Project Euler
Posted Wed Apr 16 08:39:24 -0700 2008
Bill Wood writes: "Are you familiar with the ProjectEuler site, would Aldor be a good language for solving their usual math-intensive programming problems?"
What is Project Euler?
Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems."
http://projecteuler.net/index.php?section=problems
Yes, I think Aldor is a good language in which to write programs to solve these sort of problems. If anyone here is motivated to try this, I would encourage you to post your solutions written in Aldor here, cross-referenced to the problem numbers on the above site.
I sampled a few problems there, and I think the intention was to solve the problems mathematically, rather than computationally. With today's computers, any computer language can easily solve a large portion of these problems by "brute force". I don't see why one needs Aldor or Axiom to do such numerical enumerative work. Maybe there are deeper algebraic concepts involved that are not obvious (such as for some diophantine problems) and the algebra libraries can be of help?
Do you know if the solutions (or the best ones) are posted? That may help identify which problems are suitable for Aldor/Axiom.
William
The statement at the Project Euler website includes: "Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.". So I think the intention is quite clear: mathematical insight mixed with actual computation. Since computers are enormously more powerful now than when this project was first conceived, I suppose you might dispute whether the particular problem set presented actually achieves this goal or not. In any case it seems quite reasonable to assume that at least some of the algebra built-in to Axiom and Aldor libraries is relevant to at least some of these problems.
I think it is interesting to take a look at the "statistics" section of the project web site:
http://projecteuler.net/index.php?section=statistics
26345 users have submitted 468838 correct solutions ...
In solving these problems a computer algebra system (Magma, Maple, Mathematica, Matlab or Pari/GP) was used by 493 users.
In all 42 different programming languages were used with C/C++ (3322) being the most popular, followed by Python (2482) and Java (1574).
In spite of the difference, I think 493 users of computer algebra systems is actually quite high given the probable number of programmers who are familiar with these systems compared to conventional programming languages. I think it would be great of one day Aldor and Axiom showed up on this list of languages.