  
  [1X4 [33X[0;0YRing Maps[133X[101X
  
  
  [1X4.1 [33X[0;0YRing Maps: Attributes[133X[101X
  
  [1X4.1-1 KernelSubobject[101X
  
  [33X[1;0Y[29X[2XKernelSubobject[102X( [3Xphi[103X ) [32X method[133X
  [6XReturns:[106X  [33X[0;10Ya [5Xhomalg[105X submodule[133X
  
  [33X[0;0YThe kernel ideal of the ring map [3Xphi[103X.[133X
  
  
  [1X4.2 [33X[0;0YRing Maps: Operations and Functions[133X[101X
  
  [1X4.2-1 SegreMap[101X
  
  [33X[1;0Y[29X[2XSegreMap[102X( [3XR[103X, [3Xs[103X ) [32X method[133X
  [6XReturns:[106X  [33X[0;10Ya [5Xhomalg[105X ring map[133X
  
  [33X[0;0YThe  ring  map corresponding to the Segre embedding of [22XMultiProj([3XR[103X)[122X into the
  projective space according to [22XP(W_1)× P(W_2) -> P(W_1⊗ W_2)[122X.[133X
  
  [1X4.2-2 PlueckerMap[101X
  
  [33X[1;0Y[29X[2XPlueckerMap[102X( [3Xl[103X, [3Xn[103X, [3XA[103X, [3Xs[103X ) [32X method[133X
  [6XReturns:[106X  [33X[0;10Ya [5Xhomalg[105X ring map[133X
  
  [33X[0;0YThe  ring  map  corresponding  to  the Plücker embedding of the Grassmannian
  [22XG_l(P^[3Xn[103X([3XA[103X))=G_l(P(W))[122X into the projective space [22XP(⋀^l W)[122X, where [22XW=V^*[122X is the
  [22X[3XA[103X[122X-dual of the free module [22XV=A^[3Xn[103X+1[122X of rank [22X[3Xn[103X+1[122X.[133X
  
  [1X4.2-3 VeroneseMap[101X
  
  [33X[1;0Y[29X[2XVeroneseMap[102X( [3Xn[103X, [3Xd[103X, [3XA[103X, [3Xs[103X ) [32X method[133X
  [6XReturns:[106X  [33X[0;10Ya [5Xhomalg[105X ring map[133X
  
  [33X[0;0YThe ring map corresponding to the Veronese embedding of the projective space
  [22XP^[3Xn[103X([3XA[103X)=P(W)[122X into the projective space [22XP(S^d W)[122X, where [22XW=V^*[122X is the [22X[3XA[103X[122X-dual of
  the free module [22XV=A^[3Xn[103X+1[122X of rank [22X[3Xn[103X+1[122X.[133X
  
