Reseña: Formal proofs of transcendence for e and π as an application of multivariate and symmetric polynomials
Se ha publicado un artículo de razonamiento formalizado en Coq sobre teoría de números titulado Formal proofs of transcendence for e and π as an application of multivariate and symmetric polynomials.
Sus autores son
- Sophie Bernard (del grupo Marelle en el Inria Sophia Antipolis – Méditerranée, Francia).
- Yves Bertot (del grupo Marelle en el Inria Sophia Antipolis – Méditerranée, Francia),
- Laurence Rideau (del grupo Marelle en el Inria Sophia Antipolis – Méditerranée, Francia) y
- Pierre-Yves Strub (del Instituto IMDEA Software en Madrid).
Su resumen es
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.
El trabajo se presentará el 18 de enero de 2016 en el CPP 2016 (The 5th ACM SIGPLAN Conference on Certified Programs and Proofs).
El código de las correspondientes teorías en Coq se encuentra aquí.