OrdinaryDifferentialRing(Kernels, R, var)ΒΆ

lodo.spad line 284

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
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
=: (%, %) -> Boolean
from BasicType
^: (%, Integer) -> % if R has Field
from DivisionRing
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
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: % -> OutputForm
from CoercibleTo OutputForm
coerce: % -> R
coerce(p) views p as a valie in the partial differential ring.
coerce: Fraction Integer -> % if R has Field
from Algebra Fraction Integer
coerce: Integer -> %
from NonAssociativeRing
coerce: R -> %
coerce(r) views r as a value in the ordinary differential ring.
commutator: (%, %) -> %
from NonAssociativeRng
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
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
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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
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

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

CoercibleTo OutputForm

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 %

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

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if R has Field

PrincipalIdealDomain if R has Field

RightModule %

RightModule Fraction Integer if R has Field

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

UniqueFactorizationDomain if R has Field

unitsKnown