Transcendental Numbers
Bruce Cohen
cohenb at gemstone.com
Wed Feb 4 20:05:17 UTC 1998
sqrmax at cvtci.com.ar says:
>> It wouldn't be nice to put CayleyNumber as subclass of Number. Even the
>> class Complex doesn't fit nicely under Number, because of the #> and #< that
>> also troubles Point's implementation under Number or something alike. Another
>> number set that doesn't fit under Number is the ModInteger number set. And ok,
>> they are all numbers of this kind or the other, but they won't multiply
>> between themselves in all cases. What's the sense of multiplying a modInteger by
>> aFloat? So it looks as if there are a lot of numbers (another one: Gauss'
>> integers) that don't fit as a subclass of Number. Maybe Number isn't what it's
>> named after.
Agreed, especially the last part. A really general numeric hierarchy
couldn't be based on Number as it is now implemented; there have been a
couple of designs mentioned in this thread that use a root class called
something like ArithmeticObject, which makes a lot of sense to me.
The paper that Ralph Johnson mentioned has a rather appealing hierarchy
that ought to take quaternions and such fairly easily.
>> I agree with this... although I still don't like the picture. I feel Number
>> as too big for what it is. Look at Number's subclasses. There are Integers,
>> Floats, and Fractions. All particular subsets of the rationals, which are
>> commutative. But Numbers are not only rationals.
And Floats aren't Reals either; there's no representation for Real under
Number, which I consider a problem. We have arbitrary precision
integers, so arbitrary precision floats seem reasonable (modulo all the
nasty details of implementation, of course!). In general, I favor
replacing the numeric hierarchy as given in Smalltalk-80. I'm going to
look at Ralph's double-dispatch code as soon as I get some free time
(currently scheduled for April :-( )
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Bruce Cohen, | email: cohenb at gemstone.com
GemStone Systems, Inc. | phone: (503)533-3602
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