newRPL: symbolic numbers

[Claudio L.]

Summing up this thread, here are some clear items:

To eliminate the approx/exact system mode, and to be able to emulate all its possible variations from within an expression, we need:
a) Symbolic numbers
b) Exact/approx numbers
c) Exact/approx variables or expressions.
d) Approx must "eat" exact.

We explored two alternatives:
1) Exact/approx as a property of the numbers/variables: Can be seen as a flag or a "hint" for the numeric behavior of the number/variable for evaluation purposes only.
2) Approx as an operator: A fully defined prefix operator.

Option 1):
* The hint does not change the tree structure of the expression, so it's transparent to the CAS manipulations and rules.
* Solvers can choose to use or ignore the hint when evaluating the expression.

Option 2):
* CAS needs to work with the operator explicitly.
* The operator is transparent to non-CAS solvers when they evaluate the expression.

For user interface, two proposed symbols:
a) The trailing dot.
b) The ~ prefix.

Based on all the feedback, the best path seems to be Option 1) with a ~ prefix. A flag will also be included to use a trailing dot, for people familiar with TI, Mathematica, the HP50g and any other math software that already uses a trailing dot for approx. numbers.

Now it's time to start coding all this.

Thank you all for the feedback, I think we collectively came up with a very usable feature for newRPL. You should see it all working on the next demo release.

Claudio.