Changes between Initial Version and Version 1 of Ticket #15422, comment 21


Ignore:
Timestamp:
11/29/13 08:35:20 (8 years ago)
Author:
jdemeyer
Comment:

Legend:

Unmodified
Added
Removed
Modified
  • Ticket #15422, comment 21

    initial v1  
    11Replying to [comment:20 roed]:
    22> You can '''never''' say that a p-adic polynomial has a root.
    3 That can't be true (or I am misunderstanding you). Using Hensel's Lemma, you ''can'' be certain that polynomials factor in a certain way. For example, any polynomial over `Zp` which is congruent to (t-1)(t-2) modulo p, will have a single p-adic root close to 1 and a single p-adic root close to 2. What am I missing?...
     3That can't be true (or I am misunderstanding you). Using Hensel's Lemma, you ''can'' be certain that polynomials factor in a certain way. For example, any polynomial over `Zp` which is congruent to `(t-1)(t-2)` modulo p, will have a single p-adic root close to 1 and a single p-adic root close to 2. In particular, `(t-1)(t-2) + p*f` will never be irreducible (for f in `Zp[t]`). What am I missing?...