VectorListCheckers.pl - Provides subroutines for answer checking lists MathObjects vectors with real entries.
First, load the VectorListCheckers.pl macro file.
loadMacros("PGstandard.pl","MathObjects.pl","VectorListCheckers.pl");For a MathObject list of MathObject vectors, the way to use the answer checkers is the same as using a custom answer checker inside of cmp(checker => ~~&name_of_answer_checker_subroutine) such as
ANS( List(ColumnVector(1,0,0),ColumnVector(0,1,0))->cmp( checker => ~~&basis_checker_list_of_vectors ) );
ANS( Vector("<1,0,0> + s * <0,1,0> + t * <0,0,1>")->cmp( checker => ~~&affine_subspace_checker_vectors ) );The "list of vectors" at the end of the checker name refers to the fact that the student answer is a list of vectors.
Here is an example of how to use these answer checkers.
DOCUMENT();
loadMacros('PGstandard.pl', 'PGML.pl', 'VectorListCheckers.pl', 'PGcourse.pl');
Context('Vector');
$B = Matrix([ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 0 ] ]);
$ans = List(ColumnVector(1, 0, 0), ColumnVector(0, 1, 0));
$cmp = $ans->cmp(list_checker => ~~&basis_checker_list_of_vectors);
BEGIN_PGML
A basis for the column space of [` B = [$B] `] is
[_]{$cmp}{60}
Enter your answer as a comma separated list of vectors, such as
[` \verb+<1,2,3>,<4,5,6>+ `].
END_PGML
ENDDOCUMENT();The parametric_plane_checker_columns should be used for solutions to non-homogeneous systems of linear equations for which the solution is essentially a point plus the span of several linearly independent vectors. When using the parametric plane checker, the first vector input always serves as a point on the hyperplane (i.e., the first vector input is always a particular solution), while the remaining vectors are a basis for the hyperplane (i.e., they span the homogeneous solution set).
Paul Pearson, Hope College, Department of Mathematics