Singular Manual: ellipticNFDB

| #### D.13.2.14 ellipticNFDB Procedure from library `polymake.lib` (see polymake_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 "polymake.lib";
    ==> Welcome to polymake version
    ==> Copyright (c) 1997-2015
    ==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
    ==> http://www.polymake.org
    list nf=ellipticNFDB(5);
    // the vertices of the 5th normal form are
    nf[1];
    ==> [1]:
    ==>    3,0
    ==> [2]:
    ==>    0,0
    ==> [3]:
    ==>    0,3
    // its lattice points are
    nf[2];
    ==> [1]:
    ==>    3,0
    ==> [2]:
    ==>    2,1
    ==> [3]:
    ==>    1,2
    ==> [4]:
    ==>    0,3
    ==> [5]:
    ==>    2,0
    ==> [6]:
    ==>    0,2
    ==> [7]:
    ==>    1,0
    ==> [8]:
    ==>    0,1
    ==> [9]:
    ==>    0,0

User manual for Singular version 4-1-1, 2018, generated by texi2html.