In this paper , it s applications were explained from seven different fields , the common zeros of two polynomials , the multiplicities of roots and the discrimination of a polynomial , searching the equations suitable for a algebraic number , implicating a rational curve over the plane , computing the zeros of a nonlinear algebraic equation and gathering the discrimination surface of the sas in automated theorem proving on inequalities 本文從7個(gè)方面闡述了結(jié)式的應(yīng)用,包括判斷2個(gè)多項(xiàng)式的公共零點(diǎn),判定多項(xiàng)式是否有重根,計(jì)算多項(xiàng)式的判別式,尋找代數(shù)數(shù)滿足的方程,平面有理曲線的隱式化,非線性代數(shù)方程組求解和不等式機(jī)器證明中半代數(shù)系統(tǒng)邊界曲面的獲得等。