** Using WeBWorK **

########### BEGIN CUSTOM MACRO FILE ##########

# save as parserCustomization.pl

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

# WeBWorK Online Homework Delivery System

# Copyright � 2000-2007 The WeBWorK Project, http://openwebwork.sf.net/

# $CVSHeader$

#

# This program is free software; you can redistribute it and/or modify it under

# the terms of either: (a) the GNU General Public License as published by the

# Free Software Foundation; either version 2, or (at your option) any later

# version, or (b) the "Artistic License" which comes with this package.

#

# This program is distributed in the hope that it will be useful, but WITHOUT

# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS

# FOR A PARTICULAR PURPOSE. See either the GNU General Public License or the

# Artistic License for more details.

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

=head1 NAME

parserCustomization.pl - Placeholder for site/course-local customization file.

=head1 DESCRIPTION

Copy this file to your course templates directory and put any

customization for the Parser that you want for your course

here. For example, you can make vectors display using

ijk notation (and force students to use it for entering

vectors) by using:

$context{Vector} = Parser::Context->getCopy("Vector");

$context{Vector}->flags->set(ijk=>1);

$context{Vector}->parens->remove('<');

To allow vectors to be entered with parens (and displayed with

parens) rather than angle-brakets, use

$context{Vector} = Parser::Context->getCopy("Vector");

$context{Vector}->{cmpDefaults}{Vector} = {promotePoints => 1};

$context{Vector}->lists->set(Vector=>{open=>'(', close=>')'});

(This actually just turns points into vectors in the answer checker

for vectors, and displays vectors using parens rather than angle

brackets. The student is really still entering what MathObjects

thinks is a point, but since points get promoted automatically, that

should work. But if a problem checks if a student's value is actually

a Vector, that will not be true.)

=cut

sub _parserCustomization_init {}

#$context{Vector} = Parser::Context->getCopy("Vector");

#$context{Vector}->flags->set(ijk=>1);

#$context{Vector}->parens->remove('<');

# See http://webwork.maa.org/wiki/Course-Wide_Customizations

# See https://raw.githubusercontent.com/openwebwork/pg/master/macros/parserCustomization.pl

$context{Vector} = Parser::Context->getCopy("Vector");

$context{Vector}->lists->set(Vector=>{open=>'(', close=>')'});

$context{Vector}->parens->set('('=>{type=>'Vector'});

$context{Vector}->parens->remove('<');

1;

########### END CUSTOM MACRO FILE ############

Well, yes, experience is certainly one way. The other is by the name (e.g., "Vector" for when you are using vectors, "Interval" when you are using intervals, etc.). You can also look at the list of files starting with "context" in the pg/macros directory. The documentation at the top of the files explain what they are for. You can also look at the documentation in the PG POD documentation, though it seems not to be as up-to-date as it should be (not all the files are listed).

Can you be more specific about what you are trying to accomplish? Do you mean that you want the vectors to be displayed using ijk-notation? Or do you want to allow students to enter it that way (they can enter it either way by default). Or do you want to force them to enter it that way? Or do you want to write your PG code using it?

These are all different, and require different techniques. You should not include two versions in your program, as such customizations should be done through PGcourse.pl or parserCustomization.pl in general.

Remember, MathObjects is not a CAS, and its reduction rules are not all that extensive. In your problem, you have 9x^2 in your formula, and so the derivative formulas make this be 9*d/dx(x^2), which becomes 9*(2*x). The reduction rules don't include ones that involve more than one operation, in general, so this won't be reduced, while (9*2)*x would.

The output for 9*(2*x) turns out to be 9*2*x as the parentheses don't change the result, and it turns out that you can take advantage of that. You could do

  $fx=Formula($f->D('x')->string)->reduce;

First, you don't need to load parserCustomization.pl (and shouldn't) since it is loaded automatically when MathObjects.pl is loaded. You should, however, load PGcourse.pl as the last macro file. This serves a similar function to parserCustomization.pl but will work even with problems that don't load MathObjects.pl.

Second, in terms of the values of $a and $b, you could use non_zero_random() rather than random(). This would prevent either variable from being zero (whereas yours allows one or the other to be zero).

If you do use the if-then, you don't need the extra parentheses around the equality checks. You can do

if ($a == 0 && $b == 0) {$b = 2}

$fx = $f->D('x')->reduce;

Finally, you may want to make your answer blanks a like wider, as vectors can take some space to type, especially if students are going to include computations as part of their answers (as they often do for this type of problem).

The rest looks good!