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Ore_algebra

  

skew_product

  

inner product of an Ore algebra

  

skew_power

  

power of an Ore algebra

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

skew_product(w1, w2, A)

skew_power(w, n, A)

Parameters

w1, w2, w

-

skew polynomials of the Ore algebra A

A

-

Ore algebra table

n

-

non-negative integer

Description

• 

The skew_product(w1, w2, A) function computes the noncommutative product w1w2 (in this order) in the Ore algebra A.

• 

The skew_power(w, n, A) function computes the nth power of w in the Ore algebra A.

• 

To declare an Ore algebra, use Ore_algebra[skew_algebra], Ore_algebra[shift_algebra], or Ore_algebra[diff_algebra].

• 

These functions are part of the Ore_algebra package, and so can be used in the form skew_product(..) only after performing the command with(Ore_algebra) or with(Ore_algebra,skew_product).  The functions can always be accessed in the long form Ore_algebra[skew_product](..).

Examples

withOre_algebra:

Algebras of difference operators:

Ashift_algebraSn,n:

skew_productSn,n,A

n+1Sn

(1)

skew_productSn5,n3,A

n3+15n2+75n+125Sn5

(2)

Algebras of differential operators:

Adiff_algebraDx,x,Dy,y:

skew_productDx,x,A,skew_productDy,y,A

Dxx+1,Dyy+1

(3)

skew_productDxDy,xy,A

DxDyxy+Dxx+Dyy+1

(4)

skew_productDx,x10,A

Dxx10+10x9

(5)

skew_powerDx+x,4,A

Dx4+4xDx3+6x2+6Dx2+4x3+12xDx+x4+6x2+3

(6)

Mixed differential-difference case:

Askew_algebradiff=Dx,x,shift=Sn,n:

skew_productDx,x,A,skew_productSn,n,A

Dxx+1,n+1Sn

(7)

skew_productDxSn,xn,A

nx+xDxSn+n+1Sn

(8)

skew_productSn,n5,A

n5+5n4+10n3+10n2+5n+1Sn

(9)

skew_productSn5,n,A

n+5Sn5

(10)

See Also

Ore_algebra

Ore_algebra/diff_algebra

Ore_algebra/shift_algebra

Ore_algebra/skew_algebra

Ore_algebra/Weyl_algebra

 


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