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WIP: rearrange the OPL macros for clarity
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‎OpenProblemLibrary/macros/univ/Alfredmacros.pl

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# A group of macros used in the Alfred problem library.
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sub _Alfredmacros_init {} #don't reload these macros.
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# Given a point (x,y) this macro computes the angle with respect to x-axis. The angle will be between 0 and 2pi.
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sub inversetrig
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{my $refangle = arctan(abs($_[1]/$_[0]));
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if($_[0] == 0)
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{0}
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elsif ($_[0]>0)
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{if($_[1] == 0)
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{0}
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elsif($_[1]>0)
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{$refangle;}
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else
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{2*pi-$refangle;}
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}
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else
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{if($_[1] == 0)
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{pi}
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elsif($_[1]>0)
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{pi-$refangle;}
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else
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{pi+$refangle}
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}
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}
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## Compute the max and min of an array of numbers
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#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
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#into the integration symbols.
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sub doubleclickprevent
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{TEXT(MODES(
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TeX => "",
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HTML => "<SCRIPT>if (window.jsMath) {jsMath.Click.DblClick = function () {}}</SCRIPT>"
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));
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}
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#The problems that have the answer box in the limits must be displayed in JS
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#math mode. This macro warns the user to use JS math mode if they are not.
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sub jsMathwarn
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{TEXT(MODES(
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TeX => '',
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HTML_jsMath => '',
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HTML => $HR."Warning: to use this problem, you need to".
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"select jsMath mode in the Display Options panel at the left".$HR,
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));
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}
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sub jsmathmode
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{
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TEXT(MODES(
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TeX => '',
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HTML_jsMath => '',
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HTML => $HR."Warning: to use this problem, you need to ".
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"select jsMath mode in the Display Options panel at the left".$HR,
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));
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TEXT(MODES(
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TeX => "",
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HTML => "<SCRIPT>if (window.jsMath) {jsMath.Click.DblClick = function () {}}</SCRIPT>"
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));
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}
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sub mathjaxmode
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{TEXT(MODES(
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TeX => '',
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HTML_MathJax => '',
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HTML => $HR."Warning: to use this problem, you need to ".
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"select MathJax mode in the Display Options panel at the left".$HR,
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));
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}
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#This subroutine includes the Strang's textbook into a problem, you have to
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#feed it the chapter and section. It is assumed that the book is in the course
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#directory and is labeled strangtextbook. The parameters are
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#strang(chapter,section,(optional) section title.
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#example \{&strang(16,5,"surface integrals")\}.
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$wwstrang = "http://webwork.alfred.edu/webwork2_course_files/strangcalculus";
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sub strang
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{
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htmlLink(qq!$wwstrang/Strang-$_[0]-$_[1].pdf!,"$_[0].$_[1] $_[2] from Gilbert Strang's Calculus",q/TARGET="new_window"/)
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}
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#Inserts a link to a trig table in the problem.
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#example \{&trig_table()\}
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sub trig_table
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{
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htmlLink(qq!$wwstrang/trig_identities.pdf!,"Trig Identities",q/TARGET="new_window"/)
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}
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sub strang_index
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{
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htmlLink(qq!$wwstrang/Index.pdf!,"Index",q/TARGET="new_window"/)
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}
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sub strang_TOC
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{
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htmlLink(qq!$wwstrang/TOC.pdf!,"Table of Contents",q/TARGET="new_window"/)
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}
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sub product_Rule_cmp {
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my ( $correct, $student, $self ) = @_;
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my ( $f1stu, $f2stu,$f3stu,$f4stu ) = @{$student};
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my ( $f1, $f2, $f3, $f4 ) = @{$correct};
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my @fgrade = (0,0,0,0);
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my @fstu = ($f1stu,$f2stu,$f3stu,$f4stu);
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my @fcorrect = ($f1,$f2,$f3,$f4);
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#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.
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my @prime = (2,3,5,7);
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my @answerblank = (0,0,0,0);
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for($i=0;$i<4;$i++){
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for($j=0;$j<4;$j++){
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if(($fcorrect[$i]==$fstu[$j])&&($answerblank[$j]==0)){
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{$answerblank[$j] = $prime[$i];
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$j = 4 # you have to terminate the inner loop in this case for the special case of f=e^x where f and f' are the same.
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}
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}
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}
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};
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for($i=0;$i<4;$i++){
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if(!$answerblank[$i]){
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$self->setMessage($i+1,"All of your answers should be $f, $g, or a derivative of one of these functions");
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}
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}
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#now we rely on the fact that products of primes are unique. First we check to see if all of the blanks are correct
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if ((($answerblank[0]*$answerblank[1] == 6)&&($answerblank[2]*$answerblank[3] == 35))||(($answerblank[0]*$answerblank[1] == 35)&&($answerblank[2]*$answerblank[3] == 6))){
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@fgrade = (1,1,1,1);
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}
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#now check to see if the first pair of blanks is correct, knowing one pair is not
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elsif ($answerblank[0]*$answerblank[1] == 6){
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if (($answerblank[2] == 5)||($answerblank[2] == 7)){
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@fgrade = (1,1,1,0);
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}
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elsif (($answerblank[3] == 5)||($answerblank[3] == 7)){
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@fgrade = (1,1,0,1);
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}
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else {@fgrade = (1,1,0,0);}
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}
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elsif ($answerblank[0]*$answerblank[1] == 35){
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if (($answerblank[2] == 2)||($answerblank[2] == 3)){
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@fgrade = (1,1,1,0);
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}
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elsif (($answerblank[3] == 2)||($answerblank[3] == 3)){
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@fgrade = (1,1,0,1);
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}
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else {@fgrade = (1,1,0,0);}
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}
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#if both sets are not correct, and the first set is not correct, check to see if the last pair are
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elsif ($answerblank[2]*$answerblank[3] == 6){
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if (($answerblank[0] == 5)||($answerblank[0] == 7)){
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@fgrade = (1,0,1,1);
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}
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elsif (($answerblank[1] == 5)||($answerblank[1] == 7)){
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@fgrade = (0,1,1,1);
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}
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else {@fgrade = (0,0,1,1);}
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}
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elsif ($answerblank[2]*$answerblank[3] == 35){
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if (($answerblank[0] == 2)||($answerblank[0] == 3)){
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@fgrade = (1,0,1,1);
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}
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elsif (($answerblank[1] == 2)||($answerblank[1] == 3)){
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@fgrade = (0,1,1,1);
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}
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else {@fgrade = (0,0,1,1);}
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}
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#at this point they don't have a matched set of blanks correct. look for a single function in each pair that is right. You have to make sure you only get one for each pair of answer blanks.
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else{
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if (($answerblank[0])&&($answerblank[2])&&($answerblank[0]*$answerblank[2] !=6)&&($answerblank[0]*$answerblank[2] !=35)&&($answerblank[0]!=$answerblank[2])){
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@fgrade = (1,0,1,0);
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}
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elsif (($answerblank[0])&&($answerblank[3])&&($answerblank[0]*$answerblank[3] !=6)&&($answerblank[0]*$answerblank[3] !=35)&&($answerblank[0]!=$answerblank[3])){
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@fgrade = (1,0,0,1);
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}
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elsif (($answerblank[1])&&($answerblank[2])&&($answerblank[1]*$answerblank[2] !=6)&&($answerblank[1]*$answerblank[2] !=35)&&($answerblank[1]!=$answerblank[2])){
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@fgrade = (0,1,1,0);
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}
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elsif (($answerblank[1])&&($answerblank[3])&&($answerblank[1]*$answerblank[3] !=6)&&($answerblank[1]*$answerblank[3] !=35)&&($answerblank[1]!=$answerblank[3])){
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@fgrade = (0,1,0,1);
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}
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elsif ($answerblank[0]){@fgrade = (1,0,0,0)}
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elsif ($answerblank[1]){@fgrade = (0,1,0,0)}
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elsif ($answerblank[2]){@fgrade = (0,0,1,0)}
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elsif ($answerblank[3]){@fgrade = (0,0,0,1)}
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};
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return [@fgrade];
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}
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sub check_boundary_conditions {
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my ( $correct, $student, $self ) = @_;
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return product_Rule_cmp(@_) ;
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}
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sub Snxy(){
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my %args = @_;
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my @x = @{$args{inputs}};
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my @y = @{$args{outputs}};
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my $m = $args{m};
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my $n = $args{n};
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my $i = 0;
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my $sum = 0;
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if ($#x == $#y){
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for ($i=0;$i <= $#x;$i++){
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$sum = $sum + ($x[$i])**($n)*($y[$i])**($m);
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}
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}
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else {$sum = 0};
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return $sum;
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}
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### To use the macros your problem must include unionTables.pl, and of course Alfredmacros.pl
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### Table integral returns a string that can be included in a Table to output an integral whose upper and lower limits
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### of integration can be answer blanks. There are several optional parameters:
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### width - change the width of the answer blanks. defaults to 3.
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### lowerwidth - change the width of the lower answer blank. defaults to width
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### upperwidth - change the width of the upper answer blank. defaults to width.
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### upper - the uppper limit of integration, does not have to be an answer blank, defaults to answer blank with width "width"
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### lower - the lower limit of integration, does not have to be an answer blank, defaults to answer blank with width "width"
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### limits - boolean, if 1 puts the limits of integration above and below the integral symbol, if 0 puts them after the integral symbol.
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### default is 1.
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### Your code must include unionTables.pl, and of course Alfredmacros.pl
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### An example:
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### \{BeginTable(center=>0).
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### Row([tableintegral(),
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### ],separation=>2).
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### EndTable();
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### \}
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### which will print an integral with answer blank on the upper and lower limits with the default length of 3
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###
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### This example prints out a double integral, the first integral with answer blanks with width 10, the second integral
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### has 0 for the lower limit of integration and an answer blank with width 5 for the upper limit of integration.
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### The default limits of integratin are answer blanks with width 3, in this case the default width was overridden to 5
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### and the default lower limit was changed to a zero.
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### \{BeginTable(center=>0).
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### Row([tableintegral(width=>10,limits=>'\(0\)'),tableintegral(width=>5,lower=>'\(0\)',limits=>0),
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### ],separation=>2).
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### EndTable();
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### \}
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### An example where the width of the upper and lower answer blanks have different widths.
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### \{BeginTable(center=>0).
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### Row([tableintegral(lowerwidth=>10,upperwidth=>1)
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### ],separation=>2).
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### EndTable();
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### \}
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sub tableintegral{
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my %arg = @_;
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my $width = delete $arg{width} // 3;
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my $lowerwidth = delete $arg{lowerwidth} // $width;
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my $upperwidth = delete $arg{upperwidth} // $width;
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my $lower = delete $arg{lower} // ans_rule($lowerwidth);
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my $upper = delete $arg{upper} // ans_rule($upperwidth);
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my $limits = delete $arg{limits} // 1;
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if ($limits == 1){
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return $upper.$BR.'\(\displaystyle\int\)'.$BR.$lower
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}
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else {
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return '\(\displaystyle\int\)',$upper.$BR.$BR.$lower
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}
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};
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# a sum with answer blanks for the summation variable, lower limit, and upper limit
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#\{ BeginTable(center=>0).
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# Row([tablesum(width=>10),
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# ],separation=>2).
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# EndTable();
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#\}
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# a sum with answer blanks for the upper and lower limits, and the summation variable is i
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#\{ BeginTable(center=>0).
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# Row([tablesum(width=>10,sumvariable=>'i'),
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# ],separation=>2).
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# EndTable();
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#\}
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# a sum with answer blanks for the upper and lower limits, and summation variable is not used.
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#\{ BeginTable(center=>0).
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# Row([tablesum(width=>10,usesumvariable=>0),
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# ],separation=>2).
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# EndTable();
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#\}
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# sum from n = 1 to infinity
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#\{ BeginTable(center=>0).
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# Row([tablesum(sumvariable=>'\(n\)',lower=>'\(1\)', upper=>'\(\hskip 3pt\infty\)') ],separation=>2).
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# EndTable();
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#\}
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sub tablesum{
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my %arg = @_;
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my $width = delete $arg{width} // 3;
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my $lowerwidth = delete $arg{lowerwidth} // $width;
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my $upperwidth = delete $arg{upperwidth} // $width;
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my $lower = delete $arg{lower} // ans_rule($lowerwidth);
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my $upper = delete $arg{upper} // ans_rule($upperwidth);
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my $limits = delete $arg{limits} // 1;
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my $sumvariable = delete $arg{sumvariable} // ans_rule($width);
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my $usesumvariable = delete $arg{usesumvariable} // 1;
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if ($usesumvariable == 0){
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if ($limits == 1){
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return $upper.$BR.'\(\displaystyle\sum\)'.$BR.$lower
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}
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else {
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return '\(\displaystyle\int\)',$upper.$BR.$BR.$lower
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}
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}
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else {
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if ($limits == 1){
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return $upper.$BR.'\(\displaystyle\sum\)'.$BR.$sumvariable.'\( = \)'.$lower
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}
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else {
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return '\(\displaystyle\int\)',$upper.$BR.$BR.$sumvariable.'\( = \)'.$lower
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}
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}
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};
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### Create a vertical bar with an upper and lower limit.
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sub tableevaluate{
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my %arg = @_;
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my $width = delete $arg{width} // 3;
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my $lowerwidth = delete $arg{lowerwidth} // $width;
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my $upperwidth = delete $arg{upperwidth} // $width;
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my $lower = delete $arg{lower} // ans_rule($lowerwidth);
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my $upper = delete $arg{upper} // ans_rule($upperwidth);
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return
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'\(\Bigg\vert\)',$upper.$BR.$BR.$lower
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};
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### Create a subscripted character
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sub tablesubscript{
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my %arg = @_;
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my $width = delete $arg{width} // 3;
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my $lower = delete $arg{lower} // ans_rule($width);
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my $variable = delete $arg{variable} // 'c';
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return
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$variable,$BR.$BR.$lower
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};
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### Create a superscripted character
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sub tablesuperscript{
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my %arg = @_;
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my $width = delete $arg{width} // 3;
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my $upper = delete $arg{upper} // ans_rule($width);
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my $variable = delete $arg{variable} // 'c';
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return
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$variable,$upper.$BR.$BR.$BR
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};
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### A fraction
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sub tablefrac{
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my %arg = @_;
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my $width = delete $arg{width} // 3;
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my $lower = delete $arg{lower} // ans_rule($width);
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my $upper = delete $arg{upper} // ans_rule($width);
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my $barwidth = delete $arg{barwidth} // 10+$width;
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my $divisionbar = "";
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for ($count = 1;$count <= $barwidth; $count++){
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$divisionbar = $divisionbar."-";
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}
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return $upper.$BR.$divisionbar.$BR.$lower
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};
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‎OpenProblemLibrary/macros/univ/BrockPhysicsMacros.pl

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# this file defines all Brock-Physics-specific macros.

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