Number of zeros in [a,b) : sturmab

### 5.28.16 Number of zeros in [a,b) : sturmab

sturmab takes four arguments: a polynomial expression P, a variable name and two real or complex numbers a and b

- if a and b are reals, sturmab returns the number of sign changes of P on (a, b]. In other words, it returns the number of zeros in [a,b) of the polynomial P/G where G=gcd(P,diff(P)).
- if a or b are complex, sturmab returns the number of complex roots of P in the rectangle having a and b as opposite vertices.

Input :

sturmab(x`^`2*(x`^`3+2),x,-2,0)

Output :

1

Input :

sturmab(x`^`3-1,x,-2-i,5+3i)

Output :

3

Input :

sturmab(x`^`3-1,x,-i,5+3i)

Output :

1

Warning !!!!
P is defined by its symbolic expression.
Input :
sturmab([1,0,0,2,0,0],x,-2,0),
Output :
Bad argument type.