Construct - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim


RegularChains[ChainTools]

  

Construct

  

constructs regular chains

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Construct(p, rc, R)

Construct(p, rc, R, 'normalized'='yes')

Construct(p, rc, R, 'normalized'='strongly')

Parameters

p

-

polynomial of R

rc

-

regular chain of R

R

-

polynomial ring

'normalized'='yes'

-

(optional) boolean flag

'normalized'='strongly'

-

(optional) boolean flag

Description

• 

The command Construct(p, rc, R) returns a list of regular chains  which form a triangular decomposition of the regular chain obtained by extending rc with p.

• 

This assumes that p is a non-constant with main variable greater than any algebraic variable of rc, and that the initial of p is regular modulo the saturated ideal of rc. Hence p and rc form together a regular chain.

• 

Although rc with p is assumed to form a regular chain, several regular chains may be returned; this is because the polynomial p may be factorized with respect to rc in order to simplify the expressions in the regular chains .

• 

Such factorizations will happen if they can be performed quickly. For instance, if p involves only one variable.

• 

To avoid these possible factorizations, use RegularChains[ChainTools][Chain]

• 

If 'normalized'='yes' is present, then rc must be normalized. In addition, every returned regular chain is normalized.

• 

If 'normalized'='strongly' is present, then rc must be strongly normalized. In addition, every returned regular chain is strongly normalized.

• 

This command is part of the RegularChains[ChainTools] package, so it can be used in the form Construct(..) only after executing the command with(RegularChains[ChainTools]).  However, it can always be accessed through the long form of the command by using RegularChains[ChainTools][Construct](..).

Examples

with(RegularChains): with(ChainTools):

R := PolynomialRing([t, x, y, z]);

(1)

pz := z^2+2*z+1;

(2)

py := y^2+z;

(3)

pt := t^3 + y*z;

(4)

rc := Empty(R);

(5)

rc1 := Construct(pz, rc, R);

(6)

rc1 := rc1[1]; Equations(rc1, R);

(7)

rc2 := Construct(py, rc1, R);

(8)

rc2 := rc2[1]; Equations(rc2, R);

(9)

rc3 := Construct(pt, rc2, R);

(10)

map(Equations, rc3, R);

(11)

See Also

Chain

ChainTools

Empty

Equations

ListConstruct

PolynomialRing

RegularChains

 


Download Help Document