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