[GiNaC-devel] Creating non-commutative symbols

[Alexei Sheplyakov]

Hi again,

> maybe I should explain why I need non-commutative symbols. Without them,
> this code:
> 
> #include <ginac/ginac.h>
> 
> using namespace GiNaC;
> 
> int main() {
>   symbol M1("M1");
> 
>   symbol x("x"), y("y");
>   matrix M2(2,2);
>   M2 = x, 0, y, 0;
> 
>   matrix M3(2,2);
>   M3 = 0, x, x, 0;
> 
>   symbol M4("M3");
> 
>   ex nc;
>   nc = M1 * M4;

>   nc = nc.subs(M1 == M2);
>   nc = nc.subs(M4 == M3);
>   nc.evalm();

Perhaps you meant nc = nc.evalm();

> }
> 
> throws 
> matrix::mul_scalar(): non-commutative scalar
> 
> Is that the expected behaviour?

Yes, sort of. Substituting a commutative object with a non-commutative one
is ill defined. I.e. the order of terms in the expression `x*y' does not
matter, and GiNaC can (and does) shuffle terms to canonicalize the expression
(in order to make the internal representation of `x*y' and 'y*x' exactly
the same, so the check for equality x*y == y*x is very fast, as it boils
down to comparing two pointers). Now if one substitutes both x and y with 
non-commutative objects (say, X, and Y, respectively), the result is undefined:
it can be either X*Y or Y*X (and it might change from run to run).

> OK, I will do that. But if I read your other explanations correctly,
> even a separate class will not really solve the problem I described
> above?

I guess explaining GiNaC that those symbols does not commute with matrices
would help (override return_type_tinfo()). I haven't checked it (yet), though.

Best regards,
	Alexei