return the root index in a parametric box - Maple Help

Online Help

All Products    Maple    MapleSim


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

RegularChains[SemiAlgebraicSetTools][RepresentingRootIndex] - return the root index in a parametric box

Calling Sequence

RepresentingRootIndex(pbx,R)

Parameters

pbx

-

parametric box

R

-

polynomial ring

Description

• 

The command RepresentingRootIndex(pbx,R) returns the representing root index in a parametric box.

  

See the page SemiAlgebraicSetTools for the definitions of a regular semi-algebraic set, a parametric box and a box.

Examples

withRegularChains:

withParametricSystemTools:

withSemiAlgebraicSetTools:

R:=PolynomialRingx,d,a,b,c

R:=polynomial_ring

(1)

Determine under which conditions on a,b,c,d the equation x2+d=0 has 2 distinct real solutions provided that d satisfies ad2+bd+c=0.

F:=x2+d,ad2+bd+c

F:=x2+d,ad2+bd+c

(2)

N:=

N:=

(3)

P:=

P:=

(4)

H:=

H:=

(5)

rrc:=RealRootClassificationF,N,P,H,4,2,R

rrc:=regular_semi_algebraic_set,border_polynomial

(6)

rsas:=rrc11

rsas:=regular_semi_algebraic_set

(7)

rbx:=RepresentingBoxrsas,R

rbx:=parametric_box

(8)

DisplayParametricBoxrbx:

d<0

AND

c1&colon;d2a+db+c&equals;0

(9)

RepresentingRootIndexrbx

1

(10)

See Also

IsParametricBox, RealRootClassification , RegularChains, RepresentingBox, RepresentingChain, RepresentingChain, RepresentingQuantifierFreeFormula, RepresentingRootIndex, VariableOrdering


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam