For a multivariate polynomial equation with coefficients in a computable ordered field, two criteria of this equation having real solutions are given. Based on the criteria, decision methods for the existence of real ...For a multivariate polynomial equation with coefficients in a computable ordered field, two criteria of this equation having real solutions are given. Based on the criteria, decision methods for the existence of real zeros and the semidefiniteness of binaly polynomials are provided. With the aid of computers, these methods are used to solve several examples. The technique is to extend the original field involved in the question to a computable non-Archimedean ordered field containing infinitesimal elements.展开更多
For an ordered field (K,T) and an idealI of the polynomial ring $K\left[ {x_1 , \cdots ,x_n } \right]$ , the construction of the generalized real radical $^{\left( {T,U,W} \right)} \sqrt I $ ofI is investigated. When ...For an ordered field (K,T) and an idealI of the polynomial ring $K\left[ {x_1 , \cdots ,x_n } \right]$ , the construction of the generalized real radical $^{\left( {T,U,W} \right)} \sqrt I $ ofI is investigated. When (K,T) satisfies some computational requirements, a method of computing $^{\left( {T,U,W} \right)} \sqrt I $ is presented.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 19661002)the Climbing Project
文摘For a multivariate polynomial equation with coefficients in a computable ordered field, two criteria of this equation having real solutions are given. Based on the criteria, decision methods for the existence of real zeros and the semidefiniteness of binaly polynomials are provided. With the aid of computers, these methods are used to solve several examples. The technique is to extend the original field involved in the question to a computable non-Archimedean ordered field containing infinitesimal elements.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19661002)the Climbing Project
文摘For an ordered field (K,T) and an idealI of the polynomial ring $K\left[ {x_1 , \cdots ,x_n } \right]$ , the construction of the generalized real radical $^{\left( {T,U,W} \right)} \sqrt I $ ofI is investigated. When (K,T) satisfies some computational requirements, a method of computing $^{\left( {T,U,W} \right)} \sqrt I $ is presented.
