RegularChains[ChainTools][ListConstruct] - constructs regular chains
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Calling Sequence
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ListConstruct(lp, rc, R)
ListConstruct(p, rc, R, 'normalized'='yes')
ListConstruct(p, rc, R, 'normalized'='strongly')
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Parameters
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lp
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list of polynomials of R
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rc
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regular chain of R
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R
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polynomial ring
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'normalized'='yes'
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(optional) boolean flag
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'normalized'='strongly'
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(optional) boolean flag
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Description
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The command ListConstruct(lp, rc, R) returns a list of regular chains which form a triangular decomposition of the regular chain obtained by extending rc with lp.
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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.
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It is also assumed that the polynomials of rc together with those of lp form a regular chain.
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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.
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To avoid these possible factorizations, use RegularChains[ChainTools][Chain]
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If 'normalized'='yes' is present, then rc must be normalized. In addition, every returned regular chain is normalized.
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If 'normalized'='strongly' is present, then rc must be strongly normalized. In addition, every returned regular chain is strongly normalized.
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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](..).
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Examples
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