I found a reference for this:

<http://citeseer.nj.nec.com/aardal98solving.html>

It says they do lattice base reduction as a step to solving the equations.

Whereas we're trying to do a twist on base reduction. Here's a paper

about that:

<http://citeseer.nj.nec.com/248763.html>

It says "The Gram-Schmidt vectors, however, do not necessarily belong to

the lattice, but they do span the same real vector space as b1, ..., bi,

so they are used as a "reference" for the basis reduction algorithm."

Also defines a lattice: "The lattice L spanned by b1, ..., bi is the set

of vectors that can be obtained by taking integer linear combinations of

the vectors b1, ..., bi."

It looks like what we want is between the Gram-Schmidt space (integer

combinations) and lattice (real combinations) because it has rational

combinations. Or is that the same as Gram-Schmidt?

I don't know, it's starting to get complicated. I think I'll ignore it

for a while.

Graham

--- In tuning-math@y..., graham@m... wrote:

> I found a reference for this:

>

> <http://citeseer.nj.nec.com/aardal98solving.html>

>

> It says they do lattice base reduction as a step to solving the

equations.

> Whereas we're trying to do a twist on base reduction. Here's a

paper

> about that:

That's a fancy new method for an old classic problem, and presumably

becomes interesting mostly when the number of simultaneous

Diophantine equations are high. Can you solve a system of linear

equations over the rationals in Python?

In-Reply-To: <9v35h4+amle@eGroups.com>

In article <9v35h4+amle@eGroups.com>, genewardsmith@juno.com

(genewardsmith) wrote:

> That's a fancy new method for an old classic problem, and presumably

> becomes interesting mostly when the number of simultaneous

> Diophantine equations are high. Can you solve a system of linear

> equations over the rationals in Python?

With Numeric, you can solve for floating point numbers (using a wrapper

around the Fortran LAPACK) but there's no support for integers or

rationals.

Graham