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

  ⎤ ⎦

  ⎤ ⎦