# 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)
• list of variables.

### 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]); 