Macaulay2 » Documentation
Packages » Permanents :: pminors
next | previous | forward | backward | up | index | toc

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

- Usage:
    `I = pminors(k,M)`
- Inputs:
  - M, a matrix, 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

## Caveat

## See also

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

## Ways to use pminors:

- `pminors(ZZ,Matrix)`

## For the programmer

The object pminors is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Permanents.m2:570:0.