Re: [Axiom-developer] exact quotient

[Martin Rubey]

Dear Waldek,

just to make sure:

> Oh, I think I made a stupid mistake.  I defined 
> 
> mon(n,k) == (random k * x + random k * y)^n
> 
> which makes the coefficients not of size log k, but rather of size 
> 
> log(binomial(n,j)* k^j).  Stupid me.

I just ran the test with

mon(n,k) == reduce(+, [random k * x^i*y^(n-i) for i in 0..n])

instead, and get the "expected" O(k^2) output:

(6) -> [test(kappa, 500, 5) for kappa in 10..100 by 10]

   [[10,1],[10,0],[10,1],[10,0],[10,1]]
   [[20,2],[20,2],[20,2],[20,2],[20,2]]
   [[30,4],[30,4],[30,3],[30,3],[30,5]]
   [[40,7],[40,7],[40,7],[40,7],[40,6]]
   [[50,11],[50,10],[50,11],[50,10],[50,11]]
   [[60,18],[60,15],[60,14],[60,15],[60,15]]
   [[70,19],[70,20],[70,20],[70,20],[70,22]]
 
I also modified William Sit's test (using Expand), and obtained

Out[11]= {{10, 0.272878}, {10, 0.273776}, {10, 0.273362}, {20, 0.902124}, 
 
>    {20, 0.899902}, {20, 0.899222}, {30, 1.920647}, {30, 1.922753}, 
 
>    {30, 1.916153}, {40, 3.617779}, {40, 3.708420}, {40, 3.608447}, 
 
>    {50, 6.507658}, {50, 6.525488}, {50, 6.509765}, {60, 10.755069}, 
 
>    {60, 10.809554}, {60, 10.868204}, {70, 16.384399}, {70, 16.461227}, 
 
>    {70, 16.337861}}

(on a much faster machine) which corresponds to Axiom's performance.

So, it remains to check, what situation is realistic for my problem, and
whether I can do anything about it...

Many thanks,

Martin