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hasSLP -- Checks whether a monomial complete intersection over a field of characteristic p has the Strong Lefschetz Property (SLP)

Description

Check if the monomial complete intersections $A=k[x_1,...,x_n]/(x_1^{a_1}, …, x_n^{a_n})$, where k is a field of characteristic p has the Strong Lefschetz property using Theorem 3.4 of [Nicklasson,18].

i1 : p = 3;
i2 : L = {4,5,7}

o2 = {4, 5, 7}

o2 : List
i3 : hasSLP(p, L)

o3 = false
i4 : p = 13;
i5 : L = {3,3,19}

o5 = {3, 3, 19}

o5 : List
i6 : hasSLP(p, L)

o6 = true

By default, this method does not use the Han-Monsky multiplication. When UseConjecture is set to true, the method uses the Han-Monsky obtained from Conjecture 4.1 [KMRR,25].

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

o8 = {3, 7, 8}

o8 : List
i9 : hasSLP(p, L, UseConjecture =>true)

o9 = false

Ways to use hasSLP:

  • hasSLP(ZZ,List)

For the programmer

The object hasSLP is a method function with options.


The source of this document is in IncidenceCorrespondenceCohomology.m2:1539:0.