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PushForward :: pushFwd(RingMap,ModuleMap)

pushFwd(RingMap,ModuleMap) -- push forward of a map of modules

Synopsis

Description

i1 : kk = QQ

o1 = QQ

o1 : Ring
i2 : R = kk[a,b]

o2 = R

o2 : PolynomialRing
i3 : S = kk[z,t]

o3 = S

o3 : PolynomialRing
i4 : f = map(S,R,{z^2,t^2})

               2   2
o4 = map(S,R,{z , t })

o4 : RingMap S <--- R
i5 : M = S^1/ideal(z^3,t^3)

o5 = cokernel | z3 t3 |

                            1
o5 : S-module, quotient of S
i6 : g = map(M,M,matrix{{z*t}})

o6 = | zt |

o6 : Matrix
i7 : p = pushFwd(f,g)

o7 = {0} | 0 0 ab 0 |
     {1} | 0 0 0  b |
     {2} | 1 0 0  0 |
     {1} | 0 a 0  0 |

o7 : Matrix
i8 : kerg = pushFwd(f,ker g)

o8 = cokernel {2} | b a  0 0 0 0 0 |
              {2} | 0 -b a 0 0 0 0 |
              {3} | 0 0  0 b a 0 0 |
              {3} | 0 0  0 0 0 b a |

                            4
o8 : R-module, quotient of R
i9 : kerp = prune ker p

o9 = cokernel {1} | b a  0 0 0 0 0 |
              {1} | 0 -b a 0 0 0 0 |
              {2} | 0 0  0 b a 0 0 |
              {2} | 0 0  0 0 0 b a |

                            4
o9 : R-module, quotient of R