Exact bounds for real roots of a polynomial: VAS

### 6.29.3 Exact bounds for real roots of a polynomial: VAS

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

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

Examples.

- Input:
  VAS(x^3 - 7*x + 7)
  Output:

  | ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ |
  −4 | 0
  1 |
  3
  2
  3
  2
  | 2
  | ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

- Input:
  VAS(x^5 + 2*x^4 - 6*x^3 - 7*x^2 + 7*x + 7)
  Output:

  ⎡ ⎢ ⎢ ⎣ | ⎡ ⎣ | −5,−1 | ⎤ ⎦ | ,−1, | ⎡ ⎢ ⎢ ⎣ | 1, |
  3
  2
  | ⎤ ⎥ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎣ |
  3
  2
  | ,2 | ⎤ ⎥ ⎥ ⎦ | ⎤ ⎥ ⎥ ⎦

- Input:
  VAS(x^3 - x^2 -2*x + 2)
  Output:

  ⎡ ⎣ | ⎡ ⎣ | −3,0 | ⎤ ⎦ | ,1, | ⎡ ⎣ | 1,3 | ⎤ ⎦ | ⎤ ⎦