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OreTools[Modular]

  

ModularOrePoly

  

compute the normal form of an Ore polynomial modulo a prime

  

Content

  

compute the content of an Ore polynomial modulo a prime

  

Primitive

  

compute the primitive part of an Ore polynomial modulo a prime

  

MonicAssociate

  

compute the left associate of an Ore polynomial modulo a prime

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Modular[ModularOrePoly](Ore, p)

Modular[Content](Ore, p, 'pp')

Modular[Primitive](Ore, p, 'c')

Modular[MonicAssociate](Ore, p)

Parameters

Ore

-

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

p

-

prime

c, pp

-

unevaluated names

Description

• 

The Modular[ModularOrePoly](Ore, p) calling sequence computes the normal form of the Ore polynomial Ore modulo the prime p

• 

The Modular[Content](Ore, p) calling sequence computes the content of the Ore polynomial Ore modulo the prime p. If the third (optional) argument is present, it is assigned the primitive part of Ore.

• 

The Modular[Primitive](Ore, p) calling sequence computes the primitive part of Ore modulo the prime p. If the third (optional) argument is present, it is assigned the content of Ore.

• 

The Modular[MonicAssociate](Ore, p) calling sequence computes the left monic associate of the Ore polynomial Ore modulo the prime p.

Examples

withOreTools:

Ore'OrePoly'nn1,5n+n2+3n1,n3,38n3

Ore:=OrePolynn1,n25n+3n1,n3,38n3

(1)

Modular[ModularOrePoly]Ore,19

OrePoly18nn+18,18n2+14n+3n+18,n+16

(2)

Modular[ModularOrePoly]Ore,11

OrePoly10nn+10,10n2+6n+3n+10,n+8,5n+8

(3)

Ore'OrePoly'n,3nn21,n12

Ore:=OrePolyn,n2+3n1,n12

(4)

Modular[Primitive]Ore,7,'c'

OrePoly6n,6n2+3n+6,n2+5n+1

(5)

c

1

(6)

Modular[Content]'OrePoly'n21,n+10,11,'pp'

n+10

(7)

pp

OrePolyn+1,1

(8)

Ore'OrePoly'n2,3nn21,n172

Ore:=OrePolyn2,n2+3n1,n172

(9)

Modular[MonicAssociate]Ore,17

OrePoly1,16n2+3n+16n2,1

(10)

See Also

OreTools

OreTools/Modular

OreTools/OreAlgebra

OreTools/OrePoly

OreTools/SetOreRing

 


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