weak popov form does not compute weak popov form

[ketzu]

While working on the sage.matrix.matrix2.weak_popov_form (for sage.matrix.matrix_misc.weak_popov_form applies the same) method for performance issues I noticed something.

The weak Popov form as defined in [MS] is not computed by this method. The other references do not call this form weak Popov form, it is a les restrictive definition for a certain row reduced form of matrix.

Followup ticket for reimplementation of wpf: #16742 and #16896.

[MS] T. Mulders, A. Storjohann, "On lattice reduction for polynomial
matrices," J. Symbolic Comput. 35 (2003), no. 4, 377--401

Comment of weak_popov_form:

OUTPUT:

A 3-tuple `(W,N,d)` consisting of:

1. `W` - a matrix over `k(x)` giving a weak the Popov form of self
2. `N` - a matrix over `k[x]` representing row operations used to
transform `self` to `W`
3. `d` - degree of respective columns of W; the degree of a column is
the maximum of the degree of its elements

[ketzu]

I think there should be a keyword ("transposition=False" oder something) to indicate the matrix N is wanted. Also I am not completely sure I did the deprecations right in any way.

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New commits:

​970fde5

Rename of weak_popov_form() to row_reduced_form() added deprecation warning, rework of the use of the ascend parameter, removed sorting and returning d if ascend is not set.

[git]

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

​12755f1

Reduced to be a renaming only.

[ketzu]

New commits:

​12755f1

Reduced to be a renaming only.

---

New commits:

​12755f1

Reduced to be a renaming only.

[ketzu]

See also #16896

[chapoton]

one doctest is failing

[git]

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

​7820917

Fixed the doctest of matrix/matrix_misc.py.

[ketzu]

Unfortunately I was sick for a long time, so i fixed the commit.

[dlucas]

I just changed some minor things into documentation : I removed any reference related to weak Popov form, because it does not compute the weak Popov form and I added a new reference related to the row reduced form. I also removed the name "weak Popov form" from the output field.