[GAP Forum] Linear Diophantine Equations

[Bill Allombert]

On Tue, Sep 08, 2015 at 08:59:36AM -0600, Alexander Hulpke wrote:
> Dear Forum,
> 
> > On Sep 8, 2015, at 8:52 AM, fahime babaee <f.alibabaee at gmail.com> wrote:
> > 
> > Dear forum
> > 
> > Is it possible to solve Linear Diophantine Equations over integers in Gap?
> 
> Yes. GAP has the extended Gcd algorithm (e.g using the function Gcdex for
> integers, or GcdRepresentation over arbitrary rings) required for the
> standard method for solving such equations, hoever there is no turnkey
> interface that would simply take a set of equations and return their
> solutions.

Well, GAP has also more elaborated functions like
HermiteNormalFormIntegerMatTransform()
which can be used to solve higher-dimensional linear Diophantine equations over
the integers.

Cheers,
Bill.