On Fri, 1 Mar 2024 at 11:15, John Cremona <john.crem...@gmail.com> wrote: > > On Fri, 1 Mar 2024 at 11:03, Dima Pasechnik <dimp...@gmail.com> wrote: >> >> On Fri, Mar 1, 2024 at 10:24 AM John Cremona <john.crem...@gmail.com> wrote: >>> >>> On Fri, 1 Mar 2024 at 10:04, Dima Pasechnik <dimp...@gmail.com> wrote: >>>> >>>> >>>> >>>> On 1 March 2024 09:07:26 GMT, 'Martin R' via sage-devel >>>> <sage-devel@googlegroups.com> wrote: >>>> >I'd be OK with raising an exception or with -oo, but it should be uniform, >>>> >and I think it should be the same for polynomials, Laurent polynomials and >>>> >in the same spirit for degree and valuation. >>>> > >>>> >It might be best to raise an exception, because this ensures that the zero >>>> >polynomial gets special treatment. >>>> >>>> Exceptions are expensive, performance-wise, and using them as a regular >>>> means of controlling the flow of the algorithm execution is not a good >>>> idea. >>>> A simple if/then/else is much cheaper. >>> >>> >>> Isn't this suggestion to have f.degree() raise an exception when f is zero, >>> but also then that any code which needs the degree to treat 0 as a special >>> case (where that makes sense)? To it would be the caller's responsibility >>> to do that with a test of f.is_zero() or whatever, rather than by seeing if >>> an exception is triggered. >> >> >> Letting degree(0) throw an exception means that every place where you want >> to test whether the degree of fg satisfies something needs a testing whether >> f or g is 0, in order to avoid an exception. > > > Fair enough. I had been assuming that for the types we are talking about > testing for equality with 0 would be fast, but perhaps it is not.
If p.degree() can do this quickly then there is no reason that some other function couldn't be made to return the equivalent of p.degree() < 0 quickly. It would sometimes be a bit awkward though for deg(0) to raise an exception. I see examples of code in sympy where e.g. the degrees of polynomials are reduced in a loop and having deg(0) < 0 naturally captures the the control flow that is needed. >> OTOH, setting the degree of 0 to be -oo has an obvious advantage: it >> automaticlly gives mathematically correct degree of fg, by using >> degree(fg)=degree(f)+degree(g), regardless of f or g being 0. And checking >> the degree is (or at least ought to be) faster than comparing for equality >> to 0. Do you see examples where arithmetic with degree(0) is used in practice? When I looked for these in the sympy code I didn't find any even though the -oo convention was used. I just don't think it comes up in real code. > It's a little dangerous to talk of -oo being "mathematically correct", but I > have given this definition myself in undergraduate course (and for the reason > you give) so that's ok, especially as in Sage we do have -oo as a possible > return value and no requiremt for the value to always be of the same type > (e.g. Integer). There might not be any "requirement" for degree() to return objects of the same type but from a computational perspective it is generally better to use well defined types. Python allows mixing types up but that doesn't make it a good idea to do so especially in performance sensitive code. -- Oscar -- 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/CAHVvXxRDh1y6h3PiRZNAzT50DJAfgLGMxzhdMVrV1SiNWHO24w%40mail.gmail.com.
