Take a multiplicative monoid of sequences in which the multiplication is given by Hadamard product. The set of linear combinations of interleaving monoid elements then yields a ring. We consider such a construction for the monoid of hypergeometric sequences, yielding what we call the ring of hypergeometric-type sequences -- a subring of the ring of holonomic sequences. We present two algorithms in this setting: one for computing holonomic recurrence equations from hypergeometric-type normal forms and the other for finding products of hypergeometric-type terms. These are newly implemented commands in our Maple package $\texttt{HyperTypeSeq}$, which we also describe.

翻译：考虑一个序列的乘法幺半群，其中乘法由阿达玛积定义。交错幺半群元素的线性组合集构成一个环。我们针对超几何序列幺半群进行此类构造，得到所谓的超几何型序列环——完整序列环的一个子环。我们在此框架下提出两种算法：一种从超几何型范式计算完整递推方程，另一种用于寻找超几何型项的乘积。这些算法是我们Maple软件包$\texttt{HyperTypeSeq}$中新增的命令，本文亦对该软件包进行了描述。