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

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[edit] December 24

[edit] Computing with modular forms

Two questions regarding modular forms:

  1. Using SAGE or MAGMA, is there a (relatively) painless way to work with modular forms associated with the principal congruence subgroup Γ(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 Γ0(N), or Γ1(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.

Help with either or both is appreciated! --PeruvianLlama(spit) 00:51, 24 December 2007 (UTC)

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)

[edit] 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 α, point D is r(1 − cosα) 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 α=45° this is 11.86 − 0.4142r. -- Meni Rosenfeld (talk) 21:27, 24 December 2007 (UTC)