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‎.gitattributes

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* text=auto !eol
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/4ti2_manual.pdf -text
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/IMA_25Oct2006.pdf -text
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/Tutorial-Problems.pdf -text
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/back.jpg -text

‎4ti2_manual.pdf

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‎IMA_25Oct2006.pdf

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‎Tutorial-Problems.pdf

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‎back.jpg

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‎circuits.html

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<HTML>
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<HEAD>
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<TITLE>4ti2 -- A software package for algebraic, geometric and combinatorial problems
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on linear spaces</TITLE>
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</HEAD>
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<BODY bgcolor = white>
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<center>
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<table border=0 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th>
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<font size=6>circuits</font>
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</th>
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</tr>
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</table>
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</center>
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This code computes the circuits of a matrix.<p>
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<b>Usage</b>
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<pre>
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./circuits [--options] foo
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</pre>
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<p>
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<b>Examples</b>
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<pre>
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./circuits foo
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./circuits --quiet foo
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</pre>
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<p>
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<table border=1 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th align=left>
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Option<br>
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(not on SUN)
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</th>
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<th align=left>
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Short-hand<br>
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(also on SUN)
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</th>
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<th align=left>
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Effect
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</th>
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</tr>
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<tr>
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<th align=left>
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--quiet
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</th>
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<th align=left>
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-q
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</th>
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<th align=left>
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no output is written to the screen
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</th>
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</tr>
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</table><p>
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<table border=1 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th align=left>
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Output file
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</th>
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<th align=left>
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Content
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</th>
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</tr>
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<tr>
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<th align=left>
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foo.cir
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</th>
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<th align=left>
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list of circuits
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</th>
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</tr>
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</table>
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</BODY>

‎citations.html

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<HTML>
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<HEAD>
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<TITLE>4ti2 -- A software package for algebraic, geometric and combinatorial problems
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on linear spaces</TITLE>
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</HEAD>
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<BODY bgcolor = white>
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<center>
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<table border=0 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th>
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<font size=6>Articles and books citing 4ti2</font>
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</th>
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</tr>
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</table>
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</center>
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Please let us know when you cite 4ti2 in an article or book so we can
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keep this list as complete as possible! Please let us know if we have
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missed a citation.<p>
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<ul>
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<li> R. Hemmecke and P. Malkin. Computing generating sets of lattice
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ideals. e-print arXiv:math.CO/0508359, 2005.
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<li> R. Hemmecke. Test Sets for Integer Programs with Z -Convex
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Objective. e-print arXiv:math.CO/0309154, 2003.
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<li> R. Hemmecke. Exploiting Symmetries in the Computation of Graver
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Bases. e-print arXiv:math.CO/0410334, 2004.
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<li> R. Hemmecke. Computation of Atomic Fibers of Z-Linear
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Maps. e-print arXiv:math.CO/0410289, 2004.
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<li> K. Fukuda, A.N. Jensen, N. Lauritzen, R. Thomas. The generic
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Gr&ouml;bner walk. e-print arXiv:math.AC/0501345, 2005.
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<li> N. Eriksson. Toric ideals of homogeneous phylogenetic
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models. Proceedings of the 2004 international symposium on
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Symbolic and algebraic computation, pages 149--154. ACM Press,
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2004.
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<li> P. Diaconis and N. Eriksson. Markov bases for noncommutative
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Fourier analysis of ranked data. to appear in the Journal of
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Symbolic Computation.
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<li> M. Ahmed. Magic graphs and the faces of the Birkhoff
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polytope. e-print arXiv:math.CO/0405181, 2004.
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<li> Y. Chen, I.H. Dinwoodie, and S. Sullivant. Sequential
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Importance Sampling for Multiway Tables. Annals of
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Statistics, in press, 2006.
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<li> Y. Chen, I.H. Dinwoodie, A. Dobra, and M. Huber. Lattice
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Points, Contingency Tables, and Sampling. In Contemporary
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Mathematics, Vol. 374, 65-78. American Mathematical Society,
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2005.
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<li> F. Rapallo. Toric Statistical Models: Binomial and Parametric
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Representations. Preprint #498 Dipartimento di Matematica,
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Universita' di Genova. Submitted, 2004.
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<li> S. Aoki and A. Takemura. Invariant minimal Markov basis for
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sampling contingency tables with fixed marginals. METR
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Technical Report, 03-25, University of Tokyo, Japan.
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<li> Computational Algebra and Combinatorics of Toric
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Ideals. Lectures and tutorials from the workshop on
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"Computational Algebra and Combinatorics", Harish Chandra
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Research Institute, Allahabad, India, Dec 8-13, 2003, (Rekha
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Thomas, Diane Maclagan, Sara Faridi, Leah Gold, A.V. Jayanthan,
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Amit Khetan and Tony Puthenpurakal). To be published by the
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Bhaskaracharya Prathisthana, Pune, India.
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</ul>
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</BODY>

‎cite.html

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<HTML>
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<HEAD>
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<TITLE>4ti2 -- A software package for algebraic, geometric and combinatorial problems
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on linear spaces</TITLE>
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</HEAD>
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<BODY bgcolor = white>
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<center>
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<table border=0 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th>
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<font size=6>How to cite 4ti2</font>
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</th>
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</tr>
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</table>
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</center>
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4ti2 team. 4ti2 -- A software package for algebraic, geometric and
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combinatorial problems on linear spaces. Available at www.4ti2.de.<p>
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<pre>
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@Misc{4ti2,
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author = {4ti2 team},
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title = {4ti2---A software package for algebraic, geometric and
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combinatorial problems on linear spaces},
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howpublished = {{A}vailable at www.4ti2.de}
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}
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</pre>
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</BODY>

‎credits.html

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<HTML>
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<HEAD>
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<TITLE>4ti2 -- A software package for algebraic, geometric and combinatorial problems
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on linear spaces</TITLE>
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</HEAD>
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<BODY bgcolor = white>
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<center>
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<table border=0 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th>
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<font size=6>Credits</font>
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</th>
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</tr>
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</table>
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</center>
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Many thanks to Kris Nairn for suggesting the name '4ti2'. Cool. :-)<p>
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Moreover, lots of thanks to many 4ti2 users for suggesting many interesting and
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useful improvements.
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</BODY>

‎data.html

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<HTML>
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<HEAD>
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<TITLE>4ti2 -- Computation of Hilbert bases, Graver bases, toric Groebner bases, and more</TITLE>
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</HEAD>
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<BODY bgcolor = white>
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<center>
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<table border=0 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th>
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<font size=6>Data structure</font>
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</th>
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</tr>
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</table>
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</center>
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The main concept of 4ti2 remains the same: a project is defined via a file
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'foo' containing the problem matrix. Related sets such as Graver basis
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or Markov basis are put into 'foo.gra' and 'foo.mar', respectively.<p>
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Input files and output files usually contain a matrix or a list of
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vectors (written as a matrix) in a standard encoding such as<br>
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<pre>
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2 4
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1 1 1 1
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1 2 3 4
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</pre><p>
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There are only few exceptions, for example in a file
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'foo.vars' containing user specified variable names:<br>
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<pre>
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3
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a b x
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</pre>
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</BODY>

‎download.html

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<HTML>
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<HEAD>
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<TITLE>4ti2 -- A software package for algebraic, geometric and combinatorial problems
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on linear spaces</TITLE>
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</HEAD>
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<BODY bgcolor = white>
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<center>
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<table border=0 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th>
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<font size=6>4ti2 download</font>
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</th>
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</tr>
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</table>
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<table border=5 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th>
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<font color="blue">Please register as a 4ti2 user!!!</font>
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</tr>
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</table>
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<table border=5 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th align="left" width=50%>
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Simply send<p>
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- your name (last, first),<br>
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- your affiliation (for example: UC Davis, USA), and<br>
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- your email address<p>
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to <a href="mailto:[email protected]">[email protected]</a>.
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</th>
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<th align="left" width=50%>
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For registered 4ti2 users we offer the following free services:<p>
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- e-mail information about updates, <br>
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- support for installation and computational questions.
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</th>
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</tr>
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</table>
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<table border=5 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th>
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<a href="download_4ti2.html" target=text>Go to download</a>
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</th>
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</tr>
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</table>
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</center>
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</BODY>

‎download2.html

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<HTML>
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<HEAD>
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<TITLE>4ti2 -- Computation of Hilbert bases, Graver bases, toric Gröbner bases, and more</TITLE>
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</HEAD>
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<BODY background="back.jpg"
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bgcolor = "#EEEEFF"
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TEXT=FFCC00
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LINK=FFFFF
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VLINK=#FFFCC
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ALINK=#000066>
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<center>
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<table border=0 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th>
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<font size=6 color=red>4ti2 download</font>
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</th>
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</tr>
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</table>
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<table border=5 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th width=25%>
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<a href="tutorial_4ti2.html">Brief tutorial</a>
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</th>
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<th width=25%>
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<a href="download.html">Download</a>
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</th>
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<th width=25%>
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<a href="team.html">Team</a>
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</th>
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<th width=25%>
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<a href="credits.html">Credits</a>
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</th>
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</table>
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<table border=5 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th>
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Version 1.1, released September 22, 2003</th>
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</tr>
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</table>
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<table border=5 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th width=50%>
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<a href="version_1.1/4ti2_sun_1.1.tar.gz">4ti2 version 1.1 for SUN machines</a>
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</th>
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<th width=50%>
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<a href="install_sun_1.1.html">Installation guide for SUN machines</a>
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</th>
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<tr>
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<th width=50%>
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<a href="version_1.1/4ti2_linux_1.1.tar.gz">4ti2 version 1.1 for linux machines</a>
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</th>
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<th width=50%>
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<a href="install_linux_1.1.html">Installation guide for linux machines</a>
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</th>
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</table>
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<table border=0 width=90% cellspacing=5 cellpadding=5>
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<tr>
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<th align=right>
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<a href="http://www.4ti2.de">back to www.4ti2.de</a>
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</th>
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</tr>
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</table>
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</center>
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</BODY>

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