Given an ideal J defining a curve C in *ℙ ^{3}*, curveFromP3toP1P2 produces the ideal of the curve in

This computation is done by first constructing the graph in *ℙ ^{3}×(ℙ^{1}xℙ^{2})* of the product of the two projections

Note the curve in *ℙ ^{1}×ℙ^{2}* will have degree and genus equal to the degree and genus of C as long as C does not intersect the base locus of the projection. If the option PreserveDegree is set to true, curveFromP3toP1P2 will check whether C intersects the base locus. If it does, the function will return an error. If PreserveDegree is set to false, this check is not performed and the output curve in

i1 : R = ZZ/101[z_0,z_1,z_2,z_3]; |

i2 : J = ideal(z_0*z_2-z_1^2, z_1*z_3-z_2^2, z_0*z_3-z_1*z_2); o2 : Ideal of R |

i3 : curveFromP3toP1P2(J) 2 o3 = ideal (x - x x , - x x + x x , - x x + x x ) 1,1 1,0 1,2 0,1 1,1 0,0 1,2 0,1 1,0 0,0 1,1 ZZ o3 : Ideal of ---[x , x , x , x , x ] 101 0,0 0,1 1,0 1,1 1,2 |

This creates a ring *F[x _{0,0},x_{0,1},x_{1,0},x_{1,1},x_{1,2}]* in which the resulting ideal is defined.

- curveFromP3toP1P2(Ideal)