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

Online Help

All Products    Maple    MapleSim


MultivariatePowerSeries

  

GetPuiseuxSeriesOrder

  

get the variable order of a Puiseux series

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

GetPuiseuxSeriesOrder(s)

Parameters

s

-

Puiseux series generated by this package

Description

• 

This command returns the variable order of a Puiseux series.

• 

A Puiseux series is a power series in rational powers of the variables. More precisely:

– 

Let  and  be ordered lists of variables.

– 

Let  be a list of  grevlex-positive -dimensional rational vectors.

– 

Let  be a point in .

– 

Let  be a multivariate power series in  with homogeneous components .

  

For any  in  and any list , we write  for . Moreover, we write  for the list  of  products of powers of the variables in . Then  is a Puiseux series, and every Puiseux series can be written in this way. This can be understood as evaluating  at  and then multiplying the result by .

• 

We call  the internal power series of the Puiseux series ;  the variable order of ;  the variable order of ; and  the rays of . The rays generate the cone containing the support of , meaning the set of exponent vectors of  that occur in  with a nonzero coefficient, as in the paper by Monforte and Kauers (see References). The vertex of this cone is .

• 

When using the MultivariatePowerSeries package, do not assign anything to the variables occurring in the power series, Puiseux series, and univariate polynomials over these series. If you do, you may see invalid results.

Examples

Create two Puiseux series.

(1)

(2)

(3)

We get the variable order of s1.

(4)

When we create a Puiseux series using a list of equations, Maple internally chooses a Puiseux series order. Now, we get the variable order of s2.

(5)

Next, notice that after adding s1 and s2, the new variable order is a mix between the orders of s1 and s2.

(6)

(7)

Compatibility

• 

The MultivariatePowerSeries[GetPuiseuxSeriesOrder] command was introduced in Maple 2023.

• 

For more information on Maple 2023 changes, see Updates in Maple 2023.

See Also

MultivariatePowerSeries

PuiseuxSeries

 


Download Help Document