Quote:
Originally Posted by wblipp
I'm just beginning to learn about polynomial Ideals and groebner basis...Is there a book for applied algebraic topology that covers topics like this?

Scilab and some other available software (GAP, Singular..) have such functions available.
There are also some worksheets in other CAS's that are available which may provide some perspective.
Grobner Bases, SpringerVerlag..Thomas Becker. (1993), is a good a starting place as any.
I would suggest you look at Buchberger's algorthm first and fit the pieces you have into place.
This is an interesting topic..solvable and unsolvable Thue equations is one arena you may wish to enter and tangle with a few equations for some sport and here are two references:
The Algorithmic Resolution of Diophantine Equations by Nigel Smart.
https://projecteuclid.org/download/p....em/1048515872