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Macaulay2Doc :: kernel(ChainComplexMap)

kernel(ChainComplexMap) -- kernel of a chain complex map

Synopsis

Description

If f is a graded module map, then the result will be a graded module.

i1 : R = QQ[a..d]

o1 = R

o1 : PolynomialRing
i2 : I = ideal(a^3,b^3,c^3)

             3   3   3
o2 = ideal (a , b , c )

o2 : Ideal of R
i3 : C = res coker gens I

      1      3      3      1
o3 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o3 : ChainComplex
i4 : D = res coker gens (I + ideal(a*b*c))

      1      4      6      3
o4 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o4 : ChainComplex
i5 : F = extend(D,C,map(D_0,C_0,1))

          1             1
o5 = 0 : R  <--------- R  : 0
               | 1 |

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

          6                     3
     2 : R  <----------------- R  : 2
               {5} | 0 0 0 |
               {5} | 0 0 0 |
               {5} | 0 0 0 |
               {6} | 1 0 0 |
               {6} | 0 1 0 |
               {6} | 0 0 1 |

          3                   1
     3 : R  <--------------- R  : 3
               {7} | c2  |
               {7} | -b2 |
               {7} | a2  |

     4 : 0 <----- 0 : 4
              0

o5 : ChainComplexMap

See also