Has anyone ever considered randomised testing of Sage against Mathematica? As long as the result is either
a) True or False b) An integer then comparison should be very easy. As a dead simple example, 1) Generate a large random number n. 2) Use is_prime(n) in Sage to determine if n is prime or composite. 3) Use PrimeQ[n] in Mathematica to see if n is prime or composite. 4) If Sage and Mathematica disagree, write it to a log file. Something a bit more complex. 1) Generating random equation f(x) - something that one could integrate. 2) Generate generate random upper and lower limits, 'a' and 'b' 3) Perform a numerical integration of f(x) between between 'a' and 'b' in Sage 4) Perform a numerical integration of f(x) between between 'a' and 'b' in Mathematica 5) Compare the outputs of the Sage and Mathematica A floating point number, would be more difficult to compare, as one would need to consider what is a reasonable level of difference. Comparing symbolic results directly would be a much more difficult task, and probably impossible without a huge effort, since you can often write an equation in several different ways which are equal, but a computer program could not easily be programmed to determine if they are equal. One could potentially let a computer crunch away all the time, looking for differences. Then when they are found, a human would had to investigate why the difference occurs. One could then add a trac item for "Mathematica bugs" There was once a push for a public list of Mathematica bugs. I got involved a bit with that, but it died a death and I became more interested in Sage. Some of you may know of Vladimir Bondarenko, who is a strange character who regularly used to publish Mathematica and Maple bugs he had found. In some discussions I've had with him, he was of the opinion that Wolfram Research took bug reports more seriously than Maplesoft. I've never worked out what technique he uses, but I believe is doing some randomised testing, though it is more sophisticated that what I'm suggesting above. There must be a big range of problem types where this is practical - and a much larger range where it is not. You could at the same also compare the time taken to execute the operation to find areas where Sage is much faster or slower than Mathematica. Dave -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
