Re: [Boost-users] [Proto] implementing an computer algebra system with proto

I think the attached program solves that problem. eq_solver.cpp

Thank you for posting the compile-time solver code. Specially thanks to Eric N. for writing proto and proposing the sketch of the solution. I few years ago, I tried to experiment writing a mini computer algebra in-C++-for-C++. Think for example, if we want to *implicitly* define a differential equation in the C++-code to be solved numerically by any existing routine which only takes *explicit* differential equation. There were two approaches: A) Every expression could be dynamic (like an dynamic expression-tree generated from a C++-code via a DSEL) and the solver in this case was some run-time transformation between expression-trees. But then I was missing the compile-time efficiency of simple operations (like passing addition terms as described in this topic). In order to improve that, very soon I realized that, *in principle*, B) many (if not all) of the operations could be done at compile-time (using metaprogramming) provided that the problem is well defined at compile time. For the static version (case B), the code became very obfuscated very soon and the my code itself began to be unmanageable. I guess that to really go forward I should have to have invented Proto first. That was of course in the pre-Proto era. It seems that having Proto now opens the opportunity to enjoyably continuing with that project. But I see two problems ahead, 1) The (meta-)code is still obfuscated (but may be the best we can do, at worst it looks like LISP), 2) Even if we manage to write a fairly complete (compile-time) computer algebra there will be two problems 2a) the compilation can become really slow if not overflown (compilers are not yet optimized to do this kind of job). Imagine for example, an automatic derivation meta-code, it will create an unmanageable number of template-expressions very rapidly. (Think of the fourth derivative of sin(exp(x^2)) ) For an automatic integrator is even worst. 2b) as soon as we want to introduce some run-time aspect to the problem, all the static expression-templates should be converted to some dynamic-expression. In case I am not missing something (let me know), it seems that a completely compile-time solution is doomed to become unusable except for very simple operation and difficult to extend. On the other hand a completely dynamic solution is more of what we already have (e.g. maple, mathematica, reduce) and will be no better than them (in any single aspect), an will not take advantage of compilation optimizations (think of interfacing the results with numeric libraries) So I think that a combination of a compile-time solvers and dynamic- time solvers is the only way to make something useful and innovative. Say for example, if we transform template expression only to some degree during compilation and as soon as the problem becomes too complicated (e.g. the expression is too long, or there are many expressions in the compilation stack) we let the run-time code handle the rest of the problem. Any one has any ideas on how to do this in practice? For example, in the original example of this posting, we can handle the outer-most sums at compile time and the product at runtime 1) at compile-time transform "2+var_*5=4" into this "var_*5=4-2" 2) at run-time transform the type "var_*5=4-2" (expression template) into a dynamic-tree (not expression template) representing the same equation"var_*5 = 4-2" and then this into another dynamic-tree "var_= (4-2)/5". It will naturally look like a runtime extension of Proto plus some transformation rules (some of them duplicated from the meta-program part). From the few features I understood from the Proto manual, there is a printing of expression capability that gives me the clue that constructing a run-time tree of an expression is doable. Is that dynamic tree-generation implemented in Proto? Am I trying to reinvent the wheel here? Thanks, Alfredo On Jan 30, 8:38 am, "Dave Jenkins" wrote:

"Kim Kuen Tang" wrote in messagenews:497F760C.1030408@vodafone.de...

...

The next step will be to extend the grammar with the feature of transforming such expression "1+2+var_+3=4" into this "var_=4-1-2-3".

Hi Kim Tang,

I think the attached program solves that problem.

The problem I've been working on is to use the distributive law to simplify expressions at compile time. For example, I'd like to transform "var_ * 2 + var_ * 3 = 4" to "var_ * (2 + 3) = 4". Then, you could transform it to "var_ = 4 / (2 + 3)", all at compile time. Wouldn't that be cool? I think it's possible using Proto, but I haven't worked out the details yet. Any suggestions are welcome.

Regards, Dave Jenkins

 eq_solver.cpp 3KViewDownload

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