Mathematics Branches, Topics, and Sub-Topics

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26Cxx Polynomials and rational functions

This subtopic studies polynomials and rational functions, focusing on algebraic structure, factorization, approximation, and extremal behavior.

Specific topics

26C05 Polynomials: analytic properties, etc.

Overview

26C05 studies polynomials: analytic properties, etc. in polynomials and rational functions. It studies algebraic and analytic properties of polynomials and rational functions, including zeros, factorization, and approximation.

Related Wikipedia Page

Polynomials And Rational Functions (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for polynomials: analytic properties, etc.
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in approximation theory, algebraic geometry, and classical analysis.

Applications

  • Root location and factorization
  • Approximation by polynomials
  • Rational-function methods

References

Recommended Textbooks

26C10 Polynomials: location of zeros

Overview

26C10 studies polynomials: location of zeros in polynomials and rational functions. It studies algebraic and analytic properties of polynomials and rational functions, including zeros, factorization, and approximation.

Related Wikipedia Page

Polynomials And Rational Functions (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for polynomials: location of zeros
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in approximation theory, algebraic geometry, and classical analysis.

Applications

  • Root location and factorization
  • Approximation by polynomials
  • Rational-function methods

References

Recommended Textbooks

26C15 Rational functions of one real variable

Overview

26C15 studies rational functions of one real variable in polynomials and rational functions. It studies algebraic and analytic properties of polynomials and rational functions, including zeros, factorization, and approximation.

Related Wikipedia Page

Polynomials And Rational Functions (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for rational functions of one real variable
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in approximation theory, algebraic geometry, and classical analysis.

Applications

  • Root location and factorization
  • Approximation by polynomials
  • Rational-function methods

References

Recommended Textbooks