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Re: Non-commutative algebra

  • To: mathgroup at
  • Subject: [mg13280] Re: Non-commutative algebra
  • From: Daniel Lichtblau <danl>
  • Date: Fri, 17 Jul 1998 03:18:28 -0400
  • Organization: Wolfram Research, Inc.
  • References: <6ocuue$>
  • Sender: owner-wri-mathgroup at

> ...Wolfram Research Inc. strongly disapproves of clearing any Attributes or
> otherwise modifying low level built-in functions, such as Times, Plus etc.,
> and in particular removing their Orderless attribute. If you do this terrible
> things may happen to your programs...

and cause cancer in laboratory mice

> ...either immediately or in the future. It is not made clear why we are
> actually given the opportunity to engage in such unhygienic behaviour, but
> perhaps it is just to provide a little excitement for those who like
> living dangerously.

That's about correct.

In some sense the situation is thus: Mathematica supports several
attributes, and modification thereof can be useful. Mathematica also is
implemented largely in terms of itself (even the functions written in C
call Mathematica). Hence modification of default attributes of
low-level functionsmay be dangerous.

So why do we allow this? Well, one can argue that actually we do not. As
you saw, removing Orderless for Times is only partially supported. Way
back someone apparently decided it should not be supported at all, and
until version 3 it was not. Whether this was a good change (to support
non-commutative Times in this way) is unclear. We did it mostly for
purposes of logical consistency, and not because we wanted people to
actually use it (silly us). Generally it is safe for quick localized
applications that rely on structural rather than mathematical
transformations, for example the one you showed. Were you instead to
Collect with respect to some product you might not have such good
results, because Collect will rely on Times internally.

Daniel Lichtblau
Wolfram Research

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