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hanMonsky -- Computes the multiplication in the graded Han-Monsky representation ring

Description

Computes the Han-Monsky multiplication $\delta_{a_1}*\delta_{a_2}*....*\delta_{a_n}$. In positive characteristic, the default instance employs Conjecture 4.1 [KMRR,25] to allow faster computations.

i1 : p = 5;
i2 : L = {3,7,8};
i3 : hanMonsky(p, L)

                      7
o3 = HashTable{2 => 2q            }
                     6
               4 => q
                      6     5
               5 => 2q  + 2q
                     5
               6 => q
                      4
               8 => 2q
                      4     3    2
               10 => q  + 3q  + q
                       2
               12 => 2q
               14 => q
               15 => q + 1

o3 : HashTable
i4 : p = 0;
i5 : L = {3,7,8};
i6 : hanMonsky(p, L)

                      7
o6 = HashTable{2 => 2q  }
                      6
               4 => 3q
                      5
               6 => 3q
                      4
               8 => 3q
                       3
               10 => 3q
                       2
               12 => 3q
               14 => 2q
               16 => 1

o6 : HashTable

It is possible to compute it without employing Conjecture 4.1 [KMRR,25] setting the option “UseConjecture” to be false.

i7 : p = 5;
i8 : L = {3,7,8}

o8 = {3, 7, 8}

o8 : List
i9 : hanMonsky(p, L, UseConjecture =>false)

                      7
o9 = HashTable{2 => 2q            }
                     6
               4 => q
                      6     5
               5 => 2q  + 2q
                     5
               6 => q
                      4
               8 => 2q
                      4     3    2
               10 => q  + 3q  + q
                       2
               12 => 2q
               14 => q
               15 => q + 1

o9 : HashTable

Ways to use hanMonsky:

  • hanMonsky(ZZ,List)

For the programmer

The object hanMonsky is a method function with options.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/IncidenceCorrespondenceCohomology.m2:1389:0.