WeBWorK Problems

Some WeBWorK (Perl) code for Matrix Math Objects

Re: Some WeBWorK (Perl) code for Matrix Math Objects

by Christopher Heckman -
In this post: a Mat2System that works with MathObjects.

Syntax: Mat2System ($A, @variable_list, $b) displays a system of linear equations, where

$A is a Matrix
$b is a Matrix or a Vector (or a ColumnVector)
@variable_list is a (Perl) list of strings (variable names)

Example usage: 

Mat2System (Matrix ([[1,2],[3,4]], "x", "y", Vector([5,6]))
Mat2System (Matrix ([[1,2,3],[4,5,6]], qw ("x_1 x_2 x_3 "), Matrix([[1],[2]]))

Code: (Free to use, as long as you credit me and Thomas Hagedorn (who wrote the original version))

sub Mat2System{ # Mat2System (A, qw(x y z w), b)
   my $coeffs = shift;
   my @vec = @_;
   my $vname = pop @vec;
   my ($srow, $scol) = $coeffs->dimensions;
   my $vnamerow = scalar @vec;
   my $vrow;
   if ($vname -> class eq "Matrix") { $vrow = ($vname->dimensions)[0] }
   if ($vname -> class eq "Vector") { $vrow = $vname -> length; }
   die "Wrong number of rows or columns2" if  ($vrow != $srow);
   die "Wrong number of rows or columns4" if ($scol != $vnamerow);
   my $outstr="\begin{array}";
   my $s;
   $outstr .= '{' . ('r' x (2 * $scol + 2)) . '}';
   for (my $j = 0; $j < $srow; $j ++) { 
      $s = 0; 
      for (my $i = 0; $i < $scol; $i++) { 
         my $varname = $vec [$i]; 
         my $a = $coeffs->element ($j + 1, $i + 1); 
         if ($a == 0) {
            if (($s > 0) || ($i < $scol - 1)) { $outstr .= '&&'; }
            else { $outstr .= '&0'; }
            }
         elsif ($a > 0) { 
            if ($a == 1) { $a = ""; } 
            if ($s==0) {$outstr .= "& $a \,$varname"; $s = 1; }
            else {$outstr .= "&+& $a \, $varname"; } 
            }
         else { 
            if ($s == 1) { 
               $a = -$a; 
               if ($a == 1) { $a = ""; } 
               $outstr .= "&- &$a \,$varname"; 
               }
            else {
               if ($a == -1) { $a = "-"; }
               $outstr = $outstr . "& $a \, $varname"; $s = 1;
               }
            } 
         } 
      if ($vname -> class eq "Matrix") { $outstr .= "&=&" . $vname->element($j+1, 1). "\\"; }
      if ($vname -> class eq "Vector") { $outstr .= "&=&" . $vname->extract ($j+1). "\\"; }
      } 
   $outstr . ' \end{array}'; 
   }