--- located in the courseScripts directory

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 --- located in the courseScripts directory



Answer blank macros:

These produce answer blanks of various sizes or pop up lists or radio answer buttons. The names for the answer blanks are generated implicitly.

        ans_rule( width )
        tex_ans_rule( width )
        ans_radio_buttons(value1=>label1, value2,label2 => value3,label3=>...)
        pop_up_list(@list)   # list consists of (value => label,  PR => "Product rule",...)
        pop_up_list([@list]) # list consists of values

In the last case, one can use pop_up_list(['?', 'yes', 'no']) to produce a pop-up list containing the three strings listed, and then use str_cmp to check the answer.

To indicate the checked position of radio buttons put a '%' in front of the value: ans_radio_buttons(1, 'Yes','%2','No') will have 'No' checked. tex_ans_rule works inside math equations in HTML_tth mode. It does not work in Latex2HTML mode since this mode produces gif pictures.

The following method is defined in for entering the answer evaluators corresponding to answer rules with automatically generated names. The answer evaluators are matched with the answer rules in the order in which they appear on the page.

        ANS(ans_evaluator1, ans_evaluator2,...);

These are more primitive macros which produce answer blanks for specialized cases when complete control over the matching of answers blanks and answer evaluators is desired. The names of the answer blanks must be generated manually, and it is best if they do NOT begin with the default answer prefix (currently AnSwEr).

        labeled_ans_rule(name, width)  # an alias for NAMED_ANS_RULE where width defaults to 20 if omitted.
        NAMED_ANS_RULE(name, width)
        NAMED_ANS_BOX(name, rows, cols)
        NAMED_ANS_RADIO(name, value,label,)
        NAMED_ANS_RADIO_EXTENSION(name, value,label)
        check_box('-name' =>answer5,'-value' =>'statement3','-label' =>'I loved this course!'   )
        NAMED_POP_UP_LIST($name, @list) # list consists of (value => tag,  PR => "Product rule",...)
        NAMED_POP_UP_LIST($name, [@list]) # list consists of a list of values (and each tag will be set to the corresponding value)

(Name is the name of the variable, value is the value given to the variable when this option is selected, and label is the text printed next to the button or check box. Check box variables can have multiple values.)

NAMED_ANS_RADIO_BUTTONS creates a sequence of NAMED_ANS_RADIO and NAMED_ANS_RADIO_EXTENSION items which are output either as an array or, in scalar context, as the array glued together with spaces. It is usually easier to use this than to manually construct the radio buttons by hand. However, sometimes extra flexibility is desiredin which case:

When entering radio buttons using the "NAMED" format, you should use NAMED_ANS_RADIO button for the first button and then use NAMED_ANS_RADIO_EXTENSION for the remaining buttons. NAMED_ANS_RADIO requires a matching answer evalutor, while NAMED_ANS_RADIO_EXTENSION does not. The name used for NAMED_ANS_RADIO_EXTENSION should match the name used for NAMED_ANS_RADIO (and the associated answer evaluator).

The following method is defined in for entering the answer evaluators corresponding to answer rules with automatically generated names. The answer evaluators are matched with the answer rules in the order in which they appear on the page.

      NAMED_ANS(name1 => ans_evaluator1, name2 => ans_evaluator2,...);

These auxiliary macros are defined in

        NEW_ANS_NAME(        );   # produces a new anonymous answer blank name  by appending a number to the prefix (AnSwEr)
                                  # and registers this name as an implicitly labeled answer
                                  # Its use is paired with each answer evaluator being entered using ANS()
    ANS_NUM_TO_NAME(number);  # prepends the prefix (AnSwEr) to the number, but does nothing else.
        RECORD_ANS_NAME( name );  # records the order in which the answer blank  is rendered
                                  # This is called by all of the constructs above, but must
                                  # be called explicitly if an input blank is constructed explictly
                                  # using HTML code.

These are legacy macros:

        ANS_RULE( number, width );                                              # equivalent to NAMED_ANS_RULE( NEW_ANS_NAME(  ), width)
        ANS_BOX( question_number,height, width );                       # equivalent to NAMED_ANS_BOX( NEW_ANS_NAME(  ), height, width)
        ANS_RADIO( question_number, value,tag );                    # equivalent to NAMED_ANS_RADIO( NEW_ANS_NAME( ), value,tag)
        ANS_RADIO_OPTION( question_number, value,tag );         # equivalent to NAMED_ANS_RADIO_EXTENSION( ANS_NUM_TO_NAME(number), value,tag)

                Usage   \[ \{   answer_matrix(rows,columns,width_of_ans_rule, @options) \} \]
                Creates an array of answer blanks and passes it to display_matrix which returns
                text which represents the matrix in TeX format used in math display mode. Answers
                are then passed back to whatever answer evaluators you write at the end of the problem.
                (note, if you have an m x n matrix, you will need mn answer evaluators, and they will be
                returned to the evaluaters starting in the top left hand corner and proceed to the left
                and then at the end moving down one row, just as you would read them.)
                The options are passed on to display_matrix.

Hints and solutions macros

        SOLUTION('text','text2',...);   # equivalent to TEXT(solution(...));
        hint('text', 'text2', ...);
        HINT('text', 'text2',...);      # equivalent to TEXT("$BR$HINT" . hint(@_) . "$BR") if hint(@_);

Solution prints its concatenated input when the check box named 'ShowSol' is set and the time is after the answer date. The check box 'ShowSol' is visible only after the answer date or when the problem is viewed by a professor.

$main::envir{'displaySolutionsQ'} is set to 1 when a solution is to be displayed.

Hints are shown only after the number of attempts is greater than $:showHint ($main::showHint defaults to 1) and the check box named 'ShowHint' is set. The check box 'ShowHint' is visible only after the number of attempts is greater than $main::showHint.

Hints are always shown immediately to instructors to facilitate editing the hint section.

$main::envir{'displayHintsQ'} is set to 1 when a hint is to be displayed.

Comments to instructors


Takes the text to be lines of a comment to be shown only in the Library Browser below the rendered problem.

The function COMMENT stores the needed html in the variable pgComment, which gets transfered to the flag 'comment' in PG_FLAGS.

Pseudo-random number generator

        random(0,5,.1)                  # produces a random number between 0 and 5 in increments of .1
        non_zero_random(0,5,.1) # gives a non-zero random number
        list_random(2,3,5,6,7,8,10) # produces random value from the list
        list_random(2,3, (5..8),10) # does the same thing
        SRAND(seed)     # resets the main random generator -- use very cautiously

SRAND(time) will create a different problem everytime it is called. This makes it difficult to check the answers :-).

SRAND($envir->{'inputs_ref'}->{'key'} ) will create a different problem for each login session. This is probably what is desired.

Display Macros

These macros produce different output depending on the display mode being used to show the problem on the screen, or whether the problem is being converted to TeX to produce a hard copy output.

        MODES   ( TeX =>        "Output this in TeX mode",
                  HTML =>       "output this in HTML mode",
                  HTML_tth =>   "output this in HTML_tth mode",
                  HTML_dpng =>   "output this in HTML_dpng mode",
                  Latex2HTML => "output this in Latex2HTML mode",
        TEX     (tex_version, html_version) #obsolete
        M3      (tex_version, latex2html_version, html_version) #obsolete

Display constants

        @ALPHABET               ALPHABET()                      capital letter alphabet -- ALPHABET[0] = 'A'
        $PAR                            PAR()                           paragraph character (\par or <p>)
        $BR                     BR()                            line break character
        $BRBR                   BRBR()                          line break character
        $LQ                                     LQ()                            left double quote
        $RQ                                     RQ()                            right double quote
        $BM                                     BM()                            begin math
        $EM                                     EM()                            end math
        $BDM                            BDM()                           begin display math
        $EDM                            EDM()                           end display math
        $LTS                            LTS()                           strictly less than
        $GTS                            GTS()                           strictly greater than
        $LTE                            LTE()                           less than or equal
        $GTE                            GTE()                           greater than or equal
        $BEGIN_ONE_COLUMN       BEGIN_ONE_COLUMN()      begin one-column mode
        $END_ONE_COLUMN         END_ONE_COLUMN()        end one-column mode
        $SOL                            SOLUTION_HEADING()      solution headline
        $SOLUTION                       SOLUTION_HEADING()      solution headline
        $HINT                           HINT_HEADING()          hint headline
        $US                                     US()                            underscore character
        $SPACE                          SPACE()                         space character (tex and latex only)
        $NBSP                           NBSP()                          non breaking space character
        $NDASH                          NDASH()                         en dash character
        $MDASH                          MDASH()                         em dash character
        $BLABEL                         BLABEL()                        begin label (for input)
        $ELABEL                         ELABEL()                        end label (for input)
        $BBOLD                          BBOLD()                         begin bold typeface
        $EBOLD                          EBOLD()                         end bold typeface
        $BITALIC                BITALIC()                       begin italic typeface
        $EITALIC                EITALIC()                       end italic typeface
        $BUL                            BUL()                           begin underlined type
        $EUL                            EUL()                           end underlined type
        $BCENTER                BCENTER()               begin centered environment
        $ECENTER                ECENTER()                       end centered environment
        $HR                                     HR()                            horizontal rule
        $LBRACE                         LBRACE()                        left brace
        $LB                                     LB ()                           left brace
        $RBRACE                         RBRACE()                        right brace
        $RB                                     RB ()                           right brace
        $DOLLAR                         DOLLAR()                        a dollar sign
        $PERCENT                        PERCENT()                       a percent sign
        $CARET                          CARET()                         a caret sign
        $PI                                     PI()                            the number pi
        $E                                      E()                                     the number e

TEXT macros


This is the simplest way to print text from a problem. The strings in the array @text are concatenated with spaces between them and printed out in the text of the problem. The text is not processed in any other way. TEXT is defined in


This is the most common way to enter text into the problem. All of the text between BEGIN_TEXT and END_TEXT is processed by the EV3 macro described below and then printed using the TEXT command. The two key words must appear on lines by themselves. The preprocessing that makes this construction work is done in See EV3 below for details on the processing.

Evaluation macros


        TEXT(EV3("This is a formulat \( \int_0^5 x^2 \, dx \) ");
                        text stuff...

The BEGIN_TEXT/END_TEXT construction is translated into the construction above by END_TEXT must appear on a line by itself and be left justified. (The << construction is known as a "here document" in UNIX and in PERL.)

The single quotes around END_TEXT mean that no automatic interpolation of variables takes place in the text. Using EV3 with strings which have been evaluated by double quotes may lead to unexpected results.

The evaluation macro E3 first evaluates perl code inside the braces: \{ code \}. Any perl statment can be put inside the braces. The result of the evaluation (i.e. the last statement evaluated) replaces the \{ code \} construction.

Next interpolation of all variables (e.g. $var or @array ) is performed.

Then mathematical formulas in TeX are evaluated within the \( tex math mode \) and \[ tex display math mode \] constructions, in that order:



Prevents equations generated in "image mode" from being cached. This can be useful for debugging. It has no effect in the other modes.


        addToTeXPreamble("\newcommand{\myVec}[1]{\vec{#1}} ");
Defines C<\myVec > for all the equations in the file. You can change the vector notation for an entire PG question
by changing just this line.

If you place this macro in remember to use double backslashes because it is a .pl file. In .pg files use single backslashes. This is in accordance with the usual rules for backslash in PG.

For the moment this change only works in image mode. It does not work in jsMath or MathJax mode. Stay tuned.

Adding this command

to TeX(hardcopy) portion of the ( or to the
for each homework set will take care of the TeX hardcopy version

You can also modify the TexPreamble file in webwork2/conf/snippets to set the definition of \myVec for hardcopy for the entire site.

There are ways you can use course.conf to allow course by course modification by choosing different TeXPreamble files for different courses


        FEQ($string);   # processes and outputs the string

The mathematical formulas are run through the macro FEQ (Format EQuations) which performs several substitutions (see below). In HTML_tth mode the resulting code is processed by tth to obtain an HTML version of the formula. (In the future processing by WebEQ may be added here as another option.) The Latex2HTML mode does nothing at this stage; it creates the entire problem before running it through TeX and creating the GIF images of the equations.

The resulting string is output (and usually fed into TEXT to be printed in the problem).

                $string2 = FEQ($string1);

This is a filter which is used to format equations by EV2 and EV3, but can also be used on its own. It is best understood with an example.

                $string1 = "${a}x^2 + ${b}x + {$c:%.1f}"; $a = 3;, $b = -2; $c = -7.345;

when interpolated becomes:

                $string1 = '3x^2 + -2x + {-7.345:%0.1f}

FEQ first changes the number of decimal places displayed, so that the last term becomes -7.3 Then it removes the extraneous plus and minus signs, so that the final result is what you want:

                $string2 = '3x^2 - 2x -7.3';

(The %0.1f construction is the same formatting convention used by Perl and nearly identical to the one used by the C printf statement. Some common usage: %0.3f 3 decimal places, fixed notation; %0.3e 3 significant figures exponential notation; %0.3g uses either fixed or exponential notation depending on the size of the number.)

Two additional legacy formatting constructions are also supported:

!{$c:%0.3f} will give a number with 3 decimal places and a negative sign if the number is negative, no sign if the number is positive. Since this is identical to the behavior of {$c:%0.3f} the use of this syntax is depricated.

?{$c:%0.3f} determines the sign and prints it whether the number is positive or negative. You can use this to force an expression such as +5.456.


                        text stuff...

This is a precursor to EV3. In this case the constants are interpolated first, before the evaluation of the \{ ...code...\} construct. This can lead to unexpected results. For example \{ join(" ", @text) \} with @text = ("Hello","World"); becomes, after interpolation, \{ join(" ",Hello World) \} which then causes an error when evaluated because Hello is a bare word. EV2 can still be useful if you allow for this, and in particular it works on double quoted strings, which lead to unexpected results with EV3. Using single quoted strings with EV2 may lead to unexpected results.

The unexpected results have to do with the number of times backslashed constructions have to be escaped. It is quite messy. For more details get a good Perl book and then read the code. :-)


        #  New version of EV3 that allows `...` and ``...`` to insert TeX produced
        #  by the new Parser (in math and display modes).
        #  Format:  EV3P(string,...);
        #           EV3P({options},string,...);
        #           `x^2/5` will become \(\frac{x^2}{5}\) and then rendered for hardcopy or screen output
        #  where options can include:
        #    processCommands => 0 or 1     Indicates if the student's answer will
        #                                  be allowed to process \{...\}.
        #                                    Default: 1
        #    processVariables => 0 1       Indicates whether variable substitution
        #                                  should be performed on the student's
        #                                  answer.
        #                                    Default: 1
        #    processMath => 0 or 1         Indicates whether \(...\), \[...\],
        #                                  `...` and ``...`` will be processed
        #                                  in the student's answer.
        #                                    Default: 1
        #    processParser => 0 or 1       Indicates if `...` and ``...`` should
        #                                  be processed when math is being
        #                                  processed.
        #                                    Default: 1
        #    fixDollars => 0 or 1          Specifies whether dollar signs not followed
        #                                  by a letter should be replaced by ${DOLLAR}
        #                                  prior to variable substitution (to prevent
        #                                  accidental substitution of strange Perl
        #                                  values).
        #                                    Default: 1

Formatting macros

        beginproblem()  # generates text listing number and the point value of
                        # the problem. It will also print the file name containing
                        # the problem for users listed in the PRINT_FILE_NAMES_FOR PG_environment
                        # variable.
        OL(@array)      # formats the array as an Ordered List ( <OL> </OL> ) enumerated by letters.
                                        # See BeginList()  and EndList in for a more powerful version
                                        # of this macro.
        knowlLink($display_text, url => $url,value =>'' )
                        # Places a reference to a knowl for the URL with the specified text in the problem.
                        # A common usage is \{ 'for help', url =>knowlLink(alias('prob1_help.html') \} )
                        # where alias finds the full address of the prob1_help.html file in the same directory
                        # as the problem file
        knowlLink($display_text,  url => '', value = <<EOF );  # this starts a here document that ends at EOF (left justified)
                        help text goes here .....
                        # This version of the knowl reference facilitates immediate reference to a HERE document 
                        # The function should be called either with value specified (immediate reference) or 
                        # with url specified in which case the revealed text is taken from the URL $url.
                        # The $display_text is always visible and is clicked to see the contents of the knowl.
        htmlLink($url, $text)
                        # Places a reference to the URL with the specified text in the problem.
                        # A common usage is \{ htmlLink(alias('prob1_help.html') \}, 'for help')
                        # where alias finds the full address of the prob1_help.html file in the same directory
                        # as the problem file
        iframe($url, height=>'', width=>'', id=>'', name=>'' )
                        # insert the web page referenced by $url in a space defined by height and width
                        # if the webpage contains a form then this must be inserted between
                        # BEGIN_POST_HEADER_TEXT/END_POST_HEADER_TEXT  to avoid having one 
                        # form(from the webpage) inside another (the defining form for the problem
A wide variety of google widgets, youtube videos, and other online resources can be imbedded using this macro. In HTML mode it creates an iframe, in TeX mode it prints the url.
        appletLink( { name => "xFunctions", 
                      codebase => '',    # use this to specify the complete url
                                         # otherwise libraries specified in global.conf are searched
                      archive  => '', # name the archive containing code (.jar files go here also)
                      code     => 'xFunctionsLauncher.class',  
                      width    => 100,
                      height   => 14,
                      params   => { param1 =>value1, param2 => value2},
        helpLink($type)     allows site specific help. specified in global.conf or course.conf
                       The parameter localHelpURL  must be defined in the environment
                       and is set by default to webwork2/htdocs/helpFiles
                       Standard helpFile types
                      deprecated coding method
                                        appletLink      ($url, $parameters)
                        # For example
                        # appletLink(q!  archive="http: //"
                                        code="xFunctionsLauncher.class"  width=100 height=14!,
                        " parameter text goes here")
                        # will link to xFunctions.
        low level:
        spf($number, $format)   # prints the number with the given format
        sspf($number, $format)  # prints the number with the given format, always including a sign.
        nicestring($coefficients, $terms) # print a linear combinations of terms using coefficients
        nicestring($coefficients) # uses the coefficients to make a polynomial
                        # For example
                        # nicestring([1,-2, 0]) produces 'x^2-2x'
                        # nicestring([2,0,-1],['', 't', 't^2']) produces '2-t^2'
        protect_underbar($string) # protects the underbar (class_name) in strings which may have to pass through TeX.

Sorting and other list macros

        lex_sort(@list);   # outputs list in lexigraphic (alphabetical) order
        num_sort(@list);   # outputs list in numerical order
        uniq( @list);      # outputs a list with no duplicates.  Order is unspecified.
        PGsort( \&sort_subroutine, @list);
        # &sort_subroutine defines order. It's output must be 1 or 0 (true or false)

Macros for handling tables

        begintable( number_of_columns_in_table)

Example of useage:

                This problem tests calculating new functions from old ones:$BR
                From the table below calculate the quantities asked for:$BR
                \{row(" \(x\) ",@firstrow)\}
                \{row(" \(f(x)\) ", @secondrow)\}
                \{row(" \(g(x)\) ", @thirdrow)\}
                \{row(" \(f'(x)\) ", @fourthrow)\}
                \{row(" \(g'(x)\) ", @fifthrow)\}
         (The arrays contain numbers which are placed in the table.)

Macros for displaying static images

        $string = image($image, width => 100, height => 100, tex_size => 800)
        $string = image($image, width => 100, height => 100, extra_html_tags => 'align="middle"', tex_size => 800)
        $string = image([$image1, $image2], width => 100, height => 100, tex_size => 800)
        $string = caption($string);
        $string = imageRow([$image1, $image2 ], [$caption1, $caption2]);
                 # produces a complete table with rows of pictures.