linalg(deprecated)/permanent - Maple Help

linalg(deprecated)

 permanent
 compute the permanent of a matrix

 Calling Sequence permanent(A)

Parameters

 A - square matrix

Description

 • 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.

Examples

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

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $A≔\left[\begin{array}{rrr}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$
 ${A}{≔}\left[\begin{array}{ccc}{1}& {2}& {3}\\ {4}& {5}& {6}\\ {7}& {8}& {9}\end{array}\right]$ (1)
 > $\mathrm{permanent}\left(A\right)$
 ${450}$ (2)
 > $B≔\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$
 ${B}{≔}\left[\begin{array}{ccc}{a}& {b}& {c}\\ {d}& {e}& {f}\\ {g}& {h}& {i}\end{array}\right]$ (3)
 > $\mathrm{permanent}\left(B\right)$
 ${a}{}{e}{}{i}{+}{a}{}{f}{}{h}{+}{b}{}{d}{}{i}{+}{b}{}{f}{}{g}{+}{c}{}{d}{}{h}{+}{c}{}{e}{}{g}$ (4)