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# 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

## See also

- hurwitzMatrix -- the principal submatrix of the Hurwitz matrix of a univariate polynomial

## Ways to use isHurwitzStable:

- `isHurwitzStable(RingElement)`

## For the programmer

The object isHurwitzStable is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RealRoots.m2:1129:0.