Jingzhong Zhang
Exact Bivariate Polynomial Factorization in Q by Approximation of Roots.
Tue, 08/24/2010 - 15:01 — SomNambulAuthors: Yong Feng, Jingzhong Zhang, Wenyuan Wu
Subjects: Algebraic Geometry
AbstractFactorization of polynomials is one of the foundations of symbolic
computation. Its applications arise in numerous branches of mathematics and
other sciences. However, the present advanced programming languages such as C++
and J++, do not support symbolic computation directly. Hence, it leads to
difficulties in applying factorization in engineering fields. In this paper, we
present an algorithm which use numerical method to obtain exact factors of a
bivariate polynomial with rational coefficients.Parallel computation of real solving bivariate polynomial systems by zero-matching method.
Tue, 01/19/2010 - 16:01 — SomNambulAuthors: Xiaolin Qin, Yong Feng, Jingwei Chen, Jingzhong Zhang
Subjects: Symbolic Computation
AbstractWe present a new algorithm for solving the real roots of a bivariate
polynomial system $\Sigma=\{f(x,y),g(x,y)\}$ with a finite number of solutions
by using a zero-matching method. The method is based on a lower bound for
bivariate polynomial system when the system is non-zero. Moreover, the
multiplicities of the roots of $\Sigma=0$ can be obtained by a given
neighborhood. From this approach, the parallelization of the method arises
naturally. By using a multidimensional matching method this principle can be
generalized to the multivariate equation systems.A complete algorithm to find exact minimal polynomial by approximations.
Wed, 01/06/2010 - 16:01 — SomNambulAuthors: Xiaolin Qin, Yong Feng, Jingwei Chen, Jingzhong Zhang
Subjects: Symbolic Computation
AbstractWe present a complete algorithm for finding an exact minimal polynomial from
its approximate value by using an improved parameterized integer relation
construction method. Our result is superior to the existence of error
controlling on obtaining an exact rational number from its approximation. The
algorithm is applicable for finding exact minimal polynomial of an algebraic
number by its approximate root.
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