minors(ZZ,Matrix)

Synopsis

Usage:
minors(n,M)
Function: minors
Inputs:
- n, an integer, order of the minor
- M, a matrix, a map between free modules
Outputs:
- an ideal, the ideal generated by the n by n minors of the matrix M.
Optional inputs:
- First => ...,
- Limit => ..., -- the maximum number of minors to compute
- Strategy => ..., -- choose between Bareiss and Cofactor algorithms

Minors are generated in the same order as that used by subsets(ZZ,ZZ).

i1 : R = ZZ[a..f];

i2 : M = matrix{{a,b,c},{d,e,f}}

o2 = | a b c |
     | d e f |

             2       3
o2 : Matrix R  <--- R

i3 : minors(2,M)

o3 = ideal (- b*d + a*e, - c*d + a*f, - c*e + b*f)

o3 : Ideal of R

i4 : minors(2,M,Limit=>1)

o4 = ideal(- b*d + a*e)

o4 : Ideal of R