Sage Embedding

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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.)



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">

\{ 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 2-space

Special to the Sage embedding:

This <div> section contains the Sage code needed to implement the desired function. The id attribute of the <div> must match the value of inputLocation in the server script below.

We want to pass two answers from Sage to WeBWorK, so we need to include two ans_rules inside the <div></, but outside the <script> section. The numerical value for the size of the "answer blank" is unimportant since this blank will eventually be overwritten by the Sage Cell.

The type attribute of the <script> tag is not currently checked, but may be in the future. Its suggested value is application/sage. The <script> ... </script> tags delimit the code that will be passed to the Sage Cell Server.

The content of the <script> section is preprocessed by WeBWorK before being written into the web page, so the $a11, $a12 etc. constructs are replaced by their randomized values and comments preceded by # ... are not ever seen by Sage. 


~~@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 <input> boxes (hidden since the student doesn't need to see them). Using \{ANS_NUM_TO_NAME()\} ensures they are given the correct names by WeBWorK. 

###########################################################
##
## 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 <div> to the Sage Cell Server and writes the output into the question page. 

####################################################
##
## 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 = $x1-1/3;
$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.

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