stylistic:tone, information:filtering, structural:expansion
Generic properties

In this section, we consider two polynomials A = a 0 x d + a 1 x d − 1 + ⋯ + a d {\displaystyle A=a_{0}x^{d}+a_{1}x^{d-1}+\cdots +a_{d}} and B = b 0 x e + b 1 x e − 1 + ⋯ + b e {\displaystyle B=b_{0}x^{e}+b_{1}x^{e-1}+\cdots +b_{e}} whose d + e + 2 coefficients are distinct indeterminates. Let R = Z {\displaystyle R=\mathbb {Z} } be the polynomial ring over the integers defined by these indeterminates.The resultant res (A, B) {\displaystyle \operatorname {res} (A,B)} is often called the generic resultant for the degrees d and e. It has the following properties.