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:
“Eloquence must be grounded on the plainest narrative. Afterwards, it may warm itself until it exhales symbols of every kind and color, speaks only through the most poetic forms; but first and last, it must still be at bottom a biblical statement of fact.”
—Ralph Waldo Emerson (1803–1882)
“After the first powerful plain manifesto
The black statement of pistons, without more fuss
But gliding like a queen, she leaves the station.”
—Stephen Spender (1909–1995)
“Children should know there are limits to family finances or they will confuse “we can’t afford that” with “they don’t want me to have it.” The first statement is a realistic and objective assessment of a situation, while the other carries an emotional message.”
—Jean Ross Peterson (20th century)