44 research outputs found
Implementation of prime decomposition of polynomial ideals over small finite fields
AbstractAn algorithm for the prime decomposition of polynomial ideals over small finite fields is proposed and implemented on the basis of previous work of the second author. To achieve better performance, several improvements are added to the existing algorithm, with strategies for computational flow proposed, based on experimental results. The practicality of the algorithm is examined by testing the implementation experimentally, which also reveals information about the quality of the implementation
Implementation of prime decomposition of polynomial ideals over small finite fields
AbstractAn algorithm for the prime decomposition of polynomial ideals over small finite fields is proposed and implemented on the basis of previous work of the second author. To achieve better performance, several improvements are added to the existing algorithm, with strategies for computational flow proposed, based on experimental results. The practicality of the algorithm is examined by testing the implementation experimentally, which also reveals information about the quality of the implementation
Holonomic Gradient Descent and its Application to Fisher-Bingham Integral
We give a new algorithm to find local maximum and minimum of a holonomic
function and apply it for the Fisher-Bingham integral on the sphere ,
which is used in the directional statistics. The method utilizes the theory and
algorithms of holonomic systems.Comment: 23 pages, 1 figur