normalized p_minimal_polynomials

[rrissner]

In general (p^t)-minimal polynomials of a matrix B are not uniquely determined but two different (p^t)-minimal polynomials are congruent modulo p (N_{p^{t-1})}(B) where N_{(p^{t-1})}(B) is (p^{t-1})-ideal of B.

The new method normalize_nu computes the representative whose coefficients are minimal among \{0, \ldots, p^t-1\}.

Note: The new method p_t_part(f, p, t) replaces p_part(f, p) with t = 1.

[rrissner]

New commits:

​b096cc2

normalize_nu, p_part replaced by p_t_part

[saraedum]

rrissner, I could not find your handle on the wiki home page.

[aly.deines]

Hi! I've been looking at your ticket. The code looks great. I have a few comments/questions about the documentation.

• First, in the method normalize_nu, you don't have any examples or tests of this function. You only have an indirect doctest. You should have tests such that every line of code is run via one of the tests.

• In the normalize_nu documentation you should try to keep lines to 79 characters or less (72 is prefered for documentation in the python PEP 8 style guide.)

• In the documentation, I think B should be self

  - ``nu`` -- a `(p^t)`-minimal polynomial of `B`
  

• Also, what is S?

  - ``p_min_polys`` -- a dictionary, keys are elements `s \in \mathcal{S}` with
    `s \le t`, the values are the associated normalized `(p^s)`-minimal 
    polynomials `\nu_s`
  

• Finally, in the doctest you currently have, you should indicate that it is an indirect doctest.

---

New commits:

​fb743b4	Merging branch 'u/rrissner/normalized_p_minimal_polynomials' of git://trac.sagemath.org/sage into t/22539/normalized_p_minimal_polynomials to sage 8.1.beta3.
​15cba83	Removed trailing whitespace.