.coeff (s, l); + for (int k = 0; k < h2; ++k) + m (k, k+h1-l) = e; + } + for (int l = h2; l >= l2; --l) + { + const ex e = e2.coeff (s, l); + for (int k = 0; k < h1; ++k) + m (k+h2, k+h2-l) = e; + } + + return m.determinant(); +} + } // namespace GiNaC diff -u --recursive GiNaC-1.2.1-orig/ginac/normal.h GiNaC-1.2.1/ginac/normal.h --- GiNaC-1.2.1-orig/ginac/normal.h Thu Jan 8 16:06:50 2004 +++ GiNaC-1.2.1/ginac/normal.h Sun Jun 20 11:57:22 2004 @@ -66,6 +66,9 @@ // Collect common factors in sums. extern ex collect_common_factors(const ex & e); +// Resultant of two polynomials e1,e2 with respect to symbol s +extern ex resultant (const ex& e1, const ex& e2, const symbol& s); + } // namespace GiNaC #endif // ndef __GINAC_NORMAL_H__