Hi John, My point is that once the deprecated top-level function is removed, non-expert users wanting to compute these dimensions are unlikely to spot that they can import extra stuff from "sage.modular.dims"; they're much more likely to end up using CuspForms(...).dimension(), which is hugely slower (and the docstring for that method does not say anything about the existence of a faster alternative).
(My email was prompted by a discussion on MathOverflow with a Sage newbie who wanted to compute some modular form space dimensions.) David On Tue, 20 Sept 2022 at 11:21, John Cremona <[email protected]> wrote: > In 9.6 and 9.7.rc1, I follow the suggestions at ticket #32647 and all > seems well: > > sage: from sage.modular.dims import dimension_cusp_forms > sage: time dimension_cusp_forms(Gamma0(99), 100) > CPU times: user 4 ms, sys: 0 ns, total: 4 ms > Wall time: 5.19 ms > 1184 > > -- in particular it is fast and I see no deprecation warning. David, > you didn't say which Sage version you were running. > > John > > On Tue, 20 Sept 2022 at 09:07, David Loeffler <[email protected]> > wrote: > > > > How should one go about *quickly* computing the dimension of a space of > cuspidal modular forms (of weight >= 2) in Sage, without actually computing > a basis of the space? > > > > The standalone method "dimension_cusp_forms" used to be really good for > this, and was a command I personally used very very frequently. However, > ticket #32647 slapped a deprecation warning on it. If this indeed gets > removed, then the simplest way of getting at this functionality is by > typing "CuspForms(...).dimension()". > > > > Unfortunately, this approach is vastly slower than the old standalone > function was, since it seems to be doing some kind of unnecessary > O(dimension) loop over the basis elements at initialisation time: > > > > sage: time dimension_cusp_forms(Gamma0(99), 100) # deprecated > > > > [ deprecation warning text ] > > > > CPU times: user 8 ms, sys: 0 ns, total: 8 ms > > > > Wall time: 8.94 ms > > > > 1184 > > > > > > sage: time CuspForms(Gamma0(99), 100).dimension() > > > > CPU times: user 1.06 s, sys: 124 ms, total: 1.18 s > > > > Wall time: 1.18 s > > > > 1184 > > > > > > Note the huge difference in timings: 9 milliseconds vs 1.2 seconds! So > the non-deprecated method is 130 times slower than the deprecated one, > which seems a bit problematic to me. > > > > IMHO, Sage has shot itself in the foot here, axing a fast and effective > command in one of its "core competences" (modular forms) because some > developer's notion of code aesthetics has been prioritised over ease-of-use > and functionality. I'd like to call for this change made in #32647 to be > reversed, and not reintroduced unless CuspForms.__init__() has been > re-engineered to make the new code path as quick as the old one was. > > > > (This problem only affects cusp form spaces, not the full modular form > space; "ModularForms(...).dimension()" takes about the same time as > "dimension_modular_forms()", as it should. If you're crafty, you can work > around this by importing "dimension_cusp_forms" from sage.modular.dims, or > using the dimension_cusp_forms() method of the Gamma0 group class; but > these won't be easy to find for non-expert Sage users.) > > > > Regards, David > > > > -- > > You received this message because you are subscribed to the Google > Groups "sage-nt" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected]. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-nt/CANDN%3DhzJRoKzD09Rn8pfwhMXOnU5tgTeD1j1yhCcPAKeCxYziw%40mail.gmail.com > . > > -- > You received this message because you are subscribed to the Google Groups > "sage-nt" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-nt/CAD0p0K5KCo08r0bZz_YtWja3Sr%2BcuaRSprtBXGZF-UMahOEyEQ%40mail.gmail.com > . > -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-nt/CANDN%3DhyqUbg6w4ZZvtCq46KqbohaFnF2KDoMZYQpyvFFGEzP1A%40mail.gmail.com.
