nonWeierstrassSemigroups -- Find possibly non Weierstrass Semigroups

Synopsis

Usage:

LL=nonWeierstrassSemgroups(m,g)

LL=nonWeierstrassSemgroups(m,g,LLdifficult)
Inputs:
- m, an integer, the multiplicity of a semigroup
- g, an integer, the genus of a semigroup
- LLdifficult, a list, List of difficult semigroups which we exclude from the test
Optional inputs:
- BaseField
- Verbose => ..., default value false
Outputs:
- LL, a list, List of possible non Weierstrass semigroups including LLdifficult

Description

We test which semigroups of multiplicity m and genus g are smoothable. If no smoothing was found then L is a candidate for a non Weierstrass semigroup. In this search certain semigroups L in LLdifficult, where the computation is particular heavy are excluded.

i1 : elapsedTime nonWeierstrassSemigroups(6,7)
(6, 7,  all semigroups are smoothable) -- 1.0928s elapsed


o1 = {}

o1 : List

i2 : LLdifficult={{6, 8, 9, 11}}

o2 = {{6, 8, 9, 11}}

o2 : List

i3 : elapsedTime nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true)
(17, 5)
{6, 7, 8, 17}
unfolding
 -- .340453s elapsed
flatteningRelations
 -- .129428s elapsed
next gb
 -- .00202887s elapsed
true
 -- .784939s elapsed
{6, 7, 9, 17}
unfolding
 -- .332146s elapsed
flatteningRelations
 -- .145655s elapsed
next gb
 -- .00295802s elapsed
decompose
 -- .135462s elapsed
number of components: 2
support c, codim c: {(2, 2), (5, 2)}
{0, -1}
 -- 2.24668s elapsed
{6, 8, 9, 10}
unfolding
 -- .0893476s elapsed
flatteningRelations
 -- .0971071s elapsed
next gb
 -- .000473719s elapsed
true
 -- .552764s elapsed
{6, 8, 10, 11, 13}
unfolding
 -- .420298s elapsed
flatteningRelations
 -- .184803s elapsed
next gb
 -- .00434237s elapsed
decompose
 -- .729439s elapsed
number of components: 1
support c, codim c: {(5, 1)}
{-1}
 -- 2.19494s elapsed
 -- 5.77948s elapsed
0

 -- .000003649s elapsed
 -- 5.81595s elapsed
{}

o3 = {{6, 8, 9, 11}}

o3 : List

In the verbose mode we get timings of various computation steps and further information. The first line, (17,5), indicates that there 17 semigroups of multiplicity 6 and genus 8 of which only 5 is not flagged as smoothable by the function knownExample. The second line, {6, 7, 8, 17}, gives the current semigroup. The timing under various headers tells how much time was used in each of the steps.

Ways to use nonWeierstrassSemigroups:

nonWeierstrassSemigroups(ZZ,ZZ)
nonWeierstrassSemigroups(ZZ,ZZ,List)

For the programmer

The object nonWeierstrassSemigroups is a method function with options.

nonWeierstrassSemigroups -- Find possibly non Weierstrass Semigroups

Synopsis

Description

See also

Ways to use nonWeierstrassSemigroups:

For the programmer