algorithm for non-dimensionalization

[gyromagnetic at gmail.com]

Hi,
I am trying to non-dimensionalize some data I have obtained. There are
no 'standard' dimensionless groups for my application, so I would like
to obtain the 'best' non-dimensional groups based on some statistical
measures of the resulting transformed data.

At this point, I am looking for a way to generate dimensionless
groupings from a set of base units. I would like to have a way to
output all dimensionless groups that comprise no more than some
specified number of fundamental (or base) units.

For instance, if I have data like the following:

dat1(length), dat2(time), dat3(length), dat4(length/time),
dat5(length^2)

and I want dimensionless groups with no more than four base units, I
would like a result like the following:

dat1/dat3, dat1/(dat2*dat4), dat5/(dat1*dat3), dat5/(dat2*dat4*dat1),
...

I plan to code this in Python, and would appreciate any thoughts you
might have about algorithms or approaches to carry out this task.

Thank you.

-g