* algebra/vector.spad.pamphlet (DualBasis): New.

	(LinearBasis): Likewise.
	(LinearElement): Use them.
	(LinearForm): New.

4 files changed, 122 insertions, 16 deletions

diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index 5d04110f..690e7630 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -612,7 +612,6 @@ $(OUT)/DIRPROD.$(FASLEXT): $(OUT)/DIRPCAT.$(FASLEXT)
 $(OUT)/DIRPCAT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/IVECTOR.$(FASLEXT)
 $(OUT)/MATRIX.$(FASLEXT): $(OUT)/MATCAT.$(FASLEXT)
 $(OUT)/BTAGG.$(FASLEXT): $(OUT)/BOOLE.$(FASLEXT)
-$(OUT)/LINELT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/FM.$(FASLEXT)
 
 axiom_algebra_layer_10 = \
   RESULT   BFUNCT   BPADIC   ANY      \
@@ -641,7 +640,7 @@ axiom_algebra_layer_10 = \
   FUNDESC  XPBWPOLY SMATCAT  SMATCAT- \
   RMATRIX  RMATCAT  RMATCAT- DIRPROD \
   DIRPCAT  DIRPCAT- IVECTOR  MATRIX  \
-  MATCAT   MATCAT-  IIARRAY2 LINELT
+  MATCAT   MATCAT-  IIARRAY2 
 
 
 axiom_algebra_layer_10_nrlibs = \
@@ -983,7 +982,8 @@ axiom_algebra_layer_user =  \
         ASP78    ASP9     ASP12    ASP55    ASP8     ASP19    \
         ASP20    ASP30    ASP31    ASP35    ASP41    ASP42    \
 	ASP74    ASP77    ASP80    ASP29    IRFORM   COMPILER \
-	ITFORM   ELABOR   TALGOP   YDIAGRAM
+	ITFORM   ELABOR   TALGOP   YDIAGRAM LINELT   DBASIS   \
+	LINFORM  LINBASIS
 
 axiom_algebra_layer_user_nrlibs = \
 	$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user))
@@ -1064,6 +1064,13 @@ $(OUT)/ELABOR.$(FASLEXT): $(OUT)/ITFORM.$(FASLEXT) $(OUT)/ENV.$(FASLEXT) \
 	$(OUT)/IRFORM.$(FASLEXT)
 
 
+$(OUT)/LINBASIS.$(FASLEXT): $(OUT)/ORDFIN.$(FASLEXT) $(OUT)/OVAR.$(FASLEXT)
+$(OUT)/LINELT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/FM.$(FASLEXT)
+$(OUT)/DBASIS.$(FASLEXT): $(OUT)/ORDFIN.$(FASLEXT) $(OUT)/KVTFROM.$(FASLEXT)
+$(OUT)/LINFORM.$(FASLEXT): $(OUT)/DBASIS.$(FASLEXT) \
+	$(OUT)/VSPACE.$(FASLEXT) $(OUT)/LINELT.$(FASLEXT)
+
+
 .PHONY: all all-algebra mkdir-output-directory
 all: all-ax
 
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index 2a600ccb..d0d6cc7e 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -619,7 +619,6 @@ $(OUT)/DIRPROD.$(FASLEXT): $(OUT)/DIRPCAT.$(FASLEXT)
 $(OUT)/DIRPCAT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/IVECTOR.$(FASLEXT)
 $(OUT)/MATRIX.$(FASLEXT): $(OUT)/MATCAT.$(FASLEXT)
 $(OUT)/BTAGG.$(FASLEXT): $(OUT)/BOOLE.$(FASLEXT)
-$(OUT)/LINELT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/FM.$(FASLEXT)
 
 axiom_algebra_layer_10 = \
   RESULT   BFUNCT   BPADIC   ANY      \
@@ -648,7 +647,7 @@ axiom_algebra_layer_10 = \
   FUNDESC  XPBWPOLY SMATCAT  SMATCAT- \
   RMATRIX  RMATCAT  RMATCAT- DIRPROD \
   DIRPCAT  DIRPCAT- IVECTOR  MATRIX  \
-  MATCAT   MATCAT-  IIARRAY2 LINELT
+  MATCAT   MATCAT-  IIARRAY2 
 
 
 axiom_algebra_layer_10_nrlibs = \
@@ -1062,7 +1061,8 @@ axiom_algebra_layer_user =  \
         ASP78    ASP9     ASP12    ASP55    ASP8     ASP19    \
         ASP20    ASP30    ASP31    ASP35    ASP41    ASP42    \
 	ASP74    ASP77    ASP80    ASP29    IRFORM   COMPILER \
-	ITFORM   ELABOR   TALGOP   YDIAGRAM
+	ITFORM   ELABOR   TALGOP   YDIAGRAM LINELT   DBASIS   \
+	LINFORM  LINBASIS
 
 axiom_algebra_layer_user_nrlibs = \
 	$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user))
@@ -1142,6 +1142,13 @@ $(OUT)/ITFORM.$(FASLEXT): $(OUT)/IRFORM.$(FASLEXT)
 $(OUT)/ELABOR.$(FASLEXT): $(OUT)/ITFORM.$(FASLEXT) $(OUT)/ENV.$(FASLEXT) \
 	$(OUT)/IRFORM.$(FASLEXT)
 
+
+$(OUT)/LINBASIS.$(FASLEXT): $(OUT)/ORDFIN.$(FASLEXT) $(OUT)/OVAR.$(FASLEXT)
+$(OUT)/LINELT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/FM.$(FASLEXT)
+$(OUT)/DBASIS.$(FASLEXT): $(OUT)/ORDFIN.$(FASLEXT) $(OUT)/KVTFROM.$(FASLEXT)
+$(OUT)/LINFORM.$(FASLEXT): $(OUT)/DBASIS.$(FASLEXT) \
+	$(OUT)/VSPACE.$(FASLEXT) $(OUT)/LINELT.$(FASLEXT)
+
 @
 
 \section{Broken Files}
diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet
index ba666e3a..3acfbcfe 100644
--- a/src/algebra/exposed.lsp.pamphlet
+++ b/src/algebra/exposed.lsp.pamphlet
@@ -126,6 +126,7 @@
   (|DrawComplex| . DRAWCX)
   (|DrawNumericHack| . DRAWHACK)
   (|DrawOption| . DROPT)
+  (|DualBasis| . DBASIS)
   (|EigenPackage| . EP)
   (|ElaboratedExpression| . ELABEXPR)
   (|ElementaryFunctionDefiniteIntegration| . DEFINTEF)
@@ -231,7 +232,9 @@
   (|LetAst| . LETAST)
   (|Library| . LIB)
   (|LieSquareMatrix| . LSQM)
+  (|LinearBasis| . LINBASIS)
   (|LinearElement| . LINELT)
+  (|LinearForm| . LINFORM)
   (|LinearOrdinaryDifferentialOperator| . LODO)
   (|LinearSystemMatrixPackage| . LSMP)
   (|LinearSystemMatrixPackage1| . LSMP1)
diff --git a/src/algebra/vector.spad.pamphlet b/src/algebra/vector.spad.pamphlet
index 05474370..a708524a 100644
--- a/src/algebra/vector.spad.pamphlet
+++ b/src/algebra/vector.spad.pamphlet
@@ -450,11 +450,49 @@ DirectProductFunctions2(dim, A, B): Exports == Implementation where
 
 \section{Vector space of finite dimension given by a basis}
 
+
+<<domain LINBASIS LinearBasis>>=
+++ Author: Gabriel Dos Reis
+++ Date Created: July 2, 2010
+++ Date Last Modified: July 2, 2010
+++ Descrption:
+++   Representation of a vector space basis, given by symbols.
+)abbrev domain LINBASIS LinearBasis
+LinearBasis(vars: List Symbol): Public == Private where
+  Public == Join(OrderedFinite,CoercibleFrom OrderedVariableList vars) with
+    dual: DualBasis vars -> %
+      ++ \spad{dual f} constructs the dual vector of a linear form
+      ++ which is part of a basis.
+  Private == OrderedVariableList vars add
+    coerce(s: Rep): % == per s
+    dual f == index(lookup f)@%
+
+@
+
+<<domain DBASIS DualBasis>>=
+++ Author: Gabriel Dos Reis
+++ Date Created: July 2, 2010
+++ Date Last Modified: July 2, 2010
+++ Descrption:
+++   Representation of a dual vector space basis, given by symbols.
+)abbrev domain DBASIS DualBasis
+DualBasis(vars: List Symbol): Public == Private where
+  Public == Join(OrderedFinite) with
+    dual: LinearBasis vars -> %
+      ++ \spad{dual x} constructs the dual vector of a linear element
+      ++ which is part of a basis.
+  Private == OrderedVariableList vars add
+    dual v == index(lookup v)@%
+    coerce(x: %): OutputForm ==
+      superscript(convert(rep x)@Symbol,['_*::OutputForm])::OutputForm
+
+@
+
 <<domain LINELT LinearElement>>=
 )abbrev domain LINELT LinearElement
 ++ Author: Gabriel Dos Reis
 ++ Date Created: June 30, 2010
-++ Date Last Modified: June 30, 2010
+++ Date Last Modified: July 2, 2010
 ++ Description:
 ++   A simple data structure for elements that form a
 ++   vector space of finite dimension over a given field,
@@ -462,12 +500,13 @@ DirectProductFunctions2(dim, A, B): Exports == Implementation where
 LinearElement(K,B): Public == Private where
   K: Field
   B: List Symbol
-  macro Basis == OrderedVariableList B
-  Public == Join(VectorSpace K,CoercibleFrom Basis) with
-    linearElement: (List K,List Basis) -> %
-      ++ \spad{linearElement([x1,..,xn],[b1,..,bn]) constructs
-      ++ a linear element with coordinates \spad{[x1,..,xn]} with
-      ++ respect to the basis elements \spad{b1},...\spad{bn}.
+  macro Basis == LinearBasis B
+  Public == Join(VectorSpace K,CoercibleFrom Basis,_
+                 IndexedDirectProductCategory(K,Basis)) with
+    linearElement: List K -> %
+      ++ \spad{linearElement [x1,..,xn]} returns a linear element
+      ++  with coordinates \spad{[x1,..,xn]} with respect to
+      ++ the basis elements \spad{B}.
     coordinates: % -> Vector K
       ++ \spad{coordinates x} returns the coordinates of the linear
       ++ element with respect to the basis \spad{B}.
@@ -478,10 +517,9 @@ LinearElement(K,B): Public == Private where
     dimension() ==
       size()$Basis::CardinalNumber
 
-    linearElement(cs,bs) ==
-      null cs or null bs => per 0$Rep
+    linearElement cs ==
       reduce(_+@(%,%)->%,
-         [per monomial(c,b) for c in cs for b in bs])
+         [per monomial(c,index(i)$Basis) for c in cs for i in 1..],0)
 
     coordinates x ==
       n := #B
@@ -496,7 +534,53 @@ LinearElement(K,B): Public == Private where
 @
 
 
+<<domain LINFORM LinearForm>>=
+)abbrev domain LINFORM LinearForm
+++ Author: Gabriel Dos Reis
+++ Date Created: July 2, 2010
+++ Date Last Modified: July 2, 2010
+++ Description:
+++   A simple data structure for linear forms on a vector space of
+++   finite dimension over a given field, with a given symbolic basis.
+LinearForm(K,B): Public == Private where
+  K: Field
+  B: List Symbol
+  macro Basis == DualBasis B
+  Public == Join(VectorSpace K,Eltable(LinearElement(K,B),K)) with
+    linearForm: List K -> %
+      ++ \spad{linearForm [x1,..,xn]} constructs
+      ++ a linear form with coordinates \spad{[x1,..,xn]} with
+      ++ respect to the basis elements \spad{DualBasis B}.
+    coordinates: % -> Vector K
+      ++ \spad{coordinates x} returns the coordinates of the linear
+      ++ form with respect to the basis \spad{DualBasis B}.
+  Private == FreeModule(K,Basis) add
+    dimension() ==
+      size()$Basis::CardinalNumber
+
+    linearForm cs ==
+      reduce(_+@(%,%)->%,
+         [per monomial(c,index(i)$Basis) for c in cs for i in 1..],0)
+
+    coordinates f ==
+      n := #B
+      v: Vector K := new(n,0$K)
+      ts := terms rep f
+      for i in 1..n repeat
+        t := first ts
+        lookup first t = i => 
+          v.i := second t
+          ts := rest ts
+      v
+
+    elt(f,x) ==
+      dot(coordinates f, coordinates x)$Vector(K)
+
+@
+
+
 \section{License}
+
 <<license>>=
 --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
 --All rights reserved.
@@ -541,7 +625,12 @@ LinearElement(K,B): Public == Private where
 <<category DIRPCAT DirectProductCategory>>
 <<domain DIRPROD DirectProduct>>
 <<package DIRPROD2 DirectProductFunctions2>>
+
+<<domain LINBASIS LinearBasis>>
+<<domain DBASIS DualBasis>>
+
 <<domain LINELT LinearElement>>
+<<domain LINFORM LinearForm>>
  
 @
 \eject