isWeierstrassSemigroup -- Experimentally decide whether L is a Weierstrass semigroup

Synopsis

Usage:

b=isWeierstrassSemgroup(L,r)
Inputs:
- L, a list, the generators of a semigroup
- r, a real number, numbers which influences the truncation
Optional inputs:
- BaseField
- Verbose => ..., default value false
Outputs:
- b, a Boolean value, true if a smoothing family was found, false no smoothing family was found

Description

After computing an unfolding we successivly restricting the unfolding to variables of degree larger an integer n for an n with

n<=(maximal degree of a parameter)*r,

compute the flattening relations J of the restricted unfolding. If J defines a union of components X, we check whether the fiber over a random closed point of each X is smooth. If we find a smooth fiber we return true, else we continue with n-1 until we checked the full unfolding.

i1 : L={6,8,9,11}

o1 = {6, 8, 9, 11}

o1 : List

i2 : genus L

o2 = 8

i3 : elapsedTime isWeierstrassSemigroup(L,0.15)
 -- 2.13184s elapsed

o3 = true

Ways to use isWeierstrassSemigroup:

isWeierstrassSemigroup(List,RR)

For the programmer

The object isWeierstrassSemigroup is a method function with options.

isWeierstrassSemigroup -- Experimentally decide whether L is a Weierstrass semigroup

Synopsis

Description

See also

Ways to use isWeierstrassSemigroup:

For the programmer