RegularChains[SemiAlgebraicSetTools] - Maple Programming Help

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RegularChains[SemiAlgebraicSetTools]

 DisplayParametricBox
 pretty printing of a parametric box object

 Calling Sequence DisplayParametricBox(pbx)

Parameters

 pbx - parametric box object

Description

 • Print a parametric box object

Examples

 > $\mathrm{with}\left(\mathrm{RegularChains}\right):$
 > $\mathrm{with}\left(\mathrm{ParametricSystemTools}\right):$
 > $\mathrm{with}\left(\mathrm{SemiAlgebraicSetTools}\right):$
 > $R≔\mathrm{PolynomialRing}\left(\left[x,d,a,b,c\right]\right)$
 ${R}{≔}{\mathrm{polynomial_ring}}$ (1)

Determine under which conditions on $a,b,c,d$ the equation ${x}^{2}+d=0$ has 2 distinct real solutions, provided that $d$ satisfies $a{d}^{2}+bd+c=0$.

 > $F≔\left[{x}^{2}+d,a{d}^{2}+bd+c\right]$
 ${F}{≔}\left[{{x}}^{{2}}{+}{d}{,}{a}{}{{d}}^{{2}}{+}{b}{}{d}{+}{c}\right]$ (2)
 > $N≔\left[\right]$
 ${N}{≔}\left[{}\right]$ (3)
 > $P≔\left[\right]$
 ${P}{≔}\left[{}\right]$ (4)
 > $H≔\left[\right]$
 ${H}{≔}\left[{}\right]$ (5)
 > $\mathrm{rrc}≔\mathrm{RealRootClassification}\left(F,N,P,H,4,2,R\right)$
 ${\mathrm{rrc}}{≔}\left[\left[{\mathrm{regular_semi_algebraic_set}}\right]{,}{\mathrm{border_polynomial}}\right]$ (6)
 > $\mathrm{rsas}≔{{\mathrm{rrc}}_{1}}_{1}$
 ${\mathrm{rsas}}{≔}{\mathrm{regular_semi_algebraic_set}}$ (7)
 > $\mathrm{rbx}≔\mathrm{RepresentingBox}\left(\mathrm{rsas},R\right)$
 ${\mathrm{rbx}}{≔}{\mathrm{parametric_box}}$ (8)
 > $\mathrm{IsParametricBox}\left(\mathrm{rbx}\right)$
 ${\mathrm{true}}$ (9)
 > $\mathrm{DisplayParametricBox}\left(\mathrm{rbx}\right):$
 ${d}{<}{0}$
 ${\mathrm{AND}}$
 ${{c}}_{{1}}{:}{{d}}^{{2}}{}{a}{+}{d}{}{b}{+}{c}{=}{0}$ (10)