1# gap> LoadPackage( "ToricVarieties" ); 2# true 3# gap> sigma := Cone( [[ 15,-1 ],[0,1]] ); 4# <A cone in |R^2> 5# gap> C15 := ToricVariety( sigma ); 6# polymake: used package cddlib 7# Implementation of the double description method of Motzkin et al. 8# Copyright by Komei Fukuda. 9# http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html 10# 11# <An affine normal toric variety of dimension 2> 12# gap> TorusInvariantDivisorGroup(C15); 13# <A free left module of rank 2 on free generators> 14# gap> ClassGroup(C15); 15# <A left module presented by 2 relations for 2 generators> 16# gap> Display(ByASmallerPresentation(last)); 17# Z/< 15 > 18# gap> PicardGroup(C15); 19# <A zero left module> 20# gap> CartierTorusInvariantDivisorGroup(C15); 21# <A free left submodule given by 2 generators> 22# gap> Display(last); 23# [ [ 15, 0 ], 24# [ -1, 1 ] ] 25# 26# A left submodule generated by the 2 rows of the above matrix 27# gap> ImageSubobject(MapFromCharacterToPrincipalDivisor(C15)); 28# <A free left submodule given by 2 generators> 29# gap> Display(last); 30# [ [ 15, 0 ], 31# [ -1, 1 ] ] 32# 33# A left submodule generated by the 2 rows of the above matrix 34# gap> IsSmooth(C15); 35# false 36 37 38LoadPackage( "ToricVarieties" ); 39sigma := Cone( [[ 15,-1 ],[0,1]] ); 40C15 := ToricVariety( sigma ); 41TorusInvariantDivisorGroup(C15); 42ClassGroup(C15); 43Display(ByASmallerPresentation(last)); 44PicardGroup(C15); 45CartierTorusInvariantDivisorGroup(C15); 46Display(last); 47ImageSubobject(MapFromCharacterToPrincipalDivisor(C15)); 48Display(last); 49IsSmooth(C15);