gives the number of real roots of the univariate function f in x.
gives the number of roots between a and b.
- CountRoots counts roots with multiplicities.
- The function f can be polynomial, holomorphic or meromorphic etc.
- Roots that lie exactly at x=a or x=b are counted.
- The limits a and b can be complex, in which case the range is taken to be the closed rectangle Re[a]≤Re[x]≤Re[b]∧Im[a]≤Im[x]≤Im[b].
Basic Examples (4)
Count the number of polynomial roots between 0 and 10:
Count roots of a polynomial in a closed rectangle:
Count roots of a real elementary function in a real interval:
Count roots of a holomorphic function in a closed rectangle:
Properties & Relations (5)
Introduced in 2007
Updated in 2017