OrderlyDifferentialVariable(S)

dpolcat.spad line 112 [edit on github]

• S : OrderedSet

OrderlyDifferentialVariable adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking < of the derivatives with the property that for two derivatives u and v, u < v if the order of u is less than that of v. This domain belongs to DifferentialVariableCategory. It defines weight to be just order, and it defines an orderly ranking < on derivatives u via the lexicographic order on the pair (order(u), variable(u)).

< : (%, %) -> Boolean

from PartialOrder

<= : (%, %) -> Boolean

from PartialOrder

= : (%, %) -> Boolean

from BasicType

> : (%, %) -> Boolean

from PartialOrder

>= : (%, %) -> Boolean

from PartialOrder

coerce : S -> %

from DifferentialVariableCategory(S)

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

differentiate : % -> %

from DifferentialVariableCategory(S)

differentiate : (%, NonNegativeInteger) -> %

from DifferentialVariableCategory(S)

latex : % -> String

from SetCategory

makeVariable : (S, NonNegativeInteger) -> %

from DifferentialVariableCategory(S)

max : (%, %) -> %

from OrderedSet

min : (%, %) -> %

from OrderedSet

order : % -> NonNegativeInteger

from DifferentialVariableCategory(S)

retract : % -> S

from RetractableTo(S)

retractIfCan : % -> Union(S, "failed")

from RetractableTo(S)

smaller? : (%, %) -> Boolean

from Comparable

variable : % -> S

from DifferentialVariableCategory(S)

weight : % -> NonNegativeInteger

from DifferentialVariableCategory(S)

~= : (%, %) -> Boolean

from BasicType

RetractableTo(S)

CoercibleTo(OutputForm)

Comparable

OrderedSet

CoercibleFrom(S)

SetCategory

BasicType

DifferentialVariableCategory(S)

PartialOrder