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 = {{1, 1, 3}, {1, 0, 4}, {3, 2, 0}, {0, 5, 0}, {5, 0, 0}, {0, 3, 2}, {0,
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1, 4}, {1, 4, 0}, {2, 3, 0}, {2, 1, 2}}
o1 : List
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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,
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5, 0}, {4, 1, 0}, {2, 0, 3}, {4, 0, 1}}
o2 : List
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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,
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5, 0}, {4, 1, 0}, {2, 0, 3}, {4, 0, 1}}
o3 : List
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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,
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5, 0}, {4, 1, 0}, {2, 0, 3}, {4, 0, 1}}, {{1, 3, 1}, {1, 4, 0}, {2, 3,
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0}, {0, 5, 0}, {1, 2, 2}, {3, 1, 1}, {0, 0, 5}, {1, 1, 3}, {4, 0, 1},
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{0, 2, 3}}}
o4 : List
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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,
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3, 1}, {2, 3, 0}, {2, 0, 3}, {1, 4, 0}}
o5 : List
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