gfanMinors -- minors of a matrix of indeterminates

Synopsis

Usage:

L = gfanMinors(r,d,n)
Inputs:
- r, an integer, size of the minor
- d, an integer, number of rows
- n, an integer, number of columns
Optional inputs:
- d
- dressian
- M2
- n
- names
- pluckersymmetries
- r
Outputs:
- L, a list, a list of the rxr minors of a dxn matrix of indeterminates

Description

The method produces the rxr minors of a dxn matrix of indeterminates. Note that the variables in the output are indexed by strings.

i1 : gfanMinors(2,3,3)

o1 = {- m  m   + m  m  , - m  m   + m  m  , - m  m   + m  m  , - m  m   +
         01 10    00 11     02 10    00 12     02 11    01 12     01 20  
     ------------------------------------------------------------------------
     m  m  , - m  m   + m  m  , - m  m   + m  m  , - m  m   + m  m  , -
      00 21     02 20    00 22     02 21    01 22     11 20    10 21   
     ------------------------------------------------------------------------
     m  m   + m  m  , - m  m   + m  m  }
      12 20    10 22     12 21    11 22

o1 : List

gfan Documentation

This program will generate the r*r minors of a d*n matrix of indeterminates.
Options:
-r value:
 Specify r.
-d value:
 Specify d.
-n value:
 Specify n.
-M2:
 Use Macaulay2 conventions for order of variables.
--names:
 Assign names to the minors.
--dressian:
 Produce tropical defining the Dressian(3,n) instead. (The signs may not be correct, that is the equations may not be Pluecker relations.)
--pluckersymmetries:
 Do nothing but produce symmetry generators for the Pluecker ideal.
--symmetry:
 Produces a list of generators for the group of symmetries keeping the set of minors fixed. (Only without --names).
--parametrize:
 Parametrize the set of d times n matrices of Barvinok rank less than or equal to r-1 by a list of tropical polynomials.

Ways to use gfanMinors:

gfanMinors(ZZ,ZZ,ZZ)

For the programmer

The object gfanMinors is a method function with options.