quiz5.mws

MCS 320 Quiz 5 Friday 23 September 2005

> restart;

1. Type

> r := (x^2-1)^2/(y-1);

r := (x^2-1)^2/(y-1)

followed by

> dismantle(r);

PROD(5)
  SUM(5)
     PROD(3)
        NAME(4): x
        INTPOS(2): 2
     INTPOS(2): 1
     INTNEG(2): -1
     INTPOS(2): 1
  INTPOS(2): 2
  SUM(5)
     NAME(4): y
     INTPOS(2): 1
     INTNEG(2): -1
     INTPOS(2): 1
  INTNEG(2): -1

Use the output of dismantle to draw the directed acyclic graph of the internal representation of r.

Answer: see the handout.

2. Type

> subs(-1=Pi,r);

(x^2+Pi)^2*(y+Pi)^Pi

Explain why you see Pi three times in the output.

Answer:

Every object in Maple is stored only once.  The -1 occurs three times in r, twice as coefficient and once as the exponent for the division.