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Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index f3963ea3..a7807009 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -353,6 +353,36 @@ CommutativeRing():Category == Join(Ring,BiModule(%,%)) with @ +\section{Differential Domain} + +<<category DIFFDOM DifferentialDomain>>= +)abbrev category DIFFDOM DifferentialDomain +++ Author: Gabriel Dos Reis +++ Date Created: June 13, 2010 +++ Date Last Modified: June 13, 2010 +++ Description: +++ This category captures the interface of domains with a distinguished +++ operation named \spad{differentiate}. Usually, additional properties +++ are wanted. For example, that it obeys the usual Leibniz identity +++ of differentiation of product, in case of differential rings. One +++ could also want \spad{differentiate} to obey the chain rule when +++ considering differential manifolds. +++ The lack of specific requirement in this category is an implicit +++ admission that currently \Language{} is not expressive enough to +++ express the most general notion of differentiation in an adequate +++ manner, suitable for computational purposes. +DifferentialDomain(T: Type): Category == Type with + differentiate: % -> T + ++ \spad{differentiate x} compute the derivative of \spad{x}. + D: % -> T + ++ \spad{D x} is a shorthand for \spad{differentiate x} + add + D x == + differentiate x + +@ + + \section{category DIFRING DifferentialRing} <<category DIFRING DifferentialRing>>= )abbrev category DIFRING DifferentialRing @@ -1875,6 +1905,7 @@ VectorSpace(S:Field): Category == Module(S) with <<category ORDRING OrderedRing>> <<category OINTDOM OrderedIntegralDomain>> <<category OAMONS OrderedAbelianMonoidSup>> +<<category DIFFDOM DifferentialDomain>> <<category DIFRING DifferentialRing>> <<category PDRING PartialDifferentialRing>> <<category DIFEXT DifferentialExtension>> |