# determinants and minors

The command determinant can be used to compute the determinant of a square matrix.
 i1 : R = ZZ[a..d]; i2 : f = matrix{{a,b},{c,d}} o2 = | a b | | c d | 2 2 o2 : Matrix R <--- R i3 : det f o3 = - b*c + a*d o3 : R
The command minors can be used to construct the ideal generated by the n by n minors of a matrix. Recall that the n by n minors of a matrix are the determinants of the n by n submatrices of a matrix.
 i4 : R = QQ[x,y,z]; i5 : f = matrix{{x,y,z},{y,z,x^2}} o5 = | x y z | | y z x2 | 2 3 o5 : Matrix R <--- R i6 : I = minors(2,f) 2 3 2 2 o6 = ideal (- y + x*z, x - y*z, x y - z ) o6 : Ideal of R