Spring 2001 CS100M       Solutions to Exercise E5

1. function p = addpoly(p1,p2)
   p = p1 + p2;

note: in p3.4 we always assume coefficients are stored right-to-left;
canonical refers only to whether there are leading 0s in the polynomial,
which corresponds to trailing zeros in the vector of coefficients.

   a) $addpoly([0 1], [0 -1])$ produces $[0 0]$ instead of $[0]$.
      (sum of $x$ and $-x$ is $0x+0$, which we want simplified to $0$.)

or
      $addpoly([5], [0 1]$ produces $[5 6]$ instead $[5 1]$
      because $[5]$=$5$ is a scalar added to a vector $[0 1]$.

note: the sum of a non-canonical poly with a canonical poly can be canonical,
      e.g. [0 1] + [0 0] = [0 1], i.e. x + 0 = x.

   b) $addpoly([0 1], [0 0 1])$ tries to add two vectors of different
      sizes, which is an error in Matlab.  (the answer should be $[0 1 1]$.)

2. loop invariant $X*Y = x*y + z$ holds at: (a), (b), (d), (f), (h), (k), (m)

note: for questions like this, please provide a list, as above, not a
list of true/false values (do that for partial credit, but not your
final answer).

snapshot:  (a) (b)  (c) (d)  (e) (f)  (g) (h)  (i) (k)  (l) (m)
            |   |    |   |    |   |    |   |    |   |    |   |
       #  1 | 2 |  3 | 4 |  5 | 6 |  7 | 8 |  5 | 6 |  7 | 8 |
       X  6 |   |    |   |    |   |    |   |    |   |    |   |
       Y 11 |   |    |   |    |   |    |   |    |   |    |   |
       x  6 |   | 11 |   | 22 |   |    |   | 44 |   |    |   |
       y 11 |   |    | 6 |    | 3 |    | 2 |    | 1 |    | 0 |
       z  0 |   |    |   |    |   | 22 |   |    |   | 66 |   |
       t    | 6 |    |   |    |   |    |   |    |   |    |   |

a student asked:

> % PS 	The answers to this exercise are fully text, without any code. 
> %		Why was there a need for us to submit our answers as an .m file?

+ to make sure people know how to use the matlab editor
+ to make sure people submit text files, not word documents