RegularChains[SemiAlgebraicSetTools] - Maple Help

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RegularChains[SemiAlgebraicSetTools]

 IsParametricBox
 check if an input is a parametric box

 Calling Sequence IsParametricBox(b)

Parameters

 b - any value

Description

 • The command IsParametricBox(b) returns $\mathrm{true}$ if b is a parametric box, and $\mathrm{false}$ otherwise.
 • See the page SemiAlgebraicSetTools for the definitions of a regular semi-algebraic system, a parametric box and a box.

Examples

 > $\mathrm{with}\left(\mathrm{RegularChains}\right):$
 > $\mathrm{with}\left(\mathrm{ParametricSystemTools}\right):$
 > $\mathrm{with}\left(\mathrm{SemiAlgebraicSetTools}\right):$
 > $R≔\mathrm{PolynomialRing}\left(\left[x,b,a,c\right]\right)$
 ${R}{:=}{\mathrm{polynomial_ring}}$ (1)
 > $F≔\left[a{x}^{2}+bx+c\right]$
 ${F}{:=}\left[{a}{}{{x}}^{{2}}{+}{b}{}{x}{+}{c}\right]$ (2)
 > $N≔\left[\right]$
 ${N}{:=}\left[{}\right]$ (3)
 > $P≔\left[x\right]$
 ${P}{:=}\left[{x}\right]$ (4)
 > $H≔\left[a\right]$
 ${H}{:=}\left[{a}\right]$ (5)
 > $\mathrm{rrc}≔\mathrm{RealRootClassification}\left(F,\left[\right],\left[x\right],\left[a\right],3,2,R\right)$
 ${\mathrm{rrc}}{:=}\left[\left[{\mathrm{regular_semi_algebraic_set}}\right]{,}{\mathrm{border_polynomial}}\right]$ (6)
 > $\mathrm{rsas}≔{{\mathrm{rrc}}_{1}}_{1}$
 ${\mathrm{rsas}}{:=}{\mathrm{regular_semi_algebraic_set}}$ (7)
 > $\mathrm{pbx}≔\mathrm{RepresentingBox}\left(\mathrm{rsas},R\right)$
 ${\mathrm{pbx}}{:=}{\mathrm{parametric_box}}$ (8)
 > $\mathrm{IsParametricBox}\left(\mathrm{pbx}\right)$
 ${\mathrm{true}}$ (9)
 > $\mathrm{IsParametricBox}\left(\mathrm{rsas}\right)$
 ${\mathrm{false}}$ (10)