| On solving equations of algebraic sum of equal powers |
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| 引用本文： | WANG Xinghua & YANG Shijun Department of Mathematics,Zhejiang University,Hangzhou 310028,China, Department of Mathematics,Hangzhou Normal College,Hangzhou 310036,China. On solving equations of algebraic sum of equal powers[J]. 中国科学A辑(英文版), 2006, 49(9): 1153-1157. DOI: 10.1007/s11425-006-1153-y |
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| 作者姓名： | WANG Xinghua & YANG Shijun Department of Mathematics Zhejiang University Hangzhou 310028 China Department of Mathematics Hangzhou Normal College Hangzhou 310036 China |
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| 作者单位： | WANG Xinghua & YANG Shijun Department of Mathematics，Zhejiang University，Hangzhou 310028，China; Department of Mathematics，Hangzhou Normal College，Hangzhou 310036，China |
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| 摘 要： | It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics, it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.
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| 收稿时间： | 2005-12-03 |
| 修稿时间： | 2006-02-07 |
On solving equations of algebraic sum of equal powers |
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| WANG Xinghua,YANG Shijun. On solving equations of algebraic sum of equal powers[J]. Science in China(Mathematics), 2006, 49(9): 1153-1157. DOI: 10.1007/s11425-006-1153-y |
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| Authors: | WANG Xinghua YANG Shijun |
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| Affiliation: | 1. Department of Mathematics, Zhejiang University, Hangzhou 310028, China
2. Department of Mathematics, Hangzhou Normal College, Hangzhou 310036, China |
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| Abstract: | It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics, it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers. |
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| Keywords: | algebraic sum of equal powers Newton's identities system of equations roots of a polynomial |
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