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RegularChains[SemiAlgebraicSetTools]

 VariableOrdering
 return the variable ordering defined in a quantifier-free formula

 Calling Sequence VariableOrdering(qff)

Parameters

 qff - a quantifier-free formula

Description

 • The command VariableOrdering(qff) returns the variable ordering (in decreasing order) defined in quantifier-free formula $\mathrm{qff}$.

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)
 > $\mathrm{qff}≔\mathrm{RepresentingQuantifierFreeFormula}\left(\mathrm{rbx}\right)$
 ${\mathrm{qff}}{:=}{\mathrm{quantifier_free_formula}}$ (9)
 > $\mathrm{VariableOrdering}\left(\mathrm{qff}\right)$
 $\left[{c}{,}{d}{,}{a}{,}{b}\right]$ (10)

 See Also

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