# permanents -- ideal generated by square permanents of a matrix

## Synopsis

• Usage:
permanents(n,M)
• Inputs:
• n, an integer, the size of the permanents
• M,
• 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