论文标题
矩阵因子化的精制乘法张量产物
Refined multiplicative tensor product of matrix factorizations
论文作者
论文摘要
在\ cite {fomatati20222tensor}中提出了用于多项式基质分解的算法，并且表明该算法在总体上分解多项式的标准方法的结果更好。在本文中，我们通过完善其两种主要成分之一的构建来改善该算法，即矩阵因子化的乘法张量产品$ \ widetilde {\ otimes} $，以获取另一个不同的双functorial操作，我们调用了减少的矩阵因素$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ fline的均方根tensor tensor tensor tensor tensor tensor tensor。 In fact, we observe that in the algorithm for matrix factorization of polynomials developed in \cite{fomatati2022tensor}, if we replace $\widetilde{\otimes}$ by $\overline{\otimes}$, we obtain better results on the class of summand-reducible polynomials in the sense that the refined algorithm produces大小较小的矩阵因子。
An algorithm for matrix factorization of polynomials was proposed in \cite{fomatati2022tensor} and it was shown that this algorithm produces better results than the standard method for factoring polynomials on the class of summand-reducible polynomials. In this paper, we improve this algorithm by refining the construction of one of its two main ingredients, namely the multiplicative tensor product $\widetilde{\otimes}$ of matrix factorizations to obtain another different bifunctorial operation that we call the reduced multiplicative tensor product of matrix factorizations denoted by $\overline{\otimes}$. In fact, we observe that in the algorithm for matrix factorization of polynomials developed in \cite{fomatati2022tensor}, if we replace $\widetilde{\otimes}$ by $\overline{\otimes}$, we obtain better results on the class of summand-reducible polynomials in the sense that the refined algorithm produces matrix factors which are of smaller sizes.
