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# UseConjecture -- An option that, whenever the Han-Monsky is computed, allows the user to choose if employ Conjecture 4.1 [KMRR,25] or not

## Description

The default value in hanMonsky is true, so the Han-Monsky multiplication is computed based on Conjecture 4.1 [KMRR,25]. When defined to be false, the function will not use Conjecture 4.1 [KMRR,25]. This will significantly increase the time of computation for the method hanMonsky.

The default value in hasWLP(p,L) and monomialCIsWithoutWLP is true, when is set to be false the computations are done with different methods, without computing the hanMonsky multiplication. This option does not affect hasWLP(R,L) that does not use the hanMonsky multiplication. In hasSLP, instead, the default value is false.

## See also

- hanMonsky -- Computes the multiplication in the graded Han-Monsky representation ring
- hasWLP -- Checks whether a graded Artinian algebra has the Weak Lefschetz Property (WLP)
- hasSLP -- Checks whether a monomial complete intersection over a field of characteristic p has the Strong Lefschetz Property (SLP)
- monomialCIsWithoutWLP -- Lists all the monomial complete intersections of socle s and height n that fail the Weak Lefschetz Property

## Functions with optional argument named UseConjecture:

- `hanMonsky(...,UseConjecture=>...)`
- `hasSLP(...,UseConjecture=>...)`
- `hasWLP(...,UseConjecture=>...)`
- `monomialCIsWithoutWLP(...,UseConjecture=>...)`

## For the programmer

The object UseConjecture is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/IncidenceCorrespondenceCohomology.m2:1565:0.