# Re: Lists and Plus

• To: mathgroup@smc.vnet.net
• Subject: [mg10706] Re: Lists and Plus
• From: Paul Abbott <paul@physics.uwa.edu.au>
• Date: Fri, 30 Jan 1998 04:24:41 -0500
• Organization: University of Western Australia
• References: <6ahpql\$pmq@smc.vnet.net>

```Thomas Lemm wrote:

> I intend to implement routines for basic operator algebra as found in
> second quatisation. As my operators commute only under certain
> circumstances I want to put them into lists.
>
> But by default Plus and other operations are simplified into the lists:
>
> { a, b, d, g } + 1 evaluates to
>
> { a+1, b+1, d+1, g+1 }
>
> which is - in my case - not appropriate.

Why not define your own data structure instead of using List?  An
arbitrary head will do, e.g.,

foo[a,b,c,d] + 1

and then you define rules for foo.

> I already tried to clear Operator Plus but did not succeed.

And this may break a lot of other things ;-(

> If you can think of another way to takle the operator
> algebra problem, don't hesitate to give advice, too.

There are some packages available for non-commutative algebra, e.g., a
search on MathSource <http://www.mathsource.com> for Noncommutative
finds

Noncommutative Algebra Package and Systems:

Although processing of commutative expressions is built into
Mathematica, relatively no support is given to noncommutative
expression manipulation. These packages have been developed to fill
this void. Commands for noncommuting algebra that are analogous to
Mathematica commands are implemented, as well as others. The
development of these packages has been directed by needs that arose
from research in Control Theory, Systems Theory, and in Operator
Theory. Also attached to the NCAlgebra package are files SYS* for doing
calculations with engineering systems that are common in Hinfinity
control and in differential games. See the NCAlgebra homepage
<http://math.ucsd.edu/~ncalg> for more information and heavier
software.

URL:
http://www.mathsource.com/cgi-bin/MathSource/Enhancements/Algebraic/0208-998

Cheers,
Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907
mailto:paul@physics.uwa.edu.au  AUSTRALIA
http://www.pd.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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