Comments on exploration 5

Grading comments on exploration 5

I: Symbolic expressions

• Does multiplying x times zero give zero?
• Does adding y+2 and y+3 produce x+y+5?
• Does adding 2*x and x*2 combine the terms?
• Does adding x*y*x to x*x*y combine the terms?

Things are much harder if you consider fractions and common denominators: there have been Ph.D. thesis written on that topic.

In order to get significant points on this problem, you had to not only implement the basic code, but also include test cases and give explanations. You also had to have a good set of test cases that exhibited the different properties of your system, not just two or three expressions.

One of the big dimensions on which the class answers diff-erred was the amount of simplification. Most people handled the cases of adding zero and multiplying by zero. But few people dealt with things like x*y=y*x.

There were several really excellent papers turned in. But one area where almost everyone fell down was in using data abstraction. Typically, people represented algebraic expressions as strings. As a result, the various operations had to continually parse their inputs, which made them both cumbersome to implements as non very extensible.

A better idea would be to keep the expressions as data abstractions. For example, a "sum" is an object that has a list of terms, and a "term" is an object that has a list of "factors", and a "factor" is either a number or a symbol or a sum (note the recursion). Then define addition and multiplication as operations on the list of terms, to generate new lists of terms and factors. And then define print methods separately from all of this.

Professional level algebraic manipulation systems are often implemented with the aid of pattern matchers that abstract away the details of manipulating expressions and picking out the pieces. You can learn about this in courses on symbolic computing, including 6.945.

II: Buying toothbrushes