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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
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