|
|
代数曲面对应多项式的质公因子存在性研究
|
Abstract:
Bezout定理在证明二元插值适定结点组构造方法时起到了重要的作用，但不能直接简单推广至三维空间，该文针对这个问题以平面中的相关理论为参照，以代数曲面与多项式相关理论为基础，对何时代数曲面对应多项式有质公因子进行了研究，给出了判断空间代数曲面对应多项式是否有质公因子的一种方法。
Bezout’s theorem plays an important role in proving the constructive methods of properly posed set of nodes for binary interpolation, but it cannot be directly extended to three-dimensional space. In order to address this problem, this paper investigated relevant theories on the plane, explored relevant theories of algebraic surfaces and polynomials to explain the instances during which polynomial corresponding to algebraic surface can have common prime factors, and proposed a method to judge whether the polynomial corresponding to algebraic surface has common prime factors.
| [1] | 崔利宏. 多元Lagrange插值与Kergin插值[M]. 大连: 辽宁师范大学出版社, 2018: 6-7. |
| [2] | 梁学章. 关于多元函数的插值与逼近[D]: [硕士学位论文]. 长春: 吉林大学, 1965. |
| [3] | 余震果, 李丽, 李婷, 崔利宏. 关于多元插值适定性问题研究[J]. 吉林师范大学学报(自然科学版), 2011(2): 17-25 |
| [4] | 梁学章. 关于多元函数的插值与逼近[J]. 高等学校计算数学学报, 1979(1): 123-124 |
| [5] | De Boor, C. and Ron, A. (1990) On Multivariate Polynomial Interpolation. Constructive Approximation, 6, 287-302.
https://doi.org/10.1007/BF01890412 |
| [6] | Liang, X.Z., Wang, R.H., Cui, L.H., et al. (2006) Some Researches on Trivariate Lagrange Interpolation. Journal of Computational and Applied Mathematics, 195, 192-205. https://doi.org/10.1016/j.cam.2005.03.083 |
| [7] | 樊凯. 关于多元多项式可除性的讨论[J]. 武汉教育学院学报, 1997, 27(1): 1-8. |
| [8] | 梁学章, 李强. 多元逼近[M]. 北京: 国防工业出版社, 2005: 22-24. |
