I don't have much understanding of how floating point arithmetic works, but
the argument
>If you're writing python code, you should expect 2*0.5 to return a
>float. But if you're learning linear algebra for the first time and
>typing a matrix into the Sage notebook, typing 0.5 instead of 1/2
>should not ruin the entire assignment without so much as a warning.
seems important to me. I also sometimes worry that Sage seems to be written
for users who are both experts in [insert mathematical field here] and
Python. This prevents (a) mathematical experts who don't know python from
using Sage and (b) more junior students from using sage. Maybe one can make
the argument that mathematical experts should just learn python (although I
would disagree), but I think (b) is a genuine problem. Mathematica doesn't
seem to require the user to be expert in either math or Wolfram language
(or maybe I haven't used it enough). I don't have an actionable complaint
here, but it is something I encounter when helping folks around my math
department with their code. I'm trying to keep it in mind as I develop
code.
I see that
sage: A = matrix([[-3, 2, 1 ],[ 2,-4, 4 ], [ 1, 2,-5 ]])
sage: B = (2*0.5*A)
sage: rank(B)
3
What about floating point arithmetic makes this break? I print (B) and see
[-3.00000000000000 2.00000000000000 1.00000000000000]
[ 2.00000000000000 -4.00000000000000 4.00000000000000]
[ 1.00000000000000 2.00000000000000 -5.00000000000000]
which doesn't have any obvious reason to be not rank-2. Could someone ELI5?
It is also not unprecedented for an error to be thrown for the rank method.
>From the documentation:
sage: m = matrix(Integers(4), 2, [2,2,2,2])
sage: m.rank()
Traceback (most recent call last):
...
NotImplementedError: Echelon form not implemented over 'Ring of
integers modulo 4'.
It seems reasonable to me that a similar NotImplementedError could be
thrown for generic dense matrices. Is that an acceptable solution @Dima and
@Michael? It seems easy enough to add a `.rank()` method in
`matrix/matrix_generic_dense.pyx` which throws the error. I'd be happy to
make this PR if that is reasonable to folks.
On Sunday, April 16, 2023 at 6:53:36 AM UTC-5 Dima Pasechnik wrote:
> On Sun, Apr 16, 2023 at 12:25 AM Michael Orlitzky <mic...@orlitzky.com>
> wrote:
> >
> > On Sat, 2023-04-15 at 18:20 -0400, David Roe wrote:
> > > I agree with William that you should refrain from insulting the Sage
> > > developers, especially when the underlying problem comes from your
> > > misunderstanding of how floating point arithmetic works.
> >
> > I was given this response many times, and I think it's condescending
> > (no offense). My favorite permabug:
> >
> > sage: A = matrix([[-3, 2, 1 ],
> > ....: [ 2,-4, 4 ],
> > ....: [ 1, 2,-5 ]])
> > sage: B = (2 * 0.5 * A)
> > sage: B == A
> > True
> > sage: B.rank() == A.rank()
> > False
> >
>
> that's a bug in B.rank() - in my book at least. It's perfectly
> possible to either reliably derive that rank(B)=2,
> as far as it makes sense in the given precision, or throw an error.
> It's just not implemented.
>
>
> > I promise you that I know what a floating point number is, and that
> > they aren't the problem. The problem is that reasonable expectations
> > are not met by the Sage user interface. It shouldn't be that easy to
> > get the computer to lie to me. An explanation is of course possible,
> > but only after the fact, and only with a level of knowledge about the
> > preprocessor that is beyond most users.
> >
> > --
> > You received this message because you are subscribed to the Google
> Groups "sage-devel" group.
> > To unsubscribe from this group and stop receiving emails from it, send
> an email to sage-devel+...@googlegroups.com.
> > To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-devel/c8531f5211ebfe590ed2b38390b33ef26df1d1eb.camel%40orlitzky.com
> .
>
--
You received this message because you are subscribed to the Google Groups
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sage-devel/cc5a27a3-e855-43e1-a494-b411c613497dn%40googlegroups.com.
