** Using WeBWorK **

1) Any idea on how would one test whether the "alttext" for the graph
in the problem below is working? (Here at UM they are very concerned about accessibility issues).
2) I'm not sure how to interpret the error (see attachment)
I got when "testing the randomization" of the following problem:

# DESCRIPTION
# Recognizing values of the parameters k and p from the graph of y=k x^p (with p<0)
# ENDDESCRIPTION
#Right now stored at MAA-PREP2015
# Homework/Workshop3/Souza/problem4.pg
## DBsubject(’Precalculus’)
## DBchapter(’’)
## DBsection(’’)
## Date(’mm/dd/15’)
## Level(’’)
## Keywords(’’)
## Author(’Regina Souza’)
## Institution(’University of Montana, Missoula’)
## TitleText1(’Functions Modeling Change’)
## EditionText1(5)
## AuthorText1(’Connally’)
## Section1(11.1)
## Problem1()

DOCUMENT();
loadMacros("PGstandard.pl",
"MathObjects.pl",
"PGgraphmacros.pl",
"parserPopUp.pl",
"PGML.pl",
"PGcourse.pl");
Context("Numeric");
#Context()->variables->add(t => "Real");
TEXT(beginproblem());
$showPartialCorrectAnswers = 1;
$refreshCachedImages = 1;
Context("Numeric");
$pixels = 200;
# Create the canvas
$gr = init_graph(-1,-1,6,6, # xmin, ymin, xmax, ymax
axes=>[0,0], grid=>[7,7], size=>[$pixels, $pixels]);
$gr -> lb('reset'); # remove default labels
# axes labels
$gr->lb( new Label(5.5,0,'x', 'black', 'center', 'bottom'));
$gr->lb( new Label(0.1,5.5,'y', 'black', 'left', 'middle'));
# axes labels
foreach my $i (1..5) {
$gr->lb( new Label($i,0, $i, 'black', 'center', 'top'));
$gr->lb( new Label(-0.1,$i, $i, 'black', 'right', 'middle'));
}
# randomize the graph
$c = random(2,4,0.5);
# plot a function
$f = Formula("$c/x");
add_functions($gr, "$f for x in <0,6> using color:blue and weight:2");
install_problem_grader(~~&std_problem_grader);
$showPartialCorrectAnswers = 0;
$popup1 = PopUp(
["choose","a linear function","a quadratic function","an exponential function","a power function"],
"a power function",
);
$popup2 = PopUp(
["choose","0","1","2","2.5","3","3.5","4.0"],
"$c",
);
$popup3 = PopUp(
["choose","d is less than 0", "d is between 0 and 1", "d is greater than 1"],
"d is less than 0",
);
BEGIN_PGML
Consider the function given by the following graph:
>> [@ image(insertGraph($gr), width=>$pixels, height=>$pixels, tex_size=>900,extra_html_tags=>'alt="Graph of a decreasing, concave up function in quadrant I, which passes through (1,'.$c.') " ' ) @]*
[` f(x)=c\cdot x^d `] <<
a. Which type of function is this? This is [_________]{$popup1}
b. What is the value of [` c `] ? [` c = `][____]{$popup2}
c. Choose the best option for [` d `]: [_________]{$popup3}
END_PGML
BEGIN_PGML_SOLUTION
*SOLUTION*
a. This is [@ $popup1->correct_ans() @]* .
b. [` c = [$c] `], the value of the function at 1, and
c. [@ $popup3->correct_ans() @]* , since [` c>0 `] and the power function is decreasing when [` x>0 `].
END_PGML_SOLUTION
ENDDOCUMENT();

Hi Gavin,

Hi,

Question 1: Is there an intelligent solution to avoid the label zero on the axes when creating a graph (other than interrupting the counter)?

Question 2: What is wrong with my popups? Code follows:

#---------------------------------------------------------------------------------------------------------------------
# tagging and description section
#---------------------------------------------------------------------------------------------------------------------

# DESCRIPTION
# Recognizing properties of the parameters k and p from the graph of y=kx^p
# ENDDESCRIPTION
# Homework/Workshop3/Souza/problem3.pg

#---------------------------------------------------------------------------------------------------------------------
# initialization section
#---------------------------------------------------------------------------------------------------------------------


DOCUMENT();

loadMacros("PGstandard.pl",
"MathObjects.pl",
"PGgraphmacros.pl",
"parserPopUp.pl",
"PGML.pl",
"PGcourse.pl");

Context("Numeric");

#Context()->variables->add(t => "Real");

#---------------------------------------------------------------------------------------------------------------------
# problem set-up section
#---------------------------------------------------------------------------------------------------------------------

#---------------------------------------------------------------------------------------------------------------------
# text section
#---------------------------------------------------------------------------------------------------------------------

TEXT(beginproblem());

$showPartialCorrectAnswers = 1;
$refreshCachedImages = 1;

Context("Numeric");

$pixels = 200;

# Create the canvas
$gr = init_graph(-3,-3,3,6, # xmin, ymin, xmax, ymax
axes=>[0,0], grid=>[6,9], size=>[$pixels, $pixels]);
$gr -> lb('reset'); # remove default labels

# axes labels
$gr->lb( new Label(2.5,0,'x', 'black', 'center', 'bottom'));
$gr->lb( new Label(0.1,5.5,'y', 'black', 'left', 'middle'));

# axes labels
foreach my $i (-2..2) {
$gr->lb( new Label($i,0, $i, 'black', 'center', 'top'));
}
foreach my $i (-2..5) {
$gr->lb( new Label(-0.1,$i, $i, 'black', 'right', 'middle'));
}

######
###### Maybe randomize the graph?
######

# plot a function
$f = Formula("2*sqrt(x)");
add_functions($gr, "$f for x in <-1,4> using color:blue and weight:2");

#########
### Problem worked up to here
#########

install_problem_grader(~~&std_problem_grader);
$showPartialCorrectAnswers = 0;

$popup1 = PopUp(
["choose","linear","quadratic","exponential"],
"power function",
);

$popup2 = PopUp(
["choose","d less than 0","d greater than 1"],
"d between 0 and 1",
);


BEGIN_PGML

>> [@ image(insertGraph($gr), width=>$pixels, height=>$pixels, tex_size=>900) @]*
[` f(x)=c\cdot x^d `] <<

a. Which type of function is this? [_________]{$popup1}

b. What is the value of [` c `] ? [` c = `] [____] {2}

c. Choose the best option for [` d `]: [@ $popup2->menu() @]*

END_PGML

ANS( $popup2->cmp() );

#---------------------------------------------------------------------------------------------------------------------
# (answer and) solution section
#---------------------------------------------------------------------------------------------------------------------

BEGIN_PGML_SOLUTION

*SOLUTION*

The correct answers are [@ $popup1->correct_ans() @]* , 2 (the value of the function at 1) and
[@ $popup2->correct_ans() @]* (since the power function is increasing and concave down).

END_PGML_SOLUTION



ENDDOCUMENT();

Hi Gary,

Hello,

I am trying to write a problem about measurement.
Using the multianswer parser I can access only the last "original_student_ans"
The pared-down code is below. hp

DOCUMENT();

loadMacros(
"PGbasicmacros.pl",
"MathObjects.pl",
"PGanswermacros.pl",
"parserMultiAnswer.pl",
);

#######################
TEXT($BEGIN_ONE_COLUMN,beginproblem()) ;
$refreshCachedImages = 1;
$showPartialCorrectAnswers = 1;
###############

$H = 0.43;
$W = 5.57;
$A = $H*$W;
$P = 2*$H + 2*$W;

$multians = MultiAnswer($H, $W, $A, $P)->with(
singleResult => 0,
checker => sub {
my ( $correct, $student, $self, $answer_hash_reference ) = @_;
my %ansH = %$answer_hash_reference;
@keys = keys %ansH;
foreach(0..@keys){
$strkeys = $strkeys.$keys[$_]." ";
}

my ($H_stu, $W_stu, $A_stu, $P_stu ) = @{$student};
# my ($H_oa, $W_oa, $A_oa, $P_oa )= @{$ansH} {original_student_ans};# unsuccessful


$H_n = Nsigfig($ansH{original_student_ans}); #last entry only one available

my ( $H_correct, $W_correct, $A_correct, $P_correct) = @{$correct};
$A_correct = $H_stu*$W_stu;
$P_correct = 2*$H_stu+2*$W_stu;

$self->setMessage(1,"number sigfigs for last only $H_n ");
$self->setMessage(2, $strkeys );
$self->setMessage(3,$W_oa);
$self->setMessage(4,$ansH{original_student_ans});
if($H_n ==3){
return [1,1,1,1]}
else {
return [0,0,0,0];
}
}

);
BEGIN_TEXT
Record the horizontal dimension. \{$multians->ans_rule(10)\} $BR
Record the vertical dimension. \{$multians->ans_rule(10)\} $BR
Calculate the area. \{$multians->ans_rule(10)\} $BR
Calculate the perimeter. \{$multians->ans_rule(10)\} $BR

END_TEXT

ANS($multians->cmp() );

sub Nsigfig{
($x) = @_;

$_=$x;
if (m/./){
$xPlus = $x."1";
$n =int ( ln($xPlus/($xPlus-$x))/ln(10) );}
else {#tba
}
return $n;
}
TEXT($END_ONE_COLUMN);
ENDDOCUMENT();

I don't know whether this is a problem with WW, or just with my server, but a problem it is: when I first log in to WW, and start to create a homework set, I can bring up a page of problems from the OPL very quickly. However, if I wish to choose some different problems - or even the next page of problems, my system takes ages to refresh the page, and sometimes just hangs with an error message.

This means that what should be a simple task (selecting 10 integration problems, say, for an elementary calculus set), can take well over an hour, with all the waits, the crashes, the logging out and back in.

Is this a known issue for anybody - and is there a work-around?

I"m trying to use dynamic graphics to display a series of graphs - real and imaging parts of a discrete complex function. I need to find the min and max of the solutions in order to set the limits on the graphs. I think I have this down using min(@vector) and max(@vector). I"m having difficulty on (at least) two points plotting the discrete points, I try 

$point1[0] = closed_circle(n_vec[0],$alpha_re[0], 'red');

which give a syntax error I cannot find. The vectors n_vec and alpha_re are defined and used elsewhere. 

commenting those lines out, I get an error at line 137

136		$graph_re[$j] -> stamps($point1[0],$point1[1]);
137		$fig_re[$j] = image(insertGraph($graph_re[$j]),width => 240,height => 180,tex_size => 200);

a divide by zero. I thought this would be problems with the computed limits. But I'm having difficulty displaying the limits, since program bombs. How do I find the offending values? 

Thanks

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

loadMacros(

"PGstandard.pl",

"MathObjects.pl",

"AnswerFormatHelp.pl",

"PGgraphmacros.pl",

"unionTables.pl",

"PGanswermacros.pl",

"PGchoicemacros.pl",

 "PGgraphmacros.pl",

  "extraAnswerEvaluators.pl",

 "parserCustomization.pl",

"PGcourse.pl"

);

TEXT(beginproblem());

$refreshCachedImages = 1;

Context("Complex");

Context()->variables->are(

n=>"Real",

t=>"Real"

);

Context()->flags->set(

  tolerance => 0.001,

  tolType => "absolute",

);

$Tover2 = random(5,10,1);

$T = 2*$Tover2;

$d0 = random(2,$T-4,1);

$t0 = -$Tover2 + $d0;

$d1 = random(1, $Tover2-$t0-2, 1);

$t1 = $t0 + $d1;

$d2 = random(1,$Tover2-$t1-1,1);

$t2 = $t1 + $d2;

$w0 = 2*pi/$T;

$a1 = non_zero_random(-6, 6, 1);

do {$a2 = non_zero_random(-6, 6, 1);} until ($a2 != $a1);

$FSeries = Formula("(1/$T)*(i*($a1/($w0*n))*(exp((-1)*i*$w0*$t1*n) - exp((-1)*i*$w0*$t0*n)) + i*($a2/($w0*n))*(exp((-1)*i*$w0*$t2*n) - exp((-1)*i*$w0*$t1*n)) ) ")->reduce;

$N = 6;

$indx = -1;

for ($k=-$N, $k<= $N,$k++) {

    $indx++;

    if ($k == 0) {$alpha[$indx]  = Compute(($d1*$a1 + $d2*$a2)/$T); }

    else {

      $alpha[$indx] = $FSeries -> eval(n=>$k);

    };

   $alpha_mag[$indx] = abs($alpha[$indx] );

   $alpha_ph[$indx] = arg($alpha[$indx] );

   $alpha_re[$indx] = Re($alpha[$indx] );

   $alpha_im[$indx] = Im($alpha[$indx] );

   $n_vec[$indx] = $k;

};

#$alpha0m = Compute(abs($alpha0));

#$alpha0p = Compute(0);

#if ($alpha0 < 0) {$alpha0p = pi;}

# check back for adding pi for correct quadrant

#$f_approx = Formula(" $alpha0 + 2*$alphap1m*cos($w0*t + $alphap1p) + 2*$alphap2m*cos($w0*2*t + $alphap2p) ")->reduce;

### generate graphics

$a = random(1,9,1);

$b = random(2,1,9);   

$c = random(2,1,9);

$n_min = -($N+1);

$n_max = ($N+1);    

$grid_n = $n_max - $n_min;          

$Fmag_min = Compute(min(@alpha_mag)); 

$Fph_min = (-1)*pi; 

$Fmag_max = Compute(max(@alpha_mag)); 

$Fph_max = pi; 

$Fre_min = Compute(min(@alpha_re)); 

$Fim_min = Compute(min(@alpha_im)); 

$Fre_max = Compute(max(@alpha_re)); 

$Fim_max = Compute(max(@alpha_im)); 

$grid_mag = $Fmag_max - $Fmag_min;   # limits are same for real and imag parts

$grid_ph = $Fph_max - $Fph_min;   # limits are same for real and imag parts

$grid_re = $Fre_max - $Fre_min;   # limits are same for real and imag parts

$grid_im = $Fim_max - $Fim_min;   # limits are same for real and imag parts

#$orig = image(insertGraph($gr),width => 400,height => 300,tex_size => 600);

# generate functions

# insert functions into graph

for ($j = 0; $j <=5; $j++) {

$graph_re[$j] = init_graph($n_min,$Fre_min,$n_max,$Fre_max,'axes'=>[0,0],'grid'=>[$grid_n,$grid_re] );

$graph_im[$j] = init_graph($n_min,$Fim_min,$n_max,$Fim_max,'axes'=>[0,0],'grid'=>[$grid_n,$grid_im] );

};

# set labels in graphs

for ($j = 0; $j <=5; $j++) {

$graph_re[$j]->lb('reset');

$graph_re[$j]->lb(new Label(-0.5,0,0,'black','right','middle'));

$graph_re[$j]->lb(new Label(-0.5,($Fre_max-1),($Fre_max-1),'black','right','middle'));

for ($i = 0; $i <= ($n_max-1); $i++) { if ($i != 0) {

    $graph_re[$j]->lb(new Label($i,-.5,$i,'black','center','top')) }};

$graph_re[$j]->lb(new Label(-.5,($Fre_max/2),"Fre",'black','right','top'));

$graph_re[$j]->lb(new Label(($n_max/2),-0.5,"n",'black','right','bottom'));

#plot_functions( $graph_re[$j], $real[$j]);

#$point1[0] = closed_circle(n_vec[0],$alpha_re[0], 'red');

#$point1[1] = closed_circle(n_vec[1],$alpha_re[1], 'red');

$point1[0] = closed_circle(-1,1, 'red');

$point1[1] = closed_circle(1,2, 'red');

$graph_re[$j] -> stamps($point1[0],$point1[1]);

$fig_re[$j] = image(insertGraph($graph_re[$j]),width => 240,height => 180,tex_size => 200); 

$graph_im[$j]->lb('reset');

$graph_im[$j]->lb(new Label(-0.5,0,0,'black','right','middle'));

$graph_im[$j]->lb(new Label(-0.5,($Fim_max-1),($Fim_max-1),'black','right','middle'));

for ($i = 0; $i <= ($w_max-1); $i++) { if ($i != 0) {

    $graph_im[$j]->lb(new Label($i,-.5,$i,'black','center','top')) }};

$graph_im[$j]->lb(new Label(-.5,($Fim_max/2),"Im(F)",'black','right','top'));

$graph_im[$j]->lb(new Label(($n_max/2),-0.5,"n",'black','right','bottom'));

#plot_functions( $graph_im[$j], $imag[$j]);

#$point2[0] = closed_circle(n_vec[0],$alpha_im[0], 'blue');

#$point2[1] = closed_circle(n_vec[1],$alpha_im[1], 'blue');

$point1[0] = closed_circle(-1,1, 'red');

$point1[1] = closed_circle(1,2, 'red');

$graph_im[$j] -> stamps($point2[0],$point2[1]);

$fig_im[$j] = image(insertGraph($graph_im[$j]),width => 240,height => 180,tex_size => 200); 

};

$mc = new_multiple_choice();

$mc->qa('Sketch  accurate graphs of the real and imaginary parts of this function, \( Real(F(n)) \) and \( Imag(F(n) )\) , for integers \( n \in [-$N, $N] \).  Which (if any) of the graphs below matches the graph you drew?','Real $fig_re[0]     Imag $fig_im[0] $BR $BITALIC(click on image to enlarge)$EITALIC ');

$mc->extra('Real $fig_re[1]    Imag  $fig_im[1] $BR $BITALIC(click on image to enlarge)$EITALIC',

'Real $fig_re[2]    Imag $fig_im[2] $BR $BITALIC(click on image to enlarge)$EITALIC',

'Real $fig_re[3]     Imag $fig_im[3] $BR $BITALIC(click on image to enlarge)$EITALIC',

'Real $fig_re[4]     Imag $fig_im[4] $BR $BITALIC(click on image to enlarge)$EITALIC',

'Real $fig_re[5]     Imag $fig_im[5]$BR $BITALIC(click on image to enlarge)$EITALIC');

$mc->makeLast('None of the above');

Context()->texStrings;

BEGIN_TEXT

Graphing discrete  complex functions, e.g., Fourier series

$PAR

Consider the periodic function with period \( $T \) given by

$BR

\[ f(t) = \left\lbrace \begin{array}{ l l } 0 & \mbox{ if } -$Tover2 \leq t < $t0 \\ $a1 & \mbox{ if } $t0 \leq t < $t1 \\ 

$a2 & \mbox{ if } $t1 \leq t < $t2 \\ 

0 & \mbox{ if } $t2 \leq t < $Tover2. \end{array} \right. \]

$PAR

Find and plot the first $N coefficients of the exponential Fourier Series for \( f(t) \), i.e., \( F(n) \) for \( n = -$N, ... 0, ... $N.\)

$BR

\{ $mc->print_q() \} $BR

\{ $mc->print_a() \}

END_TEXT

Context()->normalStrings;

ANS(radio_cmp($mc->correct_ans));

## force a refresh of the image after changes

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

 

You might try moving the $refreshCachedImages = 1 to earlier in the problem. Currently, it is after the image is referenced the problem. I'm not sure when it has its effect, but I suspect the image is created and linked in at the point where the image is referenced, and that is probably where the value of $refreshCachedImages is used. Changing it afterword would have no effect in that case.