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theory.html
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<HTML>
<HEAD>
<TITLE>4ti2 -- A software package for algebraic, geometric and combinatorial problems
on linear spaces</TITLE>
<style>
.floatright
{
float: right;
width: 300;
}
</style>
</HEAD>
<BODY bgcolor = white>
<center>
<table border=0 width=90% cellspacing=5 cellpadding=5>
<tr>
<th>
<font size=6>Theory of main algorithms implemented</font>
</th>
</tr>
</table>
</center>
<div class="floatright">
<a href="http://bookstore.siam.org/mo14/"><img width=300
src="MO14_sm.jpg" alt="Algebraic and Geometric Ideas in the Theory
of Discrete Optimization"></a>
</div>
<ul>
<li> graver
<ul>
<li> R. Hemmecke. On the Positive Sum Property and the Computation of
Graver test sets. Mathematical Programming, 96(2):247--269.
<li> R. Hemmecke. Exploiting Symmetries in the Computation of Graver
Bases. e-print arXiv:math.CO/0410334, 2004.
<li> Chapter 3 in: J. A. De Loera, R. Hemmecke, M. Köppe.
<a href="http://bookstore.siam.org/mo14/">Algebraic
and Geometric Ideas in the Theory of Discrete Optimization</a>,
MOS-SIAM Series on Optimization, Society for Industrial and
Applied Mathematics, Philadelphia, PA, 2013,
xx + 313 pages.
</ul>
<li> groebner / markov
<ul>
<li> A.M. Bigatti and R. LaScala and L. Robbiano. Computing toric
ideals. Journal of Symbolic Computation 27 (1999), 351--365.
<li> R. Gebauer and H. M. Möller. On an installation of
Buchberger's algorithm. Journal of Symbolic Computation 6 (1988),
275--286.
<li> R. Hemmecke and P. Malkin. Computing generating sets of lattice
ideals. e-print arXiv:math.CO/0508359, 2005.
<li> S. Hosten and B. Sturmfels. GRIN: An implementation of
Gröbner bases for integer programming. In: "Integer
programming and combinatorial optimisation", E. Balas and
J. Clausen, eds., LNCS 920, Springer-Verlag, 1995, 267--276.
<li> P. Malkin. Truncated Markov bases and Gröbner bases for
Integer Programming. e-print arXiv:math.OC/0612615, 2006.
<li> Chapter 11 in: J. A. De Loera, R. Hemmecke, M. Köppe.
<a href="http://bookstore.siam.org/mo14/">Algebraic
and Geometric Ideas in the Theory of Discrete Optimization</a>,
MOS-SIAM Series on Optimization, Society for Industrial and
Applied Mathematics, Philadelphia, PA, 2013,
xx + 313 pages.
</ul>
<li> hilbert
<ul>
<li> R. Hemmecke. On the Computation of Hilbert Bases of Cones.
in: "Mathematical Software, ICMS 2002", A. M. Cohen, X.-S. Gao,
N. Takayama, eds., World Scientific, 2002.
<li> Chapter 3 in: J. A. De Loera, R. Hemmecke, M. Köppe.
<a href="http://bookstore.siam.org/mo14/">Algebraic
and Geometric Ideas in the Theory of Discrete Optimization</a>,
MOS-SIAM Series on Optimization, Society for Industrial and
Applied Mathematics, Philadelphia, PA, 2013,
xx + 313 pages.
</ul>
<li> ppi
<ul>
<li> M. Köppe. Erzeugende Mengen für gemischt-ganzzahlige
Programme. Diploma thesis, Otto-von-Guericke-Universität
Magdeburg, 1999. available from URL
<a href="http://www.math.ucdavis.edu/~mkoeppe/art/mkoeppe-diplom.ps">http://www.math.ucdavis.edu/~mkoeppe/art/mkoeppe-diplom.ps</a>.
<li> U.-U. Haus, M. Köppe, and R. Weismantel. A primal
all-integer algorithm based on irreducible
solutions. Math. Programming, Series B, 96(2):205-246, 2003.
</ul>
</ul>
</BODY>