I'm sure you are aware of the Sage open-source mathematics software http://www.sagemath.org/
which has a mission of creating a viable free open source alternative to Magma, Maple, Mathematica and MATLAB. Obviously Sage has a test suite where results from Sage are compared to a set of known results. For example, one test for the factorial() function is: sage: factorial(10) 3628800 As you are no doubt aware, all non-trivial software contains bugs. It would be very useful to compare the result from Sage to that of other software which is developed independently. One way, which could be used in some circumstances, is to compare the Sage result to that obtained from Wolfram Alpha. For example http://www.wolframalpha.com/input/?i=10! shows 10 factorial is 3628800, so there is a very high probability that WolframAlpha and Sage are both correct. It would sometimes be useful to add a comment to the Sage test suite that the result has been compared to that obtained by WolframAlpha. So we could write something like: --------------------------------------------------------------------------------------- WolframAlpha gives the same result as Sage - see: http://www.wolframalpha.com/input/?i=10! sage: factorial(10) 3628800 ------------------------------------------------------------------------------------- Sage has tens of thousands of tests and that number is increasing all the time. Only a fairly small fractions of those tests could be computed with WolframAlpha, and even in cases where they could, we might not chose to do so. Looking at the terms of use of WolframAlpha, http://www.wolframalpha.com/termsofuse.html I personally can't see anything that would suggest that comparing results with Wolfram Alpha, and documenting this would breach the terms of use. But when I suggested we could verify a result in WolframAlpha http://www.wolframalpha.com/input/?i=N[Integrate[+Sin[x]%2Fx^2%2C{x%2C1%2CPi%2F2}]%2C50] one Sage developer questioned whether this would be within the terms of use. See:his comments at: http://groups.google.com/group/sage-devel/msg/1f8af294fbf40ccc?hl=en&; One section in particular of your terms of use says:: "You are not allowed to use Wolfram|Alpha to create something that is likely or intended to be reused as a data source for further processing, or that in some other way serves as a replacement or alternative to using Wolfram|Alpha itself. This applies whether what you create is in electronic or print form." Sage, has a web based interface that allows one to perform advanced mathematical calculations. Clearly there are some calculations that could be performed in WolframAlpha, but which could also be performed in Sage. If you try Sage - you can get a free account at http://t2nb.math.washington.edu:8080/ you will soon realise that Sage is quite different to WolframAlpha. Sage is certainly not intended to be a replacement for WolframAlpha - in fact, Sage existed several years before WolframAlpha. Sage has its own language, which is based on Python. Sage can only process input using that syntax. It does not attempt to process questions the way WolframAlpha does. To save any further discussions on the Sage developers list about whether the use of WolframAlpha in the way I explained would be permissible, could you please clarify the matter. Obviously using WolframAlpha to compare results with Sage would be of benefit to the Sage project. But it would also benefit Wolfram Research too. In the event that comparisons with WolframAlpha showed different results, and we concluded WolframAlpha had a bug, we would out of politeness let you know. In fact, only recently I made your technical support team aware of a documentation error in PrimePi[] and PrimeQ[], which I understand will be fixed. This documentation error was discovered when some comparisons were made between Sage and Mathematica. Dr. David Kirkby (a developer of the Sage mathematics software). -- 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
