newRPL: The complexity of complex mode

[Nigel (UK)]

(08-23-2016 07:43 PM)Claudio L. Wrote:  

(08-22-2016 03:03 PM)Nigel (UK) Wrote:  Does this help?

Nigel (UK)

The first part of your post really helped. Later you suggested we don't need to take care of this, but then you go into details on how every operation should be handled, so I'm exactly as I was before. Lots of special cases to take care of on every operation, and I'm still not sure if it's needed or not.

But once we allow directed infinities to exist (and for a future CAS this should be the case), we are forced to define a result for each operator, on each special case.
Some cases like (+∞,3) or (∞,∞) could be rejected as syntax error to enforce some discipline on the user and reduce the number of cases.

I see what you mean about my previous post! I got a little carried away. Because operators like "+" and "x" are already overloaded, I assumed that adding a new behaviour for a new object type would not be a problem. The simplifications such as \((3,2\times\infty)\) becoming \(\infty\angle{\pi\over2}\) would be handled by whatever code is called to evaluate this new object type.

However, I believe that all operations on directed infinities could be disallowed without loss. Those few operators that need them as input (e.g., limits and integrals) could look for them explicitly and provide their own means of dealing with them. Allowing only the angle notation (i.e., \(\infty\angle {\pi\over2}\) and not \((0,\infty)\)) would reduce the number of cases to consider and would not be a problem for the user. Perhaps it would be nice to allow \(\infty, \;-\infty, \;i\infty, \;-i\infty\) as equivalent notation for \(\infty\angle0,\;\infty\angle\pi,\;\infty\angle{\pi\over2},\;\infty\angle{-}{\pi\over2}\).

Nigel (UK)