[with patch] quotient spaces of vector spaces

[nbruin]

If V is a subspace of W then W.quotient(V) should give the quotient space U=W/V.

Left TODO:

• overload "/" constructor ?
• provide a section map U->W ?
• install appropriate coercions ?

[nbruin]

implementation

[was]

I think this should be replaced by Soroosh's code, which does this and much more.

[was]

What? and ditch my 2 lines of haiku-like sage code?

Seriously, though. The attached patch contains quite a bit more than
"quotient", as you are probably woefully aware of. Easiest is probably

 - apply the patch
 - delete "quotient" from sage/modules/free_module.py

Cheers,

[mabshoff]

We need to figure out if this still applies.

Cheers,

Michael

[was]

This has lingered too long -- I need to deal with it.

[was]

NOT ready: I still think "I think this should be replaced by Soroosh's code, which does this and much more." I don't know the status of Soroosh's code.

[mabshoff]

Soroosh's code, i.e. #1029 got merged. So should we invalidate this ticket?

Cheers,

Michael

[was]

Almost done:

was_: sage: R = QQ^3; S = R.span([[1,2,3]])
[10:14am] was_: sage: w = R.quotient(S)
[10:14am] was_: sage: w = R / S
[10:14am] was_: But the last goes boom.
[10:14am] was_: It would be 3-4 lines of code to fix that.
[10:14am] was_: Once that is fixed, then 787 is done

[was]

A quick comment. Even as is this is WRONG -- the algorithm used is buggy, evidently, or something, since

sage: A = QQ^3; V = A.span([[1,2,3], [4,5,6]])
sage: Q = V.quotient( V.span([V.0 + V.1]) ); Q
sage: Q[1](V.0 + V.1)
(1)

But Q[1] is the quotient map so should have V.0 + V.1 in its kernel.

[was]

This I think correctly really implements quotients of vector spaces.

[was]

This is also needed (it fixes a docstring)

[was]

this is also needed.

[was]

instead of applying those three patches, this is a clean bundle.

[mabshoff]

Merged in 2.8.15.alpha2.

[roed]

Changes _repr_

[was]

This was slightly buggy -- see Trac #1368 for a fix.