Compute Hasse invariant over number fields and fix current implementation

[annahaensch]

This patch will enhance the current functions hasse_invariant and hasse_invariant_OMeara to include computations of Hasse invariant for quadratic forms over number fields. In addition, this patch fixes an indexing error in the original hasse_invariant_OMeara code, which currently reads

for j in range(n-1):
    for k in range(j, n):

but should read

for j in range(n):
    for k in range(j, n):

to be consistent with OMeara's algorithm.

Component: quadratic forms

Author: Anna Haensch

Branch/Commit: f8fec47

Reviewer: Peter Bruin

Issue created by migration from https://trac.sagemath.org/ticket/16379

[annahaensch]

Branch: u/annahaensch/ticket/16379

[sagetrac-git]

Commit: 471f157

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

471f157

updated examples from last commit

[pjbruin]

comment:4

Looks good to me except for two minor points:

• it is best to keep existing doctests as far as possible; only add new ones, and fix old ones if necessary instead of replacing them;
• your patch introduces trailing whitespace on several lines (use e.g. git diff --color develop...YOURBRANCH to see this); this is discouraged, so could you remove it if and when you make another commit?
  (The patchbot encountered a doctest failure on 6.3.beta1, but it seems to be unrelated to your patch.)

[pjbruin]

Reviewer: Peter Bruin

[sagetrac-git]

Changed commit from 471f157 to a6fc438

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a6fc438

Removed trailing whitespace from last commit

[pjbruin]

comment:6

Coming back to this point:

• it is best to keep existing doctests as far as possible; only add new ones, and fix old ones if necessary instead of replacing them;

I now see that there were two identical doctests (with DiagonalQuadraticForm(ZZ, [1, -1, -1])) and you changed [1, -1, -1] to [1, -1, 5] in both of them. Could you change one of them back to [1, -1, -1]? Then we get both your new doctest and the old one, instead of duplicates.

[sagetrac-git]

Changed commit from a6fc438 to fb0d360

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

fb0d360

Reverted one example in doctest

[sagetrac-git]

Changed commit from fb0d360 to f8fec47

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

f8fec47

Reverts one doctest to old example, ignore last commit

[vbraun]

Changed branch from u/annahaensch/ticket/16379 to f8fec47