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MultivariatePowerSeries

  

SumOfAllMonomials

  

Get the power series representing the sum of all monomials over a set of variables

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

SumOfAllMonomials(x)

Parameters

x

-

list of variables

Description

• 

The command SumOfAllMonomials(x) returns the power series containing each monomial in the variables x with coefficient 1; that is, its homogeneous part of degree d is the sum of all monomials of degree d.

• 

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

Examples

withMultivariatePowerSeries:

We create a power series that is the sum of all monomials in x, and compute its homogeneous part of degree 2 and its truncation at precision 4.

aSumOfAllMonomialsx

aPowⅇrSⅇrⅈⅇs of 11x : 1+x+

(1)

HomogeneousParta,2

x2

(2)

Truncatea,4

x4+x3+x2+x+1

(3)

We create a power series that is the sum of all monomials in x, y, and/or z. We compute its homogeneous part of degree 2 and its truncation at precision 3.

bSumOfAllMonomialsx,y,z

bPowⅇrSⅇrⅈⅇs of 11x1y1z : 1+x+y+z+

(4)

HomogeneousPartb,2

x2+yx+zx+y2+zy+z2

(5)

Truncateb,3

x3+x2y+x2z+xy2+xyz+xz2+y3+y2z+yz2+z3+x2+yx+zx+y2+zy+z2+x+y+z+1

(6)

Compatibility

• 

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

• 

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

See Also

GeometricSeries

HomogeneousPart

Truncate