OreTools[Content] - return the content of an Ore polynomial
OreTools[Primitive] - return primitive part of an Ore polynomial
OreTools[MonicAssociate] - return left or right monic associate of an Ore polynomial
OreTools[Normalize] - return the normal form of an Ore polynomial
|
Calling Sequence
|
|
Content(Poly, 'p')
Primitive(Poly, 'c')
MonicAssociate['left'](Poly, 's')
MonicAssociate(Poly, 's')
MonicAssociate['right'](Poly, A, 's')
Normalize(Poly)
|
|
Parameters
|
|
Poly
|
-
|
Ore polynomial; to define an Ore polynomial, use the OrePoly structure.
|
A
|
-
|
Ore algebra; to define an Ore algebra, use the SetOreRing function.
|
c, p, s
|
-
|
(optional) names
|
|
|
|
|
Description
|
|
•
|
The Content(Poly, 'p') calling sequence returns the content of the Ore polynomial Poly. If the second (optional) argument p is present, the primitive part of Poly is assigned to p.
|
•
|
The Primitive(Poly, 'c') calling sequence returns the primitive part of the Ore poly Poly. If the second (optional) argument c is present, the content of Poly is assigned to c.
|
•
|
If the coefficients of Poly are integral (commutative) polynomials, then its content is the gcd of its coefficients and its primitive part is equal to (1/c) Poly.
|
•
|
If the coefficients of Poly are rational functions, then its content and primitive part pp satisfy:
|
1.
|
The primitive part pp is an Ore polynomial with integral (commutative) polynomial coefficients whose content is 1. Poly = c pp
|
•
|
The MonicAssociate['left'](Poly, 's') or MonicAssociate(Poly, 's') calling sequence returns (1/l) Poly where l is the leading coefficient of Poly. If the second (optional) argument s is present, (1/l) is assigned to l.
|
•
|
The MonicAssociate['right'](Poly, A, 's') calling sequence returns Poly a, where a belongs to the coefficient field such that the product (Poly a) is monic. If the third (optional) argument s, is present, a is assigned to s.
|
•
|
The Normalize(Poly) calling sequence returns Poly with nonzero leading coefficient when Poly is nonzero; returns 'OrePoly'(0), otherwise.
|
|
|
Examples
|
|
>
|
|
>
|
|
| (1) |
>
|
|
| (2) |
>
|
|
| (3) |
>
|
|
| (4) |
>
|
|
| (5) |
>
|
|
| (6) |
>
|
|
| (7) |
>
|
|
| (8) |
>
|
|
| (9) |
>
|
|
| (10) |
>
|
|
| (11) |
>
|
|
| (12) |
>
|
|
| (13) |
>
|
|
| (14) |
|
|