# Singular

#### D.13.2.15 picksFormula

Procedure from library `polymake.lib` (see polymake_lib).

Usage:
picksFormula(polygon); polygon list

Assume:
polygon is a list of integer vectors in the plane and consider their convex hull C

Return:
list, L of three integersthe
L[1] : the lattice area of C, i.e. twice the Euclidean area
L[2] : the number of lattice points on the boundary of C
L[3] : the number of interior lattice points of C

Note:
the integers in L are related by Pick's formula, namely: L[1]=L[2]+2*L[3]-2

Example:
 ```LIB "polymake.lib"; ==> Welcome to polymake version ==> Copyright (c) 1997-2015 ==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt) ==> http://www.polymake.org // define a polygon with lattice area 5 list polygon=intvec(1,2),intvec(1,0),intvec(2,0),intvec(1,1), intvec(2,1),intvec(0,0); list pick=picksFormula(polygon); // the lattice area of the polygon is: pick[1]; ==> 5 // the number of lattice points on the boundary is: pick[2]; ==> 5 // the number of interior lattice points is: pick[3]; ==> 1 // the number's are related by Pick's formula: pick[1]-pick[2]-2*pick[3]+2; ==> 0 ```