Tropical analysis

<h2 id="applications">Applications</h2>
<p>The max tropical semiring can be used appropriately to determine marking times within a given <a href="/facts/Petri_net/BK7eTHNm">Petri net</a> and a vector filled with marking state at the beginning: 
  
    
      
        −
        ∞
      
    
    {\displaystyle -\infty }
  
 (unit for max, tropical addition) means "never before", while 0 (unit for addition, tropical multiplication) is "no additional time".
</p><p><a href="/facts/Tropical_cryptography/K5vwsg5g">Tropical cryptography</a> is cryptography based on the tropical semiring.
</p><p><a href="/facts/Tropical_geometry/fFy8Evgv">Tropical geometry</a> is an analog to <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a>, using the tropical semiring.
</p>

<ul><li>Litvinov, G. L. (2005). "The Maslov dequantization, idempotent and tropical mathematics: A brief introduction". <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/math/0507014v1">math/0507014v1</a>.</li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li>Butkovič, Peter (2010), <a href="http://swbplus.bsz-bw.de/bsz329518011inh.htm"><i>Max-linear Systems: Theory and Algorithms</i></a>, Springer Monographs in Mathematics, Springer-Verlag, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-1-84996-299-5">10.1007/978-1-84996-299-5</a>, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1-84996-298-8</li>
<li>Bernd Heidergott; Geert Jan Olsder; Jacob van der Woude (2005). <a href="https://press.princeton.edu/titles/8120.html"><i>Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications</i></a>. Princeton University Press. p. 224. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-69111763-8.</li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Lunar_arithmetic/pxAya6Cz">Lunar arithmetic</a></li></ul>
<h2 id="external-links">External links</h2>
<ul><li><a href="http://maxplus.org/">MaxPlus algebra</a></li>
<li><a href="http://www.cmap.polytechnique.fr/~gaubert/maxplus.html">Max Plus</a> working group, INRIA Rocquencourt</li></ul>

Tropical analysis open-in-new

Tropical analysis