The command ListConstruct(lp, rc, R) returns a list of regular chains ${\mathrm{rc}}_i$ which form a triangular decomposition of the regular chain obtained by extending rc with lp.

It is assumed that lp is a list of non-constant polynomials sorted in increasing main variable, and that any main variable of a polynomial in lp is strictly greater than any algebraic variable of rc.

It is also assumed that the polynomials of rc together with those of lp form a regular chain.

Although rc with lp is assumed to form a regular chain, several regular chains may be returned; this is because the polynomials of lp may be factorized with respect to rc.

To avoid these possible factorizations, use RegularChains[ChainTools][Chain]

If 'normalized'='yes' is present, then rc must be normalized. In addition, every returned regular chain is normalized.

If 'normalized'='strongly' is present, then rc must be strongly normalized. In addition, every returned regular chain is strongly normalized.

This command is part of the RegularChains[ChainTools] package, so it can be used in the form ListConstruct(..) only after executing the command with(RegularChains[ChainTools]). However, it can always be accessed through the long form of the command by using RegularChains[ChainTools][ListConstruct](..).

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

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

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

$R≔\mathrm{polynomial\_ring}$

$\mathrm{py}≔y^2+2y+1$

$\mathrm{py}≔y^2+2y+1$

$\mathrm{pt}≔t^2+y$

$\mathrm{pt}≔t^2+y$

$\mathrm{rc}≔\mathrm{Empty}\left(R\right)$

$\mathrm{rc}≔\mathrm{regular\_chain}$

$\mathrm{lrc}≔\mathrm{ListConstruct}\left(\left[\mathrm{py}\,\mathrm{pt}\right]\,\mathrm{rc}\,R\right)$

$\mathrm{lrc}≔\left[\mathrm{regular\_chain}\,\mathrm{regular\_chain}\right]$

$\mathrm{map}\left(\mathrm{Equations}\,\mathrm{lrc}\,R\right)$

$\left[\left[t-1\,y+1\right]\,\left[t+1\,y+1\right]\right]$