# Homework 2

Due: Wednesday, September 29, 1999

• [Cox et al] Cox, Little, & O'Shea, "Ideals, Varieties, and Algorithms," (second Edition), Springer-Verlag, (1996), Chapters 1.
• [Heck] Heck, "Introduction to Maple," (Second Edition) Springer-Verlag, (1997), Chapter 15.

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

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.

```