** Using WeBWorK **

I'm trying to use equation_cmp to check an equation of the form "x/$a = $b/y".  It tells me my answer is correct, if I enter the string exactly as specified.  If I enter something equivalent, like $a/x = y/$b or x*y = $a*$b, it says incorrect.

Anybody know how to do this?

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I have just posted an experimental answer checker to the CVS repository in pg/macros/parserImplicitEquation.pl that should handle the situation you are interested in. It attempts to compare two implicitly defined equations to see if they have the same solutions. The check is not perfect, but it might be worth trying out.

Read the comments at the top of the file for some caveats about what can go wrong. Because of the algorithm used to check the answers, there are always ways for the student to write correct answers that will not be marked correct, and incorrect answers that will pass. For example, if f(x,y) = 0, then for large n the algorithm will mark (f(x,y))^n = 0 as incorrect, and it will not be able to locate the solutions for even n at all (the algorithm needs sign changes to identify solutions). It will also mark (x^2+y^2-.01)f(x,y)=0 as correct, since the algorithm is unlikely to notice the additional zeros introduced by the small circle.

But it WILL recognize xy=4, x/2=2/y, x=4/y, x-4/y=0, (x^2+y^2)(xy-4)=0, and so on as being the same thing. It will also get x^2-y^2=0 as |x|=|y|, and x^2-y^2=1 as |y|=sqrt(x^2-1). So it has some promise.

Try it out and see what you think. If you DO use it, you might want to view past answers on the problems that you use it on, and see whether it is marking things wrong.

Davide

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It might also be worth pointing out that since there are only a small number of ways of writing this particular equation in a reasonable fashion, one could simply use John Jones' pc_evaluator (in PGasu.pl) together with "equation_cmp" to check them all. This is an ad hoc solution of course.

Bob

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On one hand, I agree with Bob's response, I know it runs somewhat counter to webwork's philosophy. A basic feature of webwork is that problem writers don't have to anticipate the different forms in which an answer may appear.

Thinking about it more, it may be good to have both apporaches. One factor which might decide which approach to use in a given situation is what forms of the equation do you want to mark correct. In the example above of xy=4, you would probably always want variations such as x/2=2/y and y-4/x=0 to be correct. But, you may not want (x^2+y^2)(xy-4)=0 since it has a different solution set over R (because of (0,0)). Some people may also not want to accept (x^2+y^2+3)(xy-4)=0. While it has the same set of real solutions it rubs me the wrong way - to use a quartic equation for a hyperbola. Then again, it is unlikely a student will happen on an answer like that so worrying about it is probably moot.

John

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