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nonWeierstrassSemigroups -- Find possibly non Weierstrass Semigroups

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) -- .733466s 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
 -- .215523s elapsed
flatteningRelations
 -- .0803133s elapsed
next gb
 -- .00116185s elapsed
true
 -- .4961s elapsed
{6, 7, 9, 17}
unfolding
 -- .196911s elapsed
flatteningRelations
 -- .108763s elapsed
next gb
 -- .00160161s elapsed
decompose
 -- .0840658s elapsed
number of components: 2
support c, codim c: {(2, 2), (5, 2)}
{0, -1}
 -- 1.5055s elapsed
{6, 8, 9, 10}
unfolding
 -- .0734239s elapsed
flatteningRelations
 -- .0630948s elapsed
next gb
 -- .000346731s elapsed
true
 -- .369744s elapsed
{6, 8, 10, 11, 13}
unfolding
 -- .283207s elapsed
flatteningRelations
 -- .114458s elapsed
next gb
 -- .00242049s elapsed
decompose
 -- .483722s elapsed
number of components: 1
support c, codim c: {(5, 1)}
{-1}
 -- 1.44845s elapsed
 -- 3.8199s elapsed
0

 -- .000002392s elapsed
 -- 3.86036s 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.

See also

Ways to use nonWeierstrassSemigroups:

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

For the programmer

The object nonWeierstrassSemigroups is a method function with options.


The source of this document is in NumericalSemigroups.m2:2605:0.