decomposes a triangular set into regular chains
Extend(rc, lp, R)
Extend(rc, lp, R, 'output'='lazard')
regular chain of R
polynomial of R
(optional) boolean flag
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.
If the option 'output'='lazard' is present then the triangular decomposition is the sense of Lazard otherwise it is in the sense of Kalkbrener.
R ≔ PolynomialRing⁡z,y,x
R ≔ polynomial_ring
C ≔ Chain⁡y2−x2,Empty⁡R,R
C ≔ regular_chain
E ≔ Extend⁡C,y−x⁢z2+y+x⁢z,R;map⁡Display,E,R
E ≔ regular_chain
E ≔ Extend⁡C,y−x⁢z2+z,R;map⁡Display,E,R
E ≔ regular_chain,regular_chain
The RegularChains[ChainTools][Extend] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
Download Help Document
What kind of issue would you like to report? (Optional)
Thank you for submitting feedback on this help document. Your feedback will be used
to improve Maple's help in the future.