1. Purpose of rbf@trinitas.mju.ac.kr     [ 한글 설명 ]
Computation of the value of all the coefficients of the expansion of the product of a single Gaussian polynomial 1+t+t^2+...+t^(q-1) by m times 
(*)        (1+t+t^2+...+t^(q-1))^m
and immediate return to the e-mail sender of the computed results.

2. Introduction
When q*m is increased, it becomes very difficult to compute all the coefficients of the expansion of the product in Eq (*) above. Recently, Prof. Sun T. Soh discovered a very efficient recursive formula, called Recursive Binomial Formula, for such an expansion.

Soh's recursive binomial formula for (*)

We use Soh's formula for all the coefficients of such a product in this section of our InetCompu. The time efficiency of his algorithm is O(n^2). 

3. Contributor: The program we are using was developed in Reduce commands by Prof. Sun T. Soh, Dept of Math, Myong Ji Univ., Rep. of Korea. 

4. Note
For a trouble-free handling of your e-mail, we strongly recommend you to use MicroSoft Outlook Express, New mail > Alt+O > Alt+X (with No Encryption),  to send out an e-mail to rbf@trinitas.mju.ac.kr   .   

5. How to do: Send an e-mail with plain text style (for instance, in the case of MicroSoft Outlook Express, New mail > Alt+o > Alt+x (with No Encryption)) to rbf@trinitas.mju.ac.kr whose main body, in the case of Eq. (*) above, should consist of 

     input: 
q:=12$
m:=34$
     end input:  

Then upon the arrival of the e-mail, all the coefficients of the product in (*) above are automatically computed and sent back to the e-mail sender immediately.

[Reminder] When the requested job is computationally not very complicated, it should be quite the case that you will receive the result within a few Minutes.  But, our response consisting of the computed results can not be delivered to the sender properly, if either there is a spelling mistake in sender's e-mail address or sender's mail box is already filled with too many of other e-mails. Thus, if you do not receive the results although you have waited for some time, then please check your mail account to correct the above trouble-causing problems.  After that, try again according to the procedure described in Section 5 above.

6. Examples
If you send one of the following inputs between "input:" and "end input:" to rbf@trinitas.mju.ac.kr , then you should receive the computed results very quickly. In order to examine the details of the computed results of each example below, simply click the sub-titles.

6-1. Example 1 (Click here for the details)

     input:
     q:=101$
     m:=20$
     end input: 

output file size: 46KB 

comment The following is the timex report of the system for the above computation (in seconds):
real        1.10
user        0.95
sys         0.14
$

6-2. Example 2 (Click here for the details)

     input:
     q:=101$
     m:=40$
     end input:

output file size: 163KB 

comment The following is the timex report of the system for the above computation (in seconds):
real        3.42
user        3.12
sys         0.30
$ 

6-3. Example 3 (Click here for the details)

     input:
     q:=101$
     m:=80$
     end input:

output file size: 606KB

comment The following is the timex report of the system for the above computation (in seconds):
real       12.26
user       11.30
sys         0.88
$

6-4. Example 4 (Click here for the details)

      input:
     q:=101$
     m:=160$
     end input: 

output file size: 2.3MB 

comment The following is the timex report of the system for the above computation (in seconds):
real 45.00
user 42.77
sys 2.06
$