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

'## First Homework Problem File for

1. 1. Calculus
   2. Partial Derivatives
   3. 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);

<script type="text/code">

1. 1. 1. 1. 1. 1. 1. 1. 1. Sage code pasted starting here ##########

var('x,y,t,s')

M=x*y N=-y

@interact(layout=dict(left= [['x0'],['y0'],['delx'],['dely']], bottom=[['xx'],['yy']])) def _( x0 = input_box(0,width=5,label='$x_0$'),

       y0 = input_box(0,width=5,label='$y_0$'),
       delx = input_box(1,width=5,label='$\Delta{x}$'),
       dely = input_box(1,width=5,label='$\Delta{y}$'),
       xx = range_slider(-5, 5, 1, default=(-2,2), label='x Range'),
       yy = range_slider(-5, 5, 1, default=(-1,3), label='y Range')):
           
   G = plot_vector_field((M,N),(x,xx[0],xx[1]),(y,yy[0],yy[1]),aspect_ratio=true)
   G += arrow((x0,y0),(x0+delx,y0+dely))
   show(G)

1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. End of Sage Code ######################

</script>

  <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

1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 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;

1. 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