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## [Axiom-developer] Re: Commutative symbols

 From: Ralf Hemmecke Subject: [Axiom-developer] Re: Commutative symbols Date: Mon, 26 Mar 2007 17:02:24 +0200 User-agent: Thunderbird 2.0b2 (X11/20070116)

```On 03/26/2007 02:36 PM, Ondrej Certik wrote:
```
```Hmmm, I would have thought that commutativity is a property of the
multiplication of the domain you are working in and not a property of a
symbol.
```
```
I know - originaly I had a special class NCMul, for noncommutative
multiplication. But first it duplicates some code and second - some
symbols are commutative and some are not and I want to mix that. It's
like when computing with matrices, like:

A*3*x*B,

where x is a variable and A,B matrices, then you want this to evaluate to:

3*x *A*B
```
```
Maybe this is not what you want...

(6) -> A: Matrix Integer := [[1,2],[5,9],[7,11],[3,1]]
(6) ->
+1  2 +
|     |
|5  9 |
(6)  |     |
|7  11|
|     |
+3  1 +
Type: Matrix Integer
(7) -> B: Matrix Integer := [[1,2,3],[5,7,9]]
(7) ->
+1  2  3+
(7)  |       |
+5  7  9+
Type: Matrix Integer
(8) -> A*3*x*B
+33x   48x   63x +
|                |
|150x  219x  288x|
(8)  |                |
|186x  273x  360x|
|                |
+24x   39x   54x +
Type: Matrix Polynomial Integer
(11) -> B*3*x*A
11) ->
>> Error detected within library code:
can't multiply matrices of incompatible dimensions

```
```and when you think about it, it's actually the symbols, that have this
property - either you can commute it out of the expression, or you
cannot.
```
```
```
Yes, here A and B are actually matrices, not symbols. It depends on what you want.
```
Ralf

```