零维三角系统的多重实解隔离
Real Solution Isolation with Multiplicity of Zero-Dimensional Triangular Systems
摘要：
现有的零维多项式系统的实解分离算法不计算解的重数。本文用自然的方法定义了零维三角多项式组解的重数，并证明了我们的定义与经典的局部（交）重数的定义是等价的.然后，我们提出了一个有效的和完整的算法，隔离实解的多重零维三角多项式系统使用我们的定义。该算法基于实代数系数多项式的区间算术和无平方因子分解。文中给出了文献中一些算例的计算结果。
英文摘要：
Existing algorithms for isolating real solutions of zero-dimensional polynomial systems do not compute the multiplicities of the solutions. In this paper, we define in a natural way the multiplicity of solutions of zero-dimensional triangular polynomial systems and prove that our definition is equivalent to the classical definition of local (intersection) multiplicity. Then we present an effective and complete algorithm for isolating real solutions with multiplicities of zero-dimensional triangular polynomial systems using our definition. The algorithm is based on interval arithmetic and square-free factorization of polynomials with real algebraic coefficients. The computational results on some examples from the literature are presented.
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