Homework 2

Problem 1.  Exercise 5 on page 5 of [Cox et al]

Problem 2.  Use Maple to draw the affine varieties found 
            in Exercise 4 page 12 of [Cox et al].  Be sure 
            to used the CONSTRAINED option.  Also make sure 
            to use Maple to label your drawings with a brief 
            text description.  Be sure to show the coordinate 
            axes in your drwaings.

Problem 3.  Exercise 13, page 13 of [Cox et al]

Problem 4.  The 3-sphere

		S3 = V(x2 + y2 + z2 + t2 - 1)

             "lives" in 4-space.  Use Maple to visualize this 
             hypersurface by viewing 3 dimensional cross-sections 
             parameterized by t, i.e., draw 

		    S3t = V(x2 + y2 + z2 + t2 - 1)
             for 

	          t = 1.0,0.9,0.8,0.5,0.0,-0.5,-0.8,-0.9,-1.0

             Be sure to use Maple to label each drawing with the
             appropriate value of  t.  Also be sure to use the 
             CONSTRANED option and to show the coordinate axes.
             Finally, use Maple's animate3d procedure to view a
             "movie" of the hyperserface.

Problem 5.  Repeat problem 4 with the hypersurface

		M3 = V(x2 - y2 - z2 + t - 1)

            using an appropriate set of values for the parameter t.