Editing Dual lattice (section)

==Examples==

Using the properties listed above, the dual of a lattice can be efficiently calculated, by hand or computer.

* The dual of  <math display="inline"> \mathbb{Z}^n </math> is  <math display="inline"> \mathbb{Z}^n </math>. 
* The dual of <math display="inline"> 2\mathbb{Z} \oplus \mathbb{Z} </math> is <math display="inline"> \frac{1}{2} \mathbb{Z} \oplus \mathbb{Z} </math>.
* Let <math display="inline"> L = \{ x \in \mathbb{Z}^n : \sum x_i = 0 \mod 2 \}</math> be the lattice of integer vectors whose coordinates have an even sum. Then  <math display="inline">  L^* = \mathbb{Z}^n + (\frac{1}{2}, \ldots, \frac{1}{2}) </math>, that is, the dual is the lattice generated by the integer vectors along with the all  <math display="inline"> 1/2 </math>s vector.