> For the record, WeBWorK does not actually understand symbolic expressions, > simplifications, etc. So how does it check that the student's messed-up > unsimplified symbolic answer is "the same" as the hard-coded correct > symbolic answer to the question? It evaluates both expressions numerically > at a bunch of points (possibly randomly chosen, but I don't remember). If > they always differ by at most a specified tolerance, they're deemed to be > the same. Otherwise, the student's answer must have been wrong.
@alex: Yes, and I didn't mean to suggest otherwise - I had honestly forgotten this, in fact. Mike Gage gave a very nice explanation of this in the Q&A after the JMM open source in ed session. My point was simply that certain things might be checkable without a lot of overhead - and despite rjf's comments, I would argue that perhaps sin^2+cos^2 is so common, in and out of calculus assignments, that perhaps it would be a simplification worth checking all the time. @rjf: Maxima I'm sure is good; if I used it exclusively perhaps I would have known about Romberg instead of nintegral, though I don't like using commands in class that I can't immediately explain why they are called what they are. I had a lot of good discussions with colleagues from my consortium at the Joint Meetings about what they used, and Derive, Maple, Mathematica, Maxima all came up as ones either currently used or used in the past. But what is wonderful about the Sage project is being able to use things like Maxima along with PARI (without actually having to use PARI), GAP, nice plotting, and a programming language I can actually use as a not-very- sophisticated programmer, so that I feel comfortable using Sage in just about any course I teach - which, at a small liberal arts college, is a pretty wacky variety at times. It's all under the hood; the interface is the same for all of it, and I don't have to learn (and more importantly, my students don't have to learn) a new syntax etc. for every new class I teach (or am asked to teach). Miscellanea: 1. I think that quadpack is used only because I used the alternate .nintegral Maxima command instead of the (native Sage?) numerical_integral command, which doesn't like extra variables very much. 2. I appreciate the distinction between newly introduced bugs (which is endemic to every software package, yikes) and unimproved older functionality/bugs. At least for the philosophically inclined, that is an important distinction; a project with new bugs is still going, and one without bugs is too simple (pace TeX). - kcrisman --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
