The Contract command contracts the image of an ideal in  back to the polynomial ring .

The typical use of this command is to contract the result of a zero-dimensional decomposition back to the original ring. This is part of a process used to extend algorithms for zero-dimensional ideals to ideals of positive dimension. For additional details, see the help page for ZeroDimensionalDecomposition.

Becker, T., and Weispfenning, V. Groebner Bases. New York: Springer-Verlag, 1993.