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buchweitzSemigroups -- Finds semigroups that are not Weierstrass semigroups by the Buchweitz test

Description

Uses findSemigroups to produce lists of semigroups with the given invariants, and then uses the Buchweitz test: the following inequality holds for Weierstrass semigroups: sums(2, #gaps L) <= dim H^0(\omega_C^{2) = 2*(2g-1) - g + 1.

i1 : B = buchweitzSemigroups (13,26,16)

o1 = {{13, 14, 15, 16, 17, 18, 21, 22, 24}, {13, 14, 15, 16, 17, 18, 20, 22,
     ------------------------------------------------------------------------
     23}}

o1 : List
 
i2 : buchweitz 0

o2 = {13, 14, 15, 16, 17, 18, 20, 22, 23}

o2 : List
 
i3 : B = buchweitzSemigroups (14,28,17)

o3 = {{14, 15, 16, 17, 18, 19, 20, 23, 24, 26}, {14, 15, 16, 17, 18, 19, 20,
     ------------------------------------------------------------------------
     22, 24, 25}}

o3 : List

The second example in these two cases are part of the sequence defined in buchweitz. As g increases there are many more.

i4 : #buchweitzSemigroups (15,30,18)

o4 = 8

See also

Ways to use buchweitzSemigroups:

  • buchweitzSemigroups(ZZ)
  • buchweitzSemigroups(ZZ,ZZ)
  • buchweitzSemigroups(ZZ,ZZ,ZZ)

For the programmer

The object buchweitzSemigroups is a method function.

The source of this document is in NumericalSemigroups.m2:2825:0.