Copyright | (c) Masahiro Sakai 2012 |
---|---|

License | BSD-style |

Maintainer | masahiro.sakai@gmail.com |

Stability | provisional |

Portability | portable |

Safe Haskell | None |

Language | Haskell2010 |

Reference:

- "
*Sturm's theorem*." Wikipedia, The Free Encyclopedia. Wikimedia Foundation, Inc. 2012-06-23. http://en.wikipedia.org/wiki/Sturm%27s_theorem - Weisstein, Eric W. "
*Sturm Function*." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SturmFunction.html

- type SturmChain = [UPolynomial Rational]
- sturmChain :: UPolynomial Rational -> SturmChain
- numRoots :: UPolynomial Rational -> Interval Rational -> Int
- numRoots' :: SturmChain -> Interval Rational -> Int
- separate :: UPolynomial Rational -> [Interval Rational]
- separate' :: SturmChain -> [Interval Rational]
- halve :: UPolynomial Rational -> Interval Rational -> Interval Rational
- halve' :: SturmChain -> Interval Rational -> Interval Rational
- narrow :: UPolynomial Rational -> Interval Rational -> Rational -> Interval Rational
- narrow' :: SturmChain -> Interval Rational -> Rational -> Interval Rational
- approx :: UPolynomial Rational -> Interval Rational -> Rational -> Rational
- approx' :: SturmChain -> Interval Rational -> Rational -> Rational

# Documentation

type SturmChain = [UPolynomial Rational] Source

Sturm's chain (Sturm's sequence)

sturmChain :: UPolynomial Rational -> SturmChain Source

Sturm's sequence of a polynomial

numRoots :: UPolynomial Rational -> Interval Rational -> Int Source

The number of distinct real roots of `p`

in a given interval

numRoots' :: SturmChain -> Interval Rational -> Int Source

The number of distinct real roots of `p`

in a given interval.
This function takes `p`

's sturm chain instead of `p`

itself.

separate' :: SturmChain -> [Interval Rational] Source