Modifying Contexts (advanced)

Advanced Context Modifications

The Introduction to Contexts describes how to make basic modifications to a Context's variables, constants, strings, flags, functions, operators, and reduction rules. Here we will describe more advanced modifications and techniques involving the Context.

Number Formats

Real numbers are stored using a format that retains about 16 or 17 significant digits, making computations very accurate in most situations. When a number is displayed, you probably don't want to see all 17 digits (that would make a vector in three-space take up around 35 characters, for example). To make answers easier to read, MathObjects usually display only 6 significant digits. You can change the format used, however, to suit your needs. The format is determined by the Context()->{format}{number}, which is a printf-style string indicating how real numbers should be formatted for display.

The format always should begin with % and end with one of f, e, or g, possibly followed by #. Here, f means fixed-point notation (e.g. 452.116), e means exponential notation (e.g, 3.578E-5), and g means use the form most appropriate for the magnitude of the number. Between the % and the letter you can (optionally) include .n where n is the number of decimal digits to use for the number. If the format ends in #, then trailing zeros are removed after the number is formatted. (More sophisticated formats are possible, but this describes the basics.)

   Context()->{format}{number} = "%.2f";    # format numbers using 2-place decimals (e.g., for currency values).
   Context()->{format}{number} = "%.4f#";   # format numbers using 4-place decimals, but remove trailing zeros, if any.

The default format is "%g".

The Context also includes information about what should count as a number when an answer is parsed. There are two patterns for this, a signed number and an unsigned number. The latter is what is used in parsing numbers (and the sign is treated as unary minus); former is used in the Value::matchNumber() function. These are stored in the Context()->{pattern} hash; the default values are:

     Context()->{pattern}{number} = '(?:\d+(?:\.\d*)?|\.\d+)(?:E[-+]?\d+)?';
     Context()->{pattern}{signedNumber} = '[-+]?(?:\d+(?:\.\d*)?|\.\d+)(?:E[-+]?\d+)?';

These are fairly complicated regular expressions that match the usual fixe-point and exponential notation for numbers in WeBWorK. It is possible to change these patterns to handle things like commas instead of decimals for European usage, or to allow commas every three digits. Note, however, that you would need to include a NumberCheck routine that would translate the special format into the required internal format. For example, this allows you to enter numbers as hexadecimal values:

   #
   #  Numbers in hexadecimal
   #
   Context()->{pattern}{number} = '[0-9A-F]+'; 
   Context()->{pattern}{signedNumber = '[-+]?[0-9A-F]+';
   Context()->flags->set(NumberCheck => sub {
     my $self = shift;                              # the Number object
     $self->{value} = hex($self->{value_string});   # convert hex to decimal via perl hex() function
     $self->{isOne} = ($self->{value} == 1);        # set marker indicating if the value is 1
     $self->{isZero} = ($self->{value} == 0);       # set marker indicating if the value is 0
   });
   Context()->update;

Note that after changing the pattern you must call Context()->update to remake the tokenization patterns used by the Context.

Here is an example that lets you use commas in your numbers:

   #
   # Allow commas every three digits in numbers
   #
   Context()->{pattern}{number} = '(:?(:?\d{1,3}(:?\,\d{3})+|\d+)(?:\.\d*)?|\.\d+)(?:E[-+]?\d+)?';
   Context()->{pattern}{signedNumber} = '[-+]?(:?(:?\d{1,3}(:?\,\d{3})+|\d+)(?:\.\d*)?|\.\d+)(?:E[-+]?\d+)?';
   Context()->flags->set(NumberCheck => sub {
     my $self = shift;                              # the Number object
     my $value = $self->{value_string};             # the original string
     $value =~ s/,//g;                              # remove commas
     $self->{value} = $value + 0;                   # make sure it is converted to a number
     $self->{isOne} = ($self->{value} == 1);        # set marker indicating if the value is 1
     $self->{isZero} = ($self->{value} == 0);       # set marker indicating if the value is 0
   });
   Context()->update;

If you want to make the numbers display with commas, then you will need to subclass the Value::Real object and override the string() and TeX() methods to insert the commas again, and then tie your new class into the Context()->{value}{Real} value. For example, in addition to the changes above, you might do

   #
   #  Subclass the Value::Real class and override its string() and TeX()
   #  methods to insert commas back into the output
   #
   package my::Real;
   our @ISA = ('Value::Real');    # subclass of this Value::Real
   
   sub string {
     my $self = shift; my $x = $self->SUPER::string(@_);  # get the original string output
     my ($n,@rest) = split(/([.E])/,$x,1);                # break it into the integer part and the rest
     while ($n =~ m/[0-9]{4}(,|$)/)                       # add commas as needed
       {$n =~ s/([0-9])([0-9]{3})(,|$)/$1,$2$3/}
     return join("",$n,@rest);                            # return the final string
   }
   
   sub TeX {
     my $self = shift;
     my $n = $self->SUPER::TeX(@_);     # original TeX uses string(), so commas are already there
     $n =~ s/,/{,}/g;                   # just make sure they have the correct spacing
     return $n;
   }
   
   package main;    # end of package my::Real;
   
   Context()->{value}{Real} = "my::Real";    # make the Context use my::Real rather then Value::Real
   Context()->{format}{number} = "%f#";      # format using "f" rather than "g", so no exponential notation

This could be put into a separate macro file that you could load into your problems whenever it is needed. See Creating Custom Contexts for details.

Lists and Delimiters

This section and the next section 'Parens' are closely related. WebWork considers the following objects to be types of lists:

• Point,
• Vector,
• Matrix,
• List,
• Interval,
• Set,
• Union,
• AbsoluteValue.

The most common modification made to lists are to which type of parentheses is used to enclose them. The purpose of the following description is meant to make you aware of how the various parenthesis types are used by default.

• Points by default look like e.g. (3,4).
• Vectors by default look like e.g., <3,4,5>.
• Matrix objects by default look like ~[[2,3],[2,3]].
• A list by default looks like 3, 4, 5. An interval by default looks like (0,9), 0,9), etc.
• A set by default looks like {3,4,5}.
• A union by default looks like (-infinity,0? U (5,7].
• Absolute value by default looks like |-5|.

Next we'll discuss how to modify the type of parentheses used with the various objects.

WebWork recognizes the full range of parentheses types, as explained above (e.g., (, <, [, { ). But by default their meanings are dependent on the context. You can change how this works.

For example, this command will cause Vector objects to look like (3,4,5) instead of <3,4,5>:

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

More about Constants

The list of predefined constants is e, pi, i, j, k. The constant i denotes sqrt(-1) in Context("Complex"), denotes the vector <1,0> in Context("Vector2D"), and denotes the vector <1,0,0> in Context("Vector"), Context("Matrix"), and Context("Point"). The constant i is undefined outside of those contexts. The constants j and k are <0,1,0> and <0,0,1>, respectively, in Context("Vector") and Context("Matrix"). The constant j is <0,1> in Context("Vector2D"), and k is undefined there. The constants i, j and k are undefined outside of the contexts described above.

Context()->constants->set(i => {TeX=>'\boldsymbol{i}', perl=>'i'});
Context()->constants->remove("k");
Context()->constants->set(R => {TeX => '{\bf R}'});

See also

• Introduction to Contexts
• Context flags
• Reduction rules for MathObject Formulas
• Context Operator Table
• Common Contexts