英语语法分析

The theory of homology and cohomology is very important in mathematics.

同调与上同调理论在数学中占有很重要的地位。

Now, we obtain expectative results by apply cohomology to discussion of Analytical dynamics.

本文将上同调用于讨论动力学方程，得到了预期的结果。

The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory.

该语言是有意不断初级程度，避免层论的上同调理论。