PartialDifferentialRing(S)

catdef.spad line 1168 [edit on github]

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

* : (%, %) -> %
from Magma
* : (Integer, %) -> %
from AbelianGroup
* : (NonNegativeInteger, %) -> %
from AbelianMonoid
* : (PositiveInteger, %) -> %
from AbelianSemiGroup
+ : (%, %) -> %
from AbelianSemiGroup
- : % -> %
from AbelianGroup
- : (%, %) -> %
from AbelianGroup
0 : () -> %
from AbelianMonoid
1 : () -> %
from MagmaWithUnit
= : (%, %) -> Boolean
from BasicType
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.

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).

^ : (%, NonNegativeInteger) -> %
from MagmaWithUnit
^ : (%, PositiveInteger) -> %
from Magma
annihilate? : (%, %) -> Boolean
from Rng
antiCommutator : (%, %) -> %
from NonAssociativeSemiRng
associator : (%, %, %) -> %
from NonAssociativeRng
characteristic : () -> NonNegativeInteger
from NonAssociativeRing
coerce : Integer -> %
from NonAssociativeRing
coerce : % -> OutputForm
from CoercibleTo(OutputForm)
commutator : (%, %) -> %
from NonAssociativeRng
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.

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.

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
~= : (%, %) -> Boolean
from BasicType

RightModule(%)

Monoid

Ring

SemiGroup

CancellationAbelianMonoid

LeftModule(%)

BasicType

unitsKnown

NonAssociativeRing

Rng

NonAssociativeSemiRng

SemiRing

AbelianGroup

NonAssociativeSemiRing

SetCategory

AbelianSemiGroup

AbelianMonoid

Magma

BiModule(%, %)

NonAssociativeRng

MagmaWithUnit

CoercibleTo(OutputForm)

SemiRng