Generate a random generating set of a semigroups B in ℕd of full dimension with coordinate sum a and codimension c.
The option SetSeed can be used to control the random number generator.
The option Num can be used to return a list of semigroups.
The option Simplicial can be used to return a simplicial semigroup such that the standard vectors a*ei are among the Hilbert basis.
i1 : randomSemigroup(5,3,7) o1 = {{0, 4, 1}, {0, 3, 2}, {0, 5, 0}, {0, 2, 3}, {2, 2, 1}, {0, 0, 5}, {1, ------------------------------------------------------------------------ 3, 1}, {1, 1, 3}, {2, 1, 2}, {1, 0, 4}} o1 : List |
i2 : randomSemigroup(5,3,7,SetSeed=>true) o2 = {{5, 0, 0}, {1, 3, 1}, {1, 4, 0}, {0, 2, 3}, {3, 0, 2}, {0, 1, 4}, {0, ------------------------------------------------------------------------ 5, 0}, {4, 1, 0}, {2, 0, 3}, {4, 0, 1}} o2 : List |
i3 : randomSemigroup(5,3,7,SetSeed=>true) o3 = {{5, 0, 0}, {1, 3, 1}, {1, 4, 0}, {0, 2, 3}, {3, 0, 2}, {0, 1, 4}, {0, ------------------------------------------------------------------------ 5, 0}, {4, 1, 0}, {2, 0, 3}, {4, 0, 1}} o3 : List |
i4 : randomSemigroup(5,3,7,SetSeed=>true,Num=>2) o4 = {{{5, 0, 0}, {1, 3, 1}, {1, 4, 0}, {0, 2, 3}, {3, 0, 2}, {0, 1, 4}, {0, ------------------------------------------------------------------------ 5, 0}, {4, 1, 0}, {2, 0, 3}, {4, 0, 1}}, {{1, 3, 1}, {1, 4, 0}, {2, 3, ------------------------------------------------------------------------ 0}, {0, 5, 0}, {1, 2, 2}, {3, 1, 1}, {0, 0, 5}, {1, 1, 3}, {4, 0, 1}, ------------------------------------------------------------------------ {0, 2, 3}}} o4 : List |
i5 : randomSemigroup(5,3,7,SetSeed=>true,Simplicial=>true) o5 = {{5, 0, 0}, {0, 5, 0}, {0, 0, 5}, {0, 1, 4}, {4, 0, 1}, {1, 1, 3}, {1, ------------------------------------------------------------------------ 3, 1}, {2, 3, 0}, {2, 0, 3}, {1, 4, 0}} o5 : List |