CAS and small numbers

[Nigel (UK)]

Thanks for your answers.

(04-22-2014 07:21 PM)Tim Wessman Wrote:  Does setting your epsilon limit on page 2 in CAS settings not work for you?

No. If I set epsilon to 10^-50 the equation I gave still evaluates to e=0 (on the Prime, although not on the "real" Xcas).

It seems to me that epsilon is intended to deal with rounding errors, or to tell recursive algorithms when to stop. Setting a very small value for epsilon might cause problems on a limited precision device like the Prime. In any case, Planck's constant is small in standard units. Quantum mechanics is not a rounding error!

(04-22-2014 07:28 PM)Han Wrote:  When working in CAS, you are much better off using exact values. So instead of typing something like: 2.1E-10, I would recommend 21*10^(-11) as the value. Then you can convert to decimal form at the very end if needed. Most CAS will treat values having a fraction mark (in your case, a decimal point) as an implicit request to use approximate algorithms so that roundoff could possibly result in "useless" answers.

I've tried this and it does work. The problem is that numbers in Physics are genuinely approximate, and it feels strange to enter them as exact numbers. Also, the power of ten to use depends on how many significant figures there are. It requires extra brainpower to convert 6.63e-34 to 663*10^{-36}, and 6.626e-34 to 6626*10^{-37} without getting in a muddle!

I only have experience of two other CAS systems: the TI CAS and Mathematica. Neither treat small approximate numbers in this way by default. Some numbers really are small and approximate; it would be nice to do symbolic algebra with expressions involving them. I suppose that I could define variables with the small numbers in first, but that seems rather complicated.

Nigel (UK)