Section: New Results
Formal proof that and are transcendental
Participants : Sophie Bernard, Laurence Rideau.
We constructed formal proofs that is irrational, is transcendental, and is transcendental. These proofs share a common initial pattern, where rationality or algebraicity of the mathematical constants are shown to imply the existence of a sequence of positive integers that must decrease indefinitely.
This proof development is an opportunity to study the interplay between several existing libraries about algebraic structures and analysis: the ssreflect library for algebra and the Coquelicot library for calculus. Moreover, the proof that is transcendental was an occasion to test the newly developed module on symmetric polynomials by P.-Y. Strub at IMDEA.