I want to use Sage to simplify polynomials - I really want to learn to use Sage, so it is not just a problem of simplifying polynomials. Passing formulas is required. I tried a simple example
Context()->variables->are(
s=>"Real"
);
$a1 = random(2,9,1);
$a2 = 5;
$a3 = random(1,5,1);
$form = Formula("$a1*s + $a2*s + $a3");
Context("Numeric");
$SageCode1=<<END;
s = var('s')
print expand($form)
END
# accepted_tos=>true indicates that you agree to the terms of service:
# https://sagecell.sagemath.org/tos.html
$result = AskSage($SageCode1,{ accepted_tos=>true, debug=>0});
if (sageReturnedFail($result) ) {
$result = '123456789'; # default value for $answer
}
The printed result looks right, but I can't use it as a formula
$b =$result->eval(s=>2); # this fails - says s not defined in this context
$c = $form->eval(s=>2); # this works
I've tried using Formula($result) with the same error are above.
When you do the
Context("Numeric");
just before the sage code, that goes back to a fresh copy of the Numeric context, without the variable s. When the result of the sage computation is turned back into a Formula in WeBWorK, I would guess it uses the current context (I haven't looked at the code for the sage connection to confirm), and so you get the message you are seeing.
Using the sage.pl macro might be a small step in another direction. The code below has what you need backwards but maybe it could be modified to help you out.
Here, sageAnswer has the simplified polynomial that you want to check against. The way this is set up gives sageAnswer as the student's response (from inside Sage) rather than what you want to check their response against. It does appear to return from of SageCell though as a formula.
DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"contextLimitedPolynomial.pl",
"sage.pl"
);
TEXT(beginproblem());
Context()->variables->are(s=>"Real");
$a1 = random(2,9,1);
$a2 = 5;
$a3 = random(1,5,1);
$form = Formula("$a1*s + $a2*s + $a3");
$SageCode = <<SAGE_CODE;
s = var('s')
ans = expand($form)
record_answer((ans))
SAGE_CODE
Sage(
SageCode=>$SageCode,
);
Context()->texStrings;
BEGIN_TEXT
Expand \( $form \)
END_TEXT
$ans = $form; # Need this to be the answer student enters above
Context()->normalStrings;
Context("LimitedPolynomial");
# sageAnswer is the correctly simplified answer generated by the sagecell
# $ans needs to be what the student enters
# Perhaps these can be reversed somehow below...?
NAMED_ANS( sageAnswer=>$ans->cmp());
Context()->normalStrings;
ENDDOCUMENT(); # This should be the last executable line in the problem.
I guess I'm way behind on Sage knowledge. I do not understand what gets computed and checked internal to Sage and what and how variables get passed to Webwork. How about pointing me to the documents that discuss this and the terminology? For example, I have seen the term Sage cell but do not understand it or its implications. I probably thought I could work with examples, like I started with Webwork. Alas, this does not seem to be the case.
thanks for patience.