Copyright	(c) Masahiro Sakai 2012
License	BSD-style
Maintainer	masahiro.sakai@gmail.com
Stability	provisional
Portability	portable
Safe Haskell	None
Language	Haskell2010

ToySolver.Data.AlgebraicNumber.Sturm

Description

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

Synopsis

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 :: UPolynomial Rational -> [Interval Rational] Source

Disjoint intervals each of which contains exactly one real roots of the given polynoimal p. The intervals can be further narrowed by narrow or narrow'.

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

Disjoint intervals each of which contains exactly one real roots of the given polynoimal p. The intervals can be further narrowed by narrow or narrow'. This function takes p's sturm chain instead of p itself.

halve :: UPolynomial Rational -> Interval Rational -> Interval Rational Source

halve' :: SturmChain -> Interval Rational -> Interval Rational Source

narrow :: UPolynomial Rational -> Interval Rational -> Rational -> Interval Rational Source

narrow' :: SturmChain -> Interval Rational -> Rational -> Interval Rational Source

approx :: UPolynomial Rational -> Interval Rational -> Rational -> Rational Source

approx' :: SturmChain -> Interval Rational -> Rational -> Rational Source