Cohomologies of spaces of Schwartz test functions

We calculate cohomologies of the Schwartz algebras $\mathcal{D}$ and $\mathcal{S}$, which are basic spaces (test-function spaces) of the distribution theory. In the process, we find special cohomologies of the quotient algebras $\mathcal{E}/\mathcal{D}$ and $\mathcal{M}/\mathcal{S}$ ($\mathcal{E}$ and $\mathcal{M}$ are also test-function spaces), which are quite unusual from the standpoint of the standard functional analysis and are interesting for theoretical and mathematical physics.