Equations

In LattE, polytopes are represented by linear constraints, i.e. equalities or inequalities. By default a constraint is an inequality of type $ax\leq b$ unless we specify, by using a single additional line, the line numbers of constraints that are linear equalities.

EXAMPLE. Let $P$ be as in the previous example, but require $x+y=1$ instead of $x+y\leq 1$ , thus, $P=\{(x,y): x\leq 1, y\leq 1, x+y=1, x\geq 0, y\geq 0\}$ . Then the LattE input file that describes $P$ would be as such:

5  3
1 -1  0
1  0 -1
1 -1 -1
0  1  0
0  0  1
linearity 1 3

The last line states that among the $5$ inequalities one is to be considered an equality, the third one.