isAdditive -- whether a poset is additive

Description

See section 3.2 of https://arxiv.org/pdf/2502.15166 for a definition of additivity.

Boolean lattices are additive. Therefore, the wedge product of a Boolean lattice with itself is Macaulay.

i1 : B = booleanLattice 3

o1 = B

o1 : Poset

i2 : isAdditive B

o2 = true

i3 : isMacaulay posetWedgeProduct(B, B)

o3 = true

Here is a non-additive poset.

i4 : isAdditive poset({1,2,3,4,5,6}, {{1,2},{1,3},{2,4},{3,4},{3,5},{3,6}})

o4 = false

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/MacaulayPosets.m2:1624:0.