RegularChains[SemiAlgebraicSetTools]
RepresentingRootIndex
return the root index in a parametric box
Calling Sequence
Parameters
Description
Examples
RepresentingRootIndex(pbx,R)
pbx
-
parametric box
R
polynomial ring
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.
withRegularChains:
withParametricSystemTools:
withSemiAlgebraicSetTools:
R≔PolynomialRingx,d,a,b,c
R≔polynomial_ring
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
N≔
P≔
H≔
rrc≔RealRootClassificationF,N,P,H,4,2,R
rrc≔regular_semi_algebraic_set,border_polynomial
rsas≔rrc11
rsas≔regular_semi_algebraic_set
rbx≔RepresentingBoxrsas,R
rbx≔parametric_box
DisplayParametricBoxrbx:
d<0
AND
c1:d2a+db+c=0
RepresentingRootIndexrbx
1
See Also
IsParametricBox
RealRootClassification
RegularChains
RepresentingBox
RepresentingChain
RepresentingQuantifierFreeFormula
VariableOrdering
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