Re: Symbolic math Message #5 Posted by Speck on 11 Aug 2003, 9:55 p.m., in response to message #1 by Tizedes Csaba
On the TI92:
Solve(3*x+1/(x5)=15+1/(x5),x)
Returns x=5
The TI85 numeric solver returns X=5.00000000001, but does so with a sign change error before final resolve.
As a direct algebraic problem, x=5 doesn't really work. However, if the machine is internally doing some sort of a limit process, then the returned answer x=5 is quite correct, as it would never actually reach the discontinuity at x=5. If something like Newton's method (or bisection, or one of the better methods) is being used, then there is some sort of stop condition where, based on a preset tolerance level, the algorithm figures it's "close enough," and returns the found answer to the user, even though that answer may appear to be exact. The machine doesn't just magically pick x=5, plug it in and see what happens. You could just as easily do that on your own. The machine has to use a method more suited to it's type of "thinking." The advice posted above about always checking your answer is definately good advice. The computer can never be better than the person using it.
Unfortunately, this doesn't look like one of the problems where the conjugate trick works, either.
Speck.
