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Mathematica > Polynomial Systems >

Built-in Mathematica Symbol

Resultant

Resultant[poly₁, poly₂, var]
computes the resultant of the polynomials poly₁ and poly₂ with respect to the variable var.

Resultant[poly₁, poly₂, var, Modulus->p]
computes the resultant modulo the prime p.

The resultant of two polynomials p and q, both with leading coefficient one, is the product of all the differences p_i-q_j between roots of the polynomials. The resultant is always a number or a polynomial.

The resultant vanishes exactly when the polynomials have roots in common: