The objective within the gAIA II project has been to develop tools for constructing, manipulating and exploiting implicit representations for parametric curves and surfaces based on resultant computations.

The work in GAIA has been divided into three parts

A survey in four parts addressing:

A Resultant Approach to Detecting Intersecting Curves in P^{3}.

Implicitizing rational hypersurfaces using approximation complexes.

Using projection operators in computer aided Design.

The method of moving surface for the implicitization of rational parametric surface in P^{3}.

A report addressing sparce/toric resultant, results when the number of monomials is small compared to the number of possible monomials for polynomial of the degree in question.

Development of prototypes of tools for constructing, manipulating and exploiting implicit representations for parametric curves and surfaces based on resultant computations.