# 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.

PG problem file Explanation
DOCUMENT();
"PGstandard.pl",
"MathObjects.pl",
"sage.pl",
);


The sage.pl macro is not yet part of the standard WeBWorK distribution. You will need to download the macro file [sage.pl ] and place it in your local macros directory for this to work.

###############################################
##
##  pg initializations and regular WeBWorK code

$a = random(2,5,1);$ansList = List("(-cos(pi*$a)/$a + 1/$a)");  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 may be 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. Also, you will need to store the list of correct answers in a variable named$ansList (which is also customizable).

Finally, if your final answer is a matrix converted to a list, then do not use extra parenthesis here. Otherwise $ansList will be a List of Lists which is probably a bad thing. $SageCode = <<SAGE_CODE;

Area = integrate(sin($a*x),x,0,pi) record_answer((Area)) # leave out if you return no answer SAGE_CODE $SageCode = <<SAGE_CODE;

denotes the beginning of the Sage Python code to be inserted into the WeBWorK problem. This will be paired at the end with and ending SAGE_CODE which must be left-justified. This portion will create a perl variable $SageCode which is the complete Python text. To share values computed inside the Sage cell back to the WeBWorK problem, create a single Sage list named "sageAnswer" (which is configurable).  Sage( SageCode=>$SageCode,
);



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, converting each pair of Sage's latex $delimiters averts any conflict. The defaults for several of the customizable options:  SageCode => 'print 1+2', # This is the default code if none given. ButtonText => 'Start/Restart the Interactive Cell', CellServer => 'http://sagecell.sagemath.org', SageAnswerName => 'sageAnswer', # not used yet SageAnswerValue => 'ansList', # not used yet AutoEvaluateCell => 'true', # 'false' requires student to activate cell ShowAnswerBlank => 'hidden', # Set to 'input' to see Sage answer AnswerReturn => 1, # Set to 0 if Sage returns nothing  ## Lower WeBWorK text ## ## Problem display following the Sage cell ## Context()->texStrings; BEGIN_TEXT Determine the definite integral of $$\sin({a}x)$$ from $$a=0$$ to $$b=\pi$$. END_TEXT Context()->normalStrings; # Answer Evaluation$showPartialCorrectAnswers = 1;
NAMED_ANS( sageAnswer => $ansList->cmp ); # Leave out if no Sage answer. ENDDOCUMENT(); ${a}x allows you to place the value of $a adjacent to x without a space.$ax would be interpreted as the value of a variable called ax while $a x would produce a space between the number and x. The list of values computed inside the Sage cell are sageAnswer =>$ansList.