Arithmetic expressions

Arithmetic expressions consist of arithmetic terms that are combined by arithmetic operations.

An arithmetic expression consists of arithmetic terms, such as x, x², xy, or 3xy², combined by arithmetic operations, such as addition, subtraction, multiplication, and division.

Arithmetic expressions can appear in arithmetic relations, such as equality and inequality. Arithmetic expressions can be linear (such as x < z + 3y) or nonlinear (such as x < z² + y*z + 3y). CP Optimizer supports arithmetic constraints over integer decision variables. It also supports integer or numeric (floating-point) expressions.

There are no inherent restrictions on the magnitude of arithmetic operations that you can perform with CP Optimizer expressions and decision variables. The only limitation that you must bear in mind in your CP Optimizer application is any possibility of overflow due to the size and configuration of your platform (that is, limits on hardware and operating system). For example, if you multiply the largest possible integer available on your platform by the largest possible integer, you risk overflow because of limitations of your platform.

In the C++ API of CP Optimizer, there are overloaded operators for building arithmetic expressions and stating constraints over them. For many arithmetic operations, such as addition, exponentiation, or modular arithmetic, there are global functions that offer a variety of signatures that accommodate many combinations of decision variables and integer or numeric values in expressions.

In the Java™ API of CP Optimizer, there are methods to enable you to build arithmetic expressions to state constraints. Many such methods are defined in the interface IloModeler, implemented in the class IloCP.

Likewise, in the C# API of CP Optimizer, there are similar methods for building arithmetic expressions and stating constraints over them. The interface IModeler defines these methods, and the class CP inherits them.

An arithmetic constraint involves one or more decision variables in an arithmetic expression.

Table 1 summarizes the methods that support arithmetic operations to create expressions to use in constraints. Table 2 summarizes the methods and functions that return expressions for use in constraints. Table 3 summarizes the methods that implement arithmetic constraints. The reference manuals of the application programming interfaces (APIs) document each method, operator or global function more fully.

In those tables, the names of applications where the expressions or constraints are used appear in parentheses, like this (sports.cpp). The applications are part of the product, available in the appropriate subdirectory of the examples directory of your installation.