The following exercises use Singular.
- Read the help file for
```
Examples of ring
declarations
```

. You can access the help either on the Singular
homepage (it's section 3.3.1 of the manual), or by typing
`help;`

in Singular (provided you installed help
files). What command would you use to define `r`

to be
the ring *Q[x]*?
- Read the help file for the command
`gcd`

(you can
type `help gcd;`

if you installed the help files) and
do problem §1.5#8 from the book (hint: there's a very
similar example on page 45 of the book). Your answer should be
in the form of a printout from a Singular session.
- Do problem §1.5#9 from the book.

The following exercise is about *well orderings*. Which of
the following order relations are well orderings? If your answer
is "no", explain why.
- The subset
*[0,1]* of the real line, with the
usual ordering.
- The subset
*{-1/n | n* is a natural
number*}* of the real line, with the usual ordering.