Non-commutative symbolic multiplication in Calc

Non-commutative symbolic multiplication in Calc

[Neon Absentius]

Sorry if this is not the right list for this question. 

Is there a way to suspend some of the automatic simplifications that
calc performs? In particular I am interested in suspending the
assumption that multiplication is commutative.  This would allow for 
symbolic calculations with entities that are not necessarily numbers
or elements of some vector space.   

Thanks

-- 
Most precious among the relics remaining of Peter's skeleton in the
Vatican are 29 fragments of one of his skulls. (St. Peter's other
skull is preserved in a reliquary at the Cathedral of St. John
Lateran.)
   -- Frank R. Zindler, "Of Bones and Boners"

Re: Non-commutative symbolic multiplication in Calc

[Roland Winkler]

Neon Absentius <absent@sdf.lonestar.org> writes:

> Sorry if this is not the right list for this question. 
>
> Is there a way to suspend some of the automatic simplifications that
> calc performs? In particular I am interested in suspending the
> assumption that multiplication is commutative.  This would allow for 
> symbolic calculations with entities that are not necessarily numbers
> or elements of some vector space.   

It's a pretty tricky issue to get useful results when doing
analytical calculations with noncommuting variables. I doubt that
you will get what you want when you just remove the assumption that
multiplication is commutative.

Roland

Re: Non-commutative symbolic multiplication in Calc

[Neon Absentius]

On Tue, Sep 06, 2005 at 04:09:36PM +0200, Roland Winkler wrote:
> Neon Absentius <absent@sdf.lonestar.org> writes:
> 
> > Sorry if this is not the right list for this question. 
> >
> > Is there a way to suspend some of the automatic simplifications that
> > calc performs? In particular I am interested in suspending the
> > assumption that multiplication is commutative.  This would allow for 
> > symbolic calculations with entities that are not necessarily numbers
> > or elements of some vector space.   
> 
> It's a pretty tricky issue to get useful results when doing
> analytical calculations with noncommuting variables. 

It seems to me that is tricky to get useful results when doing any
calculations! In any case I am mostly interested in algebraic rather
than analytic results.
 
> I doubt that you will get what you want when you just remove the
> assumption that multiplication is commutative.

Depends on what do you mean by "just" by "remove" and by
"assumption".  When I say "suspend the assumption" I mean
(obviously) to also suspend its consequences, for example there
should be a "left" and a "right" division. It depends also on what I
want, which (at the moment of writing at least) is rather modest, I
will be happy if I am able to work on a free group (or a tensor
algebra) and define relations as rewrite rules.

Ideally the multiplication should not be assumed commutative (or the
variables invertible) unless explicitly declared so.

> 
> Roland

-- 
Most precious among the relics remaining of Peter's skeleton in the
Vatican are 29 fragments of one of his skulls. (St. Peter's other
skull is preserved in a reliquary at the Cathedral of St. John
Lateran.)
   -- Frank R. Zindler, "Of Bones and Boners"

Re: Non-commutative symbolic multiplication in Calc

[Roland Winkler]

Neon Absentius <absent@sdf.lonestar.org> writes:

>> I doubt that you will get what you want when you just remove the
>> assumption that multiplication is commutative.
>
> Depends on what do you mean by "just" by "remove" and by
> "assumption".  When I say "suspend the assumption" I mean
> (obviously) to also suspend its consequences, for example there
> should be a "left" and a "right" division. It depends also on what I
> want, which (at the moment of writing at least) is rather modest, I
> will be happy if I am able to work on a free group (or a tensor
> algebra) and define relations as rewrite rules.
>
> Ideally the multiplication should not be assumed commutative (or the
> variables invertible) unless explicitly declared so.

Emacs calc (the way I look at it) is designed to be a powerful,
advanced calculator. But it is not a computer algebra system which I
would use to address the kind of problem you are talking about..

For example. take a look at Maxima, http://www.ma.utexas.edu/maxima.html.
It's now under GPL, and it even has a nice emacs interface.

Roland

Re: Non-commutative symbolic multiplication in Calc

[Neon Absentius]

On Tue, Sep 06, 2005 at 08:36:49PM +0200, Roland Winkler wrote:
> Neon Absentius <absent@sdf.lonestar.org> writes:
> > Ideally the multiplication should not be assumed commutative (or the
> > variables invertible) unless explicitly declared so.
> 
> Emacs calc (the way I look at it) is designed to be a powerful,
> advanced calculator. But it is not a computer algebra system which I
> would use to address the kind of problem you are talking about..
> 

If there is a line between an advanced desk calculator and a CAS then
surely Emacs calc has crossed it! OTOH what are PC's but (glorified)
advanced desk calculators? :)

But (more) seriously what I am talking about is not really that more 
complicated than what calc does already. If it can calculate 
          2     2            2
   (x + y)   = x  + 2 y x + y

then it should be able to do 
          2     2                2
   (x + y)   = x  + x y + y x + y
   

> For example. take a look at Maxima, http://www.ma.utexas.edu/maxima.html.
> It's now under GPL, and it even has a nice emacs interface.

Yes I know about maxima and I use it. However I usually prefer calc
for a "quick and dirty" calculation. And I really like the interface.


-- 
Most precious among the relics remaining of Peter's skeleton in the
Vatican are 29 fragments of one of his skulls. (St. Peter's other
skull is preserved in a reliquary at the Cathedral of St. John
Lateran.)
   -- Frank R. Zindler, "Of Bones and Boners"

Re: Non-commutative symbolic multiplication in Calc

[Jay Belanger]

Neon Absentius <absent@sdf.lonestar.org> writes:

> Sorry if this is not the right list for this question. 
>
> Is there a way to suspend some of the automatic simplifications that
> calc performs? In particular I am interested in suspending the
> assumption that multiplication is commutative.

Does matrix mode ("m v") do what you want?

Jay