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RegularChains[SemiAlgebraicSetTools][RepresentingQuantifierFreeFormula] - return the quantifier-free formula of a parametric box or a regular semi-algebraic system
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Calling Sequence
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RepresentingQuantifierFreeFormula(pbx)
RepresentingQuantifierFreeFormula(rst, R)
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Parameters
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pbx
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a parametric box
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rsas
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a regular semi-algebraic system
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R
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a polynomial ring
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Description
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The command RepresentingQuantifierFreeFormula(pbx) returns the representing quantifier-free formula of the parametric box pbx.
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The command RepresentingQuantifierFreeFormula(rsas, R) returns the representing quantifier-free formula of the regular semi-algebraic system rsas.
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See the page SemiAlgebraicSetTools for the definition of a regular semi-algebraic system and that of a parametric box.
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Examples
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![R := PolynomialRing([x, b, a, c])](/support/helpjp/helpview.aspx?si=6398/file06532/math98.png)
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| (1) |
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![F := [a*x^2+b*x+c]](/support/helpjp/helpview.aspx?si=6398/file06532/math105.png)
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![F := [a*x^2+b*x+c]](/support/helpjp/helpview.aspx?si=6398/file06532/math108.png)
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![N := []](/support/helpjp/helpview.aspx?si=6398/file06532/math112.png)
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![N := []](/support/helpjp/helpview.aspx?si=6398/file06532/math115.png)
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![P := [x]](/support/helpjp/helpview.aspx?si=6398/file06532/math119.png)
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![P := [x]](/support/helpjp/helpview.aspx?si=6398/file06532/math122.png)
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![H := [a]](/support/helpjp/helpview.aspx?si=6398/file06532/math126.png)
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![H := [a]](/support/helpjp/helpview.aspx?si=6398/file06532/math129.png)
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![rrc := RealRootClassification(F, [], [x], [a], 3, 2, R)](/support/helpjp/helpview.aspx?si=6398/file06532/math133.png)
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![rrc := [[regular_semi_algebraic_set], border_polynomial]](/support/helpjp/helpview.aspx?si=6398/file06532/math136.png)
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![rsas := rrc[1][1]](/support/helpjp/helpview.aspx?si=6398/file06532/math140.png)
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| (10) |
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![[[c, a, b, 4*a*c-b^2], [[-1, -1, 1, -1], [1, 1, -1, -1]]]](/support/helpjp/helpview.aspx?si=6398/file06532/math171.png)
| (11) |
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![F := [a*x^2+b*x+c = 0, 0 < x, a <> 0]](/support/helpjp/helpview.aspx?si=6398/file06532/math175.png)
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![F := [a*x^2+b*x+c = 0, 0 < x, a <> 0]](/support/helpjp/helpview.aspx?si=6398/file06532/math178.png)
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![R := PolynomialRing([x, c, b, a])](/support/helpjp/helpview.aspx?si=6398/file06532/math182.png)
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| (13) |
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![out := [regular_semi_algebraic_system]](/support/helpjp/helpview.aspx?si=6398/file06532/math192.png)
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| (15) |
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![P := PositiveInequalities(out[1], R)](/support/helpjp/helpview.aspx?si=6398/file06532/math203.png)
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![P := [x]](/support/helpjp/helpview.aspx?si=6398/file06532/math206.png)
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![rc := RepresentingChain(out[1], R)](/support/helpjp/helpview.aspx?si=6398/file06532/math210.png) 
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![PIECEWISE([a*x^2+b*x+c = 0, ``], [a <> 0, ``])](/support/helpjp/helpview.aspx?si=6398/file06532/math217.png)
| (17) |
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![qff := RepresentingQuantifierFreeFormula(out[1])](/support/helpjp/helpview.aspx?si=6398/file06532/math221.png) 
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| (18) |
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![Display(out[1], R)](/support/helpjp/helpview.aspx?si=6398/file06532/math241.png)
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| (19) |
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