I author WeBWorK problems internally for my high school's Precalculus and Calculus curricula. I am currently putting some time into creating a library of macros (in /opt/webwork/pg/macros) to ease authoring of common question types. One such class of problems is review on factoring (not just polynomials), and the library of factoring techniques on the wiki is awkward; I have no interest in creating a separate answer blank for each factor.

Instead, I have created a subroutine which isolates all parenthesized expressions. I have several answer checkers which use this subroutine. It works fine when I include its definition in problem code, but it ceases to work when in a macro. After a bit of poking around, I realized that the following regex is creating the issue:

/~~((?:[^)(]+|(?R))*+~~)/g

When included in the macro, the subroutine always returns an empty array because this regex matches nothing. My guess is that the recursion element of the Regex is not supported in a macro. My question is this: is it possible to correct this and allow the execution of this regex in a macro file? Or am I doomed to having to copy-paste this code into every problem file that needs it?

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Here is an MWE if it helps. (After pasting it, I realized that I could make parentheticals() slightly more efficient, so please avoid commenting on that element - I'll deal with it later once this is sorted.) The goal is to put parentheticals() and $factorChecker in the macro.

DOCUMENT();

loadMacros(

"PGstandard.pl",

"PGML.pl",

"MathObjects.pl",

"PGcourse.pl");

TEXT(beginproblem());

sub parentheticals {

# Purpose: A subroutine to return an array with all parenthetical expressions of all levels of nesting. It seems regex isn't up to this task by itself.

# Requires: A text string which contains a WeBWorK formula (function)

# Returns: An array containing every expression contained by matched parentheses, with nesting

my ($formula) = @_;

my @return = @temp_old = @temp_new = @temp_parens = ();

my @parens = $formula =~ /~~((?:[^)(]+|(?R))*+~~)/g;

# This regex keeps parentheses in first and final positions, so remove them

unless( scalar @parens > 0 ){ return (); }

foreach(@parens){ push(@temp_new, substr $_, 1, -1); }

push(@return, @temp_new);

@temp_old = @temp_new;

@temp_new = ();

# Now recurse through the entries in @temp, collecting parenthetical expressions

until(scalar @parens == 0){

@parens = ();

foreach(@temp_old){

@temp_parens = $_ =~ /~~((?:[^)(]+|(?R))*+~~)/g;

push(@parens, @temp_parens);

foreach(@parens){ push(@temp_new, substr $_, 1, -1); }

}

push(@return, @temp_new);

@temp_old = @temp_new;

@temp_new = ();

}

return @return;

}

$factorChecker = sub {

# Purpose: Custom answer checker to make sure that a response matches a given function, as well as containing a set of specific parenthecized factors.

# Requires: parentheticals(), a list of parenthetical factors to be passed as an arg

# Usage: $ans = Formula("")->cmp(bypass_equivalence_test => 1, checker => $factorChecker, factors => \@factors);

# Note: Factors without addition/subtraction should NOT be included in the list of factors, as they are not necessarily parenthesized

my ($correct,$student,$ansHash) = @_;

return 0 if $ansHash->{isPreview};

my $cor = Formula($correct);

my $ans = Formula($student);

my $fac = $ansHash->{factors};

my @factors = @{$$fac};

my $text = $ansHash->{original_student_ans};

unless($ans == $cor){ return 0; }

# Check whether factors are present

my @parens = parentheticals($text);

foreach $factor (@factors){

$factor_present = 0;

foreach(@parens){

if(Formula($_) == Formula($factor) ||

Formula($_) == -1*Formula($factor) )

{ $factor_present = 1; } }

unless($factor_present == 1){

Value->Error("Your expression is equivalent to the original function, but you have not factored fully.");

return 0; }

}

return 1;

};

Context("Numeric");

@factors = ("x-1","x+1");

$answer = Formula("(x-1)*(x+1)")->cmp(bypass_equivalence_test => 1, checker => $factorChecker, factors => \@factors);

######################################################################

BEGIN_PGML

Factor this expression: [`x^2-1=`][____________________]{$answer}

END_PGML

######################################################################

ENDDOCUMENT();