Introduction to Contexts
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[[Category:MathObjects]]  [[Category:MathObjects]]  
[[Category:AIMWeBWorK Working Groups]]  [[Category:AIMWeBWorK Working Groups]] 
Revision as of 09:24, 19 August 2008
Contents 
Contexts
The Context of a problem determines how variables are interpreted, sets the default variable(s), determines default constants available in the problem, and sets appropriate default system values such as the tolerance for student errors, etc. It also adjusts the error messages for student responses so that, for example, "4i +5j +6k" will result in a syntax error message in "Numeric" context but not in "Vector" context.
List of Basic Contexts
Usually we select a Context by including
Context("name");
at the top of a problem file, where name
is one of:

Numeric
(variable x, no complex numbers, points, etc.)  this is the default context 
Complex
(variable z, i = \sqrt{1}, no points, etc.) 
Point
(another name for Vector context, but angle brackets are not allowed) 
Vector
(variables x, y, z, angle brackets form vectors, i, j, k are unit coordinate vectors, etc.) 
Vector2D
(same as Vector, but with i and j in 2D) 
Matrix
(square brackets form matrices: [[0,1],[1,0]] ) 
Interval
(subsets of the real line: parens and brackets form intervals, finite subsets, (5,6] ,(infinity,6), {5,6} etc. )
or one of the additional Specialized contexts that are available and defined in macros. In order to use one of these additional contexts, one needs to include the macro file for the context one wishes to use, with the syntax:
loadMacros("contextLimitedPolynomials.pl");
The specific context in this case allows one to specify that only "simplified" polynomials in the form \( a_n x^n + ... + a_0 \) will be allowed as answers. Inspecting the file "contextLimitedPolynomials.pl" is one way to learn how to modify a context to meet your requirements.
Common Context methods
Producing "TeX" strings
This is the most common use of a Context method. Suppose that you have a formula such as
$f = Formula("sin(3x^2)/cos(x)");
Normally "$f" emits the string "sin(3x^2)/cos(x)"
which defines the function. However if you set
the current context to "texStrings": Context()>texStrings;
then "$f" produces the TeX string used to typeset the function:
"\frac{ \sin(3x^2) }{\cos(x) } "
In practice this means that virtually every occurence of a BEGIN_TEXT/END_TEXT block should be written as
Context()>texStrings; BEGIN_TEXT Differentiate the function \( $f\) ... ...... END_TEXT Context()>normalStrings;
This means that the "$f" is replaced by TeX code placed between the "LaTeX math" symbols \( and \) and is then transformed into a typeset representation of the formula "$f".
It is a good idea to return to "normalStrings" outside BEGIN_TEXT blocks since the normal string representation of $f may be required inside perl macros in the rest of the problem.
Context changes for Formulas
 Adding variables
 In the Numeric Context, the default variable is
x
. Use thevariables>add(y=>'Real')
method to specify additional legitimate variables and their type in the current context.
For example: 
Context()>variables>add(y=>'Real');

Context()>variables>add(y=>'Real',z=>'Real');

Context()>variables>add(z=>'Complex');
 Setting variables
 To set the variable(s) in the current Context (replacing the default variable(s)), use the
variables>are()
method, as shown in the following: 
Context()>variables>are(y=>'Real');

Context()>variables>are(y=>'Real',z=>'Real');

Context()>variables>are(z=>'Complex');
 Setting variable limits
 The limits for the variables in the Context determine the values that may be used to determine the correctness of a Formula. If a Formula is not welldefined on the default range [2,2], it may be useful to set a different range for the variable(s) in the Context:
 If the only variable in the Context is
x
,
Context()>variables>set(x=>{limits=>[1,1]});

 We can similarly set limits for several variables at once, if they have been defined in the Context:

Context()>variables>set(x=>{limits=>[1,1]},y=>{limits=>[1,1]});

Context changes for Strings
 Adding Strings to the Context
 By default there are a limited number of Strings that are predefined in the Context. In the Numeric Context (the default) these include
inf
,infinity
, andDNE
. Because they exist in the Context, students can enter these as answers without generating error messages (though, of course, the answer may be incorrect). To add other Strings to the Context, we use thestrings>add()
method:
 To add the string "Continuous" to the Context,
Context()>strings>add(Continuous=>{});
 To add the strings "True" and "T" to the Context, making "T" be an alias for "True" (so that a student could enter either "True" or "T" as an answer and have either marked correct),
Context()>strings>add(True=>{},T=>{alias=>'True'});
 And to add "True", "False" and aliases for both,
Context()>strings>add(True=>{},False=>{},T=>{alias=>'True'},F=>{alias=>'False'});
 Changing casesensitivity of Strings
 By default, WeBWorK regards String objects as being caseinsensitive. Thus if the correct answer to a problem is the String object "True", a student could respond "True" or "true" and have either answer marked correct. To change this behavior, we set the
caseSensitive
flag while adding the variable to the Context:
Context()>strings>add(True=>{caseSensitive=>1});
Other useful Context changes
 Preserving constant values in Formulas
 This technique helps to make the correct answer shown to students educationally useful.
 The answer
0.5
might be correct but it is not as enlightening assin(pi/6)
.
By default WeBWorK will reduce constant expressions that are substituted into Formulas. This is not always what we want to do. It's a somewhat subtle point, which may be easiest to consider in the context of an example.
 Consider the WeBWorK code
$f = Formula("sin(x)"); $f0 = $f>eval(x=>pi/6); displayed as: (0.5)
By evaulating the sine function at the the Real value pi/6
we obtain a real number.
$f0
is accordingly a Real value (0.5) which will be displayed as a decimal.
We can make WeBWorK display the unreduced expression sin(pi/6)
by setting the
reduceConstants
flag in the Context and
substituting a Formula for x
instead of evaluating the expression:
Context()>flags>set(reduceConstants=>0); $f = Formula("sin(x)") $f0 = $f>substitute(x=>Formula("pi/6")); displayed as: sin(pi/6)
Here the Formula for pi/6
is substituted into the function $f
. $f0
is a new Formula which when displayed appears as sin(pi/6)
not in the reduced form (0.5).
Summary: evaluate vs. substitute
 The result of
$formula>evaluate(45)
has the type obtained by evaluating the formula at 45. It is no longer
a formula, but has the type of the range of the original formula.
 The result of
$formula>substitute(45)
is still a formula, with a string representation in which eachx
has been replaced by 45.