>>>>> "Stavros" == Stavros Macrakis <macrakis at gmail.com> writes:
>> I think it would be nice if 6*2^k became 3*2^(k+1), but that would
>> require factoring 6 (easy). In general, factoring would be hard, and
>> perhaps not worth the effort.
Stavros> Note that you don't need to factor 6, only gcd(6,2). To handle the case
Stavros> 54*3^n, you do
Stavros> gcd(54,3)=3 so => (54/3) * 3^(n+1) = 18*3^(n+1)
Stavros> gcd(18,3)=3 so => (18/3) * 3^(n+2) ... etc.
Yes, this is probably something that the times simplifier should do.
>> Maybe a separate function could be made available to try much harder
>> to simplify these numerical products.
Stavros> Yes, I think general simplification should not handle
Stavros> 3^n*6^n = 2^n*3^(2*n)
Stavros> 6^n*15^m = 2^n*3^(n+m)*5^m
Stavros> 3^n*9^m = 3^(n+2*m)
I agree. Although it would be nice if we could do this. I think some
of the limit bugs happen because maxima thinks 4^n grows much faster
than 2^(2*n). (Or vice versa. I can't remember.)
Ray