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1. 发明申请

US20100262643A1 COMPUTING MINIMAL POLYNOMIALS 有权
标题翻译：计算最小多边形
公开(公告)号：US20100262643A1
公开(公告)日：2010-10-14
申请号：US12422315
申请日：2009-04-13
申请人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye , Dongmei Zhang
发明人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye , Dongmei Zhang
IPC分类号： G06F7/38 , G06F7/552
CPC分类号： G06F7/724 , G06F7/12 , G06F7/16
摘要： Described is a technology, such as implemented in a computational software program, by which a minimal polynomial is efficiently determined for a radical expression over the ring Z of integer numbers or the ring Q of rational numbers. The levels of the radical are grouped into a level permutation group that is used to find a level permutation set. An annihilation polynomial is found based upon the level permutation set. The annihilation polynomial is factored, and a selection mechanism selects the minimal polynomial based upon the annihilation polynomial's factors.
摘要翻译：描述了一种技术，例如在计算软件程序中实现的技术，通过该技术，对于整数的环Z或有理数的环Q，对于根基表达式有效地确定最小多项式。激进的级别被分组成用于找到级别置换集合的级别置换组。湮没多项式是基于层次排列集合找到的。湮灭多项式被考虑，选择机制根据湮灭多项式的因素选择最小多项式。

2. 发明授权

US09122563B2 Computing minimal polynomials 有权
标题翻译：计算最小多项式
公开(公告)号：US09122563B2
公开(公告)日：2015-09-01
申请号：US12422315
申请日：2009-04-13
申请人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye , Dongmei Zhang
发明人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye , Dongmei Zhang
IPC分类号： G06F7/38 , G06F7/72 , G06F7/16 , G06F7/12
CPC分类号： G06F7/724 , G06F7/12 , G06F7/16
摘要： Described is a technology, such as implemented in a computational software program, by which a minimal polynomial is efficiently determined for a radical expression over the ring Z of integer numbers or the ring Q of rational numbers. The levels of the radical are grouped into a level permutation group that is used to find a level permutation set. An annihilation polynomial is found based upon the level permutation set. The annihilation polynomial is factored, and a selection mechanism selects the minimal polynomial based upon the annihilation polynomial's factors.
摘要翻译：描述了一种技术，例如在计算软件程序中实现的技术，通过该技术，对于整数的环Z或有理数的环Q，对于根基表达式有效地确定最小多项式。激进的级别被分组成用于找到级别置换集合的级别置换组。湮没多项式是基于层次排列集合找到的。湮灭多项式被考虑，选择机制根据湮灭多项式的因素选择最小多项式。

3. 发明申请

US20100198902A1 COMPUTING MINIMAL POLYNOMIALS OF RADICAL EXPRESSIONS 审中-公开
标题翻译：计算放射性表达的最小多边形
公开(公告)号：US20100198902A1
公开(公告)日：2010-08-05
申请号：US12364533
申请日：2009-02-03
申请人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye
发明人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye
IPC分类号： G06F7/552
CPC分类号： G06F17/10
摘要： Described is a technology, such as implemented in a computational software program, by which a minimal polynomial is efficiently determined for a radical expression based upon its structure of the radical expression. An annihilation polynomial is found based upon levels of the radical to obtain roots of the radical. A numerical method performs a zero test or multiple zero tests to find the minimal polynomial. In one implementation, the set of roots corresponding to a radical expression is found. The annihilation polynomial is computed by grouping roots of the set according to their conjugation relationship and multiplying factor polynomials level by level. A selection mechanism selects the minimal polynomial based upon the annihilation polynomial's factors.
摘要翻译：描述了一种技术，例如在计算软件程序中实现的技术，通过该技术，基于其基本表达式的结构，有效地确定基本表达式的最小多项式。基于获得根的根的自由基的水平找到湮灭多项式。数值方法执行零测试或多零测试以找到最小多项式。在一个实现中，找到与激进表达相对应的一组根。湮灭多项式通过根据它们的共轭关系和乘法因子多项式级别逐级分组的根来计算。选择机制根据湮灭多项式的因素选择最小多项式。

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