Karim Belabas - S-units and compact representations in number fields

Karim Belabas (1, 2) , Fanny Bastien (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 LFANT - Lithe and fast algorithmic number theory
3 IF - Institut Fourier

Huge algebraic numbers are problematic because - computing with them algebraically is expensive; - approximations via floating point embeddings into C require huge accuracy (cancellation); - they are often intermediate results: we do not want a result in K but in K∗/(K∗)2, or in - ZK/pk, or a floating point approximation to complex embeddings, or . . . - they may overflow the possibilities of the implementation: try 22100 .

Mots clés: S-units; compact representations; number fields

Mots clés: institut fourier; CNRS; UGA; Grenoble; Atelier PARI/GP 2020

Domaines: Mathématiques [math]

Karim Belabas, Fanny Bastien. Karim Belabas - S-units and compact representations in number fields. 2020. ⟨hal-02530400⟩