Is there a name for the way Maxima does algebra?

Robert,

This has prompted a question in my mind:  can we draw a clear distinction 
between "assumptions" and "theorems"?  For example, we do need to make 
basic assumptions to provide a background against which to work.  Eg,

solve(ex,z);

might assume z is complex or real.

When we are talking about what algebra is, these assumptions go back to 
things which are "obvious", eg * is commutative.

This reminds me of the problems I was having with very basic algebraic 
manipulations in Maxima, which simp:false helped to cure.

It would be very helpful if all assumptions could be explicit and 
controlled.  For me, I wanted to establish if two expressions were "the 
same".  Here I mean up to associativity and commutativity of + and *, but 
no distribution, and no functional operations,

eg 1+2=2+1 <> 3.  (This looks strange: sorry)

For the most part users will ignore them, and carry on using 
the algebra they know and love.  For others this flexibility will be 
absolutely key.

I would be very interested in a vocabulary with which we could talk more 
meaningfully about these issues.

Chris


On Wed, 27 Sep 2006, Robert Dodier wrote:

> Hello,
>
> I think a fair characterization is that Maxima implements a
> "little boxes" approach to algebra:
> variable = box with a label on it, value = content of box,
> axiom or theorem = license to replace some boxes.
> That seems pretty naive (which is OK by me; I imagine
> that's how I do algebra too). Is there a name for this approach?
> What are the names of some other general methods?
> If that's not how Maxima does algebra, what's a better
> characterization?
>
> Thanks for any light you can shed on this question.
>
> Robert Dodier
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