Today I tried to use mathematica and sage to compute a function. It has 10496 terms, each in the form of monomials of 6 variables and 4 more in the exponents. The sum is over 4 parameters in the exponents, each from 0 to infinity. So the sum would be rational functions of 6 variables, with 10496 terms. I thought it is straight forward to  run the mathematica to solve it, but it turns out that the software told me it cannot do it directly. Luckily I am currently at ICERM, so I talked to a professor today, who taught me how to use some symbolic programming to calculate. The computer doesn’t have to understand the meaning of the formula. It just match some symbols and give some results. There is a possible bug in the program I wrote, but probably it won’t happen. Calculating for about 15 minutes, the sage program eventually gave me a formula, which was so long that it did not appear on the screan, but instead generated a txt file. The file is 1134kb large. One can imagine how long the formula is by its pure txt size. I sent an email to Hundley with the formula attached. He replied, well, I have to say I can do nothing about it. But good job! Hundley is going to Newyork for the weekend, and so am I. So I will be away from the problem for a few days. Hopefully I can think of a way to attack it after coming back. Now I totally understand why Rallis doesn’t like to calculate the unramified L-function directly. Sometimes finite could be big, and brute force doesn’t work.



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