OrdinaryDifferentialRing(Kernels, R, var)

lodo.spad line 284 [edit on github]

• Kernels : SetCategory
• R : PartialDifferentialRing(Kernels)
• var : Kernels

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

* : (%, %) -> %

from LeftModule(%)

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

from RightModule(Fraction(Integer))

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

from LeftModule(Fraction(Integer))

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

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

from Field

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

D : % -> %

from DifferentialRing

D : (%, NonNegativeInteger) -> %

from DifferentialRing

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

from DivisionRing

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

annihilate? : (%, %) -> Boolean

from Rng

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

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

from EntireRing

associator : (%, %, %) -> %

from NonAssociativeRng

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

coerce : % -> % if R has Field

from Algebra(%)

coerce : R -> %

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

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

from Algebra(Fraction(Integer))

coerce : Integer -> %

from NonAssociativeRing

coerce : % -> R

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

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

from NonAssociativeRng

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

from PrincipalIdealDomain

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

from UniqueFactorizationDomain

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

from NonAssociativeAlgebra(%)

prime? : % -> Boolean if R has Field

from UniqueFactorizationDomain

principalIdeal : List(%) -> Record(coef : List(%), generator : %) if R has Field

from PrincipalIdealDomain

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

from UniqueFactorizationDomain

squareFreePart : % -> % if R has Field

from UniqueFactorizationDomain

subtractIfCan : (%, %) -> Union(%, "failed")

from CancellationAbelianMonoid

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

~= : (%, %) -> Boolean

from BasicType

IntegralDomain

Module(Fraction(Integer))

noZeroDivisors

LeftModule(Fraction(Integer))

Algebra(%)

RightModule(%)

Monoid

GcdDomain

AbelianMonoid

EuclideanDomain

EntireRing

NonAssociativeSemiRng

NonAssociativeAlgebra(Fraction(Integer))

CancellationAbelianMonoid

MagmaWithUnit

NonAssociativeRing

RightModule(Fraction(Integer))

unitsKnown

LeftModule(%)

canonicalUnitNormal

Module(%)

SetCategory

LeftOreRing

CoercibleTo(OutputForm)

Algebra(Fraction(Integer))

Rng

Field

CommutativeRing

TwoSidedRecip

Magma

UniqueFactorizationDomain

SemiGroup

DivisionRing

BiModule(%, %)

AbelianGroup

AbelianSemiGroup

CommutativeStar

NonAssociativeSemiRing

canonicalsClosed

NonAssociativeAlgebra(%)

PrincipalIdealDomain

BiModule(Fraction(Integer), Fraction(Integer))

DifferentialRing

NonAssociativeRng

Ring

SemiRng

BasicType

SemiRing