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MultivariatePowerSeries

  

Copy

  

copy a power series, a Puiseux series, or univariate polynomial over these series

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

Copy(p)

Copy(s)

Copy(u)

Parameters

p

-

power series generated by this package

s

-

Puiseux series generated by this package

u

-

univariate polynomial over power series or Puiseux series generated by this package

Description

• 

Copy(p), Copy(s), and Copy(u) return copies of p, s, and u, respectively. If the original object is subsequently modified (for example, by computing extra coefficients, or modifying the display style), these changes are not reflected in the copy, and vice versa. Note that the original object and its copy may share ancestors, such as power series or Puiseux series objects from which they were computed.

• 

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

We create two power series,  and .

The power series  keeps a record of  and  as its ancestors.

(1)

(2)

We can set the display styles for  and  independently. We ensure that enough terms are computed to show the difference.

(3)

(4)

(5)

(6)

The power series  is a copy of , however, they share  and , therefore when more terms of  are computed, the precision of  and  will be updated too. Consequently, the computation of new terms of  must be cheaper as it does not involve computing the coefficients of  and .

memory used=143.59MiB, alloc change=108.62MiB, cpu time=1.60s, real time=1.52s, gc time=216.32ms

(7)

(8)

(9)

(10)

memory used=6.70MiB, alloc change=0 bytes, cpu time=22.00ms, real time=23.00ms, gc time=0ns

(11)

References

  

Monforte, A.A., & Kauers, M. "Formal Laurent series in several variables." Expositiones Mathematicae. Vol. 31 No. 4 (2013): 350-367.

Compatibility

• 

The MultivariatePowerSeries[Copy] command was introduced in Maple 2021.

• 

For more information on Maple 2021 changes, see Updates in Maple 2021.

• 

The MultivariatePowerSeries[Copy] command was updated in Maple 2023.

See Also

HomogeneousPart

Inverse

PowerSeries

Precision

PuiseuxSeries

Truncate

 


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