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

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December 24

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Computing with modular forms

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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 of the (full) modular group, ? Looking through the documentation (here, for example), it only seems possible to define "ModularForms" objects with respect to the congruence subgroups , or . 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)[reply]

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)[reply]

Attachment point formula

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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)[reply]

Denoting the angle C by α, point D is above ground. Thus we have , and . For α=45° this is . -- Meni Rosenfeld (talk) 21:27, 24 December 2007 (UTC)[reply]