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RegularChains[SemiAlgebraicSetTools][RepresentingChain] - return the regular chain part of a regular semi-algebraic set/system
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Calling Sequence
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RepresentingChain(rst, R)
RepresentingChain(rsas, R)
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Parameters
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rst
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a regular semi-algebraic set
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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 RepresentingChain(rst, R) or the command RepresentingChain(rst, R) returns the regular chain part of its first argument.
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See the page SemiAlgebraicSetTools for the definition of a regular semi-algebraic system and that of a regular semi-algebraic set.
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Examples
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![F := [f]](/support/helpjp/helpview.aspx?si=6396/file06531/math103.png)
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![F := [a*x^2+b*x+c]](/support/helpjp/helpview.aspx?si=6396/file06531/math106.png)
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![N := []](/support/helpjp/helpview.aspx?si=6396/file06531/math110.png)
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![N := []](/support/helpjp/helpview.aspx?si=6396/file06531/math113.png)
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![P := []](/support/helpjp/helpview.aspx?si=6396/file06531/math117.png)
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![P := []](/support/helpjp/helpview.aspx?si=6396/file06531/math120.png)
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![H := []](/support/helpjp/helpview.aspx?si=6396/file06531/math124.png)
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![H := []](/support/helpjp/helpview.aspx?si=6396/file06531/math127.png)
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![R := PolynomialRing([x, a, b, c])](/support/helpjp/helpview.aspx?si=6396/file06531/math131.png)
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![rrc := [[regular_semi_algebraic_set], border_polynomial]](/support/helpjp/helpview.aspx?si=6396/file06531/math148.png)
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![rst := rrc[1][1]](/support/helpjp/helpview.aspx?si=6396/file06531/math152.png)
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| (10) |
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![[]](/support/helpjp/helpview.aspx?si=6396/file06531/math169.png)
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![F := [a*x^2+b*x+c = 0, 0 < x, a <> 0]](/support/helpjp/helpview.aspx?si=6396/file06531/math173.png)
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![F := [a*x^2+b*x+c = 0, 0 < x, a <> 0]](/support/helpjp/helpview.aspx?si=6396/file06531/math176.png)
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![R := PolynomialRing([x, c, b, a])](/support/helpjp/helpview.aspx?si=6396/file06531/math180.png)
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![out := [regular_semi_algebraic_system]](/support/helpjp/helpview.aspx?si=6396/file06531/math190.png)
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| (15) |
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![P := PositiveInequalities(out[1], R)](/support/helpjp/helpview.aspx?si=6396/file06531/math201.png)
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![P := [x]](/support/helpjp/helpview.aspx?si=6396/file06531/math204.png)
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![rc := RepresentingChain(out[1], R)](/support/helpjp/helpview.aspx?si=6396/file06531/math208.png) 
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![PIECEWISE([a*x^2+b*x+c = 0, ``], [a <> 0, ``])](/support/helpjp/helpview.aspx?si=6396/file06531/math215.png)
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![qff := RepresentingQuantifierFreeFormula(out[1])](/support/helpjp/helpview.aspx?si=6396/file06531/math219.png) 
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![Display(out[1], R)](/support/helpjp/helpview.aspx?si=6396/file06531/math239.png)
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| (19) |
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