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# adjacent2MinorIdeal -- Ideal generated by adjacent 2-minors

- Usage:
    `adjacent2MinorIdeal Q`
- Inputs:
  - Q, a collection of cells
- Optional inputs:
  - Field => ..., default value QQ, optional argument for polyoIdeal and adjacent2MinorIdeal
  - TermOrder => ..., default value Lex, optional argument for polyoIdeal and adjacent2MinorIdeal
- Outputs:
  - the ideal generated by the adjacent $2$-minors of Q

## Description

This function constructs the ideal generated by all adjacent $2$-minors of Q, as defined in [HH2012].

- [HH2012] Ideals generated by adjacent 2-minors(J. Herzog, T. Hibi, 2012, J. Commut. Algebra).

    i1 : Q = cellCollection {{1,1},{1,2},{2,1},{2,2}};

    i2 : I = adjacent2MinorIdeal Q

    o2 = ideal (x   x    - x   x   , x   x    - x   x   , x   x    - x   x   ,
                 2,2 1,1    2,1 1,2   2,3 1,2    2,2 1,3   3,2 2,1    3,1 2,2
         ------------------------------------------------------------------------
         x   x    - x   x   )
          3,3 2,2    3,2 2,3

    o2 : Ideal of QQ[x   , x   , x   , x   , x   , x   , x   , x   , x   ]
                      3,3   3,2   3,1   2,3   2,2   2,1   1,3   1,2   1,1

## See also

- cellCollection -- Create a collection of cells

## Ways to use adjacent2MinorIdeal:

- `adjacent2MinorIdeal(CollectionOfCells)`

## For the programmer

The object adjacent2MinorIdeal is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PolyominoIdeals.m2:1296:0.