The command GeneralConstruct(F, T, H, R) returns a constructible set $C$.

Assume that the quasi-component of T is $W\left(T\right)$ (see RegularChains for the definition). Then $C$ consists of points in $W\left(T\right)$ which cancel all polynomials in F, but do not cancel any polynomials in H.

If F is not specified, it is set to be the empty list.

If T is not specified, it is set to be the empty regular chain.

If H is not specified, it is set to $\left[1\right]$.

The quasi-component of the empty regular chain is the whole space.

Any other inputs will be rejected and an error message will be reported.

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](..).

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

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

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

$R≔\mathrm{PolynomialRing}\left(\left[x\,y\,t\right]\right)$

$R≔\mathrm{polynomial\_ring}$

$p≔\left(5t+5\right)x-y-\left(10t+7\right)\;$$q≔\left(5t-5\right)x-\left(t+2\right)y+\left(-7t+11\right)\;$$h≔x+t$

$p≔\left(5t+5\right)x-y-10t-7$

$q≔\left(5t-5\right)x-\left(t+2\right)y-7t+11$

$h≔x+t$

$\mathrm{rc}≔\mathrm{Empty}\left(R\right)\:$$\mathrm{rc}≔\mathrm{Chain}\left(\left[q\right]\,\mathrm{rc}\,R\right)$

$\mathrm{rc}≔\mathrm{regular\_chain}$

$\mathrm{cs}≔\mathrm{GeneralConstruct}\left(\left[p\right]\,\mathrm{rc}\,\left[h\right]\,R\right)$

$\mathrm{cs}≔\mathrm{constructible\_set}$

$\mathrm{lrs}≔\mathrm{RepresentingRegularSystems}\left(\mathrm{cs}\,R\right)$

$\mathrm{lrs}≔\left[\mathrm{regular\_system}\right]$

$\mathrm{ineqs}≔\mathrm{map}\left(\mathrm{RepresentingInequations}\,\mathrm{lrs}\,R\right)$

$\mathrm{ineqs}≔\left[\left[t-1\,t^3+4t^2+7t+5\right]\right]$

$\mathrm{Info}\left(\mathrm{cs}\,R\right)$

$\left[\left[\left(5t-5\right)x+\left(-t-2\right)y-7t+11\,\left(t^2+2t+3\right)y-3t^2-t-4\right]\,\left[t-1\,t^3+4t^2+7t+5\right]\right]$