Degenerate

A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. Forexample, the Point is a degenerate case of the Circle as the Radius approaches 0, and theCircle is a degenerate form of an Ellipse as the Eccentricity approaches 0. Another example is the twoidentical Roots of the second-order Polynomial . Since the Roots of an th degreePolynomial are usually distinct, Roots which coincide are said to be degenerate. Degenerate cases often requirespecial treatment in numerical and analytical solutions. For example, a simple search for both Roots of the aboveequation would find only a single one: 1.

The word degenerate also has several very specific and technical meanings in different branches of mathematics.

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 513-514, 1985.

• Prime Diophantine Equations
• Prime Factorization
• Prime Factorization Algorithms
• Prime Factors
• Prime Field
• Prime Gaps
• Prime-Generating Polynomial
• Prime Group
• Prime Ideal
• Prime Knot
• Prime k-Tuple
• Prime k-Tuples Conjecture
• Prime k-Tuplet
• Prime Manifold
• Prime Number
• Prime Number of Measurement
• Prime Number Theorem
• Prime Pairs
• Prime Patterns Conjecture
• Prime Polynomial
• Prime Power Conjecture
• Prime Power Symbol
• Primequad
• Prime Quadratic Effect
• Prime Quadruplet