10178

# 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.

### DETAILS

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

### PERMANENT CITATION

 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 » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.