Contributions Sebastian Gutsche helped in the implementation of inference of properties from already known properties, and also with the integration of 4ti2Interface. Max Horn adapted the definition of the objects numerical and affine semigroups; the behave like lists of integers or lists of lists of integers (affine case), and one can intersect numerical semigroups with lists of integers, or affine semigroup with cartesian products of lists of integers.
Functions implemented by A. Sammartano A. Sammartano implemented the following functions.

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,

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Functions implemented by C. O'Neill Chris implemented the following functions described in :

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,

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,

,

.

And contributed to:

. Also he implemented the new version of

.
Functions implemented by K. Stokes Klara Stokes helped with the implementation of functions related to patterns for ideals of numerical semigroups .
Functions implemented by I. Ojeda and C. J. Moreno Ávila Ignacio and Carlos Jesús implemented the algorithms given in and for the calculation of the Frobenius number and Apéry set of a numerical semigroup using Gröbner basis calculations. Since the new implementation by Chris was included, these algorithms are no longer used.
Functions implemented by I. Ojeda Ignacio also implemented the following functions.

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,

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Ignacio also implemented the new versions of

,

,
Functions implemented by A. Sánchez-R. Navarro Alfredo helped in the implementation of methods for 4ti2gap of the following functions.

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He also helped in preliminary versions of the following functions.

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Functions implemented by G. Zito Giuseppe gave the algorithms for the current version functions

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,

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Functions implemented by A. Herrera-Poyatos Andrés Herrera-Poyatos gave new implementations of

and

. Andrés is also coauthor of the dot functions, see Chapter
Functions implemented by Benjamin Heredia Benjamin Heredia implemented a preliminary version of

.
Functions implemented by Juan Ignacio García-García Juan Ignacio implemented a preliminary version of

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Functions implemented by C. Cisto Carmelo provided some functions to deal with affine semigroups given by gaps, and to compute gaps of affine semigroups with finite genus, see for instance

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Functions implemented by N. Matsuoka Naoyuki implemented the function associated to the generalized Gorenstein property, see Section .
Functions implemented by N. Maugeri Nicola fixed the implementation of . He also implemented

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. And the multiplicity and local property for good semigroups.
Functions implemented by H. Martín Cruz Helena helped in the implementation of the code for ideals of affine semigroups
Functions implemented by J. Angulo Rodríguez Jorge implemented the code corresponding to decompositions of ideals into irreducibles . He also implemented and .
Functions implemented by F. Strazzanti Francesco helped in the implementation of the following methods.

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,

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