** Using WeBWorK **

Answers 2 and 3 should be

$ans2 = ($a**2*$c/4)+$b;

$ans3 = [$a*$c+$c*sqrt($a**2+4*($b/$c))]/2;

Also, I have a query on the answer to problems like setAlgebra20QuadraticFun/vertexform.pg

This problem asks to find the vertex of the graph of a quadratic function.

It admits the answer

str_cmp($vertex)

$vertex="($H,$K)"

Now if the vertex is

(10,7)

(10, 7)

How can I fix that?

Thanks

Alberto

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Note that

$ans3 = [$a*$c+$c*sqrt($a**2+4*($b/$c))]/2;

is incorrect for a subtle reason. Square brackets are not allowed in an arithemetical expression in perl (or at least they do not do what you think they do) so you have to write

$ans3 = ($a*$c+$c*sqrt($a**2+4*($b/$c)))/2;

Better yet is to let WeBWorK parse the expression by writing

$ans3 = "[$a*$c+$c*sqrt($a^2+4*($b/$c))]/2";

Notice the quotes (and you can then also use ^ in place of ** if you want). This has the added advantage that when the student sees the answer, instaed of e.g. 29.4272486205415 they will see [2*14+14*sqrt(2^2+4*(3/14))]/2 which makes a lot more sense. Similarily, you can write

$ans2 = "($a^2*$c/4)+$b";

As for setAlgebra20QuadraticFun/vertexform.pg, there are (at least) three things you can do. The simplest is to replace

&ANS(str_cmp($vertex));

&ANS(ordered_str_cmp($vertex));

&ANS(str_cmp($vertex,'remove_whitespace'));

A better solution is to first add extraAnswerEvaluators.pl to the list of macros at the top so that it reads

loadMacros(
PG.pl,
PGbasicmacros.pl,
PGchoicemacros.pl,
PGanswermacros.pl,
PGauxiliaryFunctions.pl,
extraAnswerEvaluators.pl
);

and then to replace

&ANS(str_cmp($vertex));

&ANS(interval_cmp("($H,$K)"));

I will use the third method to fix the problem in the CVS.

Arnie

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I recall now that another instance of the problem with the spaces appears in problem setAlgebra20QuadraticFun/standardform.pg

At first I didn't notice because when looking at the past answers of the one student that brought it up I saw 2 commas instead of 1. He had erased his current answer.

Alberto

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Arnie

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"\( x=+2i,-2i,-2,-2\)"

Also, in your first reply above, regarding the use of ^2 instead of **2 in the .pg files, I seem to have problems with ^2. It doesn't give the right answer. I am using WW 1.9, is that the reason? Maybe I did something else wrong.

Thanks,

Alberto

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I updated setAlgebra23PolynomialZeros/roots1.pg in the CVS.

As long as the answer is a string, i.e. it is enclosed in quotes, e.g.

$ans3 = "[$a*$c+$c*sqrt($a^2+4*($b/$c))]/2";

you can use ^ instead of **. This works in WW 1.9 and in WW 2.

Arnie

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How do I fix this?

Thanks,

Alberto

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The fix is easy. Replace

$h=random(-2,2,2);

by

$h=non_zero_random(-2,2,2);

Arnie

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Can you help me fixing it?

Thanks,

Alberto

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##DESCRIPTION
##  Algebra problem: polynomial functions
##ENDDESCRIPTION

##KEYWORDS('algebra', 'polynomial function', 'rational zero')

DOCUMENT(); # This should be the first executable line in the problem.

loadMacros(
PG.pl,
PGbasicmacros.pl,
PGchoicemacros.pl,
PGanswermacros.pl,
PGauxiliaryFunctions.pl,
PGasu.pl,
extraAnswerEvaluators.pl,
PGcomplexmacros.pl
);

TEXT(&beginproblem);
$showPartialCorrectAnswers = 1;

$a = non_zero_random(-5,-1,1);
$b = non_zero_random(1,5,1);
# (x-a)(x-b)(x^2+2)
$b1=-($a+$b);
$c1=$a*$b+2;
$d1=-2*($a+$b);
$e1=2*$a*$b;

$p = nicestring([1,$b1, $c1, $d1, $e1]);
$p="P(x)=$p ";

BEGIN_TEXT
Find $BBOLD all $EBOLD of the zeros of the following polynomial and give them in a
comma-separated list.
[ $p ]
$BR
Its zeros are:

{ ans_rule(40) }

END_TEXT

ANS(number_list_cmp("$a, $b, sqrt(2)i, -sqrt(2)i ", complex=>'ok','tolType'=>'absolute','tolerance'=>0.001));

ENDDOCUMENT(); # This should be the last executable line in the problem.

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##DESCRIPTION
##  Algebra problem: complex roots of a polynomial
##ENDDESCRIPTION

##KEYWORDS('algebra', 'polynomial function', 'zero')

DOCUMENT(); # This should be the first executable line in the problem.

loadMacros(
PG.pl,
PGbasicmacros.pl,
PGchoicemacros.pl,
PGanswermacros.pl,
PGauxiliaryFunctions.pl,
PGasu.pl,
extraAnswerEvaluators.pl,
PGcomplexmacros.pl
);

TEXT(&beginproblem);
$showPartialCorrectAnswers = 1;

$a = non_zero_random(-5,-1,1);
$b = non_zero_random(1,5,1);
# (x-a)(x-b)(x^2+2)
$b1=-($a+$b);
$c1=$a*$b+2;
$d1=-2*($a+$b);
$e1=2*$a*$b;

$p = nicestring([1,$b1, $c1, $d1, $e1]);
$p="P(x)=$p ";

BEGIN_TEXT
Find $BBOLD all $EBOLD of the zeros of the following polynomial
and give them in a comma-separated list. If there are no zeros,
enter $BITALIC None$EITALIC.
[$p]
$BR
Its zeros are:
{ ans_rule(40) }
$BR
$BR
$BBOLD Note: $EBOLD complex numbers should be in the form
(a+bi).

END_TEXT

ANS(number_list_cmp("$a, $b, sqrt(2)*i, -sqrt(2)*i", complex=>'ok',
strings=>['none']));

ENDDOCUMENT(); # This should be the last executable line in the problem.

I think the most recent change was the note about the form of the answers. Webwork would choke on "sqrt(-2)" and "-sqrt(-2)". In fact, we may revise this problem to use the new parser which can handle answers in that form.

John

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I like your revision but I have two questions:

When I tried, 1.4142i, and -1.4142i (and the other two roots) were not accepted as correct (but 1.41421i, etc. was OK). 1.414 is accepted by num_cmp as being equal to sqrt(2). What sets the default tolerenance for number_list_cmp? Why doesn't it use the same tolerenance as num_cmp?

My other point is very minor. I prefer "sqrt(2)i, -sqrt(2)i" to "sqrt(2)*i, -sqrt(2)*i".

Arnie

PS Do you know how the library vlean up project is going?

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number_list_cmp just sends values off to other evaluators for checking. If we just had real numbers (and not specified complex=>ok), then it would use num_cmp for the checking.

Since this problem uses complex values, they go to cplx_cmp. It apparently uses a different tolerance than num_cmp does. I just check it with a problem where the answer was just sqrt(2).

I only really know about the small amount of library clean up which took place here over the summer. The other sites are where the bulk of that kind of stuff will be done.

John

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On problem setAlgebra23PolynomialZeros/FindPositiveRoot.pg, it appears that if one of the coefficients is 0, then the sign + (or -) is not printed, like x⁵ + 3x⁴ -114 x³ -292 x²0x¹ -5700

(Actually this is the problem instance that appears in the .pdf included within the UofR templates. The code for this problem is rather sophisticated).

And thanks again.

Alberto

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Alberto

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That is, if one of the coefficients is 0, no +/- sign is printed.

Please let me know how could I fix this. Thanks, Alberto

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As you say, the code is somewhat sophisticated and I haven't spent the time to understand what the problem is doing. However, assuming everything else is correct, the following change should fix the bug.

Replace

$poly = "";
foreach $i (0..$#prod){ $j = $#prod-$i;
        if ($i<$#prod) { 
                if ($i==0) {$poly=$poly."x^{$j}";}
                elsif ($prod[$i] > 0) {$poly=$poly."+$prod[$i] x^{$j}";}
                else {$poly=$poly."$prod[$i] x^{$j}";}
        }
        else {$poly=$poly."+$prod[$i]";}
}

with

$poly = "";
foreach $i (0..$#prod){ $j = $#prod-$i;
        if ($i<$#prod) { 
                if ($i==0) {$poly=$poly."x^{$j}";}
                elsif ($prod[$i] > 0) {$poly=$poly."+$prod[$i] x^{$j}";}
                elsif ($prod[$i] < 0) {$poly=$poly."$prod[$i] x^{$j}";}
        }
        else {$poly=$poly."+$prod[$i]";}
}

Thus only terms with non-zero coefficients are displayed. Let me know if this works.

Arnie

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(The one I mentioned earlier also has the same issue, but I don't know a seed # that produces it.)

I tried your suggestion on this one (that portion of the code is the same) but I still get a 0 without sign.

Thanks, Alberto

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$cplx_params{'tolerance'} = .01*$cplx_params{'tolerance'};

by

$cplx_params{'tolerance'} = .01*$cplx_params{'relTol'};

Arnie

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Sorry about that, and thank you.

Alberto

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&ANS(num_cmp($v2));
&ANS(num_cmp($v1));

This seems to work, but I am not sure of what I really did. This problem's code is too complex.

Alberto

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Alberto

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I am not sure which of the two factors corresponds to the missing asymptote and which to the hole.

Alberto

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A good way to view and download individual problems (and to see what changes have been made) is to goto http://cvs.webwork.rochester.edu/viewcvs.cgi/

Select UR Problem Library as the Project Root and then select rochester_problib.

For instructions on downloading the current version of the whole library, see

http://devel.webwork.rochester.edu/twiki/bin/view/Webwork/WeBWorKCVSReadOnly

Arnie

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I have not yet set up our server for CVS, and will not be able to do it just now.

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You don't need CVS to grab individual problems. Use the link http://cvs.webwork.rochester.edu/viewcvs.cgi/ and follow the instructions above. Once you select a problem, click on view and then copy the problem. Also you can easily just view the changes from the previous version.

Arnie

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Anyhow, setAlgebra25RationalFun/FindInfo3.pg now produces a timeout pink page with seed number 1548

It works fine with other seed nos., so I doubt that it is related to our server's speed.

Alberto

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I didn't get a timeout with seed 1548 but looking at the code, there are two places where random(9,9,1) should be replaced by random(-9,9,1). This occured in the original problem and I just copied it without looking closely. Obviously, using random(9,9,1) will result in an infinite loop.

Arnie

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Thanks for the fix.

Alberto

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I think the typos are in lines 46 and 50. They should be

$ans_c = "-$e**x";

$ans_c = "$e^**(-x)";

Alberto

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