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Add two more problem technique sample problems.
These are both problems from https://wiki.openwebwork.org/wiki/Problem_Techniques that demonstrate valid and current techniques in problems that were not added before for some reason. Add a `NamedAnswerRules.pg` problem that demonstrates how to use named answer rules to add buttons to the MathQuill toolbar for the named rule. This is an updated version of https://wiki.openwebwork.org/wiki/NamedAnswerRules. With PG 2.21 the way to do so is changing. So this is needed to demonstrate the new way to do it. Add an `AskSage.pl` problem that demonstrates how to use the `AskSage` method to send a request to a Sage cell server. This is an updated version of https://wiki.openwebwork.org/wiki/AskSage. Note that this version of the problem depends on the changes in #1399. Also note that without #1399 there is no hope for the `AskSage` method in general (so lets get that merged).
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‎tutorial/sample-problems/ProblemTechniques/AskSage.pg‎

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## DESCRIPTION
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## Make a call to a Sage cell server from within a problem.
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## ENDDESCRIPTION
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## DBsubject(WeBWorK)
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## DBchapter(WeBWorK tutorial)
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## DBsection(Problem Techniques)
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## Date(06/18/2026)
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## Institution(Missouri Western State University)
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## Author(Glenn Rice)
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## MO(1)
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## KEYWORDS('matrices', 'AskSage')
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#:% name = AskSage
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#:% type = technique
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#:% categories = [matrices]
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#:% section = preamble
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DOCUMENT();
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loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');
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#:% section = setup
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#: Determine a random number of rows, columns, and rank for the random matrix
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#: that will be generated by Sage.
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#:
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#: Send the code to generate the random matrix and its reduced row echelon form
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#: to the Sage cell service by calling the `AskSage` method. The first argument
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#: to the `AskSage` method must be the code for Sage to evaluate. The results
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#: are saved in keys of the `WEBWORK` dictionary. This is a special variable
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#: that the `AskSage` method looks for in the returned result and JSON decodes.
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#: Use this to save the data that is needed for the problem. The second optional
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#: argument is a reference to a hash of options. Generally, the only option is
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#: the `seed`. This can be used to pass the problem seed to Sage so that any
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#: random calls it makes also use that seed.
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#:
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#: After the `AskSage` method is returned check to see if the call failed with
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#: the `sageReturnedFail` method. If that is true, then the Sage cell server
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#: query failed. In that case set fallback values for the variables needed in
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#: the problem so that a workable problem is rendered in this case. If the call
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#: succeeded the the Sage `WEBWORK` dictionary will be decoded into the
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#: `webwork` hash key of the reply.
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#:
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#: Note that by default `AskSage` queries the public Sage cell service at
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#: https://sagecell.sagemath.org/service. However, that site no longer accepts
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#: public service requests. The service endpoint has been shut down due to
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#: security concerns. Thus the `AskSage` method will always fail with that URL.
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#: To fix this the WeBWorK administrator of your server can set up a local Sage
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#: cell service and configure `AskSage` to use that.
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Context('Matrix');
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my $rows = random(3, 4);
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my $columns = random(4, 5);
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my $rank = random(2, 3);
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$sageReply = AskSage(<<"END_CODE", { seed => $problemSeed });
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WEBWORK['M'] = random_matrix(
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QQ, $rows, $columns, algorithm = 'echelonizable', rank = $rank
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).rows()
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WEBWORK['RREF'] = matrix(QQ, WEBWORK['M']).rref().rows()
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END_CODE
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if (sageReturnedFail($sageReply)) {
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# Fallback values for $M and $RREF in case the AskSage call fails.
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$M = Matrix([ [ -4, 8, -12, 15 ], [ 5, -10, 15, -19 ], [ 2, -4, 6, -5 ] ]);
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$RREF = Matrix([ [ 1, -2, 3, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 0, 0 ] ]);
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} else {
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$M = Matrix($sageReply->{webwork}{M});
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$RREF = Matrix($sageReply->{webwork}{RREF});
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}
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#:% section = statement
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BEGIN_PGML
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Give the reduced row echelon form of the following matrix.
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[```[$M]```]
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The reduced row echelon form is
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[_]*{$RREF}
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END_PGML
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#:% section = solution
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BEGIN_PGML_SOLUTION
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Solution explanation goes here.
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END_PGML_SOLUTION
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ENDDOCUMENT();

‎tutorial/sample-problems/ProblemTechniques/NamedAnswerRules.pg‎

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## DESCRIPTION
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## Add buttons to the MathQuill toolbar for a particular
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## answer using a named answer rule.
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## ENDDESCRIPTION
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## DBsubject(WeBWorK)
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## DBchapter(WeBWorK tutorial)
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## DBsection(Problem Techniques)
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## Date(06/17/2026)
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## Institution(Missouri Western State University)
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## Author(Glenn Rice)
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## MO(1)
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## KEYWORDS('inequalities')
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#:% name = Named answer rules
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#:% type = technique
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#:% categories = [equations, interval]
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#:% section = preamble
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#: Load the PODLINK('parserLinearInequality.pl') macro so that a linear
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#: inequality answer can be used.
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DOCUMENT();
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loadMacros(
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'PGstandard.pl', 'PGML.pl',
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'parserLinearInequality.pl', 'PGcourse.pl'
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);
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#:% section = setup
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#: Generate random variables `$a`, `$b`, and `$c` to use for coefficients in the
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#: linear inequality to be solved.
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#:
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#: Then define a linear inequality answer in the `LinearInequality` context,
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#: and an interval answer in the `Interval` context.
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$a = random(2, 9);
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$b = random(2, 9);
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$c = random(2, 9);
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Context('LinearInequality');
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$inequalityAnswer = LinearInequality("x <= $a");
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Context('Interval');
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$intervalAnswer = Interval("(-inf, $a]");
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#:% section = statement
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#: Ask the student to solve the inequality, and give the answer as both a linear
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#: inequality and an interval.
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#:
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#: A named answer is needed for the linear inequality answer in order to add
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#: toolbar buttons to the MathQuill toolbar for that answer. Do this with the
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#: third option for a PGML answer by calling the `NEW_ANS_NAME` function and
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#: assigning that to the variable `$inequalityAnswerName`. Never use hard coded
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#: made up answer names in problems. Always obtain an answer name using the
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#: `NEW_ANS_NAME` method. Problems that use hard coded made up answer names will
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#: not work correctly in many situations. The interval answer does not need to
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#: be named.
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#:
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#: Finally inject a `script` tag to the end of the problem text. It is important
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#: that this JavaScript code be executed after the PG MathQuill JavaScript so
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#: that the `window.answerQuills` variable will be defined. One way to
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#: accomplish this is by executing the code in the `DOMContentLoaded` event.
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#:
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#: Add the buttons to the toolbar for the linear inequality answer by calling
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#: the `addToolbarButtons` function of the `options` object for the `mathField`
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#: associated to the `$inequalityAnswerName` answer quill. The first argument
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#: for the `addToolbarButtons` function can be either a single toolbar button
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#: definition or an array of toolbar button definitions (see below for a
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#: description of a toolbar button definition). The second argument can be
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#: either a number which is the zero based position at which the new toolbar
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#: buttons will be inserted, or the `id` of an existing toolbar button after
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#: which the new toolbar buttons will be inserted (note the `id`s of the default
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#: toolbar buttons in order are `frac`, `abs`, `sqrt`, `nthroot`, `exponent`,
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#: `infty`, `pi`, `vert`, `cup`, and `text`). Note that the second argument can
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#: be a negative number which counts backward from the end. In fact the second
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#: argument can be entirely omitted. In that case a position of -1 is used which
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#: will insert the new button before the last toolbar button (initially the text
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#: button).
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#:
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#: A toolbar button is defined as a JavaScript object with the four properties
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#: `id`, `latex`, `tooltip`, and `icon`.
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#:
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#: - The `id` can be any string, but should not have the same `id` of another
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#: toolbar button.
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#: - The `latex` for a button is the LaTeX code that will be inserted into the
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#: MathQuill input when the toolbar button is pressed. Make sure that
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#: backslashes are escaped with another backslash.
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#: - The `tooltip` is text that will be shown in a tooltip when the button on
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#: the toolbar has keyboard focus or is hovered over by the mouse cursor. Note
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#: that the toolbar text should include a brief textual description of what
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#: will be inserted when the button is pressed, and in parentheses after that
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#: the keyboard sequence that can be typed into the MathQuill input to insert
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#: the same thing that pressing the button will insert.
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#: - The `icon` is the LaTeX code for icon that will be shown in a static
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#: MathQuill field on the toolbar button. Make sure that backslashes are
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#: escaped with another backslash.
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#:
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#: A button can also be removed from the toolbar for an answer using the
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#: `removeToolbarButtons` function. The only argument for this function is a
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#: string `id` or array of string `id`s for existing toolbar buttons to be
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#: removed. For example,
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#: `answerQuills.$inequalityAnswerName.mathField.options.removeToolbarButtons('cup');`
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#: would remove the union button from the toolbar, and
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#: `answerQuills.$inequalityAnswerName.mathField.options.removeToolbarButtons([ 'pi', 'cup' ]);`
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#: would remove the pi and union buttons from the toolbar. It is important to
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#: note that removing a toolbar button does not prevent a student from entering
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#: what the toolbar button would insert. It merely removes the toolbar button.
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#: For example, if the `cup` button is removed, a student could still type
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#: "union" to enter a union symbol.
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BEGIN_PGML
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Solve the following inequality.
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>>[``[$b]x + [$c] \leq [$a * $b + $c]``]<<
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Express the answer as an inequality:
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[_]{$inequalityAnswer}{15}{ $inequalityAnswerName = NEW_ANS_NAME() }.
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Express the answer in interval notation: [_]{$intervalAnswer}{15}
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END_PGML
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TEXT(MODES(TeX => '', HTML => <<"END_SCRIPT"));
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<script>
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window.addEventListener('DOMContentLoaded', () => {
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if (!window.answerQuills) return;
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answerQuills.$inequalityAnswerName.mathField.options.addToolbarButtons(
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[
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{
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id: 'leq',
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latex: '\\leq',
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tooltip: 'less than or equal (<=)',
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icon: '\\leq'
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},
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{
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id: 'geq',
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latex: '\\geq',
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tooltip: 'greater than or equal (>=)',
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icon: '\\geq'
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}
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],
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9
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);
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});
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</script>
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END_SCRIPT
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#:% section = solution
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BEGIN_PGML_SOLUTION
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Solution explanation goes here.
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END_PGML_SOLUTION
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ENDDOCUMENT();

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