基于代数神经网络的多元多项式不可约判定及学习算法

Irreducibility Testing and Learning Algorithms of Multivariate Polynomials Based on Algebra Neural Networks Model

关键词:  多元多项式  代数神经网络  不可约  学习算法

Key words:  multivariate polynomials  algebra neural networks  irreducibility  learning algorithm

摘要:

把感知器作为数学模型,充分利用神经元的运算特性,以二元多项式近似求根神经网络模型为基础,设计一类多元多项式不可约判定的神经网络模型,它是单输入多输出三层前向神经网络,给出神经网络学习算法,这种学习算法在p-adic意义下,通过调整隐层与输出层的权值C_i,j完成学习,直到e≥deg_y(F)+1步,可确定出多元多项式不可约,通过算例表明,该算法有效,相比传统的判定算法,可操作性强.

Abstract:

With compute character of neural and based on the neural networks model of approximate solve roots, a kind of three layers forward algebra neural networks with single input and many outputs are designed, which can be applied to polynomials irreducibility testing.Neural networks learning algorithm was designed. Through the learning algorithm,we have tested F(x,y) irreducibility.