PartialDifferentialRing SΒΆ

catdef.spad line 1161

A partial differential ring with differentiations indexed by a parameter type S.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
=: (%, %) -> Boolean
from BasicType
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
annihilate?: (%, %) -> Boolean
from Rng
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
associator: (%, %, %) -> %
from NonAssociativeRng
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Integer -> %
from NonAssociativeRing
commutator: (%, %) -> %
from NonAssociativeRng
D: (%, List S) -> %
D(x, [s1, ...sn]) computes successive partial derivatives, i.e. D(...D(x, s1)..., sn).
D: (%, List S, List NonNegativeInteger) -> %
D(x, [s1, ..., sn], [n1, ..., nn]) computes multiple partial derivatives, i.e. D(...D(x, s1, n1)..., sn, nn).
D: (%, S) -> %
D(x, v) computes the partial derivative of x with respect to v.
D: (%, S, NonNegativeInteger) -> %
D(x, s, n) computes multiple partial derivatives, i.e. n-th derivative of x with respect to s.
differentiate: (%, List S) -> %
differentiate(x, [s1, ...sn]) computes successive partial derivatives, i.e. differentiate(...differentiate(x, s1)..., sn).
differentiate: (%, List S, List NonNegativeInteger) -> %
differentiate(x, [s1, ..., sn], [n1, ..., nn]) computes multiple partial derivatives, i.e.
differentiate: (%, S) -> %
differentiate(x, v) computes the partial derivative of x with respect to v.
differentiate: (%, S, NonNegativeInteger) -> %
differentiate(x, s, n) computes multiple partial derivatives, i.e. n-th derivative of x with respect to s.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
recip: % -> Union(%, failed)
from MagmaWithUnit
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
sample: %
from AbelianMonoid
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule %

Magma

MagmaWithUnit

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

RightModule %

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown