Re: Checking simplified algebraic expressions (the -3 test)

"michalchik@[EMAIL PROTECTED]
" <michalchik@[EMAIL PROTECTED]
> writes:

> I always teach them that there are cases when this won't work and your
> would need to test with all numbers to be sure. The remultiplying
> before cancelling allwos them to check one step in a simplification
> but not the whole process. You might be right that -2 would be a good
> choice but I will have to think about it. As for the ad hominum attack
> that I must think I am really clever for thinking of this, I do not
> and never pretended to be so. I posted here to hear if people had
> better suggestions and get an idea of what reasonable objections
> people had.

Well about your actual question, yes, -3 seems good. But as others
have pointed out, more numbers would always be safer.

Thinking about it, I'd probably instead check with 0,1,-1 and then
maybe 2. This probably doesn't take longer on most expressions than
just -3 since in lots of cases esp. 0 and 1 will be trivial to
calculate. And powers of 0,1,-1 are easy! But any coincidental
identity for 3 is getting really unlikely to hold for all of four
numbers.

Of course, this is never going to be a proof. But you (and hopefully
your pupils) know that.

Rupert