Module _ [...] -- get inclusion map into direct sum

Module _ [...] -- get inclusion map into direct sum

Synopsis:

Operator: _

Input:

an instance of class Module.

an instance of class Array.

Output:

an instance of class Matrix.

M_[i,j,k] -- get inclusion map of blocks from a module M.

The module M should be a direct sum, and the result is the matrix obtained by inclusion from the sum of the components numbered i, j, k. Free modules are regarded as direct sums.

i1 : M = ZZ^2 ++ ZZ^3



       5

o1 = ZZ



o1 : ZZ-module, free

i2 : M_[0]



o2 = | 1 0 |

     | 0 1 |

     | 0 0 |

     | 0 0 |

     | 0 0 |



              5        2

o2 : Matrix ZZ  <--- ZZ

i3 : M_[1]



o3 = | 0 0 0 |

     | 0 0 0 |

     | 1 0 0 |

     | 0 1 0 |

     | 0 0 1 |



              5        3

o3 : Matrix ZZ  <--- ZZ

i4 : M_[1,0]



o4 = | 0 0 0 1 0 |

     | 0 0 0 0 1 |

     | 1 0 0 0 0 |

     | 0 1 0 0 0 |

     | 0 0 1 0 0 |



              5        5

o4 : Matrix ZZ  <--- ZZ

See also:

submatrix -- select part of a matrix

Matrix _ [...] -- select some columns of blocks

Module ^ [...] -- projection onto some factors of a direct sum module

Module _ {...} -- map from free module to some generators