[GAP Forum] polynomial system solving

[Alexander Hulpke]

Dear Tasos Papathanasiou, Dear GAP-Forum,

> I would really appreciate it if anyone could help me find the less
> comlicated method to solve polynomial systems using GAP.Thank you.

Not knowing what your mathematical background or your application is makes
it a bit hard to give a suitable response:

If solving a system of polynomial equations is your only application, I
would not recommend to use GAP, but a dedicated system.

If you need to do it as part of a longer calculation in GAP, you might be
able to use the built-in Gr"oebner bases, however:

- There is no ``solve'' command or ``less complicated method''.
  You will have to build a Lexicographic Gr"obner basis and from there
  proceed ``by hand''.
  To see examples on how to use the `GroebnerBasis' command, you can get the
  online help via
  ?GroebnerBasis
  I would look at a textbook (e.g. Cox, Little, OShea: Ideals,
  Varieties and Algorithms) for a description of this second step. There is
  no specific facility in GAP to help with this.

- The Gr"obner basis functionality in GAP is rather basic and mainly
  intended to help with teaching (computational) algebra. If your polynomial
  system is complicated GAP might take very long to calculate. (You might be
  able to use the `Singular' package to interface to the singular system to
  speed up calculations, but personally I have no experience with using it
  under Windows.)

Best wishes,

    Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke