Prompts, contexts, blanks¶

A question can have several parts, each with its own answer blank. This one asks two things about one sequence.

# One sequence, two answer blanks.

random first = integer_between(-10, 10)
random step  = nonzero_integer_between(-6, 6)
random n     = integer_between(8, 15)

let nth = first + (n - 1) * step
let sum = n * (2 * first + (n - 1) * step) / 2

synth kind on Q

start Q

Q -> "arithmetic" { kind = "arithmetic" }

prompt "An arithmetic sequence has first term [`a_1 = {first}`] and common
difference [`d = {step}`].

(a) Find [`a_{{{n}}}`]. {answer nth}

(b) Find the sum of its first [`{n}`] terms. {answer sum}"

$ rhema run prompts.rhm --count 1
 1. An arithmetic sequence has first term [`a_1 = -2`] and common
difference [`d = 1`].

(a) Find [`a_{12}`]. [___]

(b) Find the sum of its first [`12`] terms. [___]
    answers: 9; 42

Compiled, each {answer ...} becomes a WeBWorK answer blank graded on its own:

$ rhema prompts.rhm --count 1 -o -
DOCUMENT();
loadMacros("PGstandard.pl", "MathObjects.pl", "PGML.pl");
Context("Numeric");

BEGIN_PGML
An arithmetic sequence has first term [`a_1 = -2`] and common
difference [`d = 1`].

(a) Find [`a_{12}`]. [_____]{9}

(b) Find the sum of its first [`12`] terms. [_____]{42}
END_PGML
ENDDOCUMENT();

What a prompt may contain¶

A prompt is a string, and a string may run over several lines; the line breaks are kept. Inside it, braces mark the places Rhema fills in:

Everything else is passed to WeBWorK as written. Prompts are PGML, so [`...`] is mathematics and a blank line starts a new paragraph.

The doubled braces matter in LaTeX. a_{12} needs braces around 12, and n must be filled in between them, so the prompt says a_{{{n}}}: a literal {, then the value of n, then a literal }.

Inside a string only two escapes exist, \" and \\. Every other backslash is kept as it is, so LaTeX such as \cdot, \to and \neg can be written directly.

One blank or several¶

A file with a single answer uses answer, as in the earlier chapters, and the blank goes after the prompt. A file that places its blanks with {answer ...} leaves answer out; writing both is an error, because it would not be clear where the blank goes.

Contexts¶

WeBWorK grades an answer according to a context: Numeric for numbers and formulas, Complex, Interval, Vector, Matrix, PolynomialFactors for a polynomial that must be factored, Boolean for propositions. A file names the context its questions need:

context "Interval"

The default is Numeric. The compiled file selects the context, and loads the macro file a context needs (contextPolynomialFactors.pl, contextBoolean.pl) when it is one that WeBWorK does not load by default.

When the forms of one question type need different contexts, such as a polynomial to expand (Numeric) and one to factor (PolynomialFactors), the start symbol can compute the context itself, as the library's polynomial_forms.rhm does:

synth pg_context on Q

Q -> E "expand" { pg_context = "Numeric"            ... }
Q -> E "factor" { pg_context = "PolynomialFactors"  ... }

pg_context and pg_width (the width of the answer box) are reserved names: computed by the start symbol, they apply to each question separately, and the compiled document switches context between questions that need different ones. width 30 at the top level sets one width for every blank.

Next: chapter 5 asks the parts of this question separately, from the same file.