# LinearExpression

Significant speed
improvements can sometimes be obtained using the `LinearExpression`

object
when there are long, dense, linear expressions. The arguments are

```
constant, linear_coeffs, linear_vars
```

where the second and third arguments are lists that must be of the same length. Here is a simple example that illustrates the syntax. This example creates two constraints that are the same; in this particular case the LinearExpression component would offer very little improvement because Pyomo would be able to detect that campe2 is a linear expression:

```
>>> import pyomo.environ as pyo
>>> from pyomo.core.expr.numeric_expr import LinearExpression
>>> model = pyo.ConcreteModel()
>>> model.nVars = pyo.Param(initialize=4)
>>> model.N = pyo.RangeSet(model.nVars)
>>> model.x = pyo.Var(model.N, within=pyo.Binary)
>>>
>>> model.coefs = [1, 1, 3, 4]
>>>
>>> model.linexp = LinearExpression(constant=0,
... linear_coefs=model.coefs,
... linear_vars=[model.x[i] for i in model.N])
>>> def caprule(m):
... return m.linexp <= 6
>>> model.capme = pyo.Constraint(rule=caprule)
>>>
>>> def caprule2(m):
... return sum(model.coefs[i-1]*model.x[i] for i in model.N) <= 6
>>> model.capme2 = pyo.Constraint(rule=caprule2)
```

Warning

The lists that are passed to `LinearExpression`

are not copied, so caution must
be exercised if they are modified after the component is constructed.