RegularChains[ChainTools][Extend] - decomposes a triangular set into regular chains
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Calling Sequence
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Extend(rc, lp, R)
Extend(rc, lp, R, 'output'='lazard')
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Parameters
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rc
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regular chain of R
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lp
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polynomial of R
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R
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polynomial ring
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'output'='lazard'
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-
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(optional) boolean flag
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Description
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The command Extend(rc, lp, R) returns a triangular decomposition (by means of regular chains) of the quasi-component defined by rc and lp. This assumes that polynomials of lp form a triangular set and are sorted in an ascending order according to their main variables. Moreover, it is assumed that each main variable of a polynomial in lp is larger than any variable appearing in rc. Therefore, the polynomials in rc and lp together must form a triangular set, which is, however, not necessarily a regular chain.
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If the option 'output'='lazard' is present then the triangular decomposition is the sense of Lazard otherwise it is in the sense of Kalkbrener.
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Compatibility
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The RegularChains[ChainTools][Extend] command was introduced in Maple 15.
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Examples
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See Also
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Chain, Empty, Equations, Inverse, IsRegular, IsStronglyNormalized, PolynomialRing, RegularChains, RegularizeDim0, RegularizeInitial, SparsePseudoRemainder
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