CASA Function: mvresultant
Compute the resultant system of a system of multivariate polynomials.
Calling Sequence:
- r := mvresultant(repr,vars)
Parameters:
- repr : list(polynom(casaCoeffType, vars))
- list of polynomials in vars with (optional) parameters and coefficients of type casaCoeffType
- vars : list(name)
-
Result:
- r : list(polynom)
- the resultant system of the given system of multivariate polynomials
Description:
- The function computes the resultant system of a system of multivariate polynomials in order to set up conditions for their solvability as well as formulas for calculating their solutions.
- The vanishing of the resultant system provides a solvability criterion for the existance of common solutions of the system (in projective space).
- We use the algorithm described in van der Waerden's Moderne Algebra, Springer-Verlag, 1994.
Examples:
> F1:=[x2^2+x1^2-1,x1*x2-1,x2^2 -x1]:
> mvresultant(F1,[x1,x2]);
> F2:=[v*x2^2+RootOf(x^3+1)*x1^2-1,x1*x2-1,x2^2 -x1]:
> mvresultant(F2,[x1,x2]);
> F3:=[x3-x1*x2-x2,x2*x3-x1,x1*x3-x2]:
> mvresultant(F3,[x1]);
> mvresultant(F3,[x1,x2]);
See Also:
[CASA]
[[resultant]]