* Henry Baker <hbaker1@pipeline.com> [May 06. 2011 20:25]:
You know that the Casio performs an inverse lookup for sure?
As an aside, there is an interesting trend in symbolic algebra that's been going on for 35 years or so: doing less traditional algebra & more numerical calculations. E.g., instead of using bignums to compute the inverse of an integer determinant, compute the determinant mod p for enough p's; using "black box programs" to compute polynomials & computing the coefficients (if you really want them) by interpolating enough point values.
Note this method (compute mod enough coprime moduli, then CRT) is 1) exact 2) bloody fast
Part of this trend is driven by necessity: modern computers are far better at numerical calculations than symbolic calculations, & part is driven by good mathematics & computational complexity.
Computers could be good at both. Humans (programmers) just do not happen to double in coding capacity every 18 months. Machines have left humans 20 years behind when it comes to exploiting the full potential of the machines. That gap is widening. Also the invention of algorithms tends to be time consuming...
Mathematicians & physicists have a long history of doing numerical calculations & then guessing the correct symbolic formula. In some cases (Newton springs to mind), the data are then fudged to make the symbolic formula look even better.
[...]
cheers, jj