On Sun, 16 Apr 2023, 15:52 Trevor Karn, <trevor.k.k...@gmail.com> wrote:
> 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? > probably because B.echelon_form() returns the identity matrix - obviously wrong too > 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 > <https://groups.google.com/d/msgid/sage-devel/cc5a27a3-e855-43e1-a494-b411c613497dn%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. 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