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.

$\mathrm{with}\left(\mathrm{RegularChains}\right)\:$

$\mathrm{with}\left(\mathrm{ParametricSystemTools}\right)\:$

$\mathrm{with}\left(\mathrm{SemiAlgebraicSetTools}\right)\:$

$R≔\mathrm{PolynomialRing}\left(\left[x\,b\,a\,c\right]\right)$

$R≔\mathrm{polynomial\_ring}$

$F≔\left[a{x}^2+bx+c\right]$

$F≔\left[a{x}^2+bx+c\right]$

$N≔\left[\right]$

$N≔\left[\right]$

$P≔\left[x\right]$

$P≔\left[x\right]$

$H≔\left[a\right]$

$H≔\left[a\right]$

$\mathrm{rrc}≔\mathrm{RealRootClassification}\left(F\,\left[\right]\,\left[x\right]\,\left[a\right]\,3\,2\,R\right)$

$\mathrm{rrc}≔\left[\left[\mathrm{regular\_semi\_algebraic\_set}\right]\,\mathrm{border\_polynomial}\right]$

$\mathrm{rsas}≔\mathrm{rrc}\left[1\right]\left[1\right]$

$\mathrm{rsas}≔\mathrm{regular\_semi\_algebraic\_set}$

$\mathrm{pbx}≔\mathrm{RepresentingBox}\left(\mathrm{rsas}\,R\right)$

$\mathrm{pbx}≔\mathrm{parametric\_box}$

$\mathrm{IsParametricBox}\left(\mathrm{pbx}\right)$

$\mathrm{true}$

$\mathrm{IsParametricBox}\left(\mathrm{rsas}\right)$

$\mathrm{false}$