Module ^ ZZ -- direct sum

Synopsis

• Operator: ^

• Usage:

  M^n

• Inputs:
  • M, a module
  • n, an integer
• Outputs:
  • a module, the direct sum of n copies of M

Description

i1 : M = coker matrix{{1,2,3}}

o1 = cokernel | 1 2 3 |

                              1
o1 : ZZ-module, quotient of ZZ

i2 : M^3

o2 = cokernel | 1 2 3 0 0 0 0 0 0 |
              | 0 0 0 1 2 3 0 0 0 |
              | 0 0 0 0 0 0 1 2 3 |

                              3
o2 : ZZ-module, quotient of ZZ

i3 : directSum(3:M)

o3 = cokernel | 1 2 3 0 0 0 0 0 0 |
              | 0 0 0 1 2 3 0 0 0 |
              | 0 0 0 0 0 0 1 2 3 |

                              3
o3 : ZZ-module, quotient of ZZ

See also

• directSum -- direct sum of modules or maps
• ++ -- a binary operator, usually used for direct sum