- Usage:
`randomRationalCurve(d,e,F)``randomRationalCurve(d,e)`

- Outputs:
- an ideal, defining random rational curve in
*ℙ*of degree (d,e) over F.^{1}×ℙ^{2}

- an ideal, defining random rational curve in

Given two positive integers d,e and a ring F, randomRationalCurve returns the ideal of a random curve in *ℙ ^{1}×ℙ^{2}* of degree (d,e) defined over the base ring F.

This is done by randomly generating two homogenous polynomials of degree d and three homogenous polynomials of degree three in F[s,t] defining maps *ℙ ^{1}→ℙ^{1}* and

If no base ring is specified, the computations are performed over ZZ/101.

i1 : randomRationalCurve(2,3,QQ); o1 : Ideal of QQ[x , x , x , x , x ] 0,0 0,1 1,0 1,1 1,2 |

i2 : randomRationalCurve(2,3); ZZ o2 : 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.

- randomRationalCurve(ZZ,ZZ)
- randomRationalCurve(ZZ,ZZ,Ring)