curve -- generates a random curve

Description

The method curve generates a random curve with given input.

Synopsis

Usage:

C = curve(D)
Inputs:
- D, an instance of the type Divisor
Outputs:
- C, an instance of the type Curve

i1 : X = quadricSurface(ZZ/101[x_0..x_3]);

i2 : D = divisor({1,2},X);

i3 : C = curve D

                                   2                              2   2      2              2                                 2
o3 = ideal (x x  - x x , x x  + 49x  + 24x x  + 3x x  + 5x x  + 5x , x  + 23x  + 24x x  + 5x  + 39x x  - 46x x  - 38x x  - 43x )
             1 2    0 3   0 1      1      0 3     1 3     2 3     3   0      1      0 2     2      0 3      1 3      2 3      3

o3 : Curve

Synopsis

Usage:

C = curve(d,g)
Inputs:
- d, an integer, degree
- g, an integer, genus
Outputs:
- C, an instance of the type Curve

i4 : I = curve(5,2);

i5 : degree I, genus I

o5 = (5, 2)

o5 : Sequence

Synopsis

Usage:

C = curve(d,g,R)
Inputs:
- d, an integer, degree
- g, an integer, genus
- R, a ring, ambient ring of P^3
Outputs:
- C, an instance of the type Curve

Ways to use curve:

curve(Divisor)
curve(ZZ,ZZ)
curve(ZZ,ZZ,Ring)

For the programmer

The object curve is a method function.