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