Hi! Jeremy Jay wrote:
It's not "intuitive" because I can see a plain single "1" when i print the poly, and I can call subs(1==q) on the poly with no errors, but when I print the poly again it is unchanged.
If I were to print your first example as written, I would not see a "4" in the output and I would not expect anything to be substituted. If I wanted to make sure I got the 4, I would have to call expand or whatever appropriately, before the substitution.
In the second example I would expect it to come out to (x^2+A*x+A). I see 4s and I'm substituting As in their place. If I don't want the 4x changed I'll have to do some extra work myself, but I don't expect GiNaC to differentiate between the 4s I see.
I think any of these cases are very "intuitive" for any programmer with any experience with any pattern matching. A substitution is just that, a substitution, and it is not "well-defined" mathematically and I don't really see any reason for it to be as rigorous as you imply. If someone wants to do silly things like replace 4s with As, let him!
But GiNaC is not sed! If you want to carry over a programmer's naive notion of substitution, then you could always print the expression and do the replacement in a string buffer. I recommend using boost::regex.
Alexei made his point, yes, but I don't see how it is "correct." He said that the semantics of a simple substitution rely upon the internal representation of the polynomial -- although there is no documentation on this point anywhere on the website. This make it non-intuitive.
Alexei was referring to GiNaC's actual internal representation. It could be a different representation. I'm seeing 1s all over every mathematical expression. 1+x*y could as well be written as 1^(1^1)+1^1*x^(1^1)*y^(1^1) and, upon substitution, result in q^(q^q)+q^q*x^(q^q)*y^(q^q). Or as (-1)^2+x*y and be invariant under subs(1==q). Is this really more insane than GiNaC's actual representation?
If you have a reference for a rigorous mathematical definition of substitution on numbers feel free to send it to me to correct me.
That's an interesting twist. IIRC you were the one suggesting to do this substitution on numbers. Now, we all seem to agree that it's not well-defined. Are you proposing, then, that .subs(x==y) isn't well-defined either? But every mathematician is familiar with this notion of substituting free variables and considers it sane. Is it not possible to rewrite your algorithm substituting variables instead of numbers? Cheers -richy. -- Richard B. Kreckel <http://www.ginac.de/~kreckel/>