On Mon, Feb 15, 2010 at 09:21:00PM -0800, William Stein wrote:
> On Mon, Feb 15, 2010 at 9:07 PM, Nick Alexander <ncalexan...@gmail.com> wrote:
> >>> To have an idea of the usage I went trough the code:
> >>>
> >>>  - MatrixSpace.identity_matrix implement 1.
> >>>  - MatrixSpace.zero_matrix implement 3.
> >>>
> >>> Of course, my opinion is to make those three methods implements 2. :-)
> >>
> >> +1 for doing option (2).
> >
> >
> > I very often want to start with the zero_matrix or the identity_matrix and
> > "fill in" the rest of the matrix.  But I also want the access routines to be
> > fast!  So I vote for copy-on-write semantics, if possible.

Yes ! I noticed that when preparing my patch. If we decide to let zero_matrix
return an immutable matrix, then in several places of sage, an explicit copy
must be added (I can do that if needed). So it will be somehow a backward
incompatible change forcing the user to change their code. Of course this is
because they used an undocumented feature namely that zero_matrix is
immutable.

Nevertheless, I'm still in favor of option (2). Indeed this is the safest
option and in case of bad usage (trying to modify an immutable matrix) the
error message is very explicit and explicative:
sage: MS = MatrixSpace(ZZ,4)
sage: a = MS.one()
sage: a[1,2] = 3
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
...
ValueError: matrix is immutable; please change a copy instead (i.e., use 
copy(M) to change a copy of M).

> Nick's suggestion is definitely a (4) -- it's nothing like any of
> (1)-(3) in this discussion.  It could be done, but would be a *lot* of
> work (certainly way more than 1-3), and would likely slow down all
> writes somewhat.   But it's possible.

With Adrien Boussicault, we wrote some generic code to have copy on write for
combinatorial object (see [1]). Aside performance and usability issues, the
main problem is that in Python, the assignment operator has a binding
semantics: it binds the given object to a new variable, no new object can be
created. It cannot be overloaded as in C++ for example. So that you have to
somehow explicitely write that you want a new semantic copy, the actual copy
being delayed.

Any comment or vote ?

Florent

[1] 
http://combinat.sagemath.org/hgwebdir.cgi/code/file/6a2c5038c298/sage/combinat/copyonwrite.py#l1

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