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OreTools[Modular][Add] - add two Ore polynomials

OreTools[Modular][Minus] - subtract two Ore polynomials

OreTools[Modular][ScalarMultiply] - multiply an Ore polynomial on the left by a scalar

OreTools[Modular][Multiply] - multiply two Ore polynomials

Calling Sequence

Modular[Add](Ore1, Ore2, p)

Modular[Minus](Ore1, Ore2, p)

Modular[ScalarMultiply](s, Ore1, p)

Modular[Multiply](Ore1, Ore2, p, A)

Parameters

Ore1, Ore2

-

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

s

-

scalar from the coefficient domain

p

-

prime

A

-

Ore algebra; to define an Ore algebra, use the SetOreRing command

Description

• 

The Modular[Add](Ore1, Ore2, m) calling sequence adds the two Ore polynomials Ore1 and Ore2 modulo p.

• 

The Modular[Minus](Ore1, Ore2, p) calling sequence subtracts the Ore polynomial Ore2 from the Ore polynomial Ore1 modulo p.

• 

The Modular[ScalarMultiply](s, Ore1, p) calling sequence multiplies the Ore polynomial Ore1 on the left by the scalar s modulo p.

• 

The Modular[Multiply](Ore1, Ore2, p, A) calling sequence multiplies the two Ore polynomials Ore1 and Ore2 in the Ore algebra A modulo m.

Examples

withOreTools:

Define the shift algebra.

A:=SetOreRingn,'shift'

A:=UnivariateOreRingn,shift

(1)

Ore1:=OrePolynn1,5n+n2+3n1,n3

Ore1:=OrePolynn1,n25n+3n1,n3

(2)

Ore2:=OrePolyn,3nn21,n12

Ore2:=OrePolyn,n2+3n1,n12

(3)

ModularAddOre1,Ore2,7

OrePoly6n2n+6,6n3+3n2+n+5n+6,n2+6n+5

(4)

ModularMinusOre1,Ore2,7

OrePolyn2+5nn+6,n3+2n2+2n+3n+6,6n2+3n+3

(5)

ModularScalarMultiply22,Ore1,17

OrePoly12nn+16,12n2+8n+2n+16,5n+2

(6)

ModularMultiplyOre1,Ore2,11,A

OrePolyn2n+10,2n3+4n2+10n+3n+10,n4+3n3+6n+2n+10,9n4+8n3+10n2+4n+3n+10,n+8n+12

(7)

See Also

OreTools, OreTools/Modular, OreTools/Modular/RightQuotient, OreTools/Modular/RightRemainder, OreTools/OreAlgebra, OreTools/OrePoly, OreTools[SetOreRing]


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