Difference between revisions of "DraggableProofs"

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(Created page with "<h2>Using the Sage Cell Server</h2> <!-- Header for these sections -- no modification needed --> <!-- 300px|thumb|right|Click to enlarge -->...")
 
 
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<h2>Using the Sage Cell Server</h2>
  
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{{historical}}
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<p style="font-size: 120%;font-weight:bold">This problem has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/Misc/DraggableProof.html a newer version of this problem]</p>
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<h2>Using Draggable Statements</h2>
   
 
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[[File:GraphicsFilename1.png|300px|thumb|right|Click to enlarge]]
  
[[File:GraphicsFilename1.png|300px|thumb|right|Click to enlarge]]
 
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-->
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UNDER CONSTRUCTION!!!
  
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<p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;">
  
<p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;">
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This PG code shows how to embed a call to the Sage Cell Server from within a problem.
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This PG code shows how develop a proof with random statements that need to go in the correct order.
 
</p>
  
</p>
  +
* PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Misc/DraggableProof_PGML.pg FortLewis/Authoring/Templates/Misc/DraggableProof_PGML.pg]
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<p style="text-align:center;">
  
<p style="text-align:center;">
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<tr valign="top">
  
<tr valign="top">
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<th> PG problem file </th>
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<th width="50%"> PG problem file </th>
 
<th> Explanation </th>
  
<th> Explanation </th>
 
</tr>
  
</tr>
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DOCUMENT();
  
DOCUMENT();
 
loadMacros(
  
loadMacros(
−
"PGstandard.pl",
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'PGstandard.pl',
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"MathObjects.pl",
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'MathObjects.pl',
−
"sage.pl",
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'PGML.pl',
  +
'draggableProof.pl',
  +
'PGcourse.pl'
 
);
  
);
  +
  +
TEXT(beginproblem());
 
</pre>
  
</pre>
   
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<td style="background-color:#ccffcc;padding:7px;">
  
<td style="background-color:#ccffcc;padding:7px;">
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<p> The sage.pl macro is not yet part of the standard WeBWorK distribution. You will need to download the macro file [[https://github.com/drjt/pg/blob/feature/SageMacro/macros/sage.pl sage.pl ]] and place it in your local macros directory for this to work.
  
  +
<p>Details of the draggableProof.pl macro can be found in [[https://webwork.maa.org/pod/pg/macros/draggableProof.html the POD]].
 
</p>
  
</p>
 
</td>
  
</td>
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<td style="background-color:#ffffdd;border:black 1px dashed;">
  
<td style="background-color:#ffffdd;border:black 1px dashed;">
 
<pre>
  
<pre>
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###############################################
  
  +
$statements = [
−
##
  
  +
'Assume \(\sqrt{2}=\frac{a}{b}\) where \(a,b\) are integers, with \(\text{gcd}(a,b)=1\) ',
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## pg initializations and regular WeBWorK code
  
  +
'\(2 = \frac{a^2}{b^2}\)',
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'\(a^2 = 2b^2\)',
  +
'if \(a^2\) is even, then \(a\) must be even',
  +
'Let \(a=2k\) for \(k\) some integer',
  +
'We can then write \( 2 = \frac{4k^2}{b^2}\) or \(b^2 = 2k^2\)',
  +
'Therefore \(b^2\) is even, so \(b\) is also even',
  +
'If \(a\) and \(b\) are both even, then the initial assumption that \(\text{gcd}(a,b)=1\) is contradicted.',
  +
'\(\sqrt{2}\) is therefore not rational.'
  +
];
   
−
$a = random(2,5,1);
  
  +
# These are extra statements that are not needed.
−  
  +
$extra = [
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$ansList = List("(-cos(pi*$a)/$a + 1/$a)");
  
  +
'Then \(a\) is odd',
  +
'\(b^2\) cannot be rational.',
  +
'therefore \(a = 2b\)'
  +
];
   
  +
$proof = DraggableProof(
  +
$statements,
  +
$extra
  +
);
 
</pre>
  
</pre>
 
</td>
  
</td>
  +
 
<td style="background-color:#ffffcc;padding:7px;">
  
<td style="background-color:#ffffcc;padding:7px;">
−
The WeBWorK set up for the problem is the same, but in addition you have
  
−
to consider how you will pass the problem parameters into Sage. For example,
  
−
if you want to pass
  
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<code>$f = (x-(-2))(x+2)(x+4)</code> it may be best to create two versions of <code>f</code>:
  
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<code>$f_raw = (x-(-2))*(x+2)*(x+4);</code> to pass to Sage and the math object
  
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<code>$f = Compute("$f_raw");</code> to use in WeBWorK.
  
 
<p>
  
<p>
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Also, you will need to store the list of correct answers in a variable named $ansList (which is also customizable).
  
  +
The <code>DraggableProof</code> function takes an arrayref of correct statements, followed (optionally) by extra statements. See the POD for more options.
 
</p>
  
</p>
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<p>
  
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Finally, if your final answer is a matrix converted to a list, then do not use extra parenthesis here. Otherwise $ansList will be a List of Lists which is probably a bad thing.
  
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</p>
  
 
</td>
  
</td>
 
</tr>
  
</tr>
   
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<!-- Initialize the Sage embedding -->
  
  +
  +
  +
<!-- Print Problem Statement -->
   
 
<tr valign="top">
  
<tr valign="top">
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<td style="background-color:#ffffdd;border:black 1px dashed;">
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<td style="background-color:#ffdddd;border:black 1px dashed;">
 
<pre>
  
<pre>
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BEGIN_PGML
   
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$SageCode = <<SAGE_CODE;
  
  +
[@ $proof->Print @]*
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  +
END_PGML
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Area = integrate(sin($a*x),x,0,pi)
  
−  
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record_answer((Area)) # leave out if you return no answer
  
−  
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SAGE_CODE
  
 
</pre>
  
</pre>
 
</td>
  
</td>
   
 
<td style="background-color:#ffcccc;padding:7px;">
  
<td style="background-color:#ffcccc;padding:7px;">
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<p>
  
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−
$SageCode = <<SAGE_CODE;
 
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</p>
  
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<p>
  
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denotes the beginning of the Sage Python code to be inserted into the WeBWorK problem. This will be paired at the end with and ending SAGE_CODE which must be left-justified. This portion will create a perl variable $SageCode which is the complete Python text.
  
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</p>
  
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<p>To share values computed inside the Sage cell back to the WeBWorK problem, create a single Sage list named "sageAnswer" (which is configurable).</p>
  
 
</td>
  
</td>
 
</tr>
  
</tr>
   
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<!-- Sage macro and options section -->
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<!-- Answer section -->
   
 
<tr valign="top">
  
<tr valign="top">
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<td style="background-color:#ffdddd;border:black 1px dashed;">
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<td style="background-color:#eeddff;border:black 1px dashed;">
 
<pre>
  
<pre>
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  +
ANS($proof->cmp);
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Sage(
  
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SageCode=>$SageCode,
  
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);
  
−  
 
</pre>
  
</pre>
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</td>
  
  +
<td style="background-color:#eeccff;padding:7px;">
−  
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<td style="background-color:#ffcccc;padding:7px;">
  
 
<p>
  
<p>
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<b>Main sage script:</b>
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<b>Answer Evaluation:</b>
−
</p>
  
−
<p>
  
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Working Sage code will work verbatim except for a couple of notational changes caused by conflicting syntax between perl and sage. In particular, since "@" is used for tables in perl and for interacts in sage, one will need to replace "@" with "~~@".
  
−  
−
Further, WeBWorK uses <code>\( and \)</code> to delimit latex and "$" for variables while Sage uses "$' to delimit latex. Therefore, converting each pair of Sage's latex $ delimiters averts any conflict.
  
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</p>
  
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<p>
  
−
The defaults for several of the customizable options:
  
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<pre>
  
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SageCode => 'print 1+2', # This is the default code if none given.
  
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ButtonText => 'Start/Restart the Interactive Cell',
  
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CellServer => 'http://sagecell.sagemath.org',
  
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SageAnswerName => 'sageAnswer', # not used yet
  
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SageAnswerValue => 'ansList', # not used yet
  
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AutoEvaluateCell => 'true', # 'false' requires student to activate cell
  
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ShowAnswerBlank => 'hidden', # Set to 'input' to see Sage answer
  
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AnswerReturn => 1, # Set to 0 if Sage returns nothing
  
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HideElements => [''], # List of items to hide in cell
  
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LinkedCells => 'false', # To allow for sharing between multiple cells
  
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</pre>
  
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</p>
  
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<p>
  
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You can hide various elements of the sage cell by listing them in the HideElements flag. Some options:
  
−
<pre>
  
−
Input Elements:
  
−
Editor (editor)
  
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Editor type toggle (editorToggle)
  
−
Language selection box (language)
  
−
Evaluate button (evalButton)
  
−
Output Elements:
  
−
Permalinks (permalinks)
  
−
Session output (output)
  
−
Session end message (done)
  
−
Session files (sessionFiles)
  
−
</pre>
  
 
</p>
  
</p>
 
</td>
  
</td>
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−  
  +
<!-- Solution section -->
−
<!-- Answer evaluation section -->
  
   
 
<tr valign="top">
  
<tr valign="top">
−
<td style="background-color:#eeddff;border:black 1px dashed;">
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<td style="background-color:#ddddff;border:black 1px dashed;">
 
<pre>
  
<pre>
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## Lower WeBWorK text
  
  +
BEGIN_PGML_SOLUTION
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##
  
  +
Solution explanation goes here.
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## Problem display following the Sage cell
  
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END_PGML_SOLUTION
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##
  
−  
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Context()->texStrings;
  
−  
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BEGIN_TEXT
  
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Determine the definite integral of
 
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\( \sin(${a}x) \) from \(a=0\) to \(b=\pi\).
  
−  
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END_TEXT
  
−  
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Context()->normalStrings;
  
−  
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# Answer Evaluation
  
−  
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$showPartialCorrectAnswers = 1;
  
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NAMED_ANS( sageAnswer => $ansList->cmp ); # Leave out if no Sage answer.
  
−  
   
  +
COMMENT('Allows integration in either order. Uses PGML.');
 
ENDDOCUMENT();
  
ENDDOCUMENT();
 
</pre>
  
</pre>
 
<td style="background-color:#ddddff;padding:7px;">
  
<td style="background-color:#ddddff;padding:7px;">
−
<p> ${a}x allows you to place the value of $a adjacent to x without a space. $ax would be interpreted as the value of
 
−
a variable called ax while $a x would produce a space between the number and x.
  
−
</p>
  
 
<p>
  
<p>
−
The list of values computed inside the Sage cell are sageAnswer => $ansList.
  
  +
<b>Solution:</b>
 
</p>
  
</p>
 
</td>
  
</td>
 
</tr>
  
</tr>
  +
 
</table>
  
</table>
   
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</p>
  
</p>
   
−
[[Category:Applets]]
  
 
[[Category:Sample Problems]]
  
[[Category:Sample Problems]]
 
[[Category:Subject Area Templates]]
  
[[Category:Subject Area Templates]]
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[[Category:Problem Techniques]]
  
[[Category:Problem Techniques]]
   
−
<!--
  
 
<ul>
  
<ul>
−
<li>POD documentation: [http://webwork.maa.org/pod/pg_TRUNK/macros/AppletObjects.pl.html AppletObjects.pl.html]</li>
 +
<li>POD documentation: [https://webwork.maa.org/pod/pg/macros/draggableProof.html draggableProof.html]</li>
−
<li>PG macro: [http://webwork.maa.org/viewvc/system/trunk/pg/macros/AppletObjects.pl?view=log AppletObjects.pl]</li>
  
−  
 
</ul>
  
</ul>
−
-->
  

Latest revision as of 08:08, 28 June 2023

This article has been retained as a historical document. It is not up-to-date and the formatting may be lacking. Use the information herein with caution.

This problem has been replaced with a newer version of this problem

Using Draggable Statements


This PG code shows how develop a proof with random statements that need to go in the correct order.


Problem Techniques Index

PG problem file Explanation 
DOCUMENT();
loadMacros(
  'PGstandard.pl',
  'MathObjects.pl',
	'PGML.pl',
  'draggableProof.pl',
  'PGcourse.pl'
);

TEXT(beginproblem());

Details of the draggableProof.pl macro can be found in [the POD]. 

$statements = [
	'Assume \(\sqrt{2}=\frac{a}{b}\) where \(a,b\) are integers, with \(\text{gcd}(a,b)=1\) ',
	'\(2 = \frac{a^2}{b^2}\)',
	'\(a^2 = 2b^2\)',
	'if \(a^2\) is even, then \(a\) must be even',
	'Let \(a=2k\) for \(k\) some integer',
	'We can then write \( 2 = \frac{4k^2}{b^2}\) or \(b^2 = 2k^2\)',
	'Therefore \(b^2\) is even, so \(b\) is also even',
	'If \(a\) and \(b\) are both even, then the initial assumption that  \(\text{gcd}(a,b)=1\) is contradicted.',
	'\(\sqrt{2}\) is therefore not rational.'
 ];

# These are extra statements that are not needed.
 $extra = [
 'Then \(a\) is odd',
 '\(b^2\) cannot be rational.',
 'therefore \(a = 2b\)'
 ];

 $proof = DraggableProof(
 	$statements,
 	$extra
 );

The DraggableProof function takes an arrayref of correct statements, followed (optionally) by extra statements. See the POD for more options. 

BEGIN_PGML

[@ $proof->Print @]*
END_PGML

ANS($proof->cmp);

Answer Evaluation: 

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

COMMENT('Allows integration in either order.  Uses PGML.');
ENDDOCUMENT();

Solution:

Templates by Subject Area


Problem Techniques Index

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