newRPL: symbolic numbers

[Nigel (UK)]

In Mathematica (from memory) and in the AUTO mode (i.e., neither EXACT nor APPROX) on TI calculators such as the TI-89, the status of a number as exact or approximate is indicated by the presence or absence of a decimal point. So 40320 is an exact number, while 40320. is approximate. Sin[4] in Mathematica simply returns Sin[4] (i.e., no evalulation), whereas Sin[4.] returns a real number. One approximate number in a calculation poisons the rest of the calculation, so that 3/2 +0.5 would be 2. rather than 2 , and substituting d=7. into 'r=d/2' would give 3.5 for r.

I have always found this to work well. When using my TI calculators (yes! I do use them and I'm not ashamed!!) I cannot remember ever needing the EXACT or APPROXIMATE modes.

I think that the quoting idea could work in the same way as the decimal point approach so long as one unquoted number poisons the entire expression it appears in. I think this is reasonable: if one number is inexact, anything calculated from that number must also be inexact. Maybe the decimal point approach would be easier for the user to enter, though? It is quicker to type 2*(3+4) than '2'*('3'+'4'). However, the elegance of the quoting idea is very appealing! I'm really not sure what is best.

Nigel (UK)