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# isGeometric -- determines if a lattice is geometric

- Usage:
    `i = isGeometric P`
- Inputs:
  - P, an instance of the type Poset, a lattice
- Outputs:
  - i, a Boolean value, whether $P$ is geometric

## Description

The lattice $P$ is geometric if it isAtomic and isUpperSemimodular.

The diamond poset is geometric. Also $n$ booleanLattices are geometric.

    i1 : P = poset {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}, {4, 5}};

    i2 : isLattice P

    o2 = true

    i3 : isGeometric P

    o3 = true

    i4 : isGeometric booleanLattice 4

    o4 = true

The following lattice is non-geometric.

    i5 : Q = poset {{1, 2}, {1, 3}, {2, 4}, {2, 5}, {3, 4}, {4, 6}, {5, 6}};

    i6 : isLattice Q

    o6 = true

    i7 : isGeometric

    o7 = isGeometric

    o7 : MethodFunction

## See also

- isAtomic -- determines if a lattice is atomic
- isLattice -- determines if a poset is a lattice
- isUpperSemimodular -- determines if a lattice is upper semimodular

## Ways to use isGeometric:

- `isGeometric(Poset)`

## For the programmer

The object isGeometric is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Posets.m2:5756:0.