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
C ≔ Chain⁡y2−x2,Empty⁡R,R
E ≔ Extend⁡C,y−x⁢z2+y+x⁢z,R;map⁡Display,E,R
E ≔ Extend⁡C,y−x⁢z2+z,R;map⁡Display,E,R
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