The Resultant function is a placeholder for representing the resultant of the polynomials a and b with respect to the main variable x. It is used in conjunction with either mod or evala which define the coefficient domain as described below.

The call Resultant(a, b, x) mod p computes the resultant of a and b with respect to the main variable x modulo p, a prime integer. The argument a must be a (multivariate) polynomial over the rationals or over a finite field specified by RootOfs.

The call evala(Resultant(a, b, x)) does likewise for a and b (multivariate) polynomials with algebraic number (or function) coefficients defined by RootOfs.

The call modp1(Resultant(a, b), p) computes the resultant of a and b modulo p a prime integer where a and b are in the modp1 representation.

$\mathrm{Resultant}\left(2x+1\,3x+4\,x\right)\mathbf{mod}7$

$5$

$r≔x+\mathrm{RootOf}\left({\mathrm{\_Z}}^2-2\right)\:$

$s≔\mathrm{RootOf}\left({\mathrm{\_Z}}^2-2\right)x+1\:$

$\mathrm{evala}\left(\mathrm{Resultant}\left(r\,s\,x\right)\right)$

$\mathrm{-1}$

$\mathrm{evala}\left(\mathrm{Resultant}\left(2x^2+xy+x+y+3\,3xy+y^2\,x\right)\right)$

$-y^2\left(y^2-6y-27\right)$