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

	(DifferentialModuleExtension): Likewise.

4 files changed, 80 insertions, 2 deletions

diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index 5bbaa9dd..d35fbbb8 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -343,6 +343,7 @@ $(OUT)/DIFFSPC.$(FASLEXT): $(OUT)/DIFFDOM.$(FASLEXT)
 $(OUT)/DIFFMOD.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT)
 $(OUT)/PDDOM.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT)
 $(OUT)/PDSPC.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT)
+$(OUT)/DSEXT.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT) $(OUT)/PDSPC.$(FASLEXT)
 
 axiom_algebra_layer_0 = \
   AHYP     ATTREG   CFCAT    ELTAB    KOERCE   KONVERT  \
@@ -369,7 +370,8 @@ axiom_algebra_layer_0 = \
   DIOPS    DIOPS-   STRING   STRICAT  ISTRING  ILIST    \
   LIST     DIFFDOM  DIFFDOM- DIFFSPC  DIFFSPC- DIFFMOD  \
   LINEXP   PATMAB   REAL     CHARZ    LOGIC    LOGIC-   \
-  RTVALUE  SYSPTR   PDDOM    PDDOM-   PDSPC    PDSPC-
+  RTVALUE  SYSPTR   PDDOM    PDDOM-   PDSPC    PDSPC-   \
+  DSEXT    DSEXT-
 
 axiom_algebra_layer_0_nrlibs = \
 	$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_0))
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index c65cf20b..0c64e0c3 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -297,6 +297,7 @@ $(OUT)/DIFFSPC.$(FASLEXT): $(OUT)/DIFFDOM.$(FASLEXT)
 $(OUT)/DIFFMOD.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT)
 $(OUT)/PDDOM.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT)
 $(OUT)/PDSPC.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT)
+$(OUT)/DSEXT.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT) $(OUT)/PDSPC.$(FASLEXT)
 
 axiom_algebra_layer_0 = \
   AHYP     ATTREG   CFCAT    ELTAB    KOERCE   KONVERT  \
@@ -323,7 +324,8 @@ axiom_algebra_layer_0 = \
   DIOPS    DIOPS-   STRING   STRICAT  ISTRING  ILIST    \
   LIST     DIFFDOM  DIFFDOM- DIFFSPC  DIFFSPC- DIFFMOD  \
   LINEXP   PATMAB   REAL     CHARZ    LOGIC    LOGIC-   \
-  RTVALUE  SYSPTR   PDDOM    PDDOM-   PDSPC    PDSPC-
+  RTVALUE  SYSPTR   PDDOM    PDDOM-   PDSPC    PDSPC-   \
+  DSEXT    DSEXT-
 
 axiom_algebra_layer_0_nrlibs = \
 	$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_0))
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet
index a09a99ea..bad221b9 100644
--- a/src/algebra/catdef.spad.pamphlet
+++ b/src/algebra/catdef.spad.pamphlet
@@ -376,6 +376,7 @@ DifferentialDomain(T: Type): Category == Type with
 
 @
 
+\section{Differential Space}
 
 <<category DIFFSPC DifferentialSpace>>=
 )abbrev category DIFFSPC DifferentialSpace
@@ -400,6 +401,54 @@ DifferentialSpace(): Category == DifferentialDomain % with
 
 @
 
+
+\section{Differential Space Extension}
+
+<<category DSEXT DifferentialSpaceExtension>>=
+)abbrev category DSEXT DifferentialSpaceExtension
+++ Author:  Gabriel Dos Reis
+++ Date Created: June 16, 2010
+++ Date Last Updated: Jun 16, 2010
+++ Related Constructors: Module, DifferentialSpace
+++ Also See:
+++ Description:
+++   Extension of a base differential space with a derivation.
+++
+DifferentialSpaceExtension(R: Type): Category == Type with
+    differentiate: (%,R -> R) -> %
+      ++ \spad{differentiate(x,d)} computes the derivative of
+      ++ \spad{x}, extending differentiation \spad{d} on \spad{R}.
+    differentiate: (%,R -> R,NonNegativeInteger) -> %
+      ++ \spad{differentiate(x,d,n)} computes the \spad{n}-th derivative
+      ++ of \spad{x} using a derivation extending \spad{d} on \spad{R}.
+    D: (%,R -> R) -> %
+      ++ \spad{D(x,d)} is a shorthand for \spad{differentiate(x,d)}.
+    D: (%,R -> R,NonNegativeInteger) -> %
+      ++ \spad{D(x,d,n)} is a shorthand for \spad{differentiate(x,d,n)}.
+    if R has DifferentialSpace then DifferentialSpace
+    if R has PartialDifferentialSpace Symbol then
+      PartialDifferentialSpace Symbol
+  add
+    differentiate(x: %, d: R -> R, n: NonNegativeInteger):% ==
+      for i in 1..n repeat x := differentiate(x,d)
+      x
+
+    D(x: %, d: R -> R) ==
+      differentiate(x, d)
+
+    D(x: %, d: R -> R, n: NonNegativeInteger) ==
+      differentiate(x,d,n)
+
+    if R has DifferentialSpace then
+      differentiate x == differentiate(x, differentiate$R)
+
+    if R has PartialDifferentialSpace Symbol then
+      differentiate(x:%, v: Symbol):% ==
+        differentiate(x, differentiate(#1, v)$R)
+
+@
+
+
 \section{category DIFRING DifferentialRing}
 <<category DIFRING DifferentialRing>>=
 )abbrev category DIFRING DifferentialRing
@@ -424,6 +473,7 @@ DifferentialRing(): Category == Join(Ring,DifferentialSpace)
 
 @
 
+
 \section{Differential Module}
 
 <<category DIFFMOD DifferentialModule>>=
@@ -499,6 +549,25 @@ DifferentialExtension(R:Ring): Category == Ring with
         differentiate(x, differentiate(#1, v)$R)
 
 @
+
+\section{Differential Module Extension}
+
+<<category DMEXT DifferentialModuleExtension>>=
+)abbrev category DMEXT DifferentialModuleExtension
+++ Author:  Gabriel Dos Reis
+++ Date Created: June 16, 2010
+++ Date Last Updated: Jun 16, 2010
+++ Related Constructors: Module, DifferentialSpaceExtension
+++ Also See:
+++   DifferentialExtension
+++ Description:
+++   Category of modules that extend differential rings.
+++
+DifferentialModuleExtension(R: CommutativeRing): Category ==
+  Join(Module(R),DifferentialSpaceExtension R)
+@
+
+
 \section{category DIVRING DivisionRing}
 <<category DIVRING DivisionRing>>=
 )abbrev category DIVRING DivisionRing
@@ -1981,12 +2050,15 @@ VectorSpace(S:Field): Category ==  Module(S) with
 <<category OINTDOM OrderedIntegralDomain>>
 <<category OAMONS OrderedAbelianMonoidSup>>
 <<category DIFFDOM DifferentialDomain>>
+<<category DIFFSPC DifferentialSpace>>
 <<category DIFRING DifferentialRing>>
 <<category DIFFMOD DifferentialModule>>
+<<category DMEXT DifferentialModuleExtension>>
 <<category PDDOM PartialDifferentialDomain>>
 <<category PDSPC PartialDifferentialSpace>>
 <<category PDRING PartialDifferentialRing>>
 <<category DIFEXT DifferentialExtension>>
+<<category DSEXT DifferentialSpaceExtension>>
 @
 
 \eject
diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet
index 6a09e207..ea6b06ce 100644
--- a/src/algebra/exposed.lsp.pamphlet
+++ b/src/algebra/exposed.lsp.pamphlet
@@ -630,9 +630,11 @@
   (|DifferentialDomain| . DIFFDOM)
   (|DifferentialExtension| . DIFEXT)
   (|DifferentialModule| . DIFFMOD)
+  (|DifferentialModuleExtension| . DSEXT)
   (|DifferentialPolynomialCategory| . DPOLCAT)
   (|DifferentialRing| . DIFRING)
   (|DifferentialSpace| . DIFFSPC)
+  (|DifferentialSpaceExtension| . DSEXT)
   (|DifferentialVariableCategory| . DVARCAT)
   (|DirectProductCategory| . DIRPCAT)
   (|DivisionRing| . DIVRING)