[GiNaC-list] Substitution troubles
dinkumator at gmail.com
Wed Feb 25 03:11:30 CET 2009
OK Nevermind all. I'll use a better toolkit. Jeez
On Tue 24 Feb 2009 - 11:25PM, Richard B. Kreckel wrote:
> 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?
> Richard B. Kreckel
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