decomposes a triangular set into regular chains - Maple Help

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RegularChains[ChainTools][Extend] - decomposes a triangular set into regular chains

Calling Sequence

Extend(rc, lp, R)

Extend(rc, lp, R,  'output'='lazard')

Parameters

rc

-

regular chain of R

lp

-

polynomial of R

R

-

polynomial ring

'output'='lazard'

-

(optional) boolean flag

Description

• 

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.

Examples

withRegularChains:withChainTools:

R:=PolynomialRingz,y,x

R:=polynomial_ring

(1)

C:=Chainy2x2,EmptyR,R

C:=regular_chain

(2)

E:=ExtendC,yxz2+y+xz,R;mapDisplay,E,R

E:=regular_chain

{z=0y+x=0

(3)

E:=ExtendC,yxz2+z,R;mapDisplay,E,R

E:=regular_chain,regular_chain

{z=0y+x=0,{2xz1=0y+x=02x0

(4)

See Also

Chain, Empty, Equations, Inverse, IsRegular, IsStronglyNormalized, PolynomialRing, RegularChains, RegularizeDim0, RegularizeInitial, SparsePseudoRemainder


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