return the sign of a polynomial at real point
SignAtBox(p, B, R)
a box object encoding a point with real coordinates
The command SignAtBox(p, B, R) returns the sign of the polynomial p at the point encoded by the box object B.
The box object B is assumed to be returned by the command RealRootIsolate.
The sign at B of the polynomial p is given as -1, 0, or 1 for negative, null, or positive, respectively.
R ≔ PolynomialRing⁡y,x
Isolate the real points of a polynomial system and pick one of them.
B ≔ RealRootIsolate⁡x2−2,y−x,,x,,R1
Check the sign of a polynomial at that box.
p ≔ x2+y2−4
Checking a couple other signs.
F. Boulier, C. Chen, F. Lemaire, M. Moreno Maza "Real root isolation of regular chains." ASCM'2009, Math-for-Industry, Lecture Note Series Vol. 22.
R. Rioboo "Computation of the real closure of an ordered field." ISSAC'92, Academic Press, San Francisco.
The RegularChains[SemiAlgebraicSetTools][SignAtBox] command was introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
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