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# innerInterval -- Inner interval of a collection of cells

- Usage:
    `innerInterval(a, b, Q)`
- Inputs:
  - a, a list of two integers representing a point in $\mathbb{Z}^2$
  - b, a list of two integers representing a point in $\mathbb{Z}^2$
  - Q, a collection of cells
- Outputs:
  - true if $[a,b]$ is an inner interval of Q, and false otherwise

## Description

Let $\mathcal{P}$ be a collection of cells. An interval $[a,b] \subseteq \mathbb{Z}^2$ is called an inner interval of $\mathcal{P}$ if every cell contained in $[a,b]$ also belongs to $\mathcal{P}$. This function returns true if $[a,b]$ is an inner interval of $\mathcal{P}$, and false otherwise.

    i1 : Q = cellCollection {{1,1}, {1,2}, {2,1}, {2,3}};

    i2 : innerInterval({1,1}, {3,3}, Q)

    o2 = false

    i3 : innerInterval({1,1}, {3,2}, Q)

    o3 = true

## See also

- cellCollection -- Create a collection of cells

## Ways to use innerInterval:

- `innerInterval(List,List,CollectionOfCells)`

## For the programmer

The object innerInterval is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PolyominoIdeals.m2:1087:0.