Usually means: Not expressible via polynomial relations.
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We found 5 dictionaries that define the word algebraically independent:

General (2 matching dictionaries)
  1. algebraically independent: Wiktionary
  2. Algebraically independent: Wikipedia, the Free Encyclopedia

Computing (1 matching dictionary)
  1. algebraically independent: Encyclopedia

Science (2 matching dictionaries)
  1. Algebraically Independent: Eric Weisstein's World of Mathematics
  2. algebraically independent: PlanetMath Encyclopedia

Definitions from Wiktionary (algebraically independent)

adjective:  (algebra, field theory) (Of a subset S of the extension field L of a given field extension L / K) whose elements do not satisfy any non-trivial polynomial equation with coefficients in K.

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