The work in GAIA has been divided into three parts

•  A survey in four parts addressing:

1. A Resultant Approach to Detecting Intersecting Curves in P³.
2. Implicitizing rational hypersurfaces using approximation complexes.
3. Using projection operators in computer aided Design.
4. The method of moving surface for the implicitization of rational parametric surface in P³.

• 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.