Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[Permanent], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The permanent of a matrix is computed in a way similar to the determinant. The permanent of an arbitrary 2x2 matrix, $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$, is $\mathrm{ad}+\mathrm{bc}$. To compute the permanent of larger matrices, minor expansion is used in the same manner as when computing determinants, only without alternating sign while expanding along a row or column.

The command with(linalg,permanent) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{linalg}\right)\:$

$A≔\mathrm{matrix}\left(\left[\left[1\,2\,3\right]\,\left[4\,5\,6\right]\,\left[7\,8\,9\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$

$\mathrm{permanent}\left(A\right)$

$450$

$B≔\mathrm{matrix}\left(\left[\left[a\,b\,c\right]\,\left[d\,e\,f\right]\,\left[g\,h\,i\right]\right]\right)$

$B≔\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$

$\mathrm{permanent}\left(B\right)$

$aei+afh+bdi+bfg+cdh+ceg$