### 11.3.2 Exact bounds for positive real roots of a polynomial

The VAS_positive command uses the Vincent-Akritas-Strzebonski algorithm to find intervals containing the positive real roots of polynomials.

- VAS_positive takes P, a polynomial.
- VAS_positive(P) returns a list of intervals which contain the positive real roots of P, where each interval contains exactly one root.

#### Examples

VAS_positive(x^3-7*x+7)

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

1

3
2

3
2

2

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦

VAS_positive(x^5+2*x^4-6*x^3-7*x^2+7*x+7)

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

1

3
2

3
2

2

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦

VAS_positive(x^3-x^2-2*x+2)

| ⎡ ⎣ | 1, | ⎡ ⎣ | 1,3 | ⎤ ⎦ | ⎤ ⎦