* algebra/catdef.spad.pamphlet (DifferentialDomain): New.

4 files changed, 38 insertions, 2 deletions

diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index 37f31c73..89983429 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -335,6 +335,8 @@ $(OUT)/SYSPTR.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
 $(OUT)/VOID.$(FASLEXT): $(OUT)/KOERCE.$(FASLEXT)
 $(OUT)/OUT.$(FASLEXT): $(OUT)/VOID.$(FASLEXT)
 
+$(OUT)/DIFFDOM.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT)
+
 axiom_algebra_layer_0 = \
   AHYP     ATTREG   CFCAT    ELTAB    KOERCE   KONVERT  \
   KRCFROM  KVTFROM  IEVALAB  IEVALAB- EVALAB   EVALAB-  \
@@ -358,7 +360,7 @@ axiom_algebra_layer_0 = \
   RCAGG    RCAGG-   SETAGG   SETAGG-  HOAGG    HOAGG-   \
   TBAGG    TBAGG-   KDAGG    KDAGG-   DIAGG    DIAGG-   \
   DIOPS    DIOPS-   STRING   STRICAT  ISTRING  ILIST    \
-  LIST                                                  \
+  LIST     DIFFDOM                                      \
   LINEXP   PATMAB   REAL     CHARZ    LOGIC    LOGIC-   \
   RTVALUE  SYSPTR
 
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index ec2c0682..9ed8ca3f 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -289,6 +289,8 @@ $(OUT)/SYSPTR.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
 $(OUT)/VOID.$(FASLEXT): $(OUT)/KOERCE.$(FASLEXT)
 $(OUT)/OUT.$(FASLEXT): $(OUT)/VOID.$(FASLEXT)
 
+$(OUT)/DIFFDOM.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT)
+
 axiom_algebra_layer_0 = \
   AHYP     ATTREG   CFCAT    ELTAB    KOERCE   KONVERT  \
   KRCFROM  KVTFROM  IEVALAB  IEVALAB- EVALAB   EVALAB-  \
@@ -312,7 +314,7 @@ axiom_algebra_layer_0 = \
   RCAGG    RCAGG-   SETAGG   SETAGG-  HOAGG    HOAGG-   \
   TBAGG    TBAGG-   KDAGG    KDAGG-   DIAGG    DIAGG-   \
   DIOPS    DIOPS-   STRING   STRICAT  ISTRING  ILIST    \
-  LIST                                                  \
+  LIST     DIFFDOM                                      \
   LINEXP   PATMAB   REAL     CHARZ    LOGIC    LOGIC-   \
   RTVALUE  SYSPTR
 
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>>
diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet
index b7df3dbd..2d584577 100644
--- a/src/algebra/exposed.lsp.pamphlet
+++ b/src/algebra/exposed.lsp.pamphlet
@@ -627,6 +627,7 @@
   (|DequeueAggregate| . DQAGG)
   (|Dictionary| . DIAGG)
   (|DictionaryOperations| . DIOPS)
+  (|DifferentialDomain| . DIFFEXT)
   (|DifferentialExtension| . DIFEXT)
   (|DifferentialPolynomialCategory| . DPOLCAT)
   (|DifferentialRing| . DIFRING)