listOfFactors -- finds a map f: S^2(-k)->S such that det(f|pt) factors factors for sufficiently many points pt in PP^1

Synopsis

Usage:
L=listOfFactors(k,g,n)
Inputs:
- k, an integer, the degree of the special pencil
- g, an integer, the genus of the curve we want to construct
- n, an integer, defining the characteristic of our ground field (see getFieldAndRing for details)
Outputs:
- L, a list, with g entries, each entrie consists of the linear and quadratic factors of f|pt for a pt in PP¹

Description

Searches a random map f:S²(-k)→S such that det(f|pt_i) has at least two linear or one quadratic factor for g distinct points pt_i in an affine chart of PP¹. Afterwards these factors are saved to a list.

i1 : (k,g,n)=(5,8,7);

i2 : L=listOfFactors(k,g,n)

                             2             2     2            2             
o2 = {{x  + x , x  + 5x }, {x  - 4x x  - 4x }, {x  - 5x x  + x }, {x  - 2x ,
        0    1   0     1     0     0 1     1     0     0 1    1     0     1 
     ------------------------------------------------------------------------
                                      2             2   2            2     2
     x  + 3x }, {x , x , x  + 4x }, {x  + 4x x  - 4x , x  + 3x x  - x }, {x 
      0     1     1   0   0     1     0     0 1     1   0     0 1    1     0
     ------------------------------------------------------------------------
                2
     - x x  - 4x }, {x  - x , x  - 5x }}
        0 1     1     0    1   0     1

o2 : List

i3 : #L==g

o3 = true

Ways to use `listOfFactors` :

listOfFactors(ZZ,ZZ,ZZ)

listOfFactors -- finds a map f: S^2(-k)->S such that det(f|pt) factors factors for sufficiently many points pt in PP^1

Synopsis

Description

Ways to use listOfFactors :

Ways to use `listOfFactors` :