Hi! On 02/18/2012 10:47 PM, DerManu@WorksLikeClockwork.com wrote:
Consider the following expression: (2^(2/3)*x^2)^(3/2) where x is positive. I'd expect eval() to reduce this to 2*x^3, but it happens only, when calling evalf(). However, I'd like other possible parts of the expression to stay exact, so evalf() isn't an option.
Here's the code for the above expression: possymbol x("x"); ex e = power( power(2,numeric(2)/numeric(3)) * power(x, 2) , numeric(3)/numeric(2) ); std::cout << e.eval() << " " << e.evalf() << std::endl; // I know eval is redundant, but it adds a dramatic element ;)
Note this situation is somewhat related yet much simpler than Topic [1] because we're dealing with purely numeric powers here. Still it seems, this kind of simplification is just not wanted. Is that correct? Or is there a trick to make it all work easily?
It's not that such a simplification is not wanted. It's just not implemented (yet?) Your example involves only products and rational exponents. In this case, GiNaC could indeed go a little bit further, I suppose, and do the transformation for you. In a slightly more general context, however, one might deal with sums. And then things start getting really, really hairy, even in the absence of symbols. The question is where to draw the line. Keep in mind that one crucial requirement for a transformation to be eligible for automatic .eval() is that it's complexity must be lower than O(N^2) where N is some suitable measure for the length of the expression. This is because .eval() is invoked automatically upon input and we don't want the program to explode on medium-sized input: it would impede the subsequent use of better suited specialized algorithms. BTW: In the past, GiNaC has evolved in some tiny steps into the direction you want. (C.f. commit e34ac03e77644.)
Would it be a sensible approach to write a map_function functor that grabs all powers that have positive muls as base and apply the power to all mul ops individually?
Of course! -richy. -- Richard B. Kreckel <http://www.ginac.de/~kreckel/>