Sage in WeBWorK: Difference between revisions

From WeBWorK_wiki
Jump to navigation Jump to search
No edit summary
No edit summary
 
(21 intermediate revisions by 2 users not shown)
Line 1: Line 1:
Sage is an open source, online symbolic mathematical system.  Details on Sage can be found at http://www.sagemath.org .
Sage is an open source, online symbolic mathematical system.  Details on Sage can be found at http://www.sagemath.org .


For use within WebWork, a special "single-cell" version of Sage is located at http://sagemath.org:5467
For use within WebWork, a special "single-cell" version of Sage is located at http://sagecell.sagemath.org
  <nowiki>
  <nowiki>
## Example pg file using Sage single cell from within a WebWork problem
## Template for calling Sage from within a WebWork pg file
##  
 
## BEGIN_DESCRIPTION
## Sample problem embedding Sage in WW
## END_DESCRIPTION


DOCUMENT();
DOCUMENT();
Line 10: Line 13:
loadMacros(
loadMacros(
"PGstandard.pl",
"PGstandard.pl",
"PGchoicemacros.pl",
"MathObjects.pl",
"MathObjects.pl",
"sage.pl"
);
);
Context()->strings->add(none=>{});


TEXT(beginproblem());  
TEXT(beginproblem());


$x0 = non_zero_random(-2,2,1);
Context("Numeric");
$y0 = non_zero_random(-2,2,1); 


$f0 = ($x0**3-$y0**3)/($x0**2+$y0**2+1);
#######  Answers to check by WeBWorK go in the list below.


$ansList = List("(pi)");


######### Here is where special coding for Sage starts  ########
#######   Possible Upper WeBWorK text
TEXT(<<'EOF');


Context()->texStrings;
BEGIN_TEXT


<div id="singlecell-test">
This is where WeBWorK problem text above the sage cell goes.
<script type="text/code">
#########  Actual Sage code pasted starting here ##########
#########  This code should work in regular Sage ##########


END_TEXT
Context()->normalStrings;


var('x,y,z')
####                  Sage Cell Server
####  Paste your code below fixing @ and $
####  Store any answers to send back as a list using the function below.
####  making certain that is tabbed over correctly


@interact(layout=dict(top=[['x0'],['y0']],
$SageCode = <<SAGE_CODE;
bottom=[['N'],['zoom_in']]))
def _(N=slider(5,100,1,10,label='Number of Contours'),
        zoom_in=checkbox(false,label='Zoom in'),
        x0=input_box(0,width=10,label='x coordinate of center'),
        y0=input_box(0,width=10,label='y coordinate of center')):


var('a')
a = pi
record_answer((a))


    f=(x^3-y^3)/(x^2+y^2+1)
SAGE_CODE
    offset = floor(10*random())/20


    if zoom_in:
Sage(
        surface = contour_plot(f,(x,x0-offset-1/10,x0+1/10),(y,y0-1/10,y0+offset+1/10), cmap=True,colorbar=True,fill=False,contours=N)   
  SageCode=>$SageCode,
    else:
  AutoEvaluateCell=>'true'
        surface = contour_plot(f,(x,-3,3),(y,-3,3),cmap=True,colorbar=True,fill=False,contours=N)   
);
    limit_point = point((x0,y0),color='red',size=30)  


    html.table([[surface+limit_point]])
    html('Contour Plot of $f(x,y)$ around $(%s'%str(x0)+',%s'%str(y0)+')$')


#######  WeBWorK text display following the Sage cell


##############  End of Sage Code ######################
Context()->texStrings;
BEGIN_TEXT


When you are comfortable with the coefficients that you have chosen, press
the submit button below.


##############  Necessary code for calling the single-cell server ##########
</script>
</div>
<script type="text/javascript" src="http://sagemath.org:5467/static/jquery-1.5.min.js"></script>
<script type="text/javascript" src="http://sagemath.org:5467/embedded_singlecell.js"></script>
<script type="text/javascript">
$(function() { // load only when the page is loaded
  var makecells = function() {
  singlecell.makeSinglecell({
      inputLocation: "#singlecell-test",
      editor: "codemirror",
      hide: ["editor","computationID","files","messages","sageMode"],
      evalButtonText: "Start/Restart",
      replaceOutput: true});
}
  singlecell.init(makecells); // load Single Cell libraries and then
                              // initialize Single Cell instances
  });
  </script>
EOF
############### End of the Sage specific code #######################
############### Below is normal WebWork pg stuff ################
Context()->texStrings;
BEGIN_TEXT
Using the contour plot below, determine the range value of the illustrated function at \( ($x0,$y0) \).
$BR $BR
\( f($x0,$y0) = \)\{ ans_rule(15) \}
$PAR
END_TEXT
END_TEXT
Context()->normalStrings;
Context()->normalStrings;


need to add reasonable approximation error of about 0.1 or so.
########Answer Evaluation
ANS( Compute($f0)->cmp() );
 
$showPartialCorrectAnswers = 1;
NAMED_ANS( sageAnswer => $ansList->cmp   );


ENDDOCUMENT();        # This should be the last executable line in the problem.
ENDDOCUMENT();        # This should be the last executable line in the problem.
     
  </nowiki>
  </nowiki>


To pass perl variables to the sage block if you need to from the problem initialization use:
The example shows how to pass perl variables from the problem initialization into the sage block.
 
:: TEXT(<<SAGE_CODE); 
 
where << SAGE_CODE without single quotes is necessary.  However, the Sage code will not execute if no variables are actually passed in.  Since $ and @ within the Sage code are now interpreted by perl, all latex delimiters should be converted from $ signs to \ ( and \ ) pairs.  Additionally, any @interact needs to be escaped and written as ~~@interact


:: TEXT(<<EOF);
If you are not passing any variables, use:


where <<EOF allows interpolation
:: TEXT(<<'SAGE_CODE');


otherwise use:
where <<'SAGE_CODE' tells perl not to interpret variables.  Sage code can then be pasted in verbatim without any need to convert formatting or escaping other characters.


:: TEXT(<<'EOF');
== See Also ==
* [[Sage Embedding]]


where 'EOF' tells perl not to interpolate variables
[[Category:Developers]]
[[Category:Developers]]

Latest revision as of 15:42, 24 June 2013

Sage is an open source, online symbolic mathematical system. Details on Sage can be found at http://www.sagemath.org .

For use within WebWork, a special "single-cell" version of Sage is located at http://sagecell.sagemath.org

## Template for calling Sage from within a WebWork pg file

## BEGIN_DESCRIPTION
## Sample problem embedding Sage in WW
## END_DESCRIPTION

DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"sage.pl"
);

TEXT(beginproblem());

Context("Numeric");

#######   Answers to check by WeBWorK go in the list below.

$ansList = List("(pi)");

#######   Possible Upper WeBWorK text

Context()->texStrings;
BEGIN_TEXT

This is where WeBWorK problem text above the sage cell goes.

END_TEXT
Context()->normalStrings;

####                   Sage Cell Server
####  Paste your code below fixing @ and $
####  Store any answers to send back as a list using the function below.
####  making certain that is tabbed over correctly

$SageCode = <<SAGE_CODE;

var('a')
a = pi
record_answer((a))

SAGE_CODE

Sage(
  SageCode=>$SageCode,
  AutoEvaluateCell=>'true'
);


#######  WeBWorK text display following the Sage cell

Context()->texStrings;
BEGIN_TEXT

When you are comfortable with the coefficients that you have chosen, press
the submit button below.

END_TEXT
Context()->normalStrings;

#########  Answer Evaluation

$showPartialCorrectAnswers = 1;
NAMED_ANS( sageAnswer => $ansList->cmp   );

ENDDOCUMENT();        # This should be the last executable line in the problem.
       
 

The example shows how to pass perl variables from the problem initialization into the sage block.

TEXT(<<SAGE_CODE);

where << SAGE_CODE without single quotes is necessary. However, the Sage code will not execute if no variables are actually passed in. Since $ and @ within the Sage code are now interpreted by perl, all latex delimiters should be converted from $ signs to \ ( and \ ) pairs. Additionally, any @interact needs to be escaped and written as ~~@interact

If you are not passing any variables, use:

TEXT(<<'SAGE_CODE');

where <<'SAGE_CODE' tells perl not to interpret variables. Sage code can then be pasted in verbatim without any need to convert formatting or escaping other characters.

See Also