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MultivariatePowerSeries

  

GetOrder

  

compute the order of a Puiseux series in one variable

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

GetOrder(s)

GetOrder(s, bnd)

Parameters

s

-

Puiseux series in one variable generated by this package

bnd

-

nonnegative integer or infinity

Description

• 

The GetOrder command computes the order of a Puiseux series in one variable, s.

• 

A univariate Puiseux series can be written as m=Mammn for some M, n. Then the order of s is defined as minmn|am0.

• 

If the order cannot be determined from the analytic expression for s, the command examines subsequent homogeneous components from the internal power series of s. If it has not found any nonzero components after examining bnd + 1 such components (degrees 0 through bnd), the command gives up and signals an error. The default value for bnd is 10.

• 

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

withMultivariatePowerSeries:

Create two Puiseux series.

pPowerSeriesd→ud,variables=u

pPowⅇrSⅇrⅈⅇs: 1+

(1)

sPuiseuxSeriesp,u=x2

sPuⅈsⅇuxSⅇrⅈⅇs: 1+

(2)

s2PuiseuxSeriesp,u=x231

s2PuⅈsⅇuxSⅇrⅈⅇs: 0+

(3)

We get the order of s, s2, s1 and x2+s1.

GetOrders

0

(4)

GetOrders2

23

(5)

GetOrders1

2

(6)

GetOrders1x2

4

(7)

If we try to find out the order of s212, initially it will not work. We need to specify a higher value for the bound.

GetOrders212

Error, (in MultivariatePowerSeries:-GetOrder) the order of Object(MultivariatePowerSeries:-PuiseuxSeriesObject,Object(MultivariatePowerSeries:-PowerSeriesObject,Array(0..10, [0,0,0,0,0,0,0,0,0,0,0]),10,MultivariatePowerSeries:-PowerSeriesObject:-mul_gen,{u},ancestors),[x],[u],[[2/3]],[x = 0]) cannot be determined with the current bound 10

GetOrders212,15

8

(8)

Compatibility

• 

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

• 

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

See Also

MultivariatePowerSeries

PuiseuxSeries