Sage Embedding

Using the Sage Cell Server

This code snippet shows the essential PG code to embed a call to the Sage Cell Server from within a problem. Note that these are insertions, not a complete PG file. This code will have to be incorporated into the problem file on which you are working.

Problem Techniques Index

PG problem file	Explanation
loadMacros("PGstandard.pl", "MathObjects.pl", );	No special macros file is needed now although in the future AppletObjects.pl or another macros file may be required to get additional functionality.
########################################################### ## ## 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 $f = (x-(-2))(x+2)(x+4) it is best to create two versions of f: $f_raw = (x-(-2))*(x+2)*(x+4); to pass to Sage and the math object $f = Compute("$f_raw"); to use in WeBWorK.
BEGIN_TEXT <div id="sagecell"> The solution x for Ax=b is given by x1= \{ ans_rule(15) \} and x2=\{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 2-space <b>~~@interact</b> 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) 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>	This <div> section contains the Sage code needed to implement the desired function. The id attribute of the div must match Notice, the answer call appears near the top between a <div> tag and a <script> tag. Multiple results will need to have multiple answer calls. The numerical value for the size of the "answer blank" is unimportant since this blank will eventually be overwritten by the Sage Cell. 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, perl 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. An example of they usage is illustrated in the code fragment below.
################################### # Configure applet ################################### #data to set up the equation $applet->configuration(qq{<XML expr='$function' />}); # initial points $applet->initialState(qq{<XML> <pt xval='0' yval='0'/></XML>}); ################################### #insert applet into body ################################### TEXT( MODES(TeX=>'object code', HTML=>$applet->insertAll( debug=>0, includeAnswerBox=>1, reinitialize_button=>$permissionLevel>=10, )));	Now we configure the applet. The contents of configuration is sent to the applet when setConfig is called. In this case it defines the function the student will see. The contents of initialState is used for setState if the student has never looked at the problem. After that the applet is set to the state in which the student left the flash applet in the previous session. The debug switch is an alternate to the debugMode flag in the applet definition. The includeAnswerBox should be set to one if you are using the default answerBox. The reinitialize_button allows the flash applet to be reset to its virgin state, as if the student had ever looked at the WeBWorK question. In this example the button is only visible to professors (users with permission level greater than 10) so that they can reset a student's problem if it is stuck for some reason.
BEGIN_TEXT $PAR Drag the point to the inflection point of the given curve and press the submit button. END_TEXT	The problem text section of the file is as we'd expect.
NAMED_ANS('answerBox'=>$answer_point ->with(tolType=>"absolute",tolerance=>.05) ->cmp ->withPostFilter(AnswerHints( sub { my ($correct,$student,$ans) = @_; return Vector($correct-$student)->norm<.2 ; } => ["You're close. You need to position the dot more precisely.", replaceMessage=>1] )));	The answer checker grabs the answer from the default answerBox where the applet has placed it. The answer is coordinates of the dot "(x, y)". We checke it with an absolute tolerance of 0.05. If the the student's dot is within .2 of the correct position then we give an encouraging message to show they are on the right track.

Problem Techniques Index
More on how to embed applets in WeBWorK Questions

• POD documentation: AppletObjects.pl.html
• PG macro: AppletObjects.pl