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

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

Synopsis:

Operator: ^ -- a binary operator, usually used for exponents

Input:

an instance of class Module.

an instance of class Array.

Output:

an instance of class Matrix.

M^[i,j,k] -- projection onto some factors of a direct sum module.

The module M should be a direct sum, and the result is the matrix obtained by projection onto 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 0 0 |

     | 0 1 0 0 0 |



              2        5

o2 : Matrix ZZ  <--- ZZ

i3 : M^[1]



o3 = | 0 0 1 0 0 |

     | 0 0 0 1 0 |

     | 0 0 0 0 1 |



              3        5

o3 : Matrix ZZ  <--- ZZ

i4 : M^[1,0]



o4 = | 0 0 1 0 0 |

     | 0 0 0 1 0 |

     | 0 0 0 0 1 |

     | 1 0 0 0 0 |

     | 0 1 0 0 0 |



              5        5

o4 : Matrix ZZ  <--- ZZ

See also:

Matrix ^ [...] -- select some rows of blocks

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

Module ^ {...} -- projection map from a free module