det Matrix -- determinant of a matrix

det Matrix -- determinant of a matrix

Synopsis:

Usage: d = det f

Function: det -- determinant of a matrix

Input:

f, an instance of class Matrix: a square matrix

Output:

d, an instance of class RingElement: the determinant of f

Optional arguments :

det(..., Strategy => ...) -- choose between Bareiss and Cofactor algorithms

i1 : R = QQ[a..d]



o1 = R



o1 : PolynomialRing

i2 : p = matrix {{a,b},{c,d}}



o2 = | a b |

     | c d |



             2       2

o2 : Matrix R  <--- R

i3 : det p



o3 = - b*c + a*d



o3 : R

Code:

     -- ../../../Macaulay2/m2/multilin.m2:194-199
     det Matrix := RingElement => options -> f -> (
          if rank source f != rank target f
          or not isFreeModule source f
          or not isFreeModule target f
          then error "expected a square matrix";
          (exteriorPower(numgens source f, f, options))_(0,0))