next | previous | forward | backward | up | index | toc

# gfanMinors -- minors of a matrix of indeterminates

## Synopsis

• Usage:
L = gfanMinors(r,d,n)
• Inputs:
• 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 .