-- -*- M2-comint -*- {* hash: 459262299 *}

i1 : R = ZZ[a..d];

i2 : F = (vars R) ++ ((vars R) ++ matrix{{a-1,b-3},{c,d}})

o2 = | a b c d 0 0 0 0 0   0   |
     | 0 0 0 0 a b c d 0   0   |
     | 0 0 0 0 0 0 0 0 a-1 b-3 |
     | 0 0 0 0 0 0 0 0 c   d   |

             4       10
o2 : Matrix R  <--- R

i3 : F^[1]

o3 = | 0 0 0 0 a b c d 0   0   |
     | 0 0 0 0 0 0 0 0 a-1 b-3 |
     | 0 0 0 0 0 0 0 0 c   d   |

             3       10
o3 : Matrix R  <--- R

i4 : F_[1]^[1]

o4 = | a b c d 0   0   |
     | 0 0 0 0 a-1 b-3 |
     | 0 0 0 0 c   d   |

             3       6
o4 : Matrix R  <--- R

i5 : G = (a=>R^2) ++ (b=>R^1)

      3
o5 = R

o5 : R-module, free

i6 : N = map(G,R^2, (i,j) -> (i+37*j)_R)

o6 = | 0 37 |
     | 1 38 |
     | 2 39 |

             3       2
o6 : Matrix R  <--- R

i7 : N^[a]

o7 = | 0 37 |
     | 1 38 |

             2       2
o7 : Matrix R  <--- R

i8 : N^[b]

o8 = | 2 39 |

             1       2
o8 : Matrix R  <--- R

i9 : N = directSum(x1 => matrix{{a,b-1}}, x2 => matrix{{a-3,b-17,c-35}}, x3 => vars R)

o9 = | a b-1 0   0    0    0 0 0 0 |
     | 0 0   a-3 b-17 c-35 0 0 0 0 |
     | 0 0   0   0    0    a b c d |

             3       9
o9 : Matrix R  <--- R

i10 : N^[x1,x3]

o10 = | a b-1 0 0 0 0 0 0 0 |
      | 0 0   0 0 0 a b c d |

              2       9
o10 : Matrix R  <--- R

i11 :