Wikipedia:Reference desk/Archives/Mathematics/2007 December 24

= December 24 =

Computing with modular forms
Two questions regarding modular forms: Help with either or both is appreciated! --PeruvianLlama(spit) 00:51, 24 December 2007 (UTC)
 * 1) Using SAGE or MAGMA, is there a (relatively) painless way to work with modular forms associated with the principal congruence subgroup $$\Gamma(N)$$ of the (full) modular group, $$PSL_2(\mathbb{Z})$$? Looking through the documentation (here, for example), it only seems possible to define "ModularForms" objects with respect to the congruence subgroups $$\Gamma_0(N)$$, or $$\Gamma_1(N)$$. But surely there must be some way around this?
 * 2) How does one go about computing q-expansions for specific modular forms, in a practical manner? The definition (in the wiki article) is nice from a theoretical standpoint, but I find it unwieldy from an everyday-use point of view.

You should look at the book Modular Forms, a Computational Approach by William Stein (the lead developer of SAGE). The book's ISBN is 0-8218-3960-8.

--Petekl (talk) 01:16, 26 December 2007 (UTC)

Attachment point formula
I want to weld a cyliner to a bar at point D such that when the cylinder is rolled 45 degrees the distance between A and B will equal 11.86. What formula would I use to determine the distance between point A and point D to achieve a distance of 11.86 between A and B? Multimillionaire (talk) 20:16, 24 December 2007 (UTC)
 * Denoting the angle C by &alpha;, point D is $$r(1-\cos \alpha)$$ above ground. Thus we have $$\mathrm{BD} = \frac{r(1-\cos \alpha)}{\sin \alpha}$$, and $$\mathrm{AD}=\mathrm{AB}-\mathrm{BD}=11.86-\frac{r(1-\cos \alpha)}{\sin \alpha}$$. For &alpha;=45° this is $$11.86-0.4142r$$. -- Meni Rosenfeld (talk) 21:27, 24 December 2007 (UTC)