Editing Rational function (section)

===Degree===
There are several non equivalent definitions of the degree of a rational function.

Most commonly, the ''degree'' of a rational function is the maximum of the [[degree of a polynomial|degrees]] of its constituent polynomials {{math|''P''}} and {{math|''Q''}}, when the fraction is reduced to [[lowest terms]]. If the degree of {{math|''f''}} is {{math|''d''}}, then the equation

:<math>f(z) = w \,</math>

has {{math|''d''}} distinct solutions in {{math|''z''}} except for certain values of {{math|''w''}}, called ''critical values'', where two or more solutions coincide or where some solution is rejected [[point at infinity|at infinity]] (that is, when the degree of the equation decreases after having [[clearing denominators|cleared the denominator]]).

The [[degree of an algebraic variety|degree]] of the [[graph of a function|graph]] of a rational function is not the degree as defined above: it is the maximum of the degree of the numerator and one plus the degree of the denominator.

In some contexts, such as in [[asymptotic analysis]], the ''degree'' of a rational function is the difference between the degrees of the numerator and the denominator.<ref>{{cite book |last1=Bourles |first1=Henri |title=Linear Systems |date=2010 |publisher=Wiley |isbn=978-1-84821-162-9 |page=515 |doi=10.1002/9781118619988 |url=https://onlinelibrary.wiley.com/doi/book/10.1002/9781118619988 |access-date=5 November 2022}}</ref>{{rp|at=§13.6.1}}<ref>{{cite book |last1=Bourbaki |first1=N. |authorlink = Nicolas Bourbaki|title=Algebra II |date=1990 |publisher=Springer |isbn=3-540-19375-8 |page=A.IV.20}}</ref>{{rp|at=Chapter IV}}

In [[network synthesis]] and [[Network analysis (electrical circuits)|network analysis]], a rational function of degree two (that is, the ratio of two polynomials of degree at most two) is often called a '''{{vanchor|biquadratic function}}'''.<ref>{{cite book |last1=Glisson |first1=Tildon H. |title=Introduction to Circuit Analysis and Design |publisher=Springer |date=2011 |isbn=978-9048194438}}</ref>