Sage in WeBWorK

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

##  First Homework Problem File for
##  Calculus
##  Partial Derivatives
##  Unit 1
## 

DOCUMENT();

loadMacros(
"PGstandard.pl",
"PGchoicemacros.pl",
"MathObjects.pl",
);
 
 Context()->strings->add(none=>{});
 
 TEXT(beginproblem()); 
 
 $x0 = non_zero_random(-2,2,1);  
 $y0 = non_zero_random(-2,2,1);   
 
 $f0 = ($x0**3-$y0**3)/($x0**2+$y0**2+1);
 
 TEXT(<<'EOF');

 <div id="singlecell-test">
 <script type="text/code">
  
 #########  Sage code pasted starting here ##########

 var('x,y,z')
 
 @interact(layout=dict(top=[['x0'],['y0']], 
 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 ###################### 
 
 
  </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
 
 ############### Below is the 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
 Context()->normalStrings;
 
 #  need to add reasonable approximation error of about 0.1 or so.
 ANS( Compute($f0)->cmp() );
 
 ENDDOCUMENT();        # This should be the last executable line in the problem.
 

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