DeRhamComplex(CoefRing, listIndVar)ΒΆ

derham.spad line 288

The deRham complex of Euclidean space, that is, the class of differential forms of arbitary degree over a coefficient ring. See Flanders, Harley, Differential Forms, With Applications to the Physical Sciences, New York, Academic Press, 1963.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (Expression CoefRing, %) -> %
from LeftModule Expression CoefRing
*: (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
coefficient: (%, %) -> Expression CoefRing
coefficient(df, u), where df is a differential form, returns the coefficient of df containing the basis term u if such a term exists, and 0 otherwise.
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Expression CoefRing -> %
from LeftAlgebra Expression CoefRing
coerce: Integer -> %
from NonAssociativeRing
commutator: (%, %) -> %
from NonAssociativeRng
degree: % -> NonNegativeInteger
degree(df) returns the homogeneous degree of differential form df.
exteriorDifferential: % -> %
exteriorDifferential(df) returns the exterior derivative (gradient, curl, divergence, ...) of the differential form df.
generator: NonNegativeInteger -> %
generator(n) returns the nth basis term for a differential form.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
homogeneous?: % -> Boolean
homogeneous?(df) tests if all of the terms of differential form df have the same degree.
latex: % -> String
from SetCategory
leadingBasisTerm: % -> %
leadingBasisTerm(df) returns the leading basis term of differential form df.
leadingCoefficient: % -> Expression CoefRing
leadingCoefficient(df) returns the leading coefficient of differential form df.
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
map: (Expression CoefRing -> Expression CoefRing, %) -> %
map(f, df) replaces each coefficient x of differential form df by f(x).
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
recip: % -> Union(%, failed)
from MagmaWithUnit
reductum: % -> %
reductum(df), where df is a differential form, returns df minus the leading term of df if df has two or more terms, and 0 otherwise.
retract: % -> Expression CoefRing
from RetractableTo Expression CoefRing
retractable?: % -> Boolean
retractable?(df) tests if differential form df is a 0-form, i.e. if degree(df) = 0.
retractIfCan: % -> Union(Expression CoefRing, failed)
from RetractableTo Expression CoefRing
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
sample: %
from AbelianMonoid
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
totalDifferential: Expression CoefRing -> %
totalDifferential(x) returns the total differential (gradient) form for element x.
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftAlgebra Expression CoefRing

LeftModule %

LeftModule Expression CoefRing

Magma

MagmaWithUnit

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

RetractableTo Expression CoefRing

RightModule %

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown