中文摘要：

由介绍 noncommutative 在无限 / 有限的集合和构造的函数空格的微分演算一个 homotopy 操作符，一个证明 Poincar 的类似物？？

英文摘要：

By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.