Re: the "set paradigm" is harmful
Ralph Baker Kearfott schrieb:
I see several possibilities of accommodating midpoint-radius
representations in the standard. One might be to simply
specify two representations for intervals, and specify
conversion between the two. (That might be the simplest way.)
Does anyone care to make a formal motion to that effect?
If such a motion passes, we can then work out details.
Conversions are already specified in the Vienna Proposal.
Forcing people wanting to conform to the standard to write more than
these conversion routines (namely a full set of - slow and typically
less accurate - functions for the unary and binary interval operations)
is unproductive baggage.
It is not even possible to define uniquely what should be the
floating-point midrad result of a midrad operation like the logarithm.
Thus getting reproducible results is not even guaranteed in the
''tightest'' mode, since tightest is not unique.
Note also that not a single midrad interval package for real
intervals is in use, as far as I can tell. That users in the past
haven't had enough incentive to create, maintain, and publicize
such a package (the ideas have been around for over 30 years)
should be argument enough to settle the issue - it won't be needed
in the future either.
Arnold Neumaier