generators Module -- matrix of generators

generators Module -- matrix of generators

Synopsis:

Usage: g = generators M

Function: generators -- matrix of generators

Input:

M, an instance of class Module.

Output:

g, an instance of class Matrix: the matrix of generators of M.

Every module in Macaulay2 has, at least implicitly, a generator matrix and a matrix of relations, both of which are matrices between free modules. This function returns the generator matrix.

i1 : R = GF(8)



o1 = R



o1 : GaloisField

i2 : f = R_0 ++ R_0^2 ++ R_0^3 ++ R_0^4



o2 = | $a 0    0    0       |

     | 0  $a^2 0    0       |

     | 0  0    $a+1 0       |

     | 0  0    0    $a^2+$a |



             4       4

o2 : Matrix R  <--- R

i3 : generators(image f)



o3 = | $a 0    0    0       |

     | 0  $a^2 0    0       |

     | 0  0    $a+1 0       |

     | 0  0    0    $a^2+$a |



             4       4

o3 : Matrix R  <--- R

i4 : generators(cokernel f)



o4 = | 1 0 0 0 |

     | 0 1 0 0 |

     | 0 0 1 0 |

     | 0 0 0 1 |



             4       4

o4 : Matrix R  <--- R

Caveat:

This function returns a matrix with the given generators. This set of generators may not be minimal, or sorted in any particular order. Use trim Module or mingens Module instead.

See also:

relations Module -- the defining relations

Code:

     -- ../../../Macaulay2/m2/matrix.m2:636
     generators Module := Matrix => M -> if M.?generators then M.generators else id_(ambient M)