Are there any Applications of Abstract Algebra in Engineering?

Question

As the title suggests, I was wondering whether there are any applications of abstract algebra in the engineering disciplines - and if so, what these are (not including basic linear algebra here, as that one seems trivial to answer - this is about Abstract Algebra in the sense of Dummit & Foote).

And, for those who might be knowledgeable on this particular topic, are there any areas (of engineering, that is) where there's potential for abstract algebra to make a difference, or where ongoing research is already pointing to promising results?

Answer 1

Algebraic Geometry is useful in Computer-Aided Geometric Design. See for instance this paper:

Algebraic Geometry for Computer-Aided Geometric Design, by Thomas W. Sederberg and Ronald N. Goldman, in IEEE Computer Graphics and Applications, 1986.

The whole field of Computer-Aided Geometric Design is very mathematical.

See also this book:

Solving Systems of Polynomial Equations, by Bernd Sturmfels, AMS, 2002