贝祖:西方消元理论的开拓者

Bezout: the Pioneer of Western Elimination Theory

贝祖是18世纪法国的数学家,由于公务繁忙,为了能在一个有限的领域内作出有价值的工作,热爱数学的他将自己的研究限制在代数学中的一个方向——方程理论上。贝祖消元求解方程组所用的多项式乘数法是得到最广泛认可的消元方法,并且成为现代多项式优化算法中运用多项式乘数的算法依据;贝祖求结式次数所得到的贝祖定理是其理论中最耀眼的成就之一,成为代数几何中的基础定理而应用广泛;贝祖关于结式的工作开启了现代消元理论研究的大门,在其影响和推动下,拉格朗日、柯西简化了消元过程、西尔维斯特完成了结式和惯性形式的工作。

Etienne Bezout is a French mathematician in the 18 century. With busy schedule but loving mathematics, he had to confi ne his studies to the theory of equations, one of the branches of algebra, in order to make some breakthroughs within a limited scope. Bezout's polynomial multiplier for resolving equations was the most widely recognized elimination method, and became the theoretical basis for applying the polynomial multiplier in modern polynomial optimization. Bezout Theorem acquired in solving the degree of resultant is one of his most glaring achievements, which has developed into the basic theorem in the algebraic geometry and is widely applied. What's more, Bezout's theory of resultant has inspired the studies of the modern elimination theory. Under his infl uence, Lagrange and Cauchy refi ned the elimination procedure and Sylvester fi nished the work on resultants and inertia forms.