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OreTools

  

Add

  

add several Ore polynomials

  

Minus

  

subtract two Ore polynomials

  

ScalarMultiply

  

multiply an Ore polynomial on the left by a scalar

  

Multiply

  

multiply several Ore polynomials

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Add(Ore1, ..., Orek)

Minus(Ore1, Ore2)

ScalarMultiply(s, Ore1)

Multiply(Ore1, ..., Orek, A)

Parameters

Ore1, Ore2, ..., Orek

-

Ore polynomials; to define an Ore polynomial, use the OrePoly structure.

s

-

scalar from the coefficient domain

A

-

Ore algebra; to define an Ore algebra, use the SetOreRing function.

Description

• 

The Add(Ore1, ..., Orek) calling sequence adds the Ore polynomials Ore1,..., Orek.

• 

The Minus(Ore1, Ore2) calling sequence subtracts the Ore polynomial Ore2 from the Ore polynomial Ore1.

• 

The ScalarMultiply(s, Ore1) calling sequence multiplies the Ore polynomial Ore1 on the left by the scalar s.

• 

The Multiply(Ore1, ..., Orek, A) calling sequence multiplies the t Ore polynomials Ore1, ...,  Orek in the Ore algebra A.

Examples

withOreTools:

Define the shift algebra.

ASetOreRingn,'shift'

A:=UnivariateOreRingn,shift

(1)

Perform arithmetic operations.

Ore1OrePolynn1,5n+n2+3n1,n3

Ore1:=OrePolynn1,n25n+3n1,n3

(2)

Ore2OrePolyn,3nn21,n12

Ore2:=OrePolyn,n2+3n1,n12

(3)

AddOre1,Ore2,Ore1

OrePolynn+1n1,n32n26n+5n1,n25

(4)

MinusOre1,Ore2

OrePolyn2+nn1,n35n2+9n4n1,n2+3n4

(5)

ScalarMultiply2,Ore1

OrePoly2nn1,2n25n+3n1,2n3

(6)

MultiplyOre1,Ore2,Ore1,A

OrePolyn3n12,3n512n4+10n2+n3nn12,3n618n5+2n4+62n3+8n229n3nn1n+1,n711n6+3n5+92n419n3168n2+8n+75n1n+1n+2,3n75n655n5+37n4+209n3100n2142n+57n1n+2n+3,3n6n534n4+2n3+31n22n3n1n+3,n3n+13

(7)

See Also

OreTools

OreTools/OreAlgebra

OreTools/OrePoly

OreTools/Quotient

OreTools/Remainder

OreTools[SetOreRing]

 


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