RegularChains[ChainTools]
Construct
constructs regular chains
Calling Sequence
Parameters
Description
Examples
Construct(p, rc, R)
Construct(p, rc, R, 'normalized'='yes')
Construct(p, rc, R, 'normalized'='strongly')
p
-
polynomial of R
rc
regular chain of R
R
polynomial ring
'normalized'='yes'
(optional) boolean flag
'normalized'='strongly'
The command Construct(p, rc, R) returns a list of regular chains which form a triangular decomposition of the regular chain obtained by extending rc with p.
This assumes that p is a non-constant with main variable greater than any algebraic variable of rc, and that the initial of p is regular modulo the saturated ideal of rc. Hence p and rc form together a regular chain.
Although rc with p is assumed to form a regular chain, several regular chains may be returned; this is because the polynomial p may be factorized with respect to rc in order to simplify the expressions in the regular chains .
Such factorizations will happen if they can be performed quickly. For instance, if p involves only one variable.
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 Construct(..) 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][Construct](..).
See Also
Chain
ChainTools
Empty
Equations
ListConstruct
PolynomialRing
RegularChains
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