# OrdinaryDifferentialRing(Kernels, R, var)ΒΆ

This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, Fraction Integer) -> % if R has Field
*: (Fraction Integer, %) -> % if R has Field
*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> % if R has Field

from Field

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> % if R has Field

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %
associates?: (%, %) -> Boolean if R has Field

from EntireRing

associator: (%, %, %) -> %
characteristic: () -> NonNegativeInteger
coerce: % -> % if R has Field

from Algebra %

coerce: % -> OutputForm
coerce: % -> R

`coerce(p)` views `p` as a valie in the partial differential ring.

coerce: Fraction Integer -> % if R has Field
coerce: Integer -> %
coerce: R -> %

`coerce(r)` views `r` as a value in the ordinary differential ring.

commutator: (%, %) -> %
D: % -> %

from DifferentialRing

D: (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate: % -> %

from DifferentialRing

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

divide: (%, %) -> Record(quotient: %, remainder: %) if R has Field

from EuclideanDomain

euclideanSize: % -> NonNegativeInteger if R has Field

from EuclideanDomain

expressIdealMember: (List %, %) -> Union(List %, failed) if R has Field
exquo: (%, %) -> Union(%, failed) if R has Field

from EntireRing

extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %) if R has Field

from EuclideanDomain

extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed) if R has Field

from EuclideanDomain

factor: % -> Factored % if R has Field
gcd: (%, %) -> % if R has Field

from GcdDomain

gcd: List % -> % if R has Field

from GcdDomain

gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has Field

from GcdDomain

inv: % -> % if R has Field

from DivisionRing

latex: % -> String

from SetCategory

lcm: (%, %) -> % if R has Field

from GcdDomain

lcm: List % -> % if R has Field

from GcdDomain

lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %) if R has Field

from LeftOreRing

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

multiEuclidean: (List %, %) -> Union(List %, failed) if R has Field

from EuclideanDomain

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

plenaryPower: (%, PositiveInteger) -> % if R has Field
prime?: % -> Boolean if R has Field
principalIdeal: List % -> Record(coef: List %, generator: %) if R has Field
quo: (%, %) -> % if R has Field

from EuclideanDomain

recip: % -> Union(%, failed)

from MagmaWithUnit

rem: (%, %) -> % if R has Field

from EuclideanDomain

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sizeLess?: (%, %) -> Boolean if R has Field

from EuclideanDomain

squareFree: % -> Factored % if R has Field
squareFreePart: % -> % if R has Field
subtractIfCan: (%, %) -> Union(%, failed)
unit?: % -> Boolean if R has Field

from EntireRing

unitCanonical: % -> % if R has Field

from EntireRing

unitNormal: % -> Record(unit: %, canonical: %, associate: %) if R has Field

from EntireRing

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra % if R has Field

Algebra Fraction Integer if R has Field

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer) if R has Field

CancellationAbelianMonoid

canonicalsClosed if R has Field

canonicalUnitNormal if R has Field

CommutativeRing if R has Field

CommutativeStar if R has Field

DifferentialRing

DivisionRing if R has Field

EntireRing if R has Field

EuclideanDomain if R has Field

Field if R has Field

GcdDomain if R has Field

IntegralDomain if R has Field

LeftModule Fraction Integer if R has Field

LeftOreRing if R has Field

Magma

MagmaWithUnit

Module % if R has Field

Module Fraction Integer if R has Field

Monoid

NonAssociativeAlgebra % if R has Field

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if R has Field

PrincipalIdealDomain if R has Field

RightModule Fraction Integer if R has Field

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip if R has Field

UniqueFactorizationDomain if R has Field

unitsKnown