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knownExample -- Is L a known Weierstrass semigroup?

Synopsis

Description

Certain semigroups are known to be Weierstrass. For example L has 2 or 3 generators only, by work of Pinkham and Sally. Another sort examples are semigroup with small weight ewt(L) < genus L by the work Nathan Pflueger extending work of Eisenbud-Harris.

i1 : L={7,12,13}

o1 = {7, 12, 13}

o1 : List
 
i2 : knownExample L

o2 = true
 
i3 : L={7,8,9,11,13}

o3 = {7, 8, 9, 11, 13}

o3 : List
 
i4 : ewt L, genus L

o4 = (7, 8)

o4 : Sequence
 
i5 : knownExample L

o5 = true
 
i6 : LL=findSemigroups(9,10);#LL

o7 = 29
 
i8 : select(LL,L->not knownExample L)

o8 = {{9, 10, 11, 12, 13, 16, 17}, {9, 10, 11, 12, 14, 15, 17}, {9, 10, 11,
     ------------------------------------------------------------------------
     12, 13, 15, 17}, {9, 10, 11, 12, 13, 14, 17}, {9, 10, 11, 12, 13, 14,
     ------------------------------------------------------------------------
     15}, {9, 10, 11, 13, 14, 15, 16}, {9, 10, 11, 12, 14, 15, 16}, {9, 10,
     ------------------------------------------------------------------------
     11, 12, 13, 15, 16}, {9, 10, 11, 12, 13, 14, 16}}

o8 : List
 
i9 : #oo

o9 = 9

See also

Ways to use knownExample:

For the programmer

The object knownExample is a method function.