Minimal
Minimal is a term that refers to the smallest or least possible amount or degree. In various fields, it may refer to a minimal element, minimal polynomial, minimal surface, or minimal system, among other concepts.
Mathematics[edit | edit source]
In mathematics, the term "minimal" is used in a variety of contexts, each with a different meaning.
Minimal element[edit | edit source]
A minimal element in a set is an element that is not greater than any other element in the set. This concept is used in order theory, a branch of mathematics that studies binary relations.
Minimal polynomial[edit | edit source]
The minimal polynomial of an algebraic element is the monic polynomial of least degree that has the element as a root. This concept is used in field theory and algebraic number theory.
Minimal surface[edit | edit source]
A minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature. The concept is used in differential geometry.
Minimal system[edit | edit source]
A minimal system in dynamical systems theory is a system that is not a proper extension of any other system. This concept is used in the study of topological dynamics.
Computer Science[edit | edit source]
In computer science, "minimal" can refer to a minimal automaton, which is a deterministic finite automaton such that no proper quotient of it (under the Myhill-Nerode relation) is also a deterministic finite automaton.
Music[edit | edit source]
In music, "minimal" often refers to minimal music, a style of music that employs limited or minimal musical materials.
See also[edit | edit source]
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