constructs regular chains
ListConstruct(lp, rc, R)
ListConstruct(p, rc, R, 'normalized'='yes')
ListConstruct(p, rc, R, 'normalized'='strongly')
list of polynomials of R
regular chain of R
(optional) boolean flag
The command ListConstruct(lp, rc, R) returns a list of regular chains rci 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](..).
R ≔ PolynomialRing⁡t,x,y,z
R ≔ polynomial_ring
py ≔ y2+2⁢y+1
pt ≔ t2+y
rc ≔ Empty⁡R
rc ≔ regular_chain
lrc ≔ ListConstruct⁡py,pt,rc,R
lrc ≔ regular_chain,regular_chain
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