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Analysability of finite $U$-rank types are explored both in general and inthe theory $\mathrm{DCF}_0$. The well-known fact that the equation$\delta(\mathrm{log}\delta x)=0$ is analysable in but not almost internal tothe constants is generalized to show that$\underbrace{\mathrm{log}\delta...\mathrm{log}\delta}_n x=0$ is not analysablein the constants in $(n-1)$-steps. The notion of a \emph{canonical analysis} isintroduced -- namely an analysis that is of minimal length and interalgebraicwith every other analysis of that length. Not every analysable type admits acanonical analysis. Using properties of reductions and coreductions in theorieswith the canonical base property, it is constructed, for any sequence ofpositive integers $(n_1,...,n_\ell)$, a type in $\mathrm{DCF}_0$ that admits acanonical analysis with the property that the $i$th step has $U$-rank $n_i$.

Constructing Types in Differentially Closed Fields that are Analysable in the Constants