Re: Elliptic Modular Function
- To: mathgroup at smc.vnet.net
- Subject: [mg94670] Re: Elliptic Modular Function
- From: "Steve Luttrell" <steve at _removemefirst_luttrell.org.uk>
- Date: Fri, 19 Dec 2008 07:25:58 -0500 (EST)
- References: <gidfcf$gr$1@smc.vnet.net>
I have Mathematica 6 and the following approach computes a recurrence
relation that relates each number in your sequence to the previous 7 numbers
(7 is the smallest window size that works), which I assume is what you are
asking for.
seq = {744, 196884, 21493760, 864299970, 20245856256, 333202640600,
4252023300096, 44656994071935, 401490886656000, 3176440229784420,
22567393309593600, 146211911499519294, 874313719685775360};
mat = Partition[seq, 8, 1];
sol = LinearSolve[mat[[All, 1 ;; -2]], mat[[All, -1]]]
{-(1001589493118707723252774586806783059511197069280472918819249115152\
64/19162784237829158216763570284054521827441476710874517532259905), \
42836309800185018672835382757497212537045197305584448679583102059327/\
15330227390263326573410856227243617461953181368699614025807924, -(
14374747893554933067078517692623466981004522949168644658386695684096\
/19162784237829158216763570284054521827441476710874517532259905), \
469984383473409665200209436753892258320750519894340701863349734306/\
3832556847565831643352714056810904365488295342174903506451981, -(
232495625234716475054419228695401877980102477748763484181693713664/
19162784237829158216763570284054521827441476710874517532259905), \
22990739633401504437950180817037514177602473403019849712296913267/\
38325568475658316433527140568109043654882953421749035064519810, 0}
The solution is a 7-component vector of rational fractions that you use to
form an inner product with each 7-tuple in your sequence to obtain the next
member of the sequence.
These rational fractions can be factorised, but unfortunately there is no
cancellation.
--
Stephen Luttrell
West Malvern, UK
"Artur" <grafix at csl.pl> wrote in message news:gidfcf$gr$1 at smc.vnet.net...
> Dear Mathemtica Gusrus,
> Will be possible help person which have ver. 7.
> Check which rule find Mathematica 7 for sequences
> {744, 196884, 21493760, 864299970, 20245856256, 333202640600,
> 4252023300096, 44656994071935, 401490886656000, 3176440229784420,
> 22567393309593600, 146211911499519294, 874313719685775360}
>
> I will be greatful for any help because I don't know how do that with
> use KleinInvariantJ function.
>
> Best wishes
> Artur
>