Integer Variables and Linear Constraints in CP-SAT

In CP-SAT, an integer variable is a decision variable whose value the solver must choose from a finite range of integers. We declare one with the syntax

$$\texttt{x = model.NewIntVar(lb, ub, name)}$$

This creates a variable named $\texttt{name}$ whose domain is the set of integers from $\texttt{lb}$ to $\texttt{ub}$, inclusive on both ends. Both bounds must be integers, and $\texttt{name}$ is a string used only for display.

For example, given a model object created with $\texttt{model = cp\_model.CpModel()}$, the lines

$$\begin{array}{l}\texttt{x = model.NewIntVar(0, 10, "x")} \\ \texttt{y = model.NewIntVar(-5, 5, "y")}\end{array}$$

declare $x \in \{0, 1, 2, \ldots, 10\}$ and $y \in \{-5, -4, \ldots, 5\}.$ In general, the domain of $\texttt{NewIntVar(lb, ub, name)}$ contains exactly

$$\texttt{ub} - \texttt{lb} + 1$$

integer values.