CSC151.02 2003F, Class 9: Procedures

Admin:
* Moment of silence
* A gift
* I'll probably discuss your Web sites on Monday.
* Read Conditionals
* Homework: Lab writeup on today's lab.

Topics:
* Followup questions on Tuesdays's lab
* Writing your own procedures
* Laboratory

What can you tell me about the following procedures?
* quotient, remainder, modulo
  * Divides two integers and gives you the whole portion of the result
  * Remainder gives the rest of the result  
  * Sam writes unitelligble math gobbledygook: y = qx + r s.t r < x
  * modulo does something different: Gives you a result on the modulus number scale
Normal number line:     -2__-1__0___1___2___3___4___5
Modulus 4 num line:     2___3___0___1___2___3___0___1___2___3___0___1___2__3

A "positive" remainder, in some sense.

* max: Given one or more reals, gives the highest
  min: Given one or more reals, gives the lowest
* Why not complex parameters?
  * Hard to write
  * If we treat them as vectors, use magnitude of vector
  * Some people compare by using the sum of the parts 
  * There are other metrics

* What procedures take 0 or more parameters?
  * list
  * +
  * * (times)
 
* numerator, denominator
  * One real parameter
> (numerator 2.4 1.2)
. numerator: expects 1 argument, given 2: 2.4 1.2
> (numerator 3/4)
3
> (denominator 3/4)
4
> (numerator 4/8)
1
> (numerator 1.2)
5404319552844595.0
> (denominator 1.2)
4503599627370496.0
> (numerator #e1.2)
6
> (denominator #e1.2)

* gcd, lcm
  * Great common divisor: Given one or more numbers, The largest number that evenly divides all the numbers
  * Lowest common multiple: If given more than one integer, The smallest positive integer that is evenly divisible by all the integers.  If given exactly one integer, that integer.

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Writing Your Own Procedures
* You must choose exactly how many parameters you have

(define NAME_OF_PROCEDURE
   (lambda LIST_OF_PARAMETERS
      EXPRESSION))

For example

(define square
  (lambda (x)
    (* x x)))

(define addreese
  (lambda (lst)
    (cons 'reese lst)))

You are now ready for the lab!