permanents -- ideal generated by square permanents of a matrix

Synopsis

Usage:

permanents(n,M)
Inputs:
- n, an integer, the size of the permanents
- M, a matrix
Outputs:
- an ideal, generated by the permanents of the n by n subpermanents of M

Description

The permanent of a square matrix N has the Laplace transform similar to the Laplace transform of the determinant of N: but all signs are positive. Permanents are used in combinatorics and in probability. They are computationally difficult.

i1 : R = ZZ[a..f];

i2 : M = genericMatrix(R,a,2,3)

o2 = | a c e |
     | b d f |

             2       3
o2 : Matrix R  <--- R

i3 : permanents(2,M)

o3 = ideal (b*c + a*d, b*e + a*f, d*e + c*f)

o3 : Ideal of R

Caveat

Ways to use `permanents` :

"permanents(ZZ,Matrix)"

For the programmer

The object permanents is a method function.