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Macaulay2Doc :: exteriorPower(ZZ,Matrix)

exteriorPower(ZZ,Matrix) -- exterior power of a matrix

Synopsis

Description

i1 : R = ZZ/2[x,y];
i2 : f = random(R^3,R^{3:-1})

o2 = | x   y   y   |
     | x+y y   x   |
     | x   x+y x+y |

             3       3
o2 : Matrix R  <--- R
i3 : exteriorPower_2 f

o3 = | y2       x2+xy+y2 xy+y2 |
     | x2       x2       0     |
     | x2+xy+y2 y2       x2+y2 |

             3       3
o3 : Matrix R  <--- R
The matrix may be a more general homomorphism of modules. For example,
i4 : g = map(coker matrix {{x^2},{x*y},{y^2}}, R^3, id_(R^3))

o4 = | 1 0 0 |
     | 0 1 0 |
     | 0 0 1 |

o4 : Matrix
i5 : g2 = exteriorPower(2,g)

o5 = | 1 0 0 |
     | 0 1 0 |
     | 0 0 1 |

o5 : Matrix
i6 : target g2

o6 = cokernel | xy x2 0  |
              | y2 0  x2 |
              | 0  y2 xy |

                            3
o6 : R-module, quotient of R

See also