  Neural codes are binary codes in $\{0,1\}^n$; here we focus on the ones which
represent the firing patterns of a type of neurons called place cells. There is
much interest in determining which neural codes can be realized by a collection
of convex sets. However, drawing representations of these convex sets,
particularly as the number of neurons in a code increases, can be very
difficult. Nevertheless, for a class of codes that are said to be
$k$-inductively pierced for $k=0,1,2$ there is an algorithm for drawing Euler
diagrams. Here we use the toric ideal of a code to show sufficient conditions
for a code to be 1- or 2-inductively pierced, so that we may use the existing
algorithm to draw realizations of such codes.
