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WIP: rearrange the OPL macros for clarity
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369 changes: 369 additions & 0 deletions OpenProblemLibrary/macros/univ/Alfredmacros.pl
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# A group of macros used in the Alfred problem library.

sub _Alfredmacros_init {} #don't reload these macros.


# Given a point (x,y) this macro computes the angle with respect to x-axis. The angle will be between 0 and 2pi.
sub inversetrig
{my $refangle = arctan(abs($_[1]/$_[0]));
if($_[0] == 0)
{0}
elsif ($_[0]>0)
{if($_[1] == 0)
{0}
elsif($_[1]>0)
{$refangle;}
else
{2*pi-$refangle;}
}
else
{if($_[1] == 0)
{pi}
elsif($_[1]>0)
{pi-$refangle;}
else
{pi+$refangle}
}
}

## Compute the max and min of an array of numbers



#This macro prevents students from double clicking in an answer box. This macro #is necessary for multiple integral problems where the answer box is typeset
#into the integration symbols.
sub doubleclickprevent
{TEXT(MODES(
TeX => "",
HTML => "<SCRIPT>if (window.jsMath) {jsMath.Click.DblClick = function () {}}</SCRIPT>"
));
}

#The problems that have the answer box in the limits must be displayed in JS
#math mode. This macro warns the user to use JS math mode if they are not.
sub jsMathwarn
{TEXT(MODES(
TeX => '',
HTML_jsMath => '',
HTML => $HR."Warning: to use this problem, you need to".
"select jsMath mode in the Display Options panel at the left".$HR,
));
}

sub jsmathmode
{
TEXT(MODES(
TeX => '',
HTML_jsMath => '',
HTML => $HR."Warning: to use this problem, you need to ".
"select jsMath mode in the Display Options panel at the left".$HR,
));
TEXT(MODES(
TeX => "",
HTML => "<SCRIPT>if (window.jsMath) {jsMath.Click.DblClick = function () {}}</SCRIPT>"
));

}

sub mathjaxmode
{TEXT(MODES(
TeX => '',
HTML_MathJax => '',
HTML => $HR."Warning: to use this problem, you need to ".
"select MathJax mode in the Display Options panel at the left".$HR,
));
}

#This subroutine includes the Strang's textbook into a problem, you have to
#feed it the chapter and section. It is assumed that the book is in the course
#directory and is labeled strangtextbook. The parameters are
#strang(chapter,section,(optional) section title.
#example \{&strang(16,5,"surface integrals")\}.
$wwstrang = "http://webwork.alfred.edu/webwork2_course_files/strangcalculus";
sub strang
{
htmlLink(qq!$wwstrang/Strang-$_[0]-$_[1].pdf!,"$_[0].$_[1] $_[2] from Gilbert Strang's Calculus",q/TARGET="new_window"/)
}

#Inserts a link to a trig table in the problem.
#example \{&trig_table()\}
sub trig_table
{
htmlLink(qq!$wwstrang/trig_identities.pdf!,"Trig Identities",q/TARGET="new_window"/)
}

sub strang_index
{
htmlLink(qq!$wwstrang/Index.pdf!,"Index",q/TARGET="new_window"/)
}

sub strang_TOC
{
htmlLink(qq!$wwstrang/TOC.pdf!,"Table of Contents",q/TARGET="new_window"/)
}

sub product_Rule_cmp {
my ( $correct, $student, $self ) = @_;
my ( $f1stu, $f2stu,$f3stu,$f4stu ) = @{$student};
my ( $f1, $f2, $f3, $f4 ) = @{$correct};
my @fgrade = (0,0,0,0);
my @fstu = ($f1stu,$f2stu,$f3stu,$f4stu);
my @fcorrect = ($f1,$f2,$f3,$f4);
#we will associate each student answer with a prime number, noting which student answer is in which blank. This allows us to make use of the fundamental theorem of arithmetic.
my @prime = (2,3,5,7);
my @answerblank = (0,0,0,0);

for($i=0;$i<4;$i++){
for($j=0;$j<4;$j++){
if(($fcorrect[$i]==$fstu[$j])&&($answerblank[$j]==0)){
{$answerblank[$j] = $prime[$i];
$j = 4 # you have to terminate the inner loop in this case for the special case of f=e^x where f and f' are the same.
}
}
}
};
for($i=0;$i<4;$i++){
if(!$answerblank[$i]){
$self->setMessage($i+1,"All of your answers should be $f, $g, or a derivative of one of these functions");
}
}
#now we rely on the fact that products of primes are unique. First we check to see if all of the blanks are correct
if ((($answerblank[0]*$answerblank[1] == 6)&&($answerblank[2]*$answerblank[3] == 35))||(($answerblank[0]*$answerblank[1] == 35)&&($answerblank[2]*$answerblank[3] == 6))){
@fgrade = (1,1,1,1);
}
#now check to see if the first pair of blanks is correct, knowing one pair is not
elsif ($answerblank[0]*$answerblank[1] == 6){
if (($answerblank[2] == 5)||($answerblank[2] == 7)){
@fgrade = (1,1,1,0);
}
elsif (($answerblank[3] == 5)||($answerblank[3] == 7)){
@fgrade = (1,1,0,1);
}
else {@fgrade = (1,1,0,0);}
}
elsif ($answerblank[0]*$answerblank[1] == 35){
if (($answerblank[2] == 2)||($answerblank[2] == 3)){
@fgrade = (1,1,1,0);
}
elsif (($answerblank[3] == 2)||($answerblank[3] == 3)){
@fgrade = (1,1,0,1);
}
else {@fgrade = (1,1,0,0);}
}
#if both sets are not correct, and the first set is not correct, check to see if the last pair are
elsif ($answerblank[2]*$answerblank[3] == 6){
if (($answerblank[0] == 5)||($answerblank[0] == 7)){
@fgrade = (1,0,1,1);
}
elsif (($answerblank[1] == 5)||($answerblank[1] == 7)){
@fgrade = (0,1,1,1);
}
else {@fgrade = (0,0,1,1);}
}
elsif ($answerblank[2]*$answerblank[3] == 35){
if (($answerblank[0] == 2)||($answerblank[0] == 3)){
@fgrade = (1,0,1,1);
}
elsif (($answerblank[1] == 2)||($answerblank[1] == 3)){
@fgrade = (0,1,1,1);
}
else {@fgrade = (0,0,1,1);}
}
#at this point they don't have a matched set of blanks correct. look for a single function in each pair that is right. You have to make sure you only get one for each pair of answer blanks.
else{
if (($answerblank[0])&&($answerblank[2])&&($answerblank[0]*$answerblank[2] !=6)&&($answerblank[0]*$answerblank[2] !=35)&&($answerblank[0]!=$answerblank[2])){
@fgrade = (1,0,1,0);
}
elsif (($answerblank[0])&&($answerblank[3])&&($answerblank[0]*$answerblank[3] !=6)&&($answerblank[0]*$answerblank[3] !=35)&&($answerblank[0]!=$answerblank[3])){
@fgrade = (1,0,0,1);
}
elsif (($answerblank[1])&&($answerblank[2])&&($answerblank[1]*$answerblank[2] !=6)&&($answerblank[1]*$answerblank[2] !=35)&&($answerblank[1]!=$answerblank[2])){
@fgrade = (0,1,1,0);
}
elsif (($answerblank[1])&&($answerblank[3])&&($answerblank[1]*$answerblank[3] !=6)&&($answerblank[1]*$answerblank[3] !=35)&&($answerblank[1]!=$answerblank[3])){
@fgrade = (0,1,0,1);
}
elsif ($answerblank[0]){@fgrade = (1,0,0,0)}
elsif ($answerblank[1]){@fgrade = (0,1,0,0)}
elsif ($answerblank[2]){@fgrade = (0,0,1,0)}
elsif ($answerblank[3]){@fgrade = (0,0,0,1)}
};
return [@fgrade];
}



sub check_boundary_conditions {
my ( $correct, $student, $self ) = @_;
return product_Rule_cmp(@_) ;
}

sub Snxy(){
my %args = @_;
my @x = @{$args{inputs}};
my @y = @{$args{outputs}};
my $m = $args{m};
my $n = $args{n};
my $i = 0;
my $sum = 0;
if ($#x == $#y){
for ($i=0;$i <= $#x;$i++){
$sum = $sum + ($x[$i])**($n)*($y[$i])**($m);
}
}
else {$sum = 0};
return $sum;
}

### To use the macros your problem must include unionTables.pl, and of course Alfredmacros.pl
### Table integral returns a string that can be included in a Table to output an integral whose upper and lower limits
### of integration can be answer blanks. There are several optional parameters:
### width - change the width of the answer blanks. defaults to 3.
### lowerwidth - change the width of the lower answer blank. defaults to width
### upperwidth - change the width of the upper answer blank. defaults to width.
### upper - the uppper limit of integration, does not have to be an answer blank, defaults to answer blank with width "width"
### lower - the lower limit of integration, does not have to be an answer blank, defaults to answer blank with width "width"
### limits - boolean, if 1 puts the limits of integration above and below the integral symbol, if 0 puts them after the integral symbol.
### default is 1.
### Your code must include unionTables.pl, and of course Alfredmacros.pl
### An example:
### \{BeginTable(center=>0).
### Row([tableintegral(),
### ],separation=>2).
### EndTable();
### \}
### which will print an integral with answer blank on the upper and lower limits with the default length of 3
###
### This example prints out a double integral, the first integral with answer blanks with width 10, the second integral
### has 0 for the lower limit of integration and an answer blank with width 5 for the upper limit of integration.
### The default limits of integratin are answer blanks with width 3, in this case the default width was overridden to 5
### and the default lower limit was changed to a zero.
### \{BeginTable(center=>0).
### Row([tableintegral(width=>10,limits=>'\(0\)'),tableintegral(width=>5,lower=>'\(0\)',limits=>0),
### ],separation=>2).
### EndTable();
### \}
### An example where the width of the upper and lower answer blanks have different widths.
### \{BeginTable(center=>0).
### Row([tableintegral(lowerwidth=>10,upperwidth=>1)
### ],separation=>2).
### EndTable();
### \}

sub tableintegral{
my %arg = @_;
my $width = delete $arg{width} // 3;
my $lowerwidth = delete $arg{lowerwidth} // $width;
my $upperwidth = delete $arg{upperwidth} // $width;
my $lower = delete $arg{lower} // ans_rule($lowerwidth);
my $upper = delete $arg{upper} // ans_rule($upperwidth);
my $limits = delete $arg{limits} // 1;
if ($limits == 1){
return $upper.$BR.'\(\displaystyle\int\)'.$BR.$lower
}
else {
return '\(\displaystyle\int\)',$upper.$BR.$BR.$lower
}
};

# a sum with answer blanks for the summation variable, lower limit, and upper limit
#\{ BeginTable(center=>0).
# Row([tablesum(width=>10),
# ],separation=>2).
# EndTable();
#\}
# a sum with answer blanks for the upper and lower limits, and the summation variable is i
#\{ BeginTable(center=>0).
# Row([tablesum(width=>10,sumvariable=>'i'),
# ],separation=>2).
# EndTable();
#\}
# a sum with answer blanks for the upper and lower limits, and summation variable is not used.
#\{ BeginTable(center=>0).
# Row([tablesum(width=>10,usesumvariable=>0),
# ],separation=>2).
# EndTable();
#\}
# sum from n = 1 to infinity
#\{ BeginTable(center=>0).
# Row([tablesum(sumvariable=>'\(n\)',lower=>'\(1\)', upper=>'\(\hskip 3pt\infty\)') ],separation=>2).
# EndTable();
#\}

sub tablesum{
my %arg = @_;
my $width = delete $arg{width} // 3;
my $lowerwidth = delete $arg{lowerwidth} // $width;
my $upperwidth = delete $arg{upperwidth} // $width;
my $lower = delete $arg{lower} // ans_rule($lowerwidth);
my $upper = delete $arg{upper} // ans_rule($upperwidth);
my $limits = delete $arg{limits} // 1;
my $sumvariable = delete $arg{sumvariable} // ans_rule($width);
my $usesumvariable = delete $arg{usesumvariable} // 1;
if ($usesumvariable == 0){
if ($limits == 1){
return $upper.$BR.'\(\displaystyle\sum\)'.$BR.$lower
}
else {
return '\(\displaystyle\int\)',$upper.$BR.$BR.$lower
}
}
else {
if ($limits == 1){
return $upper.$BR.'\(\displaystyle\sum\)'.$BR.$sumvariable.'\( = \)'.$lower
}
else {
return '\(\displaystyle\int\)',$upper.$BR.$BR.$sumvariable.'\( = \)'.$lower
}
}
};


### Create a vertical bar with an upper and lower limit.
sub tableevaluate{
my %arg = @_;
my $width = delete $arg{width} // 3;
my $lowerwidth = delete $arg{lowerwidth} // $width;
my $upperwidth = delete $arg{upperwidth} // $width;
my $lower = delete $arg{lower} // ans_rule($lowerwidth);
my $upper = delete $arg{upper} // ans_rule($upperwidth);
return
'\(\Bigg\vert\)',$upper.$BR.$BR.$lower
};

### Create a subscripted character
sub tablesubscript{
my %arg = @_;
my $width = delete $arg{width} // 3;
my $lower = delete $arg{lower} // ans_rule($width);
my $variable = delete $arg{variable} // 'c';
return
$variable,$BR.$BR.$lower
};

### Create a superscripted character
sub tablesuperscript{
my %arg = @_;
my $width = delete $arg{width} // 3;
my $upper = delete $arg{upper} // ans_rule($width);
my $variable = delete $arg{variable} // 'c';
return
$variable,$upper.$BR.$BR.$BR
};



### A fraction
sub tablefrac{
my %arg = @_;
my $width = delete $arg{width} // 3;
my $lower = delete $arg{lower} // ans_rule($width);
my $upper = delete $arg{upper} // ans_rule($width);
my $barwidth = delete $arg{barwidth} // 10+$width;
my $divisionbar = "";
for ($count = 1;$count <= $barwidth; $count++){
$divisionbar = $divisionbar."-";
}
return $upper.$BR.$divisionbar.$BR.$lower
};

1 change: 1 addition & 0 deletions OpenProblemLibrary/macros/univ/BrockPhysicsMacros.pl
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# this file defines all Brock-Physics-specific macros.
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