Tropical Curves

Tropical mathematics has two operations, addition, , and multiplication, , which differ from traditional addition and subtraction. Tropical addition is defined as the minimum of the numbers while tropical multiplication is defined as the ordinary sum. For example, and . A power is repeated multiplication; for example, .
The graph (not shown here) of the tropical polynomial of one variable is simply the lower envelope of the lines , , , and .
"A tropical polynomial function is given as the minimum of a finite set of linear functions. We define the hypersurface to be the set of all points at which this minimum is attained at least twice," in [1].
For example, the surface is represented by the points where occurs in at least two of the terms.
This Demonstration plots the surface of degree 6,
,
which is equivalent to plotting the points where at least two of the terms
give the minimum.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Reference
[1] D. Speyer and B. Sturmfels, "Tropical Mathematics," Mathematics Magazine, 82(3), 2009 pp. 163–173.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.