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.
