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D.13.1.19 ellipticNFDB

Procedure from library oldpolymake.lib (see oldpolymake_lib).

Usage:
ellipticNFDB(n[,#]); n int, # list

Assume:
n is an integer between 1 and 16

Purpose:
this is a database storing the 16 normal forms of planar polygons with precisely one interior point up to unimodular affine transformations
(see e.g. Bjorn Poonen, Fernando Rodriguez-Villegas: Lattice Polygons and the number 12. Amer. Math. Monthly 107 (2000), no. 3, 238--250.)

Return:
list, L such that
L[1] : list whose entries are the vertices of the nth normal form
L[2] : list whose entries are all the lattice points of the nth normal form
L[3] : only present if the optional parameter # is present, and then it is a polynomial in the variables (x,y) whose
Newton polygon is the nth normal form

Note:
the optional parameter is only allowed if the basering has the variables x and y

Example:
 
LIB "oldpolymake.lib";
list nf=ellipticNFDB(5);
// the vertices of the 5th normal form are
nf[1];
// its lattice points are
nf[2];


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