Sage in WeBWorK
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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