Sage Embedding
Using the Sage Cell Server
This PG code shows how to embed a call to the Sage Cell Server from within a problem.
 Download file: File:Axb span.txt (Change the file extension from .txt to .pg when you save it. You also need to replace every occurrence of 'REPLACE_WITH_SCRIPT' with '<script' in order for the .pg file to work.)
PG problem file  Explanation 

loadMacros("PGstandard.pl", "MathObjects.pl", ); 
No special macros file is needed now although in the future 
########################################################### ## ## pg initializations and regular WeBWorK code $a11 = random(2,3,1/2); $a12 = 1; $a21 = random(3,1,1/2); $a22 = non_zero_random(2,5,1/20); $A = Matrix([[$a11,$a12],[$a21,$a22]]); $A1 = Vector($a11,$a21); $x1 = non_zero_random(2,2,1/20); $x1ans = Compute("$x1"); $x2 = non_zero_random(2,2,1/10); $x2ans = Compute("$x2"); $x = Vector($x1,$x2); $b1 = $a11*$x1+$a12*$x2; $b2 = $a21*$x1+$a22*$x2; $b = Vector($b1,$b2); 
The WeBWorK set up for the problem is the same, but in addition you have
to consider how you will pass the problem parameters into Sage. For example,
if you want to pass

BEGIN_TEXT <div id="sagecell"> \{ ans_rule(15) \} \{ans_rule(15) \}. <script type="application/sage"> b = matrix([[$b1],[$b2]]) bt = b.transpose() A=matrix([[$a11,$a12],[$a21,$a22]]) At =A.transpose() # Notice the correct exact answer is given by x = A\b # Finding when a vector b is in the span of other vectors in 2space 
Special to the Sage embedding:
This <div> section contains the Sage code needed to implement the desired function.
The id attribute of the
We want to pass two answers from Sage to WeBWorK, so we need to include two
The type attribute of the The content of the 
~~@interact def _(x1=slider(3,3,1/20,1), x2=slider(3,3,1/20,1)): G = arrow((0,0),x1*At[0],rgbcolor=(0,0,1)) G += arrow(x1*At[0],x1*At[0]+x2*At[1],rgbcolor=(0,1,0)) G += arrow((0,0),($b1,$b2),rgbcolor=(1,0,0),width=5) G += text("A1",(x1*At[0][0]/2,x1*At[0][1]/2),fontsize=30,color='purple') G += text("A2",(x1*At[0][0]+x2*At[1][0]/2,x1*At[0][1]+x2*At[1][1]/2), fontsize=30,color='purple') G += text("b",($b1/2,$b2/2),fontsize=40,color='purple') G += point(x1*At[0],color='blue',pointsize=40) G += point(($b1,$b2),color='red',pointsize=30) G += point(x1*At[0]+x2*At[1],color='green',pointsize=40) G += point(($b1,$b2),color='red',pointsize=20) # Add fixed originals and dashed modified version of these show(G,frame=False) 
Main sage script: Working Sage code will work verbatim except for a couple of notational changes caused by conflicting syntax between perl and sage. In particular, since "@" is used for tables in perl and for interacts in sage, one will need to replace "@" with "~~@". Further, WeBWorK uses \( and \) to delimit latex and "$" for variables while Sage uses "$' to delimit latex. Therefore, changing each of Sage's latex delimiters to the \( and \) format averts any conflict. 
html('<input type=hidden size=15 name="\{ANS_NUM_TO_NAME(1)\}" id="\{ANS_NUM_TO_NAME(1)\}" value="%s">' %str(x1) ) html('<input type=hidden size=15 name="\{ANS_NUM_TO_NAME(2)\}" id="\{ANS_NUM_TO_NAME(2)\}" value="%s">' %str(x2) ) </script> </div> 
Hidden answer boxes written by the Sage Cell Server
At the end of Sage code (usually an interact) you need to manually pass the answers you want from Sage back into WeBWorK by
using Sage to write the answer 
########################################################### ## ## single cell server script ## ## script that sends the Sage code above to the ## single cell server and writes the return into ## the webpage ## TEXT(MODES(TeX=>"", HTML=><<'SAGE_SCRIPT')); <script src="http://aleph.sagemath.org/static/jquery.min.js"></script> <script src="http://aleph.sagemath.org/embedded_sagecell.js"></script> <script> $(function () { sagecell.makeSagecell({inputLocation: '#sagecell', template: sagecell.templates.minimal, autoeval: true, evalButtonText: 'Reset the interactive display'}); }); </script> SAGE_SCRIPT 
This section writes the javascript into the webpage that feeds the correct 
#################################################### ## ## Lower WeBWorK text ## ## Problem display following the Sage cell ## Context()>texStrings; BEGIN_TEXT When you are comfortable with the coefficients that you have chosen, press the submit button below. END_TEXT Context()>normalStrings; ####################### # Answer Evaluation $showPartialCorrectAnswers = 1; ANS( $x1ans>cmp() ); ANS( $x2ans>cmp() ); 
Answer Evaluation: The answers are checked in the same order as the input boxes appear in the Sage section. Some tweaking may be required to get the Sage format agreeing with the WeBWorK format of the objects the evaluator is checking 
########################################################### ## ## Hint(s), delete or comment if not used ## Context()>texStrings; $showHint = 2; BEGIN_HINT By adjusting the sliders, you are changing the length of the corresponding vector. Remember that a negative coefficient makes the vector point in the opposite direction. END_HINT $showHint = 4; $x1low = $x11/3; $x1high = $x1+1/5; BEGIN_HINT Consider choosing a value for the first coefficient somewhere between $x1low and $x1high. END_HINT Context()>normalStrings; ########################################################### ## ## Solution, delete or comment if not used ## Context()>texStrings; BEGIN_SOLUTION Notice that \(($x1) *A_1 + ($x2) *A_2 = $b\) END_SOLUTION Context()>normalStrings; ENDDOCUMENT(); # This should be the last executable line in the problem. 
