Macaulay2 » Documentation
Packages » NumericalSemigroups :: nonWeierstrassSemigroups
next | previous | forward | backward | up | index | toc

nonWeierstrassSemigroups -- Find possibly non Weierstrass Semigroups

Synopsis

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) -- .681833s 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
 -- .209343s elapsed
flatteningRelations
 -- .0769889s elapsed
next gb
 -- .00114155s elapsed
true
 -- .486779s elapsed
{6, 7, 9, 17}
unfolding
 -- .21359s elapsed
flatteningRelations
 -- .0871836s elapsed
next gb
 -- .00163454s elapsed
decompose
 -- .088119s elapsed
number of components: 2
support c, codim c: {(2, 2), (5, 2)}
{0, -1}
 -- 1.434s elapsed
{6, 8, 9, 10}
unfolding
 -- .0516792s elapsed
flatteningRelations
 -- .0608059s elapsed
next gb
 -- .0169727s elapsed
true
 -- .357932s elapsed
{6, 8, 10, 11, 13}
unfolding
 -- .273959s elapsed
flatteningRelations
 -- .111959s elapsed
next gb
 -- .00258216s elapsed
decompose
 -- .476484s elapsed
number of components: 1
support c, codim c: {(5, 1)}
{-1}
 -- 1.40866s elapsed
 -- 3.68748s elapsed
0

 -- .000002092s elapsed
 -- 3.71012s 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:

For the programmer

The object nonWeierstrassSemigroups is a method function with options.