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.
Download Help Document
What kind of issue would you like to report? (Optional)