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1. 发明申请

US20100169605A1 ARBITRARY PRECISION FLOATING NUMBER PROCESSING 有权
标题翻译：仲裁精度浮数代码处理
公开(公告)号：US20100169605A1
公开(公告)日：2010-07-01
申请号：US12346061
申请日：2008-12-30
申请人： Xu Yang , Hao Wei , Gong Cheng , ZhangZhang Song , Dongmei Zhang , Jian Wang
发明人： Xu Yang , Hao Wei , Gong Cheng , ZhangZhang Song , Dongmei Zhang , Jian Wang
IPC分类号： G06F12/02 , G06F7/38
CPC分类号： G06F7/483 , G06F7/49957
摘要： Techniques for providing arbitrary precision floating number (APFN) processing are disclosed. In some aspects, an APFN store may be used to store a large number (i.e., an APFN) having many significant digits, which in turn may enable a high degree of precision in mathematical operations. An APFN module may be used to create and define the APFN store. The APFN module may enable a user to define a precision (significant digits) for the large number that corresponds to the size of an array of bytes in the APFN store that are allocated for storing the large number. In further aspects, the APFN store may be used to store additional intermediary data and a resultant.
摘要翻译：公开了提供任意精度浮动数（APFN）处理的技术。在一些方面，可以使用APFN存储来存储具有许多有效数字的大量（即，APFN），这又可以使数学运算中的高度精度。可以使用APFN模块来创建和定义APFN存储。 APFN模块可以使用户能够为与分配用于存储大数量的APFN存储中的字节数组的大小相对应的大数量定义精确度（有效数字）。在另外的方面，APFN存储可以用于存储附加的中间数据和结果。

2. 发明授权

US08095767B2 Arbitrary precision floating number processing 有权
标题翻译：任意精度浮点数处理
公开(公告)号：US08095767B2
公开(公告)日：2012-01-10
申请号：US12346061
申请日：2008-12-30
申请人： Xu Yang , Hao Wei , Gong Cheng , ZhangZhang Song , Dongmei Zhang , Jian Wang
发明人： Xu Yang , Hao Wei , Gong Cheng , ZhangZhang Song , Dongmei Zhang , Jian Wang
IPC分类号： G06F12/02 , G06F7/38
CPC分类号： G06F7/483 , G06F7/49957
摘要： Techniques for providing arbitrary precision floating number (APFN) processing are disclosed. In some aspects, an APFN store may be used to store a large number (i.e., an APFN) having many significant digits, which in turn may enable a high degree of precision in mathematical operations. An APFN module may be used to create and define the APFN store. The APFN module may enable a user to define a precision (significant digits) for the large number that corresponds to the size of an array of bytes in the APFN store that are allocated for storing the large number. In further aspects, the APFN store may be used to store additional intermediary data and a resultant.
摘要翻译：公开了提供任意精度浮动数（APFN）处理的技术。在一些方面，可以使用APFN存储来存储具有许多有效数字的大量（即，APFN），这又可以使数学运算中的高度精度。可以使用APFN模块来创建和定义APFN存储。 APFN模块可以使用户能够为与分配用于存储大数量的APFN存储中的字节数组的大小相对应的大数量定义精确度（有效数字）。在另外的方面，APFN存储可以用于存储附加的中间数据和结果。

3. 发明申请

US20100191793A1 Symbolic Computation Using Tree-Structured Mathematical Expressions 审中-公开
标题翻译：使用树结构数学表达式的符号计算
公开(公告)号：US20100191793A1
公开(公告)日：2010-07-29
申请号：US12360853
申请日：2009-01-28
申请人： Xu Yang , Xiaolin Quan , Dongmei Zhang , Gong Cheng , Jian Wang , Hao Wei
发明人： Xu Yang , Xiaolin Quan , Dongmei Zhang , Gong Cheng , Jian Wang , Hao Wei
IPC分类号： G06F7/38 , G06F17/10
CPC分类号： G06F17/10 , G06F7/38
摘要： A method for performing symbolic computations on a mathematical expression. The mathematical expression may be converted to a tree structure having one or more parent nodes and one or more child nodes. Each parent node may be a mathematical operation. Each child node may be a mathematical expression on which the mathematical operation is performed in a specified order. Each child node may be in a hierarchical relationship to one of the parent nodes. The parent nodes, the child nodes or both may be manipulated to perform a first symbolic computation on the mathematical expression.
摘要翻译：一种用于对数学表达式执行符号计算的方法。数学表达式可以转换为具有一个或多个父节点和一个或多个子节点的树结构。每个父节点可以是数学运算。每个子节点可以是以指定顺序执行数学运算的数学表达式。每个子节点可以与父节点中的一个分层关系。可以操纵父节点，子节点或两者以对数学表达式执行第一符号计算。

4. 发明申请

US20080313211A1 Data Relationship Visualizer 失效
标题翻译：数据关系可视化器
公开(公告)号：US20080313211A1
公开(公告)日：2008-12-18
申请号：US11764354
申请日：2007-06-18
申请人： Yingnong Dang , Xu Yang , Dongmei Zhang , Min Wang , Jian Wang
发明人： Yingnong Dang , Xu Yang , Dongmei Zhang , Min Wang , Jian Wang
IPC分类号： G06F17/00
CPC分类号： G06F17/30994 , G06F17/30014
摘要： Data having express or implied relationships may be displayed by selecting a starting entity in a data structure, building a relationship tree, and building and optimizing a relationship matrix based on the relationship tree. The optimized relationship matrix may be used to layout and render a graphical image that positions various elements with respect to the starting entity based on the relationships. The distance matrix may be optimized by creating a first distance matrix based on the relationship tree, developing a dissimilarity matrix based on expressed or implied relationships, and multiplying the dissimilarity matrix by a weighting factor to determine a distance matrix that may be optimized by multi-dimensional scaling. An optimized weighting factor may be determined and used to select an optimized distance matrix.
摘要翻译：可以通过选择数据结构中的起始实体，建立关系树，以及基于关系树建立和优化关系矩阵来显示具有明确或隐含关系的数据。优化的关系矩阵可以用于基于关系来布局和渲染相对于起始实体定位各种元素的图形图像。距离矩阵可以通过基于关系树创建第一距离矩阵，基于表示或隐含的关系开发不相似矩阵，以及将不相似矩阵乘以加权因子来确定可以通过多重关系树优化的距离矩阵来优化，尺寸缩放。可以确定优化的加权因子并用于选择优化的距离矩阵。

5. 发明授权

US08060540B2 Data relationship visualizer 失效
标题翻译：数据关系可视化
公开(公告)号：US08060540B2
公开(公告)日：2011-11-15
申请号：US11764354
申请日：2007-06-18
申请人： Yingnong Dang , Xu Yang , Dongmei Zhang , Min Wang , Jian Wang
发明人： Yingnong Dang , Xu Yang , Dongmei Zhang , Min Wang , Jian Wang
IPC分类号： G06F17/30
CPC分类号： G06F17/30994 , G06F17/30014
摘要： Data having express or implied relationships may be displayed by selecting a starting entity in a data structure, building a relationship tree, and building and optimizing a relationship matrix based on the relationship tree. The optimized relationship matrix may be used to layout and render a graphical image that positions various elements with respect to the starting entity based on the relationships. The distance matrix may be optimized by creating a first distance matrix based on the relationship tree, developing a dissimilarity matrix based on expressed or implied relationships, and multiplying the dissimilarity matrix by a weighting factor to determine a distance matrix that may be optimized by multi-dimensional scaling. An optimized weighting factor may be determined and used to select an optimized distance matrix.
摘要翻译：可以通过选择数据结构中的起始实体，建立关系树，以及基于关系树建立和优化关系矩阵来显示具有明确或隐含关系的数据。优化的关系矩阵可以用于基于关系来布局和渲染相对于起始实体定位各种元素的图形图像。距离矩阵可以通过基于关系树创建第一距离矩阵，基于表示或隐含的关系开发不相似矩阵，以及将不相似矩阵乘以加权因子来确定可以通过多重关系树优化的距离矩阵来优化，尺寸缩放。可以确定优化的加权因子并用于选择优化的距离矩阵。

6. 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。

7. 发明授权

US08626812B2 Hybrid greatest common divisor calculator for polynomials 有权
标题翻译：用于多项式的混合最大公约数计算器
公开(公告)号：US08626812B2
公开(公告)日：2014-01-07
申请号：US12790645
申请日：2010-05-28
申请人： Xu Yang , Xiaolin Quan , Dongmei Zhang
发明人： Xu Yang , Xiaolin Quan , Dongmei Zhang
IPC分类号： G06F7/72
CPC分类号： G06F7/724 , G06F7/726
摘要： A hybrid greatest common divisor (GCD) calculator analyzes characteristics of polynomials and selects a particular GCD algorithm from multiple available GCD algorithms based on a combination of characteristics of the polynomials. The selected GCD algorithm is then applied to calculate the GCD of the polynomials.
摘要翻译：混合最大公约数（GCD）计算器分析多项式的特征，并且基于多项式的特征的组合从多个可用的GCD算法中选择特定的GCD算法。然后应用所选择的GCD算法来计算多项式的GCD。

8. 发明申请

US20100161701A1 POLYNOMIAL REPRESENTATION FOR SYMBOLIC COMPUTATION 审中-公开
标题翻译：符号计算的多项代表
公开(公告)号：US20100161701A1
公开(公告)日：2010-06-24
申请号：US12337630
申请日：2008-12-18
申请人： Xu Yang , Xiaolin Quan , Dongmei Zhang
发明人： Xu Yang , Xiaolin Quan , Dongmei Zhang
IPC分类号： G06F17/30 , G06F7/00
CPC分类号： G06F16/313
摘要： A method for converting a polynomial expression to a data structure for symbolic computation. One or more variables in the polynomial expression may be determined. The variables may be stored in a first array. One or more terms in the polynomial expression may be determined. One or more exponents of the variables in each term may be determined. The exponents may be stored in a second array. One or more coefficients of the terms may be determined. The coefficients may be stored in a third array.
摘要翻译：一种用于将多项式表达式转换为用于符号计算的数据结构的方法。可以确定多项式表达式中的一个或多个变量。变量可以存储在第一个数组中。可以确定多项式表达式中的一个或多个项。可以确定每个术语中的变量的一个或多个指数。指数可以存储在第二个数组中。术语的一个或多个系数可以被确定。系数可以存储在第三阵列中。

9. 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。

10. 发明授权

US08682950B2 Computer-implemented symbolic polynomial factorization 有权
标题翻译：计算机实现的符号多项式分解
公开(公告)号：US08682950B2
公开(公告)日：2014-03-25
申请号：US12790617
申请日：2010-05-28
申请人： Xu Yang , Xiaolin Quan , Zhihui Ba , Dongmei Zhang
发明人： Xu Yang , Xiaolin Quan , Zhihui Ba , Dongmei Zhang
IPC分类号： G06F7/38
CPC分类号： G06F7/724
摘要： An input polynomial, in symbolic form, is received, classified, pre-processed, and factored. The input polynomial is classified as a constant, a univariate polynomial, or a multivariate polynomial. Various pre-processing is performed depending on the classification. After the input polynomial is pre-processed, the remaining polynomial is factored using a polynomial factoring algorithm. By pre-processing the input polynomial, the complexity of the polynomial to be factored is reduced, which reduces the computational expense of the polynomial factoring algorithm.
摘要翻译：以符号形式的输入多项式被接收，分类，预处理和因子分解。输入多项式被分类为常数，单变量多项式或多元多项式。根据分类进行各种预处理。在预处理输入多项式之后，使用多项式分解算法对剩余多项式进行因子分解。通过预处理输入多项式，减少要求因子的多项式的复杂度，这降低了多项式因式分解算法的计算费用。

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