Transcendental Numbers

Bruce Cohen cohenb at gemstone.com
Mon Feb 2 18:38:02 UTC 1998


sqrmax at cvtci.com.ar wrote:

>> >IMO, any mixed math you add to the system, should be communtative.
>> 
>> I don't know... there are non commutative maths. This could be a problem 
>> later.

True, there are non-commutative maths, but the ones that I can think of
offhand that are generalizations of the ones implemented in Squeak, such
as quaternions and Cayley numbers, are built out of components which are
manipulated by commutative operators.  So it seems reasonable to build
the general number system such that the standard operators (addition and
multiplication in particular) are commutative, and then design the
non-commutative systems with the appropriate constraints, rather than
constraining the base number systems to favor the more complex and
less-used non-commutative systems.
-----------------------------------------------------------------------------
"Only a proper understanding of the constraints imposed by the
properties of our space and of the rich repertoire permitted within
these constraints allow the achievement of a balanced disciplined
freedom."  - Arthur Loeb in "Concepts and Images"
-----------------------------------------------------------------------------
Bruce Cohen,                               |  email: cohenb at gemstone.com
GemStone Systems, Inc.                     |  phone: (503)533-3602
20575 NW Von Neumann Drive                 |  fax:   (503)629-8556
Beaverton, OR USA 97006                    |  web:   http://www.gemstone.com





More information about the Squeak-dev mailing list