Sage in WeBWorK: Difference between revisions

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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://sagemath.org:5467
  <nowiki>
  <nowiki>
## Example pg file using Sage single cell from within a WebWork problem
## Template for calling Sage from within a WebWork pg file
##


DOCUMENT();
DOCUMENT();
Line 13: Line 12:
"MathObjects.pl",
"MathObjects.pl",
);
);
Context()->strings->add(none=>{});


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


$x0 = non_zero_random(-2,2,1); 
# Regular WebWork setup
$y0 = non_zero_random(-2,2,1); 


$f0 = ($x0**3-$y0**3)/($x0**2+$y0**2+1);
$funct  = Compute("x**4");
$funct_diff = $funct->D('x');


TEXT(<<'SAGE_CODE');
<div id="singlecell-test"><script type="text/code">


######### Here is where special coding for Sage starts  ########
# Example Sage Python
TEXT(<<'EOF');


var('x')
@interact
def _(f = (x^2)):
    df = diff(f,x,1)
    html('$f \prime (x) = %s$'%str(latex(df)) )


<div id="singlecell-test">
# End of Sage code - Start of scripts that call the Sage single-cell server
<script type="text/code">
#########  Actual Sage code pasted starting here ##########
#########  This code should work in regular Sage ##########


</script></div>


var('x,y,z')
  <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>


@interact(layout=dict(top=[['x0'],['y0']],
   <script type="text/javascript">
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')):
 
 
    f=(x^3-y^3)/(x^2+y^2+1)
    offset = floor(10*random())/20
 
    if zoom_in:
        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)    
    else:
        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 $(%s'%str(x0)+',%s'%str(y0)+')$')
 
 
##############  End of Sage Code ######################
 
 
##############  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
$(function() { // load only when the page is loaded
   var makecells = function() {
   var makecells = function() {
Line 77: Line 46:
       hide: ["editor","computationID","files","messages","sageMode"],
       hide: ["editor","computationID","files","messages","sageMode"],
       evalButtonText: "Start/Restart",
       evalButtonText: "Start/Restart",
      replaceOutput: true});
      replaceOutput: true});
}
  }


   singlecell.init(makecells); // load Single Cell libraries and then
   singlecell.init(makecells); // load Single Cell libraries and then
Line 85: Line 54:
   });
   });
   </script>
   </script>
EOF
SAGE_CODE
 


############### End of the Sage specific code #######################
# Continue pg file as normal


############### Below is normal WebWork pg stuff ################
Context()->texStrings;
BEGIN_TEXT
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
$PAR
Using Sage above, determine the derivative of \[ f(x) = $funct \].
$PAR
\(f '(x) = \) \{ ans_rule(20) \}
END_TEXT
END_TEXT
Context()->normalStrings;
Context()->normalStrings;


#  need to add reasonable approximation error of about 0.1 or so.
ANS($funct_diff->cmp() );
ANS( Compute($f0)->cmp() );
 
 
ENDDOCUMENT();     


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



Revision as of 01:49, 5 January 2012

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

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

DOCUMENT();

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

TEXT(beginproblem());

# Regular WebWork setup

$funct  = Compute("x**4");
$funct_diff = $funct->D('x');

TEXT(<<'SAGE_CODE');
<div id="singlecell-test"><script type="text/code">

# Example Sage Python

var('x')
@interact
def _(f = (x^2)):
    df = diff(f,x,1)
    html('$f \prime (x) = %s$'%str(latex(df)) )

# End of Sage code - Start of scripts that call the Sage 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>
SAGE_CODE

# Continue pg file as normal

BEGIN_TEXT
$PAR
Using Sage above, determine the derivative of \[ f(x) = $funct \].
$PAR
\(f '(x) = \) \{ ans_rule(20) \}
END_TEXT

Context()->normalStrings;

ANS($funct_diff->cmp() );


ENDDOCUMENT();       

 

To pass perl variables to the sage block if you need to from the problem initialization use:

TEXT(<<EOF);

where <<EOF allows interpolation

otherwise use:

TEXT(<<'EOF');

where 'EOF' tells perl not to interpolate variables