  We describe the formalisation in Coq of a proof that the numbers e and $\pi$
are transcendental. This proof lies at the interface of two domains of
mathematics that are often considered separately: calculus (real and elementary
complex analysis) and algebra. For the work on calculus, we rely on the
Coquelicot library and for the work on algebra, we rely on the Mathematical
Components library. Moreover, some of the elements of our formalized proof
originate in the more ancient library for real numbers included in the Coq
distribution. The case of $\pi$ relies extensively on properties of
multivariate polynomials and this experiment was also an occasion to put to
test a newly developed library for these multivariate polynomials.
