# findGeneratorsOfSubalgebra -- Find submonoid corresponding to the convex hull.

## Synopsis

• Usage:
findGeneratorsOfSubalgebra B
• Inputs:
• B, a list, with generators of an affine semigroup in \mathbb{N}^d.
• Outputs:
• a list, of elements of B.

## Description

Denote by C(B) the cone in \mathbb{R}^d spanned by B. This function computes on each ray of C(B) one element of B which has minimal coordinate sum, and returns a list of those elements.

 i1 : a=3 o1 = 3 i2 : B={{a, 0}, {0, a}, {1, a-1}, {a-1, 1}} o2 = {{3, 0}, {0, 3}, {1, 2}, {2, 1}} o2 : List i3 : findGeneratorsOfSubalgebra B o3 = {{{3, 0}, 0}, {{0, 3}, 1}} o3 : List

 i4 : a=4 o4 = 4 i5 : B={{a, 0}, {2, a-2}, {1, a-1}, {a-1, 1}} o5 = {{4, 0}, {2, 2}, {1, 3}, {3, 1}} o5 : List i6 : findGeneratorsOfSubalgebra B o6 = {{{4, 0}, 0}, {{1, 3}, 2}} o6 : List

 i7 : B={{3, 0}, {2, 0}, {1, 1}, {0, 2}} o7 = {{3, 0}, {2, 0}, {1, 1}, {0, 2}} o7 : List i8 : findGeneratorsOfSubalgebra B o8 = {{{2, 0}, 1}, {{0, 2}, 3}} o8 : List

## Ways to use findGeneratorsOfSubalgebra :

• "findGeneratorsOfSubalgebra(List)"

## For the programmer

The object findGeneratorsOfSubalgebra is .