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

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