Editing Ehrhart polynomial (section)

==Toric variety==
The case <math>n=d=2</math> and <math>t = 1</math> of these statements yields [[Pick's theorem]]. Formulas for the other coefficients are much harder to get; [[Todd class]]es of [[toric variety|toric varieties]], the [[Riemann–Roch theorem]] as well as [[Fourier analysis]] have been used for this purpose.

If {{math|''X''}} is the [[toric variety]] corresponding to the normal fan of {{math|''P''}}, then {{math|''P''}} defines an [[ample line bundle]] on {{math|''X''}}, and the Ehrhart polynomial of {{math|''P''}} coincides with the [[Hilbert polynomial]] of this line bundle.

Ehrhart polynomials can be studied for their own sake. For instance, one could ask questions related to the roots of an Ehrhart polynomial.<ref>{{citation|last1=Braun|first1=Benjamin|last2=Develin|first2=Mike|authorlink2=Mike Develin| title=Ehrhart Polynomial Roots and Stanley's Non-Negativity Theorem|publisher=[[American Mathematical Society]] |year=2008|volume=452|series=Contemporary Mathematics|pages=67–78| doi= 10.1090/conm/452/08773 |arxiv=math/0610399|isbn=9780821841730|s2cid=118496291}}</ref> Furthermore, some authors have pursued the question of how these polynomials could be classified.<ref>{{citation| last=Higashitani |first=Akihiro| title= Classification of Ehrhart Polynomials of Integral Simplices|journal=DMTCS Proceedings| year=2012| pages=587–594| url= http://www.math.nagoya-u.ac.jp/fpsac12/download/contributed/dmAR0152.pdf}}</ref>