公共零点 meaning in English

common zeros

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
本文从7个方面阐述了结式的应用，包括判断2个多项式的公共零点，判定多项式是否有重根，计算多项式的判别式，寻找代数数满足的方程，平面有理曲线的隐式化，非线性代数方程组求解和不等式机器证明中半代数系统边界曲面的获得等。
The piecewise algebraic curve and the piecewise algebraic variety , as the set of zeros of a bivariate spline function and the set of all common zeros of multivariate splines respectively , are new and important concepts in algebraic geometry and computational geometry . it is obvious that the piecewise algebraic curve ( variety ) is a kind of generalization of the classical algebraic curve ( variety respectively )
分片代数曲线作为二元样条函数的零点集合，分片代数簇作为一些多元样条函数的公共零点集合，它们是代数几何与计算几何中一种新的重要概念，显然也是经典代数曲线与代数簇的推广。