Our purpose is to develop algorithms for solving certain types of

diophantine equations, especially index form equations. This problem

combines some classical tools of number theory with A.Baker's effective

estimates for linear forms in the logarithms of algebraic numbers and

the lattice basis reduction method of A.J.Lenstra, H.K.Lenstra and

L.Lovasz. We implement our algorithms and develop databases from

the solutions of these diophantine equations.