# pminors -- Return ideal generated by pminors of a specified size

## Synopsis

• Usage:
I = pminors(k,M)
• Inputs:
• M, , a square matrix in any commutative ring
• k, an integer, a positive integer
• Optional inputs:
• Strategy (missing documentation) => ..., default value null,
• Outputs:
• I, an ideal, the ideal generated by the $k\times k$ permanent minors of $M$

## Description

Computes the ideal generated by $k\times k$ permanent minors of $M$ with the specified strategy. If no strategy is input then the default is Glynn's formula.

Here is the ideal generated by the $2\times 2$ permanent minors of the 3x3 generic matrix of variables.

 i1 : R = QQ[vars(0..8)] o1 = R o1 : PolynomialRing i2 : M = genericMatrix(R,a,3,3) o2 = | a d g | | b e h | | c f i | 3 3 o2 : Matrix R <--- R i3 : I = pminors(2,M) o3 = ideal (b*d + a*e, b*g + a*h, e*g + d*h, c*d + a*f, c*g + a*i, f*g + d*i, ------------------------------------------------------------------------ c*e + b*f, c*h + b*i, f*h + e*i) o3 : Ideal of R

Here is the ideal generated by the $2\times 2$ permanent minors of a $2\times 3$ matrix using the two different strategies.

 i4 : M=matrix{{1,2,3},{4,5,6}} o4 = | 1 2 3 | | 4 5 6 | 2 3 o4 : Matrix ZZ <--- ZZ i5 : pminors(2,M,Strategy=>glynn) o5 = ideal (13, 18, 27) o5 : Ideal of ZZ i6 : pminors(2,M,Strategy=>ryser) o6 = ideal (13, 18, 27) o6 : Ideal of ZZ