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monomialCIsWithoutWLP -- Lists all the monomial complete intersections of socle s and height n that fail the Weak Lefschetz Property

Description

This method lists all the n-tuples $(a_1,....,a_n)$, up to order, such that $a_1+.......+a_n-n=s$ and $k[x_1,...,x_n]/(x_1^{a_1}, …, x_n^{a_n})$ fails the WLP with characteristic p, using the method hasWLP. The default value of the option UseConjecture is true, so the computations are based on Conjecture 4.1 [KMRR,25]. When UseConjecture is set to false, the method does not use Conjecture 4.1 [KMRR,25].

i1 : p = 5;
i2 : s = 10;
i3 : n = 4;
i4 : L = monomialCIsWithoutWLP(p,n,s)

o4 = {{2, 2, 5, 5}, {2, 3, 4, 5}, {2, 4, 4, 4}, {3, 3, 3, 5}, {3, 3, 4, 4}}

o4 : List

See also

Ways to use monomialCIsWithoutWLP:

  • monomialCIsWithoutWLP(ZZ,ZZ,ZZ)

For the programmer

The object monomialCIsWithoutWLP is a method function with options.


The source of this document is in IncidenceCorrespondenceCohomology.m2:1500:0.