DOCUMENT(); loadMacros( "PG.pl", "PGbasicmacros.pl", "MathObjects.pl", ); Context("Numeric"); # INITIALIZATION $order = 5; $multiplier = 10; $ratio = Compute(1/($multiplier^$order)); TEXT(beginproblem()); Context()->texStrings; BEGIN_TEXT The method has error \(O(h^$order)\). You run the method once with \(n\) steps and then a second time with $multiplier times as many steps. You should expect the error the second time to be roughly what fraction of the error the first time? $BR \{ans_rule(8)\} END_TEXT Context()->normalStrings; # ANSWERS ANS($ratio ->cmp() ); Context()->texStrings; SOLUTION(EV3(<<'END_SOLUTION')); $PAR SOLUTIONS $PAR $PAR The ratio of the new error to the original error is roughly \[ \frac{(h/$multiplier)^$order}{h^$order}= \frac{1}{$multiplier^$order} = $ratio. \] Testing: $BR \(\text{multiplier} = $multiplier,\)$BR \(\text{order} = $order,\)$BR \( \text{ratio} = 1/($multiplier^$order), \)$BR \( \text{computed ratio} = $ratio . \) END_SOLUTION Context()->normalStrings; ENDDOCUMENT();

Compute("1/($multiplier^$order"));

since the input to Compute() should always be a string.

To see what exactly is going wrong I used the PGlabs calculator

at http://webwork.maa.org/wiki/PGLabs

$ans = 1/10000;but

TEXT(Compute($ans), $PAR);

TEXT($ans);

yields

0.0001

0.0001

$ans = 1/1000000;

TEXT(Compute($ans), $PAR);

TEXT($ans);

yields

-3.28172

1e-06

The upper number is e-6. If perl wrote 10^(-6) as

1E-06 instead of 1e-06 you would have been ok, but

I haven't figured out how to force WeBWorK to do that.

In any case it is best to use a string input to Compute() so that

you can control the exact form of the correct answer which is shown to students once they are allowed to see the correct answer.

$ordLocal = random(2,6,1); $ordLocalMinus = Compute($ordLocal - 1); $globalOrdAns = Formula("h^$ordLocalMinus");I did not use quotes in the Compute command shown above, but still the value of $globalOrdAns was correctly computed. Did the Compute in the line assigning $ordLocalMinus just get ignored but the value of $ordLocalMinus actually get calculated (so it could correctly be fed to the Formula command?

If so, when are the quotes required and when not?

If you use ^ with a MathObject, it will warn you about this, but since you were using perl reals, not MathObjects, it went ahead and did the exclusive or. Silly, but true.

Davide

When you pass a string to Compute(), it will first parse it using the MathObject parser, as controlled by the current Context object. That means that the operations and functions and so on that are defined there will be the ones that control the result, no the built-in perl expression parser. That makes the result work exactly like student answers, which is good for consistency, and also makes it easier to produce results that are not easy to produce in perl (like Intervals, and Vectors). Finally, Compute() saves the original string as the correct answer string, so that if you used

$ans = Compute("sqrt(2)");to produce a MathObject that was used for an answer checker via

ANS($ans->cmp);then the correct answer would show as

`sqrt(2)`

rather than `1.41421`

as it would have been had you used `Compute(sqrt(2))`

without the quotes.
I don't think there is a hard-and-fast rule for when to use quotes and when not to. You have to think about what result you want to have in terms of the correct answer as well as the computed result.

Hope that clears things up for you.

Davide