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RegularChains[ConstructibleSetTools][GeneralConstruct] - construct a constructible set from a regular chain, equalities, and inequalities
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Calling Sequence
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GeneralConstruct(F, T, H, R)
GeneralConstruct(F, T, R)
GeneralConstruct(T, H, R)
GeneralConstruct(F, H, R)
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Parameters
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F, H
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lists of polynomials
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T
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regular chain
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R
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polynomial ring
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Description
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The command GeneralConstruct(F, T, H, R) returns a constructible set  .
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If F is not specified, it is set to be the empty list.
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If T is not specified, it is set to be the empty regular chain.
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If H is not specified, it is set to ![[1]](/support/helpjp/helpview.aspx?si=6412/file06472/math119.png) .
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The quasi-component of the empty regular chain is the whole space.
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Any other inputs will be rejected and an error message will be reported.
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This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form GeneralConstruct(..) only after executing the command with(RegularChains[ConstructibleSetTools]). However, it can always be accessed through the long form of the command by using RegularChains[ConstructibleSetTools][GeneralConstruct](..).
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Examples
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First, define a polynomial ring and three polynomials in the ring.
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![R := PolynomialRing([x, y, t])](/support/helpjp/helpview.aspx?si=6412/file06472/math157.png)
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Build a regular chain using  , which means  vanishes but the initial  of  does not vanish.
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 ![rc := Chain([q], rc, R)](/support/helpjp/helpview.aspx?si=6412/file06472/math190.png)
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Use GeneralConstruct to figure out the points in  which cancel  but do not cancel  .
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![cs := GeneralConstruct([p], rc, [h], R)](/support/helpjp/helpview.aspx?si=6412/file06472/math207.png)
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cs is a constructible set consisting of one regular system.
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![lrs := [regular_system]](/support/helpjp/helpview.aspx?si=6412/file06472/math220.png)
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The inequalities form the following list.
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![ineqs := [[t-1, t^3+4*t^2+7*t+5]]](/support/helpjp/helpview.aspx?si=6412/file06472/math229.png)
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To see complete information, use the Info command.
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![[[(5*t-5)*x+(-2-t)*y-7*t+11, (t^2+2*t+3)*y-t-4-3*t^2], [t-1, t^3+4*t^2+7*t+5]]](/support/helpjp/helpview.aspx?si=6412/file06472/math241.png)
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