* algebra/fparfrac.spad.pamphlet (FullPartialFractionExpansion):

	Now satisfies DifferentialSpace.
	* algebra/gseries.spad.pamphlet (GeneralUnivariatePowerSeries):
	Now satisfies an instance of PartialDifferentialDomain.
	* algebra/laurent.spad.pamphlet (UnivariateLaurentSeries): Likewise.
	* algebra/puiseux.spad.pamphlet (UnivariatePuiseuxSeries): Likewise.
	* algebra/suls.spad.pamphlet (SparseUnivariateLaurentSeries): Likewise.
	* algebra/supxs.spad.pamphlet (SparseUnivariatePuiseuxSeries):
	Likewise. 
	* algebra/suts.spad.pamphlet (SparseUnivariateTaylorSeries): Likewise.
	* algebra/taylor.spad.pamphlet (UnivariateTaylorSeries): Likewise.

11 files changed, 38 insertions, 49 deletions

diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index efcfdf48..ebfc81c3 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -770,12 +770,12 @@ axiom_algebra_layer_14_objects = \
 	   $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_14)))
 $(OUT)/EXPUPXS.$(FASLEXT): $(OUT)/UPXS.$(FASLEXT)
 $(OUT)/UPXS.$(FASLEXT): $(OUT)/UPXSCAT.$(FASLEXT) $(OUT)/UPXSCONS.$(FASLEXT) \
-	$(OUT)/ULS.$(FASLEXT)
+	$(OUT)/ULS.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT)
 $(OUT)/UPXSCONS.$(FASLEXT): $(OUT)/UPXSCCA.$(FASLEXT)
-$(OUT)/ULS.$(FASLEXT): $(OUT)/ULSCONS.$(FASLEXT)
+$(OUT)/ULS.$(FASLEXT): $(OUT)/ULSCONS.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT)
 $(OUT)/ULSCONS.$(FASLEXT): $(OUT)/ULSCCAT.$(FASLEXT)
 $(OUT)/ULSCCAT.$(FASLEXT): $(OUT)/UTS.$(FASLEXT)
-$(OUT)/UTS.$(FASLEXT): $(OUT)/UTSCAT.$(FASLEXT)
+$(OUT)/UTS.$(FASLEXT): $(OUT)/UTSCAT.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT)
 
 axiom_algebra_layer_15 = \
   DSMP     EXPUPXS  UPXS     UPXSCONS \
@@ -831,6 +831,7 @@ axiom_algebra_layer_18_objects = \
 	$(addprefix $(OUT)/, \
 	   $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_18)))
 $(OUT)/TSETCAT.$(FASLEXT): $(OUT)/PSETCAT.$(FASLEXT) $(OUT)/RPOLCAT.$(FASLEXT)
+$(OUT)/FPARFRAC.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT)
 
 axiom_algebra_layer_19 = \
   ACPLOT   ANTISYM           ATTRBUT \
@@ -869,6 +870,7 @@ axiom_algebra_layer_19_objects = \
 	   $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_19)))
 $(OUT)/AN.$(FASLEXT): $(OUT)/IAN.$(FASLEXT)
 $(OUT)/IAN.$(FASLEXT): $(OUT)/EXPR.$(FASLEXT)
+$(OUT)/SUTS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT)
 
 axiom_algebra_layer_20 = \
   AF       ALGFACT  ALGFF    ALGMANIP ALGMFACT ALGPKG   \
@@ -910,6 +912,9 @@ axiom_algebra_layer_20_objects = \
 	$(addprefix $(OUT)/, \
 	   $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_20)))
 $(OUT)/FDIV.$(FASLEXT): $(OUT)/HELLFDIV.$(FASLEXT)
+$(OUT)/GSERIES.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT)
+$(OUT)/SULS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT)
+$(OUT)/SUPXS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT)
 
 axiom_algebra_layer_21 = \
   DEFINTEF DFINTTLS DEFINTRF D01TRNS  \
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index a52c8977..29e74be9 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -802,12 +802,12 @@ axiom_algebra_layer_14_objects = \
 <<layer15>>=
 $(OUT)/EXPUPXS.$(FASLEXT): $(OUT)/UPXS.$(FASLEXT)
 $(OUT)/UPXS.$(FASLEXT): $(OUT)/UPXSCAT.$(FASLEXT) $(OUT)/UPXSCONS.$(FASLEXT) \
-	$(OUT)/ULS.$(FASLEXT)
+	$(OUT)/ULS.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT)
 $(OUT)/UPXSCONS.$(FASLEXT): $(OUT)/UPXSCCA.$(FASLEXT)
-$(OUT)/ULS.$(FASLEXT): $(OUT)/ULSCONS.$(FASLEXT)
+$(OUT)/ULS.$(FASLEXT): $(OUT)/ULSCONS.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT)
 $(OUT)/ULSCONS.$(FASLEXT): $(OUT)/ULSCCAT.$(FASLEXT)
 $(OUT)/ULSCCAT.$(FASLEXT): $(OUT)/UTS.$(FASLEXT)
-$(OUT)/UTS.$(FASLEXT): $(OUT)/UTSCAT.$(FASLEXT)
+$(OUT)/UTS.$(FASLEXT): $(OUT)/UTSCAT.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT)
 
 axiom_algebra_layer_15 = \
   DSMP     EXPUPXS  UPXS     UPXSCONS \
@@ -883,6 +883,7 @@ axiom_algebra_layer_18_objects = \
 
 <<layer19>>=
 $(OUT)/TSETCAT.$(FASLEXT): $(OUT)/PSETCAT.$(FASLEXT) $(OUT)/RPOLCAT.$(FASLEXT)
+$(OUT)/FPARFRAC.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT)
 
 axiom_algebra_layer_19 = \
   ACPLOT   ANTISYM           ATTRBUT \
@@ -926,6 +927,7 @@ axiom_algebra_layer_19_objects = \
 <<layer20>>=
 $(OUT)/AN.$(FASLEXT): $(OUT)/IAN.$(FASLEXT)
 $(OUT)/IAN.$(FASLEXT): $(OUT)/EXPR.$(FASLEXT)
+$(OUT)/SUTS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT)
 
 axiom_algebra_layer_20 = \
   AF       ALGFACT  ALGFF    ALGMANIP ALGMFACT ALGPKG   \
@@ -972,6 +974,9 @@ axiom_algebra_layer_20_objects = \
 
 <<layer21>>=
 $(OUT)/FDIV.$(FASLEXT): $(OUT)/HELLFDIV.$(FASLEXT)
+$(OUT)/GSERIES.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT)
+$(OUT)/SULS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT)
+$(OUT)/SUPXS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT)
 
 axiom_algebra_layer_21 = \
   DEFINTEF DFINTTLS DEFINTRF D01TRNS  \
diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet
index ea6b06ce..80bb4c66 100644
--- a/src/algebra/exposed.lsp.pamphlet
+++ b/src/algebra/exposed.lsp.pamphlet
@@ -737,6 +737,7 @@
   (|PAdicIntegerCategory| . PADICCT)
   (|PartialDifferentialDomain| . PDDOM)
   (|PartialDifferentialRing| . PDRING)
+  (|PartialDifferentialSpace| . PDSPC)
   (|PartialTranscendentalFunctions| . PTRANFN)
   (|Patternable| . PATAB)
   (|PatternMatchable| . PATMAB)
diff --git a/src/algebra/fparfrac.spad.pamphlet b/src/algebra/fparfrac.spad.pamphlet
index ed7bce9d..b769ba05 100644
--- a/src/algebra/fparfrac.spad.pamphlet
+++ b/src/algebra/fparfrac.spad.pamphlet
@@ -15,7 +15,7 @@
 ++ Full partial fraction expansion of rational functions
 ++ Author: Manuel Bronstein
 ++ Date Created: 9 December 1992
-++ Date Last Updated: 6 October 1993
+++ Date Last Updated: June 18, 2010
 ++ References: M.Bronstein & B.Salvy,
 ++             Full Partial Fraction Decomposition of Rational Functions,
 ++             in Proceedings of ISSAC'93, Kiev, ACM Press.
@@ -34,7 +34,7 @@ FullPartialFractionExpansion(F, UP): Exports == Implementation where
   ODF ==> Fraction ODP
   FPF ==> Record(polyPart: UP, fracPart: List REC)
 
-  Exports ==> Join(SetCategory, ConvertibleTo RF)  with
+  Exports ==> Join(SetCategory, DifferentialSpace, ConvertibleTo RF)  with
     +:                 (UP, $) -> $
       ++ p + x returns the sum of p and x
     fullPartialFraction: RF -> $
@@ -46,14 +46,6 @@ FullPartialFractionExpansion(F, UP): Exports == Implementation where
       ++ fracPart(f) returns the list of summands of the fractional part of f.
     construct:           List REC -> $
       ++ construct(l) is the inverse of fracPart.
-    differentiate:       $ -> $
-      ++ differentiate(f) returns the derivative of f.
-    D:                    $ -> $
-      ++ D(f) returns the derivative of f.
-    differentiate:       ($, N) -> $
-      ++ differentiate(f, n) returns the n-th derivative of f.
-    D: ($, NonNegativeInteger) -> $
-      ++ D(f, n) returns the n-th derivative of f.
 
   Implementation ==> add
     Rep := FPF
diff --git a/src/algebra/gseries.spad.pamphlet b/src/algebra/gseries.spad.pamphlet
index d6ea733c..b9085625 100644
--- a/src/algebra/gseries.spad.pamphlet
+++ b/src/algebra/gseries.spad.pamphlet
@@ -14,7 +14,7 @@
 )abbrev domain GSERIES GeneralUnivariatePowerSeries
 ++ Author: Clifton J. Williamson
 ++ Date Created: 22 September 1993
-++ Date Last Updated: 23 September 1993
+++ Date Last Updated: June 18, 2010
 ++ Basic Operations:
 ++ Related Domains:
 ++ Also See:
@@ -40,15 +40,13 @@ GeneralUnivariatePowerSeries(Coef,var,cen): Exports == Implementation where
   EFUPXS ==> ElementaryFunctionsUnivariatePuiseuxSeries
   FS2UPS ==> FunctionSpaceToUnivariatePowerSeries
 
-  Exports ==> UnivariatePuiseuxSeriesCategory Coef with
+  Exports ==> Join(UnivariatePuiseuxSeriesCategory Coef,_
+                   PartialDifferentialDomain(%,Variable var)) with
     coerce: Variable(var) -> %
       ++ coerce(var) converts the series variable \spad{var} into a
       ++ Puiseux series.
     coerce: UPXS(Coef,var,cen) -> %
       ++ coerce(f) converts a Puiseux series to a general power series.
-    differentiate: (%,Variable(var)) -> %
-      ++ \spad{differentiate(f(x),x)} returns the derivative of
-      ++ \spad{f(x)} with respect to \spad{x}.
     if Coef has Algebra Fraction Integer then
       integrate: (%,Variable(var)) -> %
         ++ \spad{integrate(f(x))} returns an anti-derivative of the power
diff --git a/src/algebra/laurent.spad.pamphlet b/src/algebra/laurent.spad.pamphlet
index 0a22f478..1bfafeea 100644
--- a/src/algebra/laurent.spad.pamphlet
+++ b/src/algebra/laurent.spad.pamphlet
@@ -14,7 +14,7 @@
 )abbrev category ULSCCAT UnivariateLaurentSeriesConstructorCategory
 ++ Author: Clifton J. Williamson
 ++ Date Created: 6 February 1990
-++ Date Last Updated: 10 May 1990
+++ Date Last Updated: June 18, 2010
 ++ Basic Operations:
 ++ Related Domains:
 ++ Also See:
@@ -562,13 +562,11 @@ UnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where
   I   ==> Integer
   UTS ==> UnivariateTaylorSeries(Coef,var,cen)
 
-  Exports ==> UnivariateLaurentSeriesConstructorCategory(Coef,UTS) with
+  Exports ==> Join(UnivariateLaurentSeriesConstructorCategory(Coef,UTS),_
+                   PartialDifferentialDomain(%,Variable var)) with
     coerce: Variable(var) -> %
       ++ \spad{coerce(var)} converts the series variable \spad{var} into a
       ++ Laurent series.
-    differentiate: (%,Variable(var)) -> %
-      ++ \spad{differentiate(f(x),x)} returns the derivative of
-      ++ \spad{f(x)} with respect to \spad{x}.
     if Coef has Algebra Fraction Integer then
       integrate: (%,Variable(var)) -> %
         ++ \spad{integrate(f(x))} returns an anti-derivative of the power
diff --git a/src/algebra/puiseux.spad.pamphlet b/src/algebra/puiseux.spad.pamphlet
index fc5321ec..d9104a28 100644
--- a/src/algebra/puiseux.spad.pamphlet
+++ b/src/algebra/puiseux.spad.pamphlet
@@ -413,7 +413,7 @@ UnivariatePuiseuxSeriesConstructor(Coef,ULS):_
 )abbrev domain UPXS UnivariatePuiseuxSeries
 ++ Author: Clifton J. Williamson
 ++ Date Created: 28 January 1990
-++ Date Last Updated: 21 September 1993
+++ Date Last Updated: June 18, 2010
 ++ Basic Operations:
 ++ Related Domains:
 ++ Also See:
@@ -442,10 +442,8 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where
   ULS ==> UnivariateLaurentSeries(Coef,var,cen)
 
   Exports ==> Join(UnivariatePuiseuxSeriesConstructorCategory(Coef,ULS),_
+                   PartialDifferentialDomain(%,Variable var),_
                    RetractableTo UTS,CoercibleFrom Variable var) with
-    differentiate: (%,Variable(var)) -> %
-      ++ \spad{differentiate(f(x),x)} returns the derivative of
-      ++ \spad{f(x)} with respect to \spad{x}.
     if Coef has Algebra Fraction Integer then
       integrate: (%,Variable(var)) -> %
         ++ \spad{integrate(f(x))} returns an anti-derivative of the power
diff --git a/src/algebra/suls.spad.pamphlet b/src/algebra/suls.spad.pamphlet
index 2b1db3b9..efd567aa 100644
--- a/src/algebra/suls.spad.pamphlet
+++ b/src/algebra/suls.spad.pamphlet
@@ -14,7 +14,7 @@
 )abbrev domain SULS SparseUnivariateLaurentSeries
 ++ Author: Clifton J. Williamson
 ++ Date Created: 11 November 1994
-++ Date Last Updated: 10 March 1995
+++ Date Last Updated: June 18, 2010
 ++ Basic Operations:
 ++ Related Domains: InnerSparseUnivariatePowerSeries,
 ++   SparseUnivariateTaylorSeries, SparseUnivariatePuiseuxSeries
@@ -44,13 +44,11 @@ SparseUnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where
   SUTS  ==> SparseUnivariateTaylorSeries(Coef,var,cen)
   EFULS ==> ElementaryFunctionsUnivariateLaurentSeries(Coef,SUTS,%)
 
-  Exports ==> UnivariateLaurentSeriesConstructorCategory(Coef,SUTS) with
+  Exports ==> Join(UnivariateLaurentSeriesConstructorCategory(Coef,SUTS),_
+                   PartialDifferentialDomain(%,Variable var)) with
     coerce: Variable(var) -> %
       ++ \spad{coerce(var)} converts the series variable \spad{var} into a
       ++ Laurent series.
-    differentiate: (%,Variable(var)) -> %
-      ++ \spad{differentiate(f(x),x)} returns the derivative of
-      ++ \spad{f(x)} with respect to \spad{x}.
     if Coef has Algebra Fraction Integer then
       integrate: (%,Variable(var)) -> %
         ++ \spad{integrate(f(x))} returns an anti-derivative of the power
diff --git a/src/algebra/supxs.spad.pamphlet b/src/algebra/supxs.spad.pamphlet
index a8591584..a911aa38 100644
--- a/src/algebra/supxs.spad.pamphlet
+++ b/src/algebra/supxs.spad.pamphlet
@@ -14,7 +14,7 @@
 )abbrev domain SUPXS SparseUnivariatePuiseuxSeries
 ++ Author: Clifton J. Williamson
 ++ Date Created: 11 November 1994
-++ Date Last Updated: 28 February 1995
+++ Date Last Updated: June 18, 2010
 ++ Basic Operations:
 ++ Related Domains: InnerSparseUnivariatePowerSeries,
 ++   SparseUnivariateTaylorSeries, SparseUnivariateLaurentSeries
@@ -43,10 +43,8 @@ SparseUnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where
   SUPS ==> InnerSparseUnivariatePowerSeries(Coef)
 
   Exports ==> Join(UnivariatePuiseuxSeriesConstructorCategory(Coef,SULS),_
+                   PartialDifferentialDomain(%,Variable var),_
                    RetractableTo SUTS,CoercibleFrom Variable var) with
-    differentiate: (%,Variable(var)) -> %
-      ++ \spad{differentiate(f(x),x)} returns the derivative of
-      ++ \spad{f(x)} with respect to \spad{x}.
     if Coef has Algebra Fraction Integer then
       integrate: (%,Variable(var)) -> %
         ++ \spad{integrate(f(x))} returns an anti-derivative of the power
diff --git a/src/algebra/suts.spad.pamphlet b/src/algebra/suts.spad.pamphlet
index 8e5f4106..ecd46bad 100644
--- a/src/algebra/suts.spad.pamphlet
+++ b/src/algebra/suts.spad.pamphlet
@@ -14,7 +14,7 @@
 )abbrev domain SUTS SparseUnivariateTaylorSeries
 ++ Author: Clifton J. Williamson
 ++ Date Created: 16 February 1990
-++ Date Last Updated: 10 March 1995
+++ Date Last Updated: June 18, 2010
 ++ Basic Operations:
 ++ Related Domains: InnerSparseUnivariatePowerSeries,
 ++   SparseUnivariateLaurentSeries, SparseUnivariatePuiseuxSeries
@@ -47,7 +47,8 @@ SparseUnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where
   ST   ==> Stream Term
   UP   ==> UnivariatePolynomial(var,Coef)
 
-  Exports ==> UnivariateTaylorSeriesCategory(Coef) with
+  Exports ==> Join(UnivariateTaylorSeriesCategory(Coef),_
+                   PartialDifferentialDomain(%,Variable var)) with
     coerce: UP -> %
       ++\spad{coerce(p)} converts a univariate polynomial p in the variable
       ++\spad{var} to a univariate Taylor series in \spad{var}.
@@ -57,9 +58,6 @@ SparseUnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where
     coerce: Variable(var) -> %
       ++\spad{coerce(var)} converts the series variable \spad{var} into a
       ++ Taylor series.
-    differentiate: (%,Variable(var)) -> %
-      ++ \spad{differentiate(f(x),x)} computes the derivative of
-      ++ \spad{f(x)} with respect to \spad{x}.
     if Coef has Algebra Fraction Integer then
       integrate: (%,Variable(var)) -> %
         ++ \spad{integrate(f(x),x)} returns an anti-derivative of the power
diff --git a/src/algebra/taylor.spad.pamphlet b/src/algebra/taylor.spad.pamphlet
index e85c7a85..e3e01da9 100644
--- a/src/algebra/taylor.spad.pamphlet
+++ b/src/algebra/taylor.spad.pamphlet
@@ -141,7 +141,7 @@ InnerTaylorSeries(Coef): Exports == Implementation where
 )abbrev domain UTS UnivariateTaylorSeries
 ++ Author: Clifton J. Williamson
 ++ Date Created: 21 December 1989
-++ Date Last Updated: 21 September 1993
+++ Date Last Updated: June 18, 2010
 ++ Basic Operations:
 ++ Related Domains: UnivariateLaurentSeries(Coef,var,cen), UnivariatePuiseuxSeries(Coef,var,cen)
 ++ Also See:
@@ -170,7 +170,8 @@ UnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where
   STT  ==> StreamTaylorSeriesOperations Coef
   TERM ==> Record(k:NNI,c:Coef)
   UP   ==> UnivariatePolynomial(var,Coef)
-  Exports ==> UnivariateTaylorSeriesCategory(Coef) with
+  Exports ==> Join(UnivariateTaylorSeriesCategory(Coef),_
+                   PartialDifferentialDomain(%,Variable var)) with
     coerce: UP -> %
       ++\spad{coerce(p)} converts a univariate polynomial p in the variable
       ++\spad{var} to a univariate Taylor series in \spad{var}.
@@ -180,9 +181,6 @@ UnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where
     coerce: Variable(var) -> %
       ++\spad{coerce(var)} converts the series variable \spad{var} into a
       ++ Taylor series.
-    differentiate: (%,Variable(var)) -> %
-      ++ \spad{differentiate(f(x),x)} computes the derivative of
-      ++ \spad{f(x)} with respect to \spad{x}.
     lagrange: % -> %
       ++\spad{lagrange(g(x))} produces the Taylor series for \spad{f(x)}
       ++ where \spad{f(x)} is implicitly defined as \spad{f(x) = x*g(f(x))}.