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Numerical Semigroups Python's Functions

We were looking a speedy way of building a numerical semigroup (NS). Finally, we got this, helped by itertools package in Python.

We are spanish speakers, so the assigment is in spanish as well. However, here's a brief description of each function. We are sorry, but remenber, code speaks for itself.

Using geners of a numerical semigroup, we defined using itertools the following functions:

  • EsSN(geners) -> Verify if geners form a numerical semigroup.
  • PerteSN(x,geners) -> Verify if x belongs to the NS formed by geners.
  • GenInfinitoSN(geners,ini=0) -> Returns an infinite NS elements' iterator started in ini.
  • ConjApery(geners,verb=False) -> Return a Apery(geners,min(geners))'s list of the NS formed by geners.
  • GenSNMaxApery(geners,verb=False) -> returns an NS's iterator up to max(Apery(geners,min(geners))).
  • GeneradorSN(geners,verb=False) -> Verify if geners forms a NS. If so, returns an NS's iterator up to max(Apery(geners,min(geners))). Otherwise, returns an error.
  • ListaSN(geners,verb=False) -> Verify if geners forms a NS. If so, returns a NS's list up to max(Apery(geners,min(geners))). Otherwise, returns an error.

If verb = True, it returns information about the NS.

Authors:

  • Rincón, Jose
  • Sánchez, Adrián