DifferentialExtension(R)
catdef.spad line 268
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Differential extensions of a ring R. Given a differentiation on R, extend it to a differentiation on %.
- * : (%, %) -> %
- 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 : % -> % if R has DifferentialRing
- from DifferentialRing
- D : (%, List(Symbol)) -> % if R has PartialDifferentialRing(Symbol)
- from PartialDifferentialRing(Symbol)
- D : (%, List(Symbol), List(NonNegativeInteger)) -> % if R has PartialDifferentialRing(Symbol)
- from PartialDifferentialRing(Symbol)
- D : (%, Mapping(R, R)) -> %
D(x, deriv) differentiates x extending the derivation deriv on R.
- D : (%, Mapping(R, R), NonNegativeInteger) -> %
D(x, deriv, n) differentiate x n times using a derivation which extends deriv on R.
- D : (%, NonNegativeInteger) -> % if R has DifferentialRing
- from DifferentialRing
- D : (%, Symbol) -> % if R has PartialDifferentialRing(Symbol)
- from PartialDifferentialRing(Symbol)
- D : (%, Symbol, NonNegativeInteger) -> % if R has PartialDifferentialRing(Symbol)
- from PartialDifferentialRing(Symbol)
- ^ : (%, 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 : % -> % if R has DifferentialRing
- from DifferentialRing
- differentiate : (%, List(Symbol)) -> % if R has PartialDifferentialRing(Symbol)
- from PartialDifferentialRing(Symbol)
- differentiate : (%, List(Symbol), List(NonNegativeInteger)) -> % if R has PartialDifferentialRing(Symbol)
- from PartialDifferentialRing(Symbol)
- differentiate : (%, Mapping(R, R)) -> %
differentiate(x, deriv) differentiates x extending the derivation deriv on R.
- differentiate : (%, Mapping(R, R), NonNegativeInteger) -> %
differentiate(x, deriv, n) differentiate x n times using a derivation which extends deriv on R.
- differentiate : (%, NonNegativeInteger) -> % if R has DifferentialRing
- from DifferentialRing
- differentiate : (%, Symbol) -> % if R has PartialDifferentialRing(Symbol)
- from PartialDifferentialRing(Symbol)
- differentiate : (%, Symbol, NonNegativeInteger) -> % if R has PartialDifferentialRing(Symbol)
- from PartialDifferentialRing(Symbol)
- 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(%)
PartialDifferentialRing(Symbol)
DifferentialRing
unitsKnown
NonAssociativeRing
Rng
NonAssociativeSemiRng
SemiRing
AbelianGroup
NonAssociativeSemiRing
SetCategory
AbelianSemiGroup
AbelianMonoid
Magma
BiModule(%, %)
NonAssociativeRng
BasicType
MagmaWithUnit
CoercibleTo(OutputForm)
SemiRng