isHurwitzStable -- determines if a univariate polynomial with rational coefficients is Hurwitz-stable

Usage:

isHurwitzStable(f)
Inputs:
- f, a ring element, a univariate polynomial with rational coefficients
Outputs:
- a Boolean value, the Hurwitz stability of the polynomial f

Description

A real univariate polynomial is Hurwitz-stable if all its roots have negative real parts. This method determines the Hurwitz stability of a univariate polynomial f of degree $n>0$ with rational coefficients whose leading coefficient is positive. Note that ring f is allowed to be multivariate.

i1 : R = QQ[x]

o1 = R

o1 : PolynomialRing

i2 : f = 3*x^4 - 7*x^3 + 5*x - 7 

       4     3
o2 = 3x  - 7x  + 5x - 7

o2 : R

i3 : g = x^2 + 10*x + 21

      2
o3 = x  + 10x + 21

o3 : R

i4 : isHurwitzStable(f)

o4 = false

i5 : isHurwitzStable(g)	      

o5 = true

Ways to use isHurwitzStable:

isHurwitzStable(RingElement)

For the programmer

The object isHurwitzStable is a method function.

The source of this document is in RealRoots.m2:1129:0.

isHurwitzStable -- determines if a univariate polynomial with rational coefficients is Hurwitz-stable

Description

See also

Ways to use isHurwitzStable:

For the programmer