DOCUMENT();
loadMacros(
"PGstandard.pl",
"PGML.pl",
);
TEXT(beginproblem());


Context("Matrix");
Context()->constants->are(
  'e' => Matrix([[1,0],[0,1]]),
  'a' => 2*Matrix([[0,-1],[1,0]]),
);
Context()->operators->undefine("+","-","inverse");
Context()->flags->set(
    formatStudentAnswer=>'parsed'
);

$G = List("e, a, a^2");

# For debugging
TEXT($G->value, $PAR); # this has the matrices
TEXT(pretty_print($G->data), $PAR); # a perl array of the matrices
TEXT($G->TeX, $PAR); # this has a TeX version of the matrices
TEXT($G->string, $PAR); # this has the matrices

BEGIN_PGML
List all of the elements of the group [` \langle a : a^3 = e \rangle`] in the form [`a^i`] where [`i`] is a nonnegative integer that is as small as possible.  Use [`e`] to denote the identity element of the group.

    [` \langle a : a^3 = e \rangle = \big\lbrace `] [_________________]{$G} [`\big\rbrace`]
END_PGML

ENDDOCUMENT();