AN ELEMENTARY PROOF OF BARNETTS THEOREM ABOUT THE GREATEST COMMON DIVISOR OF SEVERAL UNIVARIATE POLYNOMIALS

Gonzalezvega L.

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AN ELEMENTARY PROOF OF BARNETTS THEOREM ABOUT THE GREATEST COMMON DIVISOR OF SEVERAL UNIVARIATE POLYNOMIALS

机译：关于几个单项多项式的最大公约数的Barnets定理的基本证明

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This articule provides a new proof of Barnett's theorem giving the degree of the greatest common divisor of several univariate polynomials with coefficients in a field in terms of the rank of a well-defined matrix. The new proof is elementary and self-contained (no use of Jordan form or invariant factors), and it is based on some easy to state properties of subresultants. Moreover this proof allows one to generalize Barnett's results to the case when the considered polynomials have their coefficients in an integral domain. [References: 16]

机译：这篇文章为巴尼特定理提供了新的证明，它给出了几个单变量多项式的最大公因数的程度，该单因式多项式在一个字段中的系数取决于定义良好的矩阵的秩。新的证明是基本且独立的（不使用约旦形式或不变因素），它基于子结果的一些易于陈述的性质。此外，这一证明使人们可以将Barnett的结果推广到所考虑的多项式的系数在整数域中的情况。 [参考：16]

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《Linear Algebra and its Applications》 |1996年第0期|共18页
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Gonzalezvega L.;
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正文语种 eng
中图分类数理逻辑、数学基础;
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1. AN ELEMENTARY PROOF OF BARNETTS THEOREM ABOUT THE GREATEST COMMON DIVISOR OF SEVERAL UNIVARIATE POLYNOMIALS [J] . Gonzalezvega L. Linear Algebra and its Applications . 1996,第0期

机译：关于几个单项多项式的最大公约数的Barnets定理的基本证明
2. Complexity of algorithms for computing greatest common divisors of parametric univariate polynomials [J] . A. Ayad International journal of algebra . 2010,第1a4期

机译：计算参数单变量多项式的最大公约数的算法的复杂性
3. A Note on an Elementary Proof of Fermat's LastTheorem for Polynomials [J] . P.K. Tam Southeast Asian bulletin of mathematics . 2008,第6期

机译：关于费马最后多项式定理的基本证明的一个注记
4. Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials [C] . Erich Kaltofen, Zhengfeng Yang, Lihong Zhi International symposium on Symbolic and algebraic computation . 2006

机译：具有线性约束系数和奇异多项式的几个多项式的近似最大公约数
5. An inverse kinematic solution to the 6 degree of freedom Kuka 662 robot by reduction to an 8th order univariate polynomial,or a 4th order bivariate polynomial, with up to 4 real solutions [D] . Kaufman, Richard D. 2009

机译：通过还原为8阶单变量多项式或4阶双变量多项式，对6自由度Kuka 662机器人进行逆运动学解，其中最多包含4个实解
6. On a New Method in Elementary Number Theory Which Leads to An Elementary Proof of the Prime Number Theorem [O] . P. Erdös 1949

机译：关于初等数论的新方法导致素数定理的初等证明
7. An elementary proof of Barnett's theorem about the greatest common divisor of several univarlate polynomials [O] . González-Vega Laureano 1996

机译：关于几个单变量多项式的最大公约数的巴尼特定理的基本证明
8. Infinite Elementary Divisors of a Matrix Polynomial and Implications [R] . Hayton, G. E., Pugh, A. C., Fretwell, P. 1987

机译：矩阵多项式的无穷初等除数及其启示

AN ELEMENTARY PROOF OF BARNETTS THEOREM ABOUT THE GREATEST COMMON DIVISOR OF SEVERAL UNIVARIATE POLYNOMIALS

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