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

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

- an ideal, defining random monomial curve in

Given two positive integers d,e and a ring F, randomMonomialCurve 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 a monomial m of degree e in F[s,t], which is not s^{e} or t^{e}. This allows one to define two maps *ℙ ^{1}→ℙ^{1}* and

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

i1 : randomMonomialCurve(2,3,QQ); o1 : Ideal of QQ[x , x , x , x , x ] 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.

- randomMonomialCurve(ZZ,ZZ)
- randomMonomialCurve(ZZ,ZZ,Ring)