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Macaulay2Doc :: minors(ZZ,Matrix)

minors(ZZ,Matrix) -- ideal generated by minors

Synopsis

Description

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

When n is negative, the unit ideal is returned, to preserve the expected ordering among the resulting ideals.

i5 : minors(1,M)

o5 = ideal (a, d, b, e, c, f)

o5 : Ideal of R
i6 : minors(0,M)

o6 = ideal 1

o6 : Ideal of R
i7 : minors(-1,M)

o7 = ideal 1

o7 : Ideal of R

See also