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Cremona :: composeRationalMaps

composeRationalMaps -- composition of rational maps

Synopsis

Description

We illustrate this with a simple example.
i1 : R=QQ[x_0..x_3]; S=QQ[y_0..y_4]; T=QQ[z_0..z_4];
i4 : phi=map(R,S,{x_0*x_2,x_0*x_3,x_1*x_2,x_1*x_3,x_2*x_3})

o4 = map(R,S,{x x , x x , x x , x x , x x })
               0 2   0 3   1 2   1 3   2 3

o4 : RingMap R <--- S
i5 : psi=map(S,T,{y_0*y_3,-y_2*y_3,y_1*y_2,y_2*y_4,-y_3*y_4})

o5 = map(S,T,{y y , -y y , y y , y y , -y y })
               0 3    2 3   1 2   2 4    3 4

o5 : RingMap S <--- T
i6 : phi*psi

                          2                   2          2
o6 = map(R,T,{x x x x , -x x x , x x x x , x x x , -x x x })
               0 1 2 3    1 2 3   0 1 2 3   1 2 3    1 2 3

o6 : RingMap R <--- T
i7 : composeRationalMaps(phi,psi)

o7 = map(R,T,{x , -x , x , x , -x })
               0    1   0   2    3

o7 : RingMap R <--- T

Ways to use composeRationalMaps :