Statement
Let be a Sturm chain, where p is a square-free polynomial, and let σ(ξ) denote the number of sign changes (ignoring zeroes) in the sequence
Sturm's theorem then states that for two real numbers a < b, the number of distinct roots of p in the half-open interval (a,b] is σ(a) − σ(b).
Read more about this topic: Sturm's Theorem
Famous quotes containing the word statement:
“He that writes to himself writes to an eternal public. That statement only is fit to be made public, which you have come at in attempting to satisfy your own curiosity.”
—Ralph Waldo Emerson (1803–1882)
“Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth.”
—Charles Sanders Peirce (1839–1914)
“Truth is used to vitalize a statement rather than devitalize it. Truth implies more than a simple statement of fact. “I don’t have any whisky,” may be a fact but it is not a truth.”
—William Burroughs (b. 1914)