RegularChains[ChainTools] - Maple Programming Help

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RegularChains[ChainTools]

  

Extend

  

decomposes a triangular set into regular chains

 

Calling Sequence

Parameters

Description

Examples

Compatibility

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:

RPolynomialRingz,y,x

Rpolynomial_ring

(1)

CChainy2x2,EmptyR,R

Cregular_chain

(2)

EExtendC,yxz2+y+xz,R;mapDisplay,E,R

Eregular_chain

{z=0y+x=0

(3)

EExtendC,yxz2+z,R;mapDisplay,E,R

Eregular_chain,regular_chain

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

(4)

Compatibility

• 

The RegularChains[ChainTools][Extend] command was introduced in Maple 15.

• 

For more information on Maple 15 changes, see Updates in Maple 15.

See Also

Chain

Empty

Equations

Inverse

IsRegular

IsStronglyNormalized

PolynomialRing

RegularChains

RegularizeDim0

RegularizeInitial

SparsePseudoRemainder