[GiNaC-list] BUG or incoherence: matrix A; A*pow(A,-1) =! 1

[Alexei Sheplyakov]

Hello,

On Wed, Sep 16, 2009 at 10:46:34AM -0400, jros wrote:
> We now that for matrix class objects A, GiNaC simplifies 
> 
> matrix A;
> cout << A-A << endl;
> 
> give 0
> 
> The same way that 
> 
> symbol a
> cout << a-a << endl;
> 
> gives 0
> 
> But I think that for coherence
> 
> matrix A;
> cout << A*pow(A,-1) << endl;
> 
> should give 1,

First of all, GiNaC does not evaluate matrix products and powers automatically,
one should call evalm() for that (this is documented in the manual, see
http://www.ginac.de/tutorial/Matrices.html#Matrices). Secondly, the expression
is ill defined because A is zero (on the other hand, A - A is OK).

> (I mean reduced to numeric(1) regardless the particular form of A,

The expression above is a matrix. Why should we replace it with a number?

> the  same way as
> 
> symbol a
> cout << a*pow(a,-1) << endl;
> 
> is 1
> 
> By the way it would be wonderful if A-A give matrix-es instead of
> numeric-s, although I think you've already had long discussions about
> that.

I agree, it's nice, but also it's very difficult to implement in any
*useful* way.
 
> PD: I wouldn't mind to derive a class from matrix to change this
> behavior the easy way, but I don't know if this can be done this way.

The expr - expr => 0 transformations are done by the `add' class, and
the expr/expr => 1 transformation is done by the `mul' class, respectively.
Therefore subclassing matrix won't help. 

Best regards,
	Alexei