Difference between revisions of "Sage in WeBWorK"

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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 12: 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 76: 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 84: Line 54:
 
});
 
});
 
</script>
 
</script>
EOF
 
  +
SAGE_CODE
   
  +
# Continue pg file as normal
   
############### End of the Sage specific code #######################
 
 
############### 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 21:49, 4 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