ly, it has been hopeless to find explicit solutions to such
	     systems, and mathematics has instead developed deep and
	     powerful theories about the solutions to polynomial equations.
	     Enumerative Geometry is concerned with counting the
	     number of solutions when the polynomials come from a geometric situation and
	     Intersection Theory\index{intersection theory} gives methods to accomplish the enumeration.
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	     We use <i>Macaulay2</i> to investigate some problems from enume