How do I let them know about a bug ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg83736] How do I let them know about a bug ?*From*: giovanni resta <g.restaCUT at CUTiit.cnr.it>*Date*: Thu, 29 Nov 2007 06:29:30 -0500 (EST)

Hi, first of all let me express my joy in the discovery of this newsgroup. I was playing with Mathematica 6 (which has some very very nice features!) of a collegue of mine and exploring the new features. I saw that RamanujanTau[n] has been moved into the kernel and has a much more efficient implementation. In Issues, they say that when evaluated on large prime operands it can take long time, and they make this example: RamanujanTau[214928639999] // Timing {29.7385, 336969318523447435477041542002543549208693346637507838687265285} By lazily factoring it, I realized that the computed value was obviously wrong, so I checked for other prime operands. To make a long story short I saw that for prime operands greater than about 2*10^6 the function returned results that were almost surely wrong. So I worked a little on Attributes, to see how the function was implemented. I discovered that when the operand is a prime greater or equal to 1999993 the algorithm they used is wrong. In that case they uses this formula: (1/2) p^5 HurwitzClassNumber[4*p] which is clearly broken (by the way, the nice HurwitzClassNumber function is hidden). Indeed there is a way to compute tau(n) using the Hurwitz Class Number function H(x), and it contains the term (1/2) p^5 H(4*p) but it is much more complicated than that, since it needs also the evaluation of H() in about other O(sqrt(p)) points! Thus, for a number as large as 214928639999 the right running time will be simply "too long". Anyway, the right formula for tau() using H() can be found in the paper: http://pages.cs.wisc.edu/~cdx/CompTau.pdf I hope that this will be useful to anybody which will play with the fascinating Ramanujan tau function. I wonder if I have to send a message to the Mathematica Team (how??) or if they read this newsgroup. bye, g.