newRPL: symbolic numbers

[Claudio L.]

(12-23-2014 09:49 PM)Nigel (UK) Wrote:  The trailing dot is a reasonable idea. However, is it necessary? I'm not sure why anyone would want a number like 2.5 to be treated as an exact number.
Perhaps this is because I'm a physics teacher - I insist that all calculated results are given to an appropriate number of significant figures, usually no more than three. Anyone who writes 5/2 ohms for the resistance of a resistor would lose a mark, because they are claiming to know the resistance to an infinite number of significant figures and that can never happen.

Sometimes in engineering you end up with expressions that are for the most part theoretical, then patched with some obscure real coefficients. It's not that I believe the coefficient is exact (it was likely picked arbitrarily by a committee of researchers that had too much caffeine), but I don't like that coefficient to "eat" all other exact coefficients which do have a meaning.

For example, a simple beam deflection formula at the center: d=5/384*w*L^4/EI, where 5/384 are exact numbers from symbolic integration. But then the engineers mess it up with let's say a factor of 1.5 to account for long term material behavior, making it:
d=1.5*5/384*w*L^4/EI

In cases like this, it's better if 1.5 behaves like an exact value (eventually converted to 3/2), so it's easier to preserve the 5/384 fraction that engineers quickly recognize as a "simple beam formula adjusted with some factor", rather than some obscure factor that you don't know where it comes from.

The other case is also true: sometimes you want that factor to eat all other numbers and give you a single real coefficient. For example if you are doing tables for different cases of the beam deflection above and you just want the final coefficient.
The tables can be expressed as d= m * (w*L^4/EI), where your m=k*5/384, and k varies according to different factors (it may even be integer or 1).
In that case, you want the k value to be treated as approx. and "eat" the fraction, to produce the desired expression format.

The issue is sometimes more visual than related to the significance of the number itself.

(12-23-2014 09:49 PM)Nigel (UK) Wrote:  So I would suggest:

2 or 2. is a number --> approx.
'2' is symbolic --> exact
'2.5' is symbolic --> approx because of the dot
'2.5.' is symbolic ... --> exact! Exact numbers with decimals might be needed sometimes, but for me at least they would be a rare occurrence and so they should be the harder of the two to type.

I'm not entirely happy with this either. I shall continue to think!

Nigel (UK)

Seems reasonable, but how would you type a symbolic integer that is approximated?
'2.' --> exact
'2' --> exact