论文标题
广义数值理论转换
Generalized numerical-theoretical transformation
论文作者
论文摘要
广义数字理论转换（NPT）是根据指数函数定理制定的，这使我们能够通过Modulo Operations对此功能的指数替换操作Modulo整个表达式，这使得为NPT的定理基本实现了NPT的基本定理，因为它在NPT中使用的函数是重量转换功能。根据该定理，制定并证明了整体NPT的所有主要定理，它们的双重性以及该转换的权重函数的特性。选择此函数的基础（包括一个复杂的数字）不仅可以决定一种或另一种类型的转换，还决定了转换本身的模块。这使我们能够以统一的离散转换理论的形式概括了许多知名的NPT，例如Mersen，Gauss，甚至傅立叶。
The generalized number-theoretic transformation (NPT) is formulated on the basis of the exponential function theorem, which allows us to replace operations modulo the expression as a whole by modulo operations on the exponent of this function, which makes this theorem fundamental for NPT, since it is such a function used in NPT as a weight conversion function. On the basis of this theorem, all the main theorems of the generalized NPT, their duality, as well as the properties of the weight functions of this transformation are formulated and proved. The choice of the basis of this function, as which any number can be chosen, including a complex one, determines not only one or another type of transformation, but also the module of the transformation itself. This allows us to generalize a number of well-known NPTs, such as Mersen, Gauss, and even Fourier, in the form of a unified theory of discrete transformations.
