RegularChains[SemiAlgebraicSetTools] - Maple Programming Help

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Home : Support : Online Help : Mathematics : Factorization and Solving Equations : RegularChains : SemiAlgebraicSetTools Subpackage : RegularChains/SemiAlgebraicSetTools/SignAtBox

RegularChains[SemiAlgebraicSetTools]

  

SignAtBox

  

return the sign of a polynomial at real point

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

SignAtBox(p, B, R)

Parameters

p

-

a polynomial

B

-

a box object encoding a point with real coordinates

R

-

polynomial ring

Description

• 

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.

Examples

with(RegularChains):

with(SemiAlgebraicSetTools):

R := PolynomialRing([y, x]);

Rpolynomial_ring

(1)

Isolate the real points of a polynomial system and pick one of them.

B := RealRootIsolate([x^2-2, y-x], [], [x], [], R)[1];

Bbox

(2)

Check the sign of a polynomial at that box.

p := x^2+y^2-4;

px2+y24

(3)

SignAtBox(p, B, R);

0

(4)

Checking a couple other signs.

SignAtBox(p-1, B, R);

−1

(5)

SignAtBox(p+1, B, R);

1

(6)

References

  

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.

Compatibility

• 

The RegularChains[SemiAlgebraicSetTools][SignAtBox] command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

RealRootIsolate