ToySolver.Data.AlgebraicNumber.Sturm

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

Documentation

type SturmChain = [UPolynomial Rational]

Sturm's chain (Sturm's sequence)

sturmChain :: UPolynomial Rational -> SturmChain

Sturm's sequence of a polynomial

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

The number of distinct real roots of p in a given interval

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

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]

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]

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

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