RegularChains[ChainTools] - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Factorization and Solving Equations : RegularChains : ChainTools Subpackage : RegularChains/ChainTools/Extend

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

R:=polynomial_ring

(1)

CChainy2x2,EmptyR,R

C:=regular_chain

(2)

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

E:=regular_chain

{z=0y+x=0

(3)

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

E:=regular_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

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam