期刊文献+
共找到2篇文章
< 1 >
每页显示 20 50 100
Simplification and normalization of indexed differentials involving coordinate transformation 被引量:4
1
作者 LIU Jiang LI HongBo CAO YuanHao 《Science China Mathematics》 SCIE 2009年第10期2266-2286,共21页
In nD differential geometry, basic geometric structures and properties are described locally by differentiable functions and equations with indices that obey Einstein summation convention. Although symbolic manipulati... In nD differential geometry, basic geometric structures and properties are described locally by differentiable functions and equations with indices that obey Einstein summation convention. Although symbolic manipulation of such indexed functions is one of the oldest research topics in computer algebra, so far there exists no normal form reduction algorithm to judge whether two indexed polynomials involving indices of different coordinate systems are equal or not. It is a challenging task in computer algebra. In this paper, for a typical framework—the partial derivatives in coordinate transformation matrix involved are of order no more than two (such as local computations of ordinary curvatures and tor-sion), we put forward two algorithms, one on elimination of all redundant dummy indices of indexed polynomials, the other on normalization of such indexed polynomials, by which we can judge whether two indexed polynomials are equal or not. We implement the algorithms with Maple V.10 and use them to solve tensor verification problems in differential geometry, and to derive automatically the transformation rules of locally defined indexed functions under the change of local coordinates. 展开更多
关键词 nD symbolic computation Einstein summation convention mechanical theorem-proving differential geometry tensor verification 68w30 53-99
原文传递
Three kinds of extraneous factors in Dixon resultants
2
作者 ZHAO ShiZhong FU HongGuang 《Science China Mathematics》 SCIE 2009年第1期160-172,共13页
Dixon resultant is a basic elimination method which has been used widely in the high technology fields of automatic control, robotics, etc. But how to remove extraneous factors in Dixon resultants has been a very diff... Dixon resultant is a basic elimination method which has been used widely in the high technology fields of automatic control, robotics, etc. But how to remove extraneous factors in Dixon resultants has been a very difficult problem. In this paper, we discover some extraneous factors by expressing the Dixon resultant in a linear combination of original polynomial system. Furthermore, it has been proved that the factors mentioned above include three parts which come from Dixon derived polynomials, Dixon matrix and the resulting resultant expression by substituting Dixon derived polynomials respectively. 展开更多
关键词 Dixon resultant Dixon matrix extraneous factors 00A06 13A50 13P99 68w30
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部