-- -*- M2-comint -*- {* hash: -200353717 *}

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

i5 : R = QQ[a..d];

i6 : M = (a => image vars R) ++ (b => coker vars R)

o6 = subquotient (| a b c d 0 |, | 0 0 0 0 |)
                  | 0 0 0 0 1 |  | a b c d |

                               2
o6 : R-module, subquotient of R

i7 : M^[a]

o7 = {1} | 1 0 0 0 0 |
     {1} | 0 1 0 0 0 |
     {1} | 0 0 1 0 0 |
     {1} | 0 0 0 1 0 |

o7 : Matrix

i8 : isWellDefined oo

o8 = true

i9 : M^[b]

o9 = | 0 0 0 0 1 |

o9 : Matrix

i10 : isWellDefined oo

o10 = true

i11 : isWellDefined(M^{2})

o11 = false

i12 : C = res coker vars R

       1      4      6      4      1
o12 = R  <-- R  <-- R  <-- R  <-- R  <-- 0
                                          
      0      1      2      3      4      5

o12 : ChainComplex

i13 : D = (a=>C) ++ (b=>C)

       2      8      12      8      2
o13 = R  <-- R  <-- R   <-- R  <-- R  <-- 0
                                           
      0      1      2       3      4      5

o13 : ChainComplex

i14 : D^[a]

           1               2
o14 = 0 : R  <----------- R  : 0
                | 1 0 |

           4                               8
      1 : R  <--------------------------- R  : 1
                {1} | 1 0 0 0 0 0 0 0 |
                {1} | 0 1 0 0 0 0 0 0 |
                {1} | 0 0 1 0 0 0 0 0 |
                {1} | 0 0 0 1 0 0 0 0 |

           6                                       12
      2 : R  <----------------------------------- R   : 2
                {2} | 1 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 1 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 1 0 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 1 0 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 1 0 0 0 0 0 0 0 |
                {2} | 0 0 0 0 0 1 0 0 0 0 0 0 |

           4                               8
      3 : R  <--------------------------- R  : 3
                {3} | 1 0 0 0 0 0 0 0 |
                {3} | 0 1 0 0 0 0 0 0 |
                {3} | 0 0 1 0 0 0 0 0 |
                {3} | 0 0 0 1 0 0 0 0 |

           1                   2
      4 : R  <--------------- R  : 4
                {4} | 1 0 |

      5 : 0 <----- 0 : 5
               0

o14 : ChainComplexMap

i15 :