Multicomplex and multidual numbers are two generalizations of complex numbers with multiple imaginary axes, useful for numerical computation of derivatives with machine precision. The similarities between multicomplex and multidual algebras allowed us to create a unified library to use either one for sensitivity analysis. This library can be used to compute arbitrary order derivates of functions of a single variable or multiple variables. The storage of matrix representations of multicomplex and multidual numbers is avoided using a combination of one-dimensional resizable arrays and an indexation method based on binary bitwise operations. To provide high computational efficiency and low memory usage, the multiplication of hypercomplex numbers up to sixth order is carried out using a hard-coded algorithm. For higher hypercomplex orders, the library uses by default a multiplication method based on binary bitwise operations. The computation of algebraic and transcendental functions is achieved using a Taylor series approximation. Fortran and Python versions were developed, and extensions to other languages are self-evident.

中文翻译：

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多Z

多复数和多对偶数是具有多个虚轴的复数的两种推广，可用于机器精度的导数数值计算。多复代数和多对偶代数之间的相似性使我们能够创建一个统一的库来使用其中任何一个进行敏感性分析。该库可用于计算单个变量或多个变量的函数的任意阶导数。使用一维可调整大小数组和基于二进制位运算的索引方法的组合，避免了多复数和多对数的矩阵表示的存储。为了提供高计算效率和低内存使用，使用硬编码算法执行高达六阶的超复数乘法。对于更高的超复杂阶，该库默认使用基于二进制位运算的乘法方法。代数和超越函数的计算是使用泰勒级数逼近实现的。开发了 Fortran 和 Python 版本，对其他语言的扩展是不言而喻的。