Homework # 4
due Tuesday, February 24, 4:00 PM

Programming

Do Exercise 7 of Chapter 7. Put the resulting function in quick.sml. (It will be easier to first do Exercise 6 and then change it.)

A polynomial \( a_n x^n + \ldots + a_1 x + a_0 \) can be represented as a list of reals \( [a_0, a_1, \ldots, a_n] \). Write functions eval, pow and polyToString so that we can evaluate: 


- val p = [1.0,2.0]; (* 2x + 1 *)
val p = [1.0,2.0] : real list
- eval(p,0.1);
val it = 1.2 : real
- val p3 = pow(3,p);
val p3 = [1.0,6.0,12.0,8.0] : real list
- eval(p3,0.1);
val it = 1.728 : real
- polyToString(p3);
val it = "8.0x^3 + 12.0x^2 + 6.0x + 1.0" : string
- polyToString [0.0,0.0,~1.0,0.0,0.0];
val it = "0.0x^4 + 0.0x^3 + ~1.0x^2 + 0.0x + 0.0" : string
- polyToString [0.0];
val it = "0.0" : string
- polyToString [];
val it = "0.0" : string
You will need to use the functions Real.toString and Int.toString to get strings for numbers. Don't ``open'' either the ``Real'' or the ``Int'' structure because it will cause overloading functions to misbehave. Do not use if in any of your code for polynomials. Put the resulting functions in poly.sml.

Our solution uses four additional functions, three of them at the top-level (useful named functions), and one a helper for the polyToString function.

Overloading and Polymorphism

Do Exercises 3 and 4 of Chapter 8.

Submitting Your Work

You submit your program work by putting it in the homework4 directory in your AFS class volume. You may do all your work in this directory, or you may wish to do your work in a different directory and copy things when correct into this directory. In any case, you will lose permission to write things in this directory after the deadline, which is 4:00pm on Tuesday, February 24th. In other words, you must be done before lecture starts.

The homework4 directory should include the following:

About this document


John Tang Boyland
2004-02-20