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semigroupsFromMatrix -- applies semigroupFromMu to the columns of a matrix

Description

If M = facetRays L then the columns of M are the values of mu applied to the first point on each ray of the minimal closed face containing L. In this case semigroupsFrom M returns the list of semigroups corresponding to the rays,

i1 : M1 = coneRays 4

o1 = | 1 1 3 1 |
     | 2 0 2 2 |
     | 3 1 1 1 |

              3       4
o1 : Matrix ZZ  <-- ZZ
 
i2 : netList semigroupsFromMatrix M1

     +-+-+--+--+
o2 = |4|5|  |  |
     +-+-+--+--+
     |4|6|9 |11|
     +-+-+--+--+
     |4|7|10|13|
     +-+-+--+--+
     |4|5|7 |  |
     +-+-+--+--+
 
i3 : (H,M) = allSemigroups 4

o3 = (| 4  0 4  |, | 5  6  7  |)
      | 4  4 4  |  | 5  6  11 |
      | 4  4 8  |  | 5  10 7  |
      | 4  8 4  |  | 5  10 11 |
      | 4  8 8  |  | 5  10 15 |
      | 4  8 12 |  | 9  6  7  |
      | 8  4 4  |  | 9  10 7  |
      | 8  8 4  |  | 9  14 7  |
      | 12 8 4  |  | 13 6  7  |
                   | 13 10 7  |
                   | 13 14 7  |
                   | 17 10 7  |
                   | 17 14 7  |
                   | 21 14 7  |

o3 : Sequence

See also

Ways to use semigroupsFromMatrix:

  • semigroupsFromMatrix(Matrix)

For the programmer

The object semigroupsFromMatrix is a method function.

The source of this document is in NumericalSemigroups.m2:3035:0.