James G. McLaughlin on Fri, 4 May 2001 12:25:24 -0500 (CDT)

 lindep command

```Has anyone used the lindep command on a large set of numbers? I am
wondering how effective this command is and what the effective limits are
on the size of the sets it can work on.

I'll describe my problem and my approach and possibly someone can suggest
a better approach.

I calculate two numbers, u and v say, to high precision - 1100/1200 digits
(by taking enough terms in a certain continued fraction expansion). I know
there is an algebraic relation between them: ie there exists f(x,y) in
Z[x,y] such that f(u,v) = 0. I have an idea how high the degree is from
work on similar numbers so say the degree is d. I compute the set of
numbers

X = {u^i*v*j: 0 <= i <= d, 0 <= j <= d}.

I then try lindep(X,1000),say.

This has worked in the past for other numbers with smaller d. My present d
is 17 so my set has 324 elements and gp has been chugging away for about
10 days now. Previously I was able to get by with the 1000 in
lindep(X,1000) replaced by something smaller.

Does anyone have a suggestion how I might speed things up or am I near
the limits of what lindep can do?

Jimmy Mc Laughlin.
```