The following document was written using Schematik, the precursor of SchematiX that developed for the Nexts. You may wish to use one of the word processors on the Nexts (say WordPerfect or WriteNow) or the SGIs (say Rapport), especially since you will probably want to include some of the images in the first lab. See one of us or one of the lab assistants if you need help using one of these word processors.
Chris Cross
MC27 Lab 1
February 31, 1995
Introduction
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The primary purpose of this lab is simply to demonstrate how one might
write an MC27 lab report. However, in order to provide a suitable
pretense, a bit of high-school algebra is dredged up. [This lab
report was done in Schematik rather than a word processing program,
and hence isn't very fancy, but it illustrates what the instructors
would be satisfied with.]
Part 1: Number of real roots of a quadratic
-------------------------------------------
In this part of the lab, I designed a procedure to compute how many
real roots a quadratic equation has. Remembering that this could be
determined by computing the discriminant of the equation and then
testing that discriminant, I broke the problem into those two parts:
(define num-real-roots
(lambda (a b c) ;how many real roots does ax\^2+bx+c=0 have?
(num-real-roots-from-discriminant (discriminant a b c))))
The two auxiliary routines used by the above both straightforwardly
reflect my memories from high school:
(define discriminant
(lambda (a b c)
(- (square b) (* 4 a c))))
(define num-real-roots-from-discriminant
(lambda (d)
(if (< d 0)
0
(if (= d 0)
1
2))))
(The procedure square used above is from the book.)
I tested the real-roots procedure using one simple example falling
into each of the three cases. Note that I took care to use examples
in which the three arguments were different from one another, to
improve the chances of catching certain bugs.
My procedure worked in all three cases, as shown below:
(real-roots 1 2 3)
;Value: 0
(real-roots 1 10 2)
;Value: 2
(real-roots 2 16 32)
;Value: 1
Conclusion
----------
The programming required for this lab was simple, not only because
there was (atypically) only one part, but also because that part
didn't require any recursion or iteration. Determining the number of
real roots of a quadratic equation is an example of an unusual
category of computations: those that are complex enough to be worth
automating, yet involve only a fixed amount of computation.