@inproceedings{91f09dddce044dab9b6cbdbb6b53fe37,
title = "Formal proofs of transcendence for e and pi as an application of multivariate and symmetric polynomials",
abstract = "We describe the formalisation in Coq of a proof that the numbers e and π 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 π 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.",
keywords = "Coq, Formal mathematics, Multivariate polynomials, Proof assistant, Transcendence",
author = "Sophie Bernard and Yves Bertot and Laurence Rideau and Strub, \{Pierre Yves\}",
note = "Publisher Copyright: {\textcopyright} 2016 ACM.; 5th ACM SIGPLAN Conference on Certified Programs and Proofs, CPP 2016 ; Conference date: 18-01-2016 Through 19-01-2016",
year = "2016",
month = jan,
day = "18",
doi = "10.1145/2854065.2854072",
language = "English",
series = "CPP 2016 - Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs, co-located with POPL 2016",
publisher = "Association for Computing Machinery, Inc",
pages = "76--87",
editor = "Jeremy Avigad and Adam Chlipala",
booktitle = "CPP 2016 - Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs, co-located with POPL 2016",
}