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

Online Help

All Products    Maple    MapleSim


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

withMultivariatePowerSeries:

We create two power series, a and b.

aInversePowerSeries1+xy:

bInversePowerSeriesy2x+1:

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

ca+b

cPowⅇrSⅇrⅈⅇs of 11+xy+1y2x+1 : 2+

(1)

dCopyc

dPowⅇrSⅇrⅈⅇs of 11+xy+1y2x+1 : 2+

(2)

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

SetDisplayStylec,'precision'=7

precision=7

(3)

SetDisplayStyled,'precision'=4

precision=4

(4)

UpdatePrecisionc,7:UpdatePrecisiond,7:

c

PowⅇrSⅇrⅈⅇs of 11+xy+1y2x+1 : 2+y+2x22xy+3x2y5y2x+y3+2x44x3y+3x2y24xy3+2y4+5x4y14x3y2+10x2y32xy4+y5+2x66x5y+10x4y220x3y3+21x2y46xy5+7x6y27x5y2+35x4y325x3y4+21x2y511xy6+y7+

(5)

d

PowⅇrSⅇrⅈⅇs of 11+xy+1y2x+1 : 2+y+2x22xy+3x2y5y2x+y3+2x44x3y+3x2y24xy3+2y4+

(6)

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

gc:

CodeTools:-UsageHomogeneousPartc,500:

memory used=143.60MiB, alloc change=113.27MiB, cpu time=1.56s, real time=1.47s, gc time=255.73ms

Precisiona

500

(7)

Precisionb

500

(8)

Precisionc

500

(9)

Precisiond

7

(10)

gc:

CodeTools:-UsageHomogeneousPartd,500:

memory used=6.70MiB, alloc change=0 bytes, cpu time=27.00ms, real time=27.00ms, gc time=0ns

Precisiond

500

(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