AngouriMath
RealRootCount(AngouriMath.Functions.IntegerPolynomial,AngouriMath.Entity.Variable,System.Int32)
Method (no overloads)
Summary
How many distinct real roots an irreducible factor of degree
two, three or four has, ornull where that could not be settled.
two, three or four has, or
Remarks
separates two real roots (negative) from four or none (positive), and the two
auxiliary quantities
those: four real where both are negative, none where either is positive. Where
neither of those holds — one of them zero and the other not positive — the
criterion says nothing, and neither does this. Rees, A note on the quartic,
Amer. Math. Monthly 29 (1922); Lazard, Quantifier elimination: optimal solution
for two classical examples, J. Symbolic Comput. 5 (1988).
not have — so it is a sign that the input was not what it was taken to be, and the
sign table declines rather than proceeds.
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