* algebra/boolean.spad.pamphlet (PropositionalLogic): New category.

	(Boolean): Assert as belonging to PropositionalLogic.
	Update cached Lisp translation.
	* algebra/Makefile.pamphlet (axiom_algebra_layer_0): Add
	PROPLOG.o
	* src/algebra: Update databases.

9 files changed, 22132 insertions, 22180 deletions

diff --git a/src/ChangeLog b/src/ChangeLog
index a99d946c..fafaf259 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,5 +1,14 @@
 2008-01-15  Gabriel Dos Reis  <gdr@cs.tamu.edu>
 
+	* algebra/boolean.spad.pamphlet (PropositionalLogic): New category.
+	(Boolean): Assert as belonging to PropositionalLogic.
+	Update cached Lisp translation.
+	* algebra/Makefile.pamphlet (axiom_algebra_layer_0): Add
+	PROPLOG.o
+	* src/algebra: Update databases.
+
+2008-01-15  Gabriel Dos Reis  <gdr@cs.tamu.edu>
+
 	* algebra/syntax.spad (autoCoerce$Syntax): Add overloads.
 	* interp/compiler.boot (coerceExtraHard): Always coerce by
 	autoCoerce. 
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index a974ad21..7fe8dd8f 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -377,7 +377,7 @@ axiom_algebra_layer_0 = \
   KOERCE.o  KONVERT.o MSYSCMD.o ODEIFTBL.o \
   OM.o      OMCONN.o  OMDEV.o   OUT.o      \
   PRIMCAT.o PRINT.o   PTRANFN.o SPFCAT.o   \
-  TYPE.o    UTYPE.o
+  TYPE.o    UTYPE.o   PROPLOG.o
 
 axiom_algebra_layer_0_nrlibs = \
 	$(axiom_algebra_layer_0:.$(OBJEXT)=.NRLIB/code.$(OBJEXT))
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index 45f1f2bd..70a3f05c 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -205,7 +205,7 @@ axiom_algebra_layer_0 = \
   KOERCE.o  KONVERT.o MSYSCMD.o ODEIFTBL.o \
   OM.o      OMCONN.o  OMDEV.o   OUT.o      \
   PRIMCAT.o PRINT.o   PTRANFN.o SPFCAT.o   \
-  TYPE.o    UTYPE.o
+  TYPE.o    UTYPE.o   PROPLOG.o
 
 axiom_algebra_layer_0_nrlibs = \
 	$(axiom_algebra_layer_0:.$(OBJEXT)=.NRLIB/code.$(OBJEXT))
diff --git a/src/algebra/boolean.spad.pamphlet b/src/algebra/boolean.spad.pamphlet
index 84632fa5..85b2c056 100644
--- a/src/algebra/boolean.spad.pamphlet
+++ b/src/algebra/boolean.spad.pamphlet
@@ -1,14 +1,39 @@
 \documentclass{article}
 \usepackage{axiom}
+
+\title{src/algebra boolean.spad}
+\author{Stephen M. Watt, Michael Monagan, Gabriel Dos~Reis}
+
 \begin{document}
-\title{\$SPAD/src/algebra boolean.spad}
-\author{Stephen M. Watt, Michael Monagan}
 \maketitle
 \begin{abstract}
 \end{abstract}
-\eject
+
 \tableofcontents
 \eject
+
+\section{category PROPLOG PropositionalLogic}
+<<category PROPLOG PropositionalLogic>>=
+)abbrev category PROPLOG PropositionalLogic
+++ Author: Gabriel Dos Reis
+++ Date Created: Januray 14, 2008
+++ Date Last Modified: January 14, 2008
+++ Description: This category declares the connectives of
+++ Propositional Logic.
+PropositionalLogic(): Category == with
+  "not": % -> %
+    ++ not p returns the logical negation of `p'.
+  "and": (%, %) -> %
+    ++ p and q returns the logical conjunction of `p', `q'.
+  "or": (%, %) -> %
+    ++ p or q returns the logical disjunction of `p', `q'.
+  implies: (%,%) -> %
+    ++ implies(p,q) returns the logical implication of `q' by `p'.
+  equiv: (%,%) -> %
+    ++ equiv(p,q) returns the logical equivalence of `p', `q'.
+@
+
+
 \section{domain REF Reference}
 <<domain REF Reference>>=
 )abbrev domain REF Reference
@@ -131,20 +156,13 @@ Logic: Category == BasicType with
 ++ Description:  \spadtype{Boolean} is the elementary logic with 2 values:
 ++ true and false
 
-Boolean(): Join(OrderedSet, Finite, Logic, ConvertibleTo InputForm) with
+Boolean(): Join(OrderedSet, Finite, Logic, PropositionalLogic, ConvertibleTo InputForm) with
     true   : constant -> %
       ++ true is a logical constant.
     false  : constant -> %
       ++ false is a logical constant.
     _^    : % -> %
       ++ ^ n returns the negation of n.
-    _not : % -> %
-      ++ not n returns the negation of n.
-    _and  : (%, %) -> %
-      ++ a and b  returns the logical {\em and} of Boolean \spad{a} and b.
-    _or  : (%, %) -> %
-      ++ a or b returns the logical inclusive {\em or}
-      ++ of Boolean \spad{a} and b.
     xor    : (%, %) -> %
       ++ xor(a,b) returns the logical exclusive {\em or}
       ++ of Boolean \spad{a} and b.
@@ -152,9 +170,6 @@ Boolean(): Join(OrderedSet, Finite, Logic, ConvertibleTo InputForm) with
       ++ nand(a,b) returns the logical negation of \spad{a} and b.
     nor    : (%, %) -> %
       ++ nor(a,b) returns the logical negation of \spad{a} or b.
-    implies: (%, %) -> %
-      ++ implies(a,b) returns the logical implication
-      ++ of Boolean \spad{a} and b.
     test: % -> Boolean
       ++ test(b) returns b and is provided for compatibility with the new compiler.
   == add
@@ -178,6 +193,7 @@ Boolean(): Join(OrderedSet, Finite, Logic, ConvertibleTo InputForm) with
     nand(a, b)    == (test a => nt b; true)
     a = b         == BooleanEquality(a, b)$Lisp
     implies(a, b) == (test a => b; true)
+    equiv(a,b)    == BooleanEquality(a, b)$Lisp
     a < b         == (test b => not(test a);false)
 
     size()        == 2
@@ -212,250 +228,157 @@ code and copy the {\bf BOOLEAN.o} file to the {\bf OUT} directory.
 This is eventually forcibly replaced by a recompiled version. 
 <<BOOLEAN.lsp BOOTSTRAP>>=
 
-(|/VERSIONCHECK| 2) 
+(/VERSIONCHECK 2) 
+
+(PUT '|BOOLEAN;test;$B;1| '|SPADreplace| '(XLAM (|a|) |a|)) 
+
+(DEFUN |BOOLEAN;test;$B;1| (|a| $) |a|) 
+
+(DEFUN |BOOLEAN;nt| (|b| $) (COND (|b| 'NIL) ('T 'T))) 
+
+(PUT '|BOOLEAN;true;$;3| '|SPADreplace| '(XLAM NIL 'T)) 
+
+(DEFUN |BOOLEAN;true;$;3| ($) 'T) 
+
+(PUT '|BOOLEAN;false;$;4| '|SPADreplace| '(XLAM NIL NIL)) 
+
+(DEFUN |BOOLEAN;false;$;4| ($) NIL) 
+
+(DEFUN |BOOLEAN;not;2$;5| (|b| $) (COND (|b| 'NIL) ('T 'T))) 
+
+(DEFUN |BOOLEAN;^;2$;6| (|b| $) (COND (|b| 'NIL) ('T 'T))) 
+
+(DEFUN |BOOLEAN;~;2$;7| (|b| $) (COND (|b| 'NIL) ('T 'T))) 
+
+(DEFUN |BOOLEAN;and;3$;8| (|a| |b| $) (COND (|a| |b|) ('T 'NIL))) 
+
+(DEFUN |BOOLEAN;/\\;3$;9| (|a| |b| $) (COND (|a| |b|) ('T 'NIL))) 
+
+(DEFUN |BOOLEAN;or;3$;10| (|a| |b| $) (COND (|a| 'T) ('T |b|))) 
+
+(DEFUN |BOOLEAN;\\/;3$;11| (|a| |b| $) (COND (|a| 'T) ('T |b|))) 
+
+(DEFUN |BOOLEAN;xor;3$;12| (|a| |b| $)
+  (COND (|a| (|BOOLEAN;nt| |b| $)) ('T |b|))) 
 
-(PUT 
-  (QUOTE |BOOLEAN;test;2$;1|) 
-  (QUOTE |SPADreplace|) 
-  (QUOTE (XLAM (|a|) |a|))) 
-
-(DEFUN |BOOLEAN;test;2$;1| (|a| |$|) |a|) 
-
-(DEFUN |BOOLEAN;nt| (|b| |$|) 
-  (COND (|b| (QUOTE NIL)) 
-  ((QUOTE T) (QUOTE T)))) 
-
-(PUT 
-  (QUOTE |BOOLEAN;true;$;3|) 
-  (QUOTE |SPADreplace|) 
-  (QUOTE (XLAM NIL (QUOTE T)))) 
-
-(DEFUN |BOOLEAN;true;$;3| (|$|) 
-  (QUOTE T)) 
-
-(PUT 
-  (QUOTE |BOOLEAN;false;$;4|) 
-  (QUOTE |SPADreplace|) 
-  (QUOTE (XLAM NIL NIL))) 
-
-(DEFUN |BOOLEAN;false;$;4| (|$|) NIL) 
-
-(DEFUN |BOOLEAN;not;2$;5| (|b| |$|) 
-  (COND 
-    (|b| (QUOTE NIL)) 
-    ((QUOTE T) (QUOTE T)))) 
-
-(DEFUN |BOOLEAN;^;2$;6| (|b| |$|) 
-  (COND 
-    (|b| (QUOTE NIL)) 
-    ((QUOTE T) (QUOTE T)))) 
-
-(DEFUN |BOOLEAN;~;2$;7| (|b| |$|) 
-  (COND 
-    (|b| (QUOTE NIL)) 
-    ((QUOTE T) (QUOTE T)))) 
-
-(DEFUN |BOOLEAN;and;3$;8| (|a| |b| |$|) 
-  (COND 
-    (|a| |b|) 
-    ((QUOTE T) (QUOTE NIL)))) 
-
-(DEFUN |BOOLEAN;/\\;3$;9| (|a| |b| |$|) 
-  (COND 
-    (|a| |b|) 
-    ((QUOTE T) (QUOTE NIL)))) 
-
-(DEFUN |BOOLEAN;or;3$;10| (|a| |b| |$|) 
-  (COND 
-    (|a| (QUOTE T)) 
-    ((QUOTE T) |b|))) 
-
-(DEFUN |BOOLEAN;\\/;3$;11| (|a| |b| |$|) 
-  (COND 
-    (|a| (QUOTE T)) 
-    ((QUOTE T) |b|))) 
-
-(DEFUN |BOOLEAN;xor;3$;12| (|a| |b| |$|) 
-  (COND 
-    (|a| (|BOOLEAN;nt| |b| |$|)) 
-    ((QUOTE T) |b|))) 
-
-(DEFUN |BOOLEAN;nor;3$;13| (|a| |b| |$|) 
-  (COND 
-    (|a| (QUOTE NIL)) 
-    ((QUOTE T) (|BOOLEAN;nt| |b| |$|)))) 
-
-(DEFUN |BOOLEAN;nand;3$;14| (|a| |b| |$|) 
-  (COND 
-    (|a| (|BOOLEAN;nt| |b| |$|)) 
-    ((QUOTE T) (QUOTE T)))) 
-
-(PUT 
-  (QUOTE |BOOLEAN;=;3$;15|) 
-  (QUOTE |SPADreplace|) 
-  (QUOTE |BooleanEquality|)) 
-
-(DEFUN |BOOLEAN;=;3$;15| (|a| |b| |$|) 
-  (|BooleanEquality| |a| |b|)) 
-
-(DEFUN |BOOLEAN;implies;3$;16| (|a| |b| |$|) 
-  (COND 
-    (|a| |b|) 
-    ((QUOTE T) (QUOTE T)))) 
-
-(DEFUN |BOOLEAN;<;3$;17| (|a| |b| |$|) 
-  (COND 
-    (|b| 
-      (COND 
-        (|a| (QUOTE NIL))
-        ((QUOTE T) (QUOTE T)))) 
-    ((QUOTE T) (QUOTE NIL)))) 
-
-(PUT 
-  (QUOTE |BOOLEAN;size;Nni;18|) 
-  (QUOTE |SPADreplace|) 
-  (QUOTE (XLAM NIL 2))) 
-
-(DEFUN |BOOLEAN;size;Nni;18| (|$|) 2) 
-
-(DEFUN |BOOLEAN;index;Pi$;19| (|i| |$|) 
-  (COND 
-    ((SPADCALL |i| (QREFELT |$| 26)) (QUOTE NIL))
-    ((QUOTE T) (QUOTE T)))) 
-
-(DEFUN |BOOLEAN;lookup;$Pi;20| (|a| |$|) 
-  (COND 
-    (|a| 1) 
-    ((QUOTE T) 2))) 
-
-(DEFUN |BOOLEAN;random;$;21| (|$|) 
-  (COND 
-    ((SPADCALL (|random|) (QREFELT |$| 26)) (QUOTE NIL)) 
-    ((QUOTE T) (QUOTE T)))) 
-
-(DEFUN |BOOLEAN;convert;$If;22| (|x| |$|) 
-  (COND 
-    (|x| (SPADCALL (SPADCALL "true" (QREFELT |$| 33)) (QREFELT |$| 35)))
-    ((QUOTE T) 
-      (SPADCALL (SPADCALL "false" (QREFELT |$| 33)) (QREFELT |$| 35))))) 
-
-(DEFUN |BOOLEAN;coerce;$Of;23| (|x| |$|) 
-  (COND 
-    (|x| (SPADCALL "true" (QREFELT |$| 38)))
-    ((QUOTE T) (SPADCALL "false" (QREFELT |$| 38))))) 
-
-(DEFUN |Boolean| NIL 
-  (PROG NIL 
-    (RETURN 
-      (PROG (#1=#:G82461) 
-        (RETURN 
-          (COND 
-            ((LETT #1# 
-                (HGET |$ConstructorCache| (QUOTE |Boolean|))
-                |Boolean|)
-              (|CDRwithIncrement| (CDAR #1#)))
-             ((QUOTE T) 
-               (|UNWIND-PROTECT| 
-                 (PROG1 
-                   (CDDAR 
-                     (HPUT 
-                       |$ConstructorCache| 
-                       (QUOTE |Boolean|) 
-                       (LIST (CONS NIL (CONS 1 (|Boolean;|))))))
-                   (LETT #1# T |Boolean|))
-                 (COND 
-                   ((NOT #1#) 
-                     (HREM |$ConstructorCache| (QUOTE |Boolean|)))))))))))) 
-
-(DEFUN |Boolean;| NIL 
-  (PROG (|dv$| |$| |pv$|) 
-    (RETURN 
-      (PROGN 
-        (LETT |dv$| (QUOTE (|Boolean|)) . #1=(|Boolean|))
-        (LETT |$| (GETREFV 41) . #1#)
-        (QSETREFV |$| 0 |dv$|)
-        (QSETREFV |$| 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #1#))
-        (|haddProp| |$ConstructorCache| (QUOTE |Boolean|) NIL (CONS 1 |$|))
-        (|stuffDomainSlots| |$|) |$|)))) 
-
-(MAKEPROP 
-  (QUOTE |Boolean|) 
-  (QUOTE |infovec|) 
-    (LIST 
-      (QUOTE 
-        #(NIL NIL NIL NIL NIL NIL 
-          (|Boolean|)
-          |BOOLEAN;test;2$;1| 
-          (CONS IDENTITY 
-            (FUNCALL (|dispatchFunction| |BOOLEAN;true;$;3|) |$|))
-          (CONS IDENTITY 
-            (FUNCALL (|dispatchFunction| |BOOLEAN;false;$;4|) |$|))
-          |BOOLEAN;not;2$;5| 
-          |BOOLEAN;^;2$;6| 
-          |BOOLEAN;~;2$;7| 
-          |BOOLEAN;and;3$;8| 
-          |BOOLEAN;/\\;3$;9| 
-          |BOOLEAN;or;3$;10| 
-          |BOOLEAN;\\/;3$;11| 
-          |BOOLEAN;xor;3$;12| 
-          |BOOLEAN;nor;3$;13| 
-          |BOOLEAN;nand;3$;14| 
-          |BOOLEAN;=;3$;15| 
-          |BOOLEAN;implies;3$;16| 
-          |BOOLEAN;<;3$;17| 
-          (|NonNegativeInteger|) 
-          |BOOLEAN;size;Nni;18| 
-          (|Integer|) 
-          (0 . |even?|) 
-          (|PositiveInteger|) 
-          |BOOLEAN;index;Pi$;19| 
-          |BOOLEAN;lookup;$Pi;20| 
-          |BOOLEAN;random;$;21| 
-          (|String|) 
-          (|Symbol|)
-          (5 . |coerce|)
-          (|InputForm|)
-          (10 . |convert|)
-          |BOOLEAN;convert;$If;22| 
-          (|OutputForm|) 
-          (15 . |message|) 
-          |BOOLEAN;coerce;$Of;23| 
-          (|SingleInteger|)))
-      (QUOTE 
-         #(|~=| 20 |~| 26 |xor| 31 |true| 37 |test| 41 |size| 46 |random| 50 
-           |or| 54 |not| 60 |nor| 65 |nand| 71 |min| 77 |max| 83 |lookup| 89 
-           |latex| 94 |index| 99 |implies| 104 |hash| 110 |false| 115 
-           |convert| 119 |coerce| 124 |and| 129 |^| 135 |\\/| 140 |>=| 146 
-           |>| 152 |=| 158 |<=| 164 |<| 170 |/\\| 176))
-      (QUOTE NIL)
-      (CONS 
-        (|makeByteWordVec2| 1 (QUOTE (0 0 0 0 0 0 0)))
-        (CONS 
-          (QUOTE 
-            #(|OrderedSet&| NIL |Logic&| |SetCategory&| NIL |BasicType&| NIL))
-          (CONS 
-            (QUOTE 
-              #((|OrderedSet|) 
-                (|Finite|)
-                (|Logic|)
-                (|SetCategory|)
-                (|ConvertibleTo| 34)
-                (|BasicType|)
-                (|CoercibleTo| 37)))
-            (|makeByteWordVec2| 
-              40 
-              (QUOTE 
-                (1 25 6 0 26 1 32 0 31 33 1 34 0 32 35 1 37 0 31 38 2 0 6 0 0 
-                 1 1 0 0 0 12 2 0 0 0 0 17 0 0 0 8 1 0 6 0 7 0 0 23 24 0 0 0 
-                 30 2 0 0 0 0 15 1 0 0 0 10 2 0 0 0 0 18 2 0 0 0 0 19 2 0 0 0 
-                 0 1 2 0 0 0 0 1 1 0 27 0 29 1 0 31 0 1 1 0 0 27 28 2 0 0 0 0
-                 21 1 0 40 0 1 0 0 0 9 1 0 34 0 36 1 0 37 0 39 2 0 0 0 0 13 1
-                 0 0 0 11 2 0 0 0 0 16 2 0 6 0 0 1 2 0 6 0 0 1 2 0 6 0 0 20 2
-                 0 6 0 0 1 2 0 6 0 0 22 2 0 0 0 0 14))))))
-      (QUOTE |lookupComplete|))) 
-
-(MAKEPROP (QUOTE |Boolean|) (QUOTE NILADIC) T) 
+(DEFUN |BOOLEAN;nor;3$;13| (|a| |b| $)
+  (COND (|a| 'NIL) ('T (|BOOLEAN;nt| |b| $)))) 
 
+(DEFUN |BOOLEAN;nand;3$;14| (|a| |b| $)
+  (COND (|a| (|BOOLEAN;nt| |b| $)) ('T 'T))) 
+
+(PUT '|BOOLEAN;=;2$B;15| '|SPADreplace| '|BooleanEquality|) 
+
+(DEFUN |BOOLEAN;=;2$B;15| (|a| |b| $) (|BooleanEquality| |a| |b|)) 
+
+(DEFUN |BOOLEAN;implies;3$;16| (|a| |b| $) (COND (|a| |b|) ('T 'T))) 
+
+(PUT '|BOOLEAN;equiv;3$;17| '|SPADreplace| '|BooleanEquality|) 
+
+(DEFUN |BOOLEAN;equiv;3$;17| (|a| |b| $) (|BooleanEquality| |a| |b|)) 
+
+(DEFUN |BOOLEAN;<;2$B;18| (|a| |b| $)
+  (COND (|b| (SPADCALL |a| (QREFELT $ 23))) ('T 'NIL))) 
+
+(PUT '|BOOLEAN;size;Nni;19| '|SPADreplace| '(XLAM NIL 2)) 
+
+(DEFUN |BOOLEAN;size;Nni;19| ($) 2) 
+
+(DEFUN |BOOLEAN;index;Pi$;20| (|i| $)
+  (COND ((SPADCALL |i| (QREFELT $ 28)) 'NIL) ('T 'T))) 
+
+(DEFUN |BOOLEAN;lookup;$Pi;21| (|a| $) (COND (|a| 1) ('T 2))) 
+
+(DEFUN |BOOLEAN;random;$;22| ($)
+  (COND ((SPADCALL (|random|) (QREFELT $ 28)) 'NIL) ('T 'T))) 
+
+(DEFUN |BOOLEAN;convert;$If;23| (|x| $)
+  (COND
+    (|x| (SPADCALL (SPADCALL "true" (QREFELT $ 35)) (QREFELT $ 37)))
+    ('T (SPADCALL (SPADCALL "false" (QREFELT $ 35)) (QREFELT $ 37))))) 
+
+(DEFUN |BOOLEAN;coerce;$Of;24| (|x| $)
+  (COND
+    (|x| (SPADCALL "true" (QREFELT $ 40)))
+    ('T (SPADCALL "false" (QREFELT $ 40))))) 
+
+(DEFUN |Boolean| ()
+  (PROG ()
+    (RETURN
+      (PROG (#0=#:G1458)
+        (RETURN
+          (COND
+            ((LETT #0# (HGET |$ConstructorCache| '|Boolean|) |Boolean|)
+             (|CDRwithIncrement| (CDAR #0#)))
+            ('T
+             (UNWIND-PROTECT
+               (PROG1 (CDDAR (HPUT |$ConstructorCache| '|Boolean|
+                                   (LIST
+                                    (CONS NIL (CONS 1 (|Boolean;|))))))
+                 (LETT #0# T |Boolean|))
+               (COND
+                 ((NOT #0#) (HREM |$ConstructorCache| '|Boolean|))))))))))) 
+
+(DEFUN |Boolean;| ()
+  (PROG (|dv$| $ |pv$|)
+    (RETURN
+      (PROGN
+        (LETT |dv$| '(|Boolean|) . #0=(|Boolean|))
+        (LETT $ (GETREFV 43) . #0#)
+        (QSETREFV $ 0 |dv$|)
+        (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#))
+        (|haddProp| |$ConstructorCache| '|Boolean| NIL (CONS 1 $))
+        (|stuffDomainSlots| $)
+        $)))) 
+
+(MAKEPROP '|Boolean| '|infovec|
+    (LIST '#(NIL NIL NIL NIL NIL NIL (|Boolean|) |BOOLEAN;test;$B;1|
+             (CONS IDENTITY
+                   (FUNCALL (|dispatchFunction| |BOOLEAN;true;$;3|) $))
+             (CONS IDENTITY
+                   (FUNCALL (|dispatchFunction| |BOOLEAN;false;$;4|) $))
+             |BOOLEAN;not;2$;5| |BOOLEAN;^;2$;6| |BOOLEAN;~;2$;7|
+             |BOOLEAN;and;3$;8| |BOOLEAN;/\\;3$;9| |BOOLEAN;or;3$;10|
+             |BOOLEAN;\\/;3$;11| |BOOLEAN;xor;3$;12|
+             |BOOLEAN;nor;3$;13| |BOOLEAN;nand;3$;14|
+             |BOOLEAN;=;2$B;15| |BOOLEAN;implies;3$;16|
+             |BOOLEAN;equiv;3$;17| (0 . |not|) |BOOLEAN;<;2$B;18|
+             (|NonNegativeInteger|) |BOOLEAN;size;Nni;19| (|Integer|)
+             (5 . |even?|) (|PositiveInteger|) |BOOLEAN;index;Pi$;20|
+             |BOOLEAN;lookup;$Pi;21| |BOOLEAN;random;$;22| (|String|)
+             (|Symbol|) (10 . |coerce|) (|InputForm|) (15 . |convert|)
+             |BOOLEAN;convert;$If;23| (|OutputForm|) (20 . |message|)
+             |BOOLEAN;coerce;$Of;24| (|SingleInteger|))
+          '#(~= 25 ~ 31 |xor| 36 |true| 42 |test| 46 |size| 51 |random|
+             55 |or| 59 |not| 65 |nor| 70 |nand| 76 |min| 82 |max| 88
+             |lookup| 94 |latex| 99 |index| 104 |implies| 109 |hash|
+             115 |false| 120 |equiv| 124 |convert| 130 |coerce| 135
+             |and| 140 ^ 146 |\\/| 151 >= 157 > 163 = 169 <= 175 < 181
+             |/\\| 187)
+          'NIL
+          (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0))
+                (CONS '#(|OrderedSet&| NIL |Logic&| |SetCategory&| NIL
+                         NIL |BasicType&| NIL)
+                      (CONS '#((|OrderedSet|) (|Finite|) (|Logic|)
+                               (|SetCategory|) (|ConvertibleTo| 36)
+                               (|PropositionalLogic|) (|BasicType|)
+                               (|CoercibleTo| 39))
+                            (|makeByteWordVec2| 42
+                                '(1 6 0 0 23 1 27 6 0 28 1 34 0 33 35 1
+                                  36 0 34 37 1 39 0 33 40 2 0 6 0 0 1 1
+                                  0 0 0 12 2 0 0 0 0 17 0 0 0 8 1 0 6 0
+                                  7 0 0 25 26 0 0 0 32 2 0 0 0 0 15 1 0
+                                  0 0 10 2 0 0 0 0 18 2 0 0 0 0 19 2 0
+                                  0 0 0 1 2 0 0 0 0 1 1 0 29 0 31 1 0
+                                  33 0 1 1 0 0 29 30 2 0 0 0 0 21 1 0
+                                  42 0 1 0 0 0 9 2 0 0 0 0 22 1 0 36 0
+                                  38 1 0 39 0 41 2 0 0 0 0 13 1 0 0 0
+                                  11 2 0 0 0 0 16 2 0 6 0 0 1 2 0 6 0 0
+                                  1 2 0 6 0 0 20 2 0 6 0 0 1 2 0 6 0 0
+                                  24 2 0 0 0 0 14)))))
+          '|lookupComplete|)) 
+
+(MAKEPROP '|Boolean| 'NILADIC T) 
 @
 \section{domain IBITS IndexedBits}
 <<domain IBITS IndexedBits>>=
@@ -579,6 +502,7 @@ Bits(): Exports == Implementation where
 <<domain BOOLEAN Boolean>>
 <<domain IBITS IndexedBits>>
 <<domain BITS Bits>>
+<<category PROPLOG PropositionalLogic>>
 @
 \eject
 \begin{thebibliography}{99}
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 555f8866..d64b8402 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(2224445 . 3409262765)       
+(2225717 . 3409435990)       
 (-18 A S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
 NIL 
 NIL 
 (-19 S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
 (-20 S) 
 ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) 
@@ -38,7 +38,7 @@ NIL
 NIL 
 (-27) 
 ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-28 S R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
@@ -46,23 +46,23 @@ NIL
 NIL 
 (-29 R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-4187 . T) (-4185 . T) (-4184 . T) ((-4192 "*") . T) (-4183 . T) (-4188 . T) (-4182 . T) (-2180 . T)) 
+((-4189 . T) (-4187 . T) (-4186 . T) ((-4194 "*") . T) (-4185 . T) (-4190 . T) (-4184 . T) (-2181 . T)) 
 NIL 
 (-30) 
 ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) 
 NIL 
 NIL 
-(-31 R -1724) 
+(-31 R -1725) 
 ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) 
 NIL 
-((|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517))))) 
+((|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517))))) 
 (-32 S) 
 ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4190))) 
+((|HasAttribute| |#1| (QUOTE -4192))) 
 (-33) 
 ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-34) 
 ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) 
@@ -70,7 +70,7 @@ NIL
 NIL 
 (-35 |Key| |Entry|) 
 ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) 
-((-4190 . T) (-4191 . T) (-2180 . T)) 
+((-4192 . T) (-4193 . T) (-2181 . T)) 
 NIL 
 (-36 S R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) 
@@ -78,20 +78,20 @@ NIL
 NIL 
 (-37 R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#1|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-38 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) 
 NIL 
 NIL 
-(-39 -1724 UP UPUP -3326) 
+(-39 -1725 UP UPUP -1673) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-4183 |has| (-377 |#2|) (-333)) (-4188 |has| (-377 |#2|) (-333)) (-4182 |has| (-377 |#2|) (-333)) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3745 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3745 (|HasCategory| (-377 |#2|) (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3745 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3745 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) 
-(-40 R -1724) 
+((-4185 |has| (-377 |#2|) (-333)) (-4190 |has| (-377 |#2|) (-333)) (-4184 |has| (-377 |#2|) (-333)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3747 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3747 (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3747 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3747 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) 
+(-40 R -1725) 
 ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -400) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -400) (|devaluate| |#1|))))) 
 (-41 OV E P) 
 ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) 
 NIL 
@@ -102,31 +102,31 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-278)))) 
 (-43 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) 
-((-4187 |has| |#1| (-509)) (-4185 . T) (-4184 . T)) 
+((-4189 |has| |#1| (-509)) (-4187 . T) (-4186 . T)) 
 ((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) 
 (-44 |Key| |Entry|) 
 ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1004))) (-12 (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-1004)))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-1004)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1860) (|devaluate| |#2|)))))) (-3745 (-12 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1860) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1860) (|devaluate| |#2|))))))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (-3747 (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|))))))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-45 S R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
 ((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333)))) 
 (-46 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4184 . T) (-4185 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-47) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (LIST (QUOTE -953) (QUOTE (-517))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (LIST (QUOTE -954) (QUOTE (-517))))) 
 (-48) 
 ((|constructor| (NIL "This domain implements anonymous functions"))) 
 NIL 
 NIL 
 (-49 R |lVar|) 
 ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-50 S) 
 ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) 
@@ -140,7 +140,7 @@ NIL
 ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) 
 NIL 
 NIL 
-(-53 |Base| R -1724) 
+(-53 |Base| R -1725) 
 ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) 
 NIL 
 NIL 
@@ -150,7 +150,7 @@ NIL
 NIL 
 (-55 R |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) 
-((-4190 . T) (-4191 . T) (-2180 . T)) 
+((-4192 . T) (-4193 . T) (-2181 . T)) 
 NIL 
 (-56 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) 
@@ -158,65 +158,65 @@ NIL
 NIL 
 (-57 S) 
 ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-58 R) 
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-59 -2987) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-59 -2989) 
 ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim}      SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT)      DOUBLE PRECISION ELAM,P,Q,X,DQDL      INTEGER JINT      P=1.0D0      Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X)      DQDL=1.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-60 -2987) 
+(-60 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim}      SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO)      DOUBLE PRECISION ELAM,FINFO(15)      INTEGER MAXIT,IFLAG      IF(MAXIT.EQ.-1)THEN        PRINT*,\"Output from Monit\"      ENDIF      PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) 
 NIL 
 NIL 
-(-61 -2987) 
+(-61 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim}      SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC)      DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N)      INTEGER M,N,LJC      INTEGER I,J      DO 25003 I=1,LJC        DO 25004 J=1,N          FJACC(I,J)=0.0D025004   CONTINUE25003 CONTINUE      FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/(     &XC(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/(     &XC(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)*     &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)*     &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+     &XC(2))      FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714     &286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666     &6667D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3)     &+XC(2))      FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      FJACC(1,1)=1.0D0      FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(2,1)=1.0D0      FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(3,1)=1.0D0      FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/(     &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)     &**2)      FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666     &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2)      FJACC(4,1)=1.0D0      FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(5,1)=1.0D0      FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399     &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999     &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(6,1)=1.0D0      FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/(     &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)     &**2)      FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333     &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2)      FJACC(7,1)=1.0D0      FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/(     &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)     &**2)      FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428     &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2)      FJACC(8,1)=1.0D0      FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(9,1)=1.0D0      FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(10,1)=1.0D0      FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(11,1)=1.0D0      FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,1)=1.0D0      FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(13,1)=1.0D0      FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(14,1)=1.0D0      FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,1)=1.0D0      FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-62 -2987) 
+(-62 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim}      DOUBLE PRECISION FUNCTION F(X)      DOUBLE PRECISION X      F=DSIN(X)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-63 -2987) 
+(-63 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim}      SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX)      DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH)      INTEGER JTHCOL,N,NROWH,NCOLH      HX(1)=2.0D0*X(1)      HX(2)=2.0D0*X(2)      HX(3)=2.0D0*X(4)+2.0D0*X(3)      HX(4)=2.0D0*X(4)+2.0D0*X(3)      HX(5)=2.0D0*X(5)      HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6))      HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6))      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-64 -2987) 
+(-64 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim}      SUBROUTINE FUNCT1(N,XC,FC)      DOUBLE PRECISION FC,XC(N)      INTEGER N      FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5     &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X     &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+     &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC(     &2)+10.0D0*XC(1)**4+XC(1)**2      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-65 -2987) 
+(-65 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim}      FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1     &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W(     &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1     &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W(     &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8))     &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7)     &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0.     &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3     &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W(     &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-66 -2987) 
+(-66 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK      W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00     &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554     &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365     &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z(     &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0.     &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050     &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z     &(1)      W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010     &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136     &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D     &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8)     &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532     &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056     &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1     &))      W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0     &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033     &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502     &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D     &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(-     &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961     &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917     &D0*Z(1))      W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0.     &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688     &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315     &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z     &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0     &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802     &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0*     &Z(1)      W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+(     &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014     &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966     &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352     &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6))     &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718     &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851     &6D0*Z(1)      W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048     &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323     &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730     &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z(     &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583     &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700     &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1)      W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0     &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843     &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017     &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z(     &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136     &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015     &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1     &)      W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05     &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338     &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869     &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8)     &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056     &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544     &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z(     &1)      W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(-     &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173     &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441     &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8     &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23     &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773     &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z(     &1)      W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0     &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246     &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609     &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8     &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032     &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688     &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z(     &1)      W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0     &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830     &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D     &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8)     &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493     &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054     &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1)      W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(-     &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162     &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889     &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8     &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0.     &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226     &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763     &75D0*Z(1)      W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+(     &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169     &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453     &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z(     &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05     &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277     &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0     &*Z(1)      W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15))     &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236     &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278     &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D     &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0     &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660     &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903     &02D0*Z(1)      W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0     &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325     &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556     &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D     &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0.     &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122     &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z     &(1)      W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0.     &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669     &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114     &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z     &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0     &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739     &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0*     &Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-67 -2987) 
+(-67 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      DOUBLE PRECISION D(K),F(K)      INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE      CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) 
 NIL 
 NIL 
-(-68 -2987) 
+(-68 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK)      INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE      DOUBLE PRECISION A(5,5)      EXTERNAL F06PAF      A(1,1)=1.0D0      A(1,2)=0.0D0      A(1,3)=0.0D0      A(1,4)=-1.0D0      A(1,5)=0.0D0      A(2,1)=0.0D0      A(2,2)=1.0D0      A(2,3)=0.0D0      A(2,4)=0.0D0      A(2,5)=-1.0D0      A(3,1)=0.0D0      A(3,2)=0.0D0      A(3,3)=1.0D0      A(3,4)=-1.0D0      A(3,5)=0.0D0      A(4,1)=-1.0D0      A(4,2)=0.0D0      A(4,3)=-1.0D0      A(4,4)=4.0D0      A(4,5)=-1.0D0      A(5,1)=0.0D0      A(5,2)=-1.0D0      A(5,3)=0.0D0      A(5,4)=-1.0D0      A(5,5)=4.0D0      IF(MODE.EQ.1)THEN        CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1)      ELSEIF(MODE.EQ.2)THEN        CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1)      ENDIF      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-69 -2987) 
+(-69 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE PEDERV(X,Y,PW)      DOUBLE PRECISION X,Y(*)      DOUBLE PRECISION PW(3,3)      PW(1,1)=-0.03999999999999999D0      PW(1,2)=10000.0D0*Y(3)      PW(1,3)=10000.0D0*Y(2)      PW(2,1)=0.03999999999999999D0      PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2))      PW(2,3)=-10000.0D0*Y(2)      PW(3,1)=0.0D0      PW(3,2)=60000000.0D0*Y(2)      PW(3,3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-70 -2987) 
+(-70 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim}      SUBROUTINE REPORT(X,V,JINT)      DOUBLE PRECISION V(3),X      INTEGER JINT      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) 
 NIL 
 NIL 
-(-71 -2987) 
+(-71 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N)      INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOUBLE PRECISION W1(3),W2(3),MS(3,3)      IFLAG=-1      MS(1,1)=2.0D0      MS(1,2)=1.0D0      MS(1,3)=0.0D0      MS(2,1)=1.0D0      MS(2,2)=2.0D0      MS(2,3)=1.0D0      MS(3,1)=0.0D0      MS(3,2)=1.0D0      MS(3,3)=2.0D0      CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG)      IFLAG=-IFLAG      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-72 -2987) 
+(-72 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N)      INTEGER LDFJAC,N,IFLAG      IF(IFLAG.EQ.1)THEN        FVEC(1)=(-1.0D0*X(2))+X(1)        FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2)        FVEC(3)=3.0D0*X(3)      ELSEIF(IFLAG.EQ.2)THEN        FJAC(1,1)=1.0D0        FJAC(1,2)=-1.0D0        FJAC(1,3)=0.0D0        FJAC(2,1)=0.0D0        FJAC(2,2)=2.0D0        FJAC(2,3)=-1.0D0        FJAC(3,1)=0.0D0        FJAC(3,2)=0.0D0        FJAC(3,3)=3.0D0      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
@@ -228,55 +228,55 @@ NIL
 ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim}      SUBROUTINE G(EPS,YA,YB,BC,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BC(N)      INTEGER N      BC(1)=YA(1)      BC(2)=YA(2)      BC(3)=YB(2)-1.0D0      RETURN      END      SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N)      DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N)      INTEGER N      AJ(1,1)=1.0D0      AJ(1,2)=0.0D0      AJ(1,3)=0.0D0      AJ(2,1)=0.0D0      AJ(2,2)=1.0D0      AJ(2,3)=0.0D0      AJ(3,1)=0.0D0      AJ(3,2)=0.0D0      AJ(3,3)=0.0D0      BJ(1,1)=0.0D0      BJ(1,2)=0.0D0      BJ(1,3)=0.0D0      BJ(2,1)=0.0D0      BJ(2,2)=0.0D0      BJ(2,3)=0.0D0      BJ(3,1)=0.0D0      BJ(3,2)=1.0D0      BJ(3,3)=0.0D0      RETURN      END      SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N)      INTEGER N      BCEP(1)=0.0D0      BCEP(2)=0.0D0      BCEP(3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-75 -2987) 
+(-75 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER)      DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*)      INTEGER N,IUSER(*),MODE,NSTATE      OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7)     &+(-1.0D0*X(2)*X(6))      OBJGRD(1)=X(7)      OBJGRD(2)=-1.0D0*X(6)      OBJGRD(3)=X(8)+(-1.0D0*X(7))      OBJGRD(4)=X(9)      OBJGRD(5)=-1.0D0*X(8)      OBJGRD(6)=-1.0D0*X(2)      OBJGRD(7)=(-1.0D0*X(3))+X(1)      OBJGRD(8)=(-1.0D0*X(5))+X(3)      OBJGRD(9)=X(4)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-76 -2987) 
+(-76 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim}      DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X)      DOUBLE PRECISION X(NDIM)      INTEGER NDIM      FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0*     &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-77 -2987) 
+(-77 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE LSFUN1(M,N,XC,FVECC)      DOUBLE PRECISION FVECC(M),XC(N)      INTEGER I,M,N      FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X     &C(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666     &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X     &C(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC     &(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X     &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142     &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999     &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2))      FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999     &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666     &67D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999     &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2))      FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-78 -2987) 
+(-78 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER     &,USER)      DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*)      INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE      IF(NEEDC(1).GT.0)THEN        C(1)=X(6)**2+X(1)**2        CJAC(1,1)=2.0D0*X(1)        CJAC(1,2)=0.0D0        CJAC(1,3)=0.0D0        CJAC(1,4)=0.0D0        CJAC(1,5)=0.0D0        CJAC(1,6)=2.0D0*X(6)      ENDIF      IF(NEEDC(2).GT.0)THEN        C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2        CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1)        CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1))        CJAC(2,3)=0.0D0        CJAC(2,4)=0.0D0        CJAC(2,5)=0.0D0        CJAC(2,6)=0.0D0      ENDIF      IF(NEEDC(3).GT.0)THEN        C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2        CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1)        CJAC(3,2)=2.0D0*X(2)        CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1))        CJAC(3,4)=0.0D0        CJAC(3,5)=0.0D0        CJAC(3,6)=0.0D0      ENDIF      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-79 -2987) 
+(-79 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N)      INTEGER N,IFLAG      FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0      FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1.     &0D0      FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1.     &0D0      FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1.     &0D0      FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1.     &0D0      FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1.     &0D0      FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1.     &0D0      FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1.     &0D0      FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-80 -2987) 
+(-80 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI)      DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI      ALPHA=DSIN(X)      BETA=Y      GAMMA=X*Y      DELTA=DCOS(X)*DSIN(Y)      EPSOLN=Y+X      PHI=X      PSI=Y      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-81 -2987) 
+(-81 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE BNDY(X,Y,A,B,C,IBND)      DOUBLE PRECISION A,B,C,X,Y      INTEGER IBND      IF(IBND.EQ.0)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(X)      ELSEIF(IBND.EQ.1)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.2)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.3)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(Y)      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-82 -2987) 
+(-82 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNF(X,F)      DOUBLE PRECISION X      DOUBLE PRECISION F(2,2)      F(1,1)=0.0D0      F(1,2)=1.0D0      F(2,1)=0.0D0      F(2,2)=-10.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-83 -2987) 
+(-83 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNG(X,G)      DOUBLE PRECISION G(*),X      G(1)=0.0D0      G(2)=0.0D0      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-84 -2987) 
+(-84 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim}      SUBROUTINE FCN(X,Z,F)      DOUBLE PRECISION F(*),X,Z(*)      F(1)=DTAN(Z(3))      F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2)     &**2))/(Z(2)*DCOS(Z(3)))      F(3)=-0.03199999999999999D0/(X*Z(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-85 -2987) 
+(-85 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR)      DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3)      YL(1)=XL      YL(2)=2.0D0      YR(1)=1.0D0      YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM))      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-86 -2987) 
+(-86 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim}      SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD)      DOUBLE PRECISION Y(N),RESULT(M,N),XSOL      INTEGER M,N,COUNT      LOGICAL FORWRD      DOUBLE PRECISION X02ALF,POINTS(8)      EXTERNAL X02ALF      INTEGER I      POINTS(1)=1.0D0      POINTS(2)=2.0D0      POINTS(3)=3.0D0      POINTS(4)=4.0D0      POINTS(5)=5.0D0      POINTS(6)=6.0D0      POINTS(7)=7.0D0      POINTS(8)=8.0D0      COUNT=COUNT+1      DO 25001 I=1,N        RESULT(COUNT,I)=Y(I)25001 CONTINUE      IF(COUNT.EQ.M)THEN        IF(FORWRD)THEN          XSOL=X02ALF()        ELSE          XSOL=-X02ALF()        ENDIF      ELSE        XSOL=POINTS(COUNT)      ENDIF      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-87 -2987) 
+(-87 -2989) 
 ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim}      DOUBLE PRECISION FUNCTION G(X,Y)      DOUBLE PRECISION X,Y(*)      G=X+Y(1)      RETURN      END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
@@ -286,8 +286,8 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-333)))) 
 (-89 S) 
 ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-90 S) 
 ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) 
 NIL 
@@ -298,15 +298,15 @@ NIL
 NIL 
 (-92) 
 ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) 
-((-4190 . T)) 
+((-4192 . T)) 
 NIL 
 (-93) 
 ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,{}b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) 
-((-4190 . T) ((-4192 "*") . T) (-4191 . T) (-4187 . T) (-4185 . T) (-4184 . T) (-4183 . T) (-4188 . T) (-4182 . T) (-4181 . T) (-4180 . T) (-4179 . T) (-4178 . T) (-4186 . T) (-4189 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4177 . T)) 
+((-4192 . T) ((-4194 "*") . T) (-4193 . T) (-4189 . T) (-4187 . T) (-4186 . T) (-4185 . T) (-4190 . T) (-4184 . T) (-4183 . T) (-4182 . T) (-4181 . T) (-4180 . T) (-4188 . T) (-4191 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4179 . T)) 
 NIL 
 (-94 R) 
 ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,{}n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f,{} g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-95 R UP) 
 ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a,{} [b1,{}...,{}bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,{}...,{}bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a,{} b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{\\spad{pi}} is balanced with respect to \\spad{b}."))) 
@@ -322,15 +322,15 @@ NIL
 NIL 
 (-98 S) 
 ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-99 R UP M |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE (-4192 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-4194 "*")))) 
 (-100) 
 ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) 
-((-4190 . T)) 
+((-4192 . T)) 
 NIL 
 (-101 A S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) 
@@ -338,23 +338,23 @@ NIL
 NIL 
 (-102 S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) 
-((-4191 . T) (-2180 . T)) 
+((-4193 . T) (-2181 . T)) 
 NIL 
 (-103) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -953) (QUOTE (-1075)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-938))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1051))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1075)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3745 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-939))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1052))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3747 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) 
 (-104) 
 ((|constructor| (NIL "This domain provides an implementation of binary files. Data is accessed one byte at a time as a small integer.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "\\spad{position!(f,{} i)} sets the current byte-position to \\spad{i}.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file \\spad{f}.")) (|readIfCan!| (((|Union| (|SingleInteger|) "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) 
 NIL 
 NIL 
 (-105) 
 ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| (-107) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-107) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-107) (QUOTE (-1004))) (-12 (|HasCategory| (-107) (QUOTE (-1004))) (|HasCategory| (-107) (LIST (QUOTE -280) (QUOTE (-107))))) (|HasCategory| (-107) (LIST (QUOTE -557) (QUOTE (-787))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| (-107) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-107) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-107) (QUOTE (-1005))) (-12 (|HasCategory| (-107) (QUOTE (-1005))) (|HasCategory| (-107) (LIST (QUOTE -280) (QUOTE (-107))))) (|HasCategory| (-107) (LIST (QUOTE -557) (QUOTE (-787))))) 
 (-106 R S) 
 ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) 
-((-4185 . T) (-4184 . T)) 
+((-4187 . T) (-4186 . T)) 
 NIL 
 (-107) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (((|Boolean|) $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|implies| (($ $ $) "\\spad{implies(a,{}b)} returns the logical implication of Boolean \\spad{a} and \\spad{b}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical inclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of Boolean \\spad{a} and \\spad{b}.")) (|not| (($ $) "\\spad{not n} returns the negation of \\spad{n}.")) (^ (($ $) "\\spad{^ n} returns the negation of \\spad{n}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
@@ -368,25 +368,25 @@ NIL
 ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) 
 NIL 
 NIL 
-(-110 -1724 UP) 
+(-110 -1725 UP) 
 ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) 
 NIL 
 NIL 
 (-111 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-112 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-111 |#1|) (QUOTE (-832))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -953) (QUOTE (-1075)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-134))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-111 |#1|) (QUOTE (-938))) (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-1051))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-207))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -478) (QUOTE (-1075)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -111) (|devaluate| |#1|)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (QUOTE (-278))) (|HasCategory| (-111 |#1|) (QUOTE (-502))) (|HasCategory| (-111 |#1|) (QUOTE (-779))) (-3745 (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-832)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-111 |#1|) (QUOTE (-832))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-134))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-111 |#1|) (QUOTE (-939))) (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-1052))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-207))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -478) (QUOTE (-1076)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -111) (|devaluate| |#1|)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (QUOTE (-278))) (|HasCategory| (-111 |#1|) (QUOTE (-502))) (|HasCategory| (-111 |#1|) (QUOTE (-779))) (-3747 (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-832)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))))) 
 (-113 A S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4191))) 
+((|HasAttribute| |#1| (QUOTE -4193))) 
 (-114 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-115 UP) 
 ((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) 
@@ -394,15 +394,15 @@ NIL
 NIL 
 (-116 S) 
 ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-117 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-118) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
 (-119 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
@@ -410,16 +410,16 @@ NIL
 NIL 
 (-120 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
-((-4190 . T) (-4191 . T) (-2180 . T)) 
+((-4192 . T) (-4193 . T) (-2181 . T)) 
 NIL 
 (-121 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-122 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-123) 
 ((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) 
 NIL 
@@ -430,20 +430,20 @@ NIL
 NIL 
 (-125) 
 ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) 
-(((-4192 "*") . T)) 
+(((-4194 "*") . T)) 
 NIL 
-(-126 |minix| -3131 S T$) 
+(-126 |minix| -3136 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-127 |minix| -3131 R) 
+(-127 |minix| -3136 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\^= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) 
 NIL 
 NIL 
 (-128) 
 ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) 
-((-4190 . T) (-4180 . T) (-4191 . T)) 
-((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1004))) (-12 (|HasCategory| (-131) (QUOTE (-1004))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3745 (-12 (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1004))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787))))) 
+((-4192 . T) (-4182 . T) (-4193 . T)) 
+((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1005))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3747 (-12 (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787))))) 
 (-129 R Q A) 
 ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) 
 NIL 
@@ -458,7 +458,7 @@ NIL
 NIL 
 (-132) 
 ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-133 R) 
 ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,{}r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) 
@@ -466,9 +466,9 @@ NIL
 NIL 
 (-134) 
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
-(-135 -1724 UP UPUP) 
+(-135 -1725 UP UPUP) 
 ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,{}y),{} p(x,{}y))} returns \\spad{[g(z,{}t),{} q(z,{}t),{} c1(z),{} c2(z),{} n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,{}y) = g(z,{}t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z,{} t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,{}y),{} f(x),{} g(x))} returns \\spad{p(f(x),{} y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p,{} q)} returns an integer a such that a is neither a pole of \\spad{p(x,{}y)} nor a branch point of \\spad{q(x,{}y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g,{} n)} returns \\spad{[m,{} c,{} P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x,{} y))} returns \\spad{[c(x),{} n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,{}y))} returns \\spad{[c(x),{} q(x,{}z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x,{} z) = 0}."))) 
 NIL 
 NIL 
@@ -479,14 +479,14 @@ NIL
 (-137 A S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{^=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasAttribute| |#1| (QUOTE -4190))) 
+((|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasAttribute| |#1| (QUOTE -4192))) 
 (-138 S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{^=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-139 |n| K Q) 
 ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,{}[i1,{}i2,{}...,{}iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,{}[i1,{}i2,{}...,{}iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) 
-((-4185 . T) (-4184 . T) (-4187 . T)) 
+((-4187 . T) (-4186 . T) (-4189 . T)) 
 NIL 
 (-140) 
 ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,{}xMin,{}xMax,{}yMin,{}yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,{}frac,{}sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,{}frac,{}sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) 
@@ -500,7 +500,7 @@ NIL
 ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) 
 NIL 
 NIL 
-(-143 R -1724) 
+(-143 R -1725) 
 ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) 
 NIL 
 NIL 
@@ -527,10 +527,10 @@ NIL
 (-149 S R) 
 ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-919))) (|HasCategory| |#2| (QUOTE (-1096))) (|HasCategory| |#2| (QUOTE (-971))) (|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasAttribute| |#2| (QUOTE -4186)) (|HasAttribute| |#2| (QUOTE -4189)) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-779)))) 
+((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-920))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasAttribute| |#2| (QUOTE -4188)) (|HasAttribute| |#2| (QUOTE -4191)) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-779)))) 
 (-150 R) 
 ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) 
-((-4183 -3745 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-832)))) (-4188 |has| |#1| (-333)) (-4182 |has| |#1| (-333)) (-4186 |has| |#1| (-6 -4186)) (-4189 |has| |#1| (-6 -4189)) (-3887 . T) (-2180 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 -3747 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-832)))) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4188 |has| |#1| (-6 -4188)) (-4191 |has| |#1| (-6 -4191)) (-3883 . T) (-2181 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-151 RR PR) 
 ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) 
@@ -542,8 +542,8 @@ NIL
 NIL 
 (-153 R) 
 ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) 
-((-4183 -3745 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-832)))) (-4188 |has| |#1| (-333)) (-4182 |has| |#1| (-333)) (-4186 |has| |#1| (-6 -4186)) (-4189 |has| |#1| (-6 -4189)) (-3887 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-333))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-1096))) (-12 (|HasCategory| |#1| (QUOTE (-919))) (|HasCategory| |#1| (QUOTE (-1096)))) (|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1075)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-971))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1096)))) (|HasCategory| |#1| (QUOTE (-502))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-278))) (-3745 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509)))) (-3745 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-832))) 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(|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-779)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-1096)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-832))))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-832))))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-333)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasAttribute| |#1| (QUOTE -4186)) (|HasAttribute| |#1| (QUOTE -4189)) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075))))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-319))))) 
+((-4185 -3747 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-832)))) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4188 |has| |#1| (-6 -4188)) (-4191 |has| |#1| (-6 -4191)) (-3883 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (QUOTE (-920))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-972))) (-12 (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-502))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-278))) (-3747 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-207))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-207))) (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-779)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-1097)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-832))))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-832))))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-333)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasAttribute| |#1| (QUOTE -4188)) (|HasAttribute| |#1| (QUOTE -4191)) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076))))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-319))))) 
 (-154 R S CS) 
 ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) 
 NIL 
@@ -554,11 +554,11 @@ NIL
 NIL 
 (-156) 
 ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) 
-(((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+(((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-157 R) 
 ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialQuotients(x) = [b0,{}b1,{}b2,{}b3,{}...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialDenominators(x) = [b1,{}b2,{}b3,{}...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialNumerators(x) = [a1,{}a2,{}a3,{}...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,{}b)} constructs a continued fraction in the following way: if \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,{}a,{}b)} constructs a continued fraction in the following way: if \\spad{a = [a1,{}a2,{}...]} and \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) 
-(((-4192 "*") . T) (-4183 . T) (-4188 . T) (-4182 . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+(((-4194 "*") . T) (-4185 . T) (-4190 . T) (-4184 . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-158 R) 
 ((|constructor| (NIL "CoordinateSystems provides coordinate transformation functions for plotting. Functions in this package return conversion functions which take points expressed in other coordinate systems and return points with the corresponding Cartesian coordinates.")) (|conical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1| |#1|) "\\spad{conical(a,{}b)} transforms from conical coordinates to Cartesian coordinates: \\spad{conical(a,{}b)} is a function which will map the point \\spad{(lambda,{}mu,{}nu)} to \\spad{x = lambda*mu*nu/(a*b)},{} \\spad{y = lambda/a*sqrt((mu**2-a**2)*(nu**2-a**2)/(a**2-b**2))},{} \\spad{z = lambda/b*sqrt((mu**2-b**2)*(nu**2-b**2)/(b**2-a**2))}.")) (|toroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{toroidal(a)} transforms from toroidal coordinates to Cartesian coordinates: \\spad{toroidal(a)} is a function which will map the point \\spad{(u,{}v,{}phi)} to \\spad{x = a*sinh(v)*cos(phi)/(cosh(v)-cos(u))},{} \\spad{y = a*sinh(v)*sin(phi)/(cosh(v)-cos(u))},{} \\spad{z = a*sin(u)/(cosh(v)-cos(u))}.")) (|bipolarCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolarCylindrical(a)} transforms from bipolar cylindrical coordinates to Cartesian coordinates: \\spad{bipolarCylindrical(a)} is a function which will map the point \\spad{(u,{}v,{}z)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))},{} \\spad{z}.")) (|bipolar| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolar(a)} transforms from bipolar coordinates to Cartesian coordinates: \\spad{bipolar(a)} is a function which will map the point \\spad{(u,{}v)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))}.")) (|oblateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{oblateSpheroidal(a)} transforms from oblate spheroidal coordinates to Cartesian coordinates: \\spad{oblateSpheroidal(a)} is a function which will map the point \\spad{(\\spad{xi},{}eta,{}phi)} to \\spad{x = a*sinh(\\spad{xi})*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(\\spad{xi})*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(\\spad{xi})*cos(eta)}.")) (|prolateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{prolateSpheroidal(a)} transforms from prolate spheroidal coordinates to Cartesian coordinates: \\spad{prolateSpheroidal(a)} is a function which will map the point \\spad{(\\spad{xi},{}eta,{}phi)} to \\spad{x = a*sinh(\\spad{xi})*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(\\spad{xi})*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(\\spad{xi})*cos(eta)}.")) (|ellipticCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{ellipticCylindrical(a)} transforms from elliptic cylindrical coordinates to Cartesian coordinates: \\spad{ellipticCylindrical(a)} is a function which will map the point \\spad{(u,{}v,{}z)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)},{} \\spad{z}.")) (|elliptic| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{elliptic(a)} transforms from elliptic coordinates to Cartesian coordinates: \\spad{elliptic(a)} is a function which will map the point \\spad{(u,{}v)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)}.")) (|paraboloidal| (((|Point| |#1|) (|Point| |#1|)) "\\spad{paraboloidal(pt)} transforms \\spad{pt} from paraboloidal coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v,{}phi)} to \\spad{x = u*v*cos(phi)},{} \\spad{y = u*v*sin(phi)},{} \\spad{z = 1/2 * (u**2 - v**2)}.")) (|parabolicCylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolicCylindrical(pt)} transforms \\spad{pt} from parabolic cylindrical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v,{}z)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v},{} \\spad{z}.")) (|parabolic| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolic(pt)} transforms \\spad{pt} from parabolic coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v}.")) (|spherical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{spherical(pt)} transforms \\spad{pt} from spherical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta,{}phi)} to \\spad{x = r*sin(phi)*cos(theta)},{} \\spad{y = r*sin(phi)*sin(theta)},{} \\spad{z = r*cos(phi)}.")) (|cylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cylindrical(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta,{}z)} to \\spad{x = r * cos(theta)},{} \\spad{y = r * sin(theta)},{} \\spad{z}.")) (|polar| (((|Point| |#1|) (|Point| |#1|)) "\\spad{polar(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta)} to \\spad{x = r * cos(theta)} ,{} \\spad{y = r * sin(theta)}.")) (|cartesian| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cartesian(pt)} returns the Cartesian coordinates of point \\spad{pt}."))) 
@@ -584,7 +584,7 @@ NIL
 ((|constructor| (NIL "This package provides tools for working with cyclic streams.")) (|computeCycleEntry| ((|#2| |#2| |#2|) "\\spad{computeCycleEntry(x,{}cycElt)},{} where \\spad{cycElt} is a pointer to a node in the cyclic part of the cyclic stream \\spad{x},{} returns a pointer to the first node in the cycle")) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) "\\spad{computeCycleLength(s)} returns the length of the cycle of a cyclic stream \\spad{t},{} where \\spad{s} is a pointer to a node in the cyclic part of \\spad{t}.")) (|cycleElt| (((|Union| |#2| "failed") |#2|) "\\spad{cycleElt(s)} returns a pointer to a node in the cycle if the stream \\spad{s} is cyclic and returns \"failed\" if \\spad{s} is not cyclic"))) 
 NIL 
 NIL 
-(-164 R -1724) 
+(-164 R -1725) 
 ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
@@ -688,19 +688,19 @@ NIL
 ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) 
 NIL 
 NIL 
-(-190 -1724 UP UPUP R) 
+(-190 -1725 UP UPUP R) 
 ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f,{} ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) 
 NIL 
 NIL 
-(-191 -1724 FP) 
+(-191 -1725 FP) 
 ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) 
 NIL 
 NIL 
 (-192) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -953) (QUOTE (-1075)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-938))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1051))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1075)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3745 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) 
-(-193 R -1724) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-939))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1052))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3747 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) 
+(-193 R -1725) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -714,19 +714,19 @@ NIL
 NIL 
 (-196 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-197 |CoefRing| |listIndVar|) 
 ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
-(-198 R -1724) 
+(-198 R -1725) 
 ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} x,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) 
 NIL 
 NIL 
 (-199) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-2202 . T) (-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-2204 . T) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-200) 
 ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) 
@@ -734,23 +734,23 @@ NIL
 NIL 
 (-201 R) 
 ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4192 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4194 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-202 A S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
 NIL 
 NIL 
 (-203 S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
-((-4191 . T) (-2180 . T)) 
+((-4193 . T) (-2181 . T)) 
 NIL 
 (-204 S R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#2| (QUOTE (-207)))) 
+((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207)))) 
 (-205 R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-206 S) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) 
@@ -758,36 +758,36 @@ NIL
 NIL 
 (-207) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-208 A S) 
 ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4190))) 
+((|HasAttribute| |#1| (QUOTE -4192))) 
 (-209 S) 
 ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) 
-((-4191 . T) (-2180 . T)) 
+((-4193 . T) (-2181 . T)) 
 NIL 
 (-210) 
 ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) 
 NIL 
 NIL 
-(-211 S -3131 R) 
+(-211 S -3136 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (QUOTE (-777))) (|HasAttribute| |#3| (QUOTE -4187)) (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (QUOTE (-659))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1004)))) 
-(-212 -3131 R) 
+((|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (QUOTE (-777))) (|HasAttribute| |#3| (QUOTE -4189)) (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (QUOTE (-659))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-963))) (|HasCategory| |#3| (QUOTE (-1005)))) 
+(-212 -3136 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
-((-4184 |has| |#2| (-962)) (-4185 |has| |#2| (-962)) (-4187 |has| |#2| (-6 -4187)) ((-4192 "*") |has| |#2| (-156)) (-4190 . T) (-2180 . T)) 
+((-4186 |has| |#2| (-963)) (-4187 |has| |#2| (-963)) (-4189 |has| |#2| (-6 -4189)) ((-4194 "*") |has| |#2| (-156)) (-4192 . T) (-2181 . T)) 
 NIL 
-(-213 -3131 A B) 
+(-213 -3136 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
-(-214 -3131 R) 
+(-214 -3136 R) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) 
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(|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-1005)))) (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-963)))) (-12 (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076))))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-215) 
 ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) 
 NIL 
@@ -798,47 +798,47 @@ NIL
 NIL 
 (-217) 
 ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) 
-((-4183 . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-218 S) 
 ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,{}v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,{}v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-219 S) 
 ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}"))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-220 M) 
 ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) 
 NIL 
 NIL 
 (-221 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-4192 "*") |has| |#2| (-156)) (-4183 |has| |#2| (-509)) (-4188 |has| |#2| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3745 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3745 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4188)) (|HasCategory| |#2| (QUOTE (-421))) (-3745 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) 
+(((-4194 "*") |has| |#2| (-156)) (-4185 |has| |#2| (-509)) (-4190 |has| |#2| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3747 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4190)) (|HasCategory| |#2| (QUOTE (-421))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) 
 (-222) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 12,{} 2007. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type")) (|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reify| (((|Syntax|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}."))) 
 NIL 
 NIL 
 (-223 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
-((-4187 -3745 (-3992 (|has| |#4| (-962)) (|has| |#4| (-207))) (-3992 (|has| |#4| (-962)) (|has| |#4| (-823 (-1075)))) (|has| |#4| (-6 -4187)) (-3992 (|has| |#4| (-962)) (|has| |#4| (-579 (-517))))) (-4184 |has| |#4| (-962)) (-4185 |has| |#4| (-962)) ((-4192 "*") |has| |#4| (-156)) (-4190 . T)) 
-((|HasCategory| |#4| (QUOTE (-333))) (|HasCategory| |#4| (QUOTE (-962))) (|HasCategory| |#4| (QUOTE (-725))) (|HasCategory| |#4| (QUOTE (-777))) (-3745 (|HasCategory| |#4| (QUOTE (-725))) (|HasCategory| |#4| (QUOTE (-777)))) (|HasCategory| |#4| (QUOTE (-156))) (-3745 (|HasCategory| |#4| (QUOTE (-156))) (|HasCategory| |#4| (QUOTE (-333))) (|HasCategory| |#4| (QUOTE (-962)))) (-3745 (|HasCategory| |#4| (QUOTE (-156))) (|HasCategory| |#4| (QUOTE (-333)))) (-3745 (|HasCategory| |#4| (QUOTE (-156))) (|HasCategory| |#4| (QUOTE (-962)))) (|HasCategory| |#4| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#4| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#4| (QUOTE (-207))) (-3745 (|HasCategory| |#4| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#4| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#4| (QUOTE (-156))) (|HasCategory| |#4| (QUOTE (-207))) (|HasCategory| |#4| (QUOTE (-962)))) (|HasCategory| |#4| (QUOTE (-1004))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#4| (QUOTE (-659))) (-12 (|HasCategory| |#4| (QUOTE (-962))) (|HasCategory| |#4| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (QUOTE (-962))) (|HasCategory| |#4| (LIST (QUOTE -823) (QUOTE (-1075))))) (-12 (|HasCategory| |#4| (QUOTE (-207))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-1004))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517))))) (-3745 (-12 (|HasCategory| |#4| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (QUOTE (-156))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (QUOTE (-207))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (QUOTE (-333))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (QUOTE (-725))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (QUOTE (-777))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (QUOTE (-962))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (QUOTE (-1004))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517)))))) (-3745 (|HasCategory| |#4| (QUOTE (-962))) (-12 (|HasCategory| |#4| (QUOTE (-1004))) (|HasCategory| |#4| (LIST (QUOTE -953) (QUOTE (-517)))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (QUOTE (-1004)))) (-3745 (-12 (|HasCategory| |#4| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -823) (QUOTE (-1075))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (QUOTE (-156)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (QUOTE (-207)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (QUOTE (-333)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (QUOTE (-338)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (QUOTE (-725)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (QUOTE (-777)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (QUOTE (-1004))))) (-3745 (|HasAttribute| |#4| (QUOTE -4187)) (-12 (|HasCategory| |#4| (QUOTE (-207))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-962))) (|HasCategory| |#4| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#4| (QUOTE (-962))) (|HasCategory| |#4| (LIST (QUOTE -823) (QUOTE (-1075)))))) (|HasCategory| |#4| (QUOTE (-123))) (|HasCategory| |#4| (QUOTE (-25))) (-12 (|HasCategory| |#4| (QUOTE (-1004))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (-3745 (-12 (|HasCategory| |#4| (QUOTE (-156))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-207))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-333))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-725))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (-12 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(|HasCategory| |#3| (QUOTE (-777))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-963))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -823) (QUOTE (-1076)))))) (|HasCategory| |#3| (LIST (QUOTE -557) (QUOTE (-787))))) 
 (-225 A R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-207)))) 
 (-226 R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
 NIL 
 (-227 S) 
 ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) 
-((-4190 . T) (-4191 . T) (-2180 . T)) 
+((-4192 . T) (-4193 . T) (-2181 . T)) 
 NIL 
 (-228) 
 ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) 
@@ -878,8 +878,8 @@ NIL
 NIL 
 (-237 R S V) 
 ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
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+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#3| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-238 A S) 
 ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
 NIL 
@@ -924,11 +924,11 @@ NIL
 ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) 
 NIL 
 NIL 
-(-249 R -1724) 
+(-249 R -1725) 
 ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) 
 NIL 
 NIL 
-(-250 R -1724) 
+(-250 R -1725) 
 ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) 
 NIL 
 NIL 
@@ -943,10 +943,10 @@ NIL
 (-253 A S) 
 ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1004)))) 
+((|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005)))) 
 (-254 S) 
 ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) 
-((-4191 . T) (-2180 . T)) 
+((-4193 . T) (-2181 . T)) 
 NIL 
 (-255 S) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
@@ -967,18 +967,18 @@ NIL
 (-259 S |Dom| |Im|) 
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4191))) 
+((|HasAttribute| |#1| (QUOTE -4193))) 
 (-260 |Dom| |Im|) 
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
 NIL 
-(-261 S R |Mod| -3334 -3798 |exactQuo|) 
+(-261 S R |Mod| -1769 -2662 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-262) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-4183 . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-263 R) 
 ((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,{}m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,{}m,{}k,{}g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,{}m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable."))) 
@@ -990,21 +990,21 @@ NIL
 NIL 
 (-265 S) 
 ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) 
-((-4187 -3745 (|has| |#1| (-962)) (|has| |#1| (-442))) (-4184 |has| |#1| (-962)) (-4185 |has| |#1| (-962))) 
-((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1075)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-273))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442)))) (-3745 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-962)))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-659))) (-3745 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3745 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-21))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-962)))) (-3745 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-25))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-962)))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-1004))))) 
+((-4189 -3747 (|has| |#1| (-963)) (|has| |#1| (-442))) (-4186 |has| |#1| (-963)) (-4187 |has| |#1| (-963))) 
+((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-273))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442)))) (-3747 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-963)))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-659))) (-3747 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-1017))) (-3747 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-21))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-963)))) (-3747 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-25))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-963)))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-1005))))) 
 (-266 |Key| |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (-12 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1860) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1004))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-1004)))) (-12 (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-267) 
 ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) 
 NIL 
 NIL 
-(-268 -1724 S) 
+(-268 -1725 S) 
 ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) 
 NIL 
 NIL 
-(-269 E -1724) 
+(-269 E -1725) 
 ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) 
 NIL 
 NIL 
@@ -1019,7 +1019,7 @@ NIL
 (-272 S) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-962)))) 
+((|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-963)))) 
 (-273) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) 
 NIL 
@@ -1042,7 +1042,7 @@ NIL
 NIL 
 (-278) 
 ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-279 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
@@ -1052,7 +1052,7 @@ NIL
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-281 -1724) 
+(-281 -1725) 
 ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,{}s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) 
 NIL 
 NIL 
@@ -1062,8 +1062,8 @@ NIL
 NIL 
 (-283 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -953) (QUOTE (-1075)))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-938))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-1051))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-207))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -478) (QUOTE (-1075)) (LIST (QUOTE -1142) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -280) (LIST (QUOTE -1142) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (LIST (QUOTE -258) (LIST (QUOTE -1142) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1142) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-278))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-502))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-779))) (-3745 (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-779)))) (-12 (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| $ (QUOTE (-132)))) (-3745 (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (-12 (|HasCategory| (-1142 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| $ (QUOTE (-132)))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-1052))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-207))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -478) (QUOTE (-1076)) (LIST (QUOTE -1143) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -280) (LIST (QUOTE -1143) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -258) (LIST (QUOTE -1143) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1143) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-278))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-502))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-779))) (-3747 (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-779)))) (-12 (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| $ (QUOTE (-132)))) (-3747 (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (-12 (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| $ (QUOTE (-132)))))) 
 (-284 R S) 
 ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) 
 NIL 
@@ -1074,9 +1074,9 @@ NIL
 NIL 
 (-286 R) 
 ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 
-((-4187 -3745 (-3992 (|has| |#1| (-962)) (|has| |#1| (-579 (-517)))) (-12 (|has| |#1| (-509)) (-3745 (-3992 (|has| |#1| (-962)) (|has| |#1| (-579 (-517)))) (|has| |#1| (-962)) (|has| |#1| (-442)))) (|has| |#1| (-962)) (|has| |#1| (-442))) (-4185 |has| |#1| (-156)) (-4184 |has| |#1| (-156)) ((-4192 "*") |has| |#1| (-509)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-509)) (-4182 |has| |#1| (-509))) 
-((|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-962))) (-3745 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517))))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-962)))) (-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509)))) (-3745 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (-3745 (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517))))) (-3745 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-21))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-962)))) (-3745 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-25))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-962)))) (-3745 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-1016))) (-3745 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-1016)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-1016)))) (-3745 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509)))) (-3745 (-12 (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))))) (|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (LIST (QUOTE -953) (QUOTE (-517))))) 
-(-287 R -1724) 
+((-4189 -3747 (-3993 (|has| |#1| (-963)) (|has| |#1| (-579 (-517)))) (-12 (|has| |#1| (-509)) (-3747 (-3993 (|has| |#1| (-963)) (|has| |#1| (-579 (-517)))) (|has| |#1| (-963)) (|has| |#1| (-442)))) (|has| |#1| (-963)) (|has| |#1| (-442))) (-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) ((-4194 "*") |has| |#1| (-509)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-509)) (-4184 |has| |#1| (-509))) 
+((|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-963))) (-3747 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517))))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-963)))) (-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (-3747 (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517))))) (-3747 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-21))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-963)))) (-3747 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-25))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-963)))) (-3747 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-1017))) (-3747 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-1017)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-1017)))) (-3747 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))))) (|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (LIST (QUOTE -954) (QUOTE (-517))))) 
+(-287 R -1725) 
 ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) 
 NIL 
 NIL 
@@ -1086,8 +1086,8 @@ NIL
 NIL 
 (-289 FE |var| |cen|) 
 ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4182 |has| |#1| (-333)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-333))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2269) (LIST (|devaluate| |#1|) (QUOTE (-1075)))))) (-3745 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1096))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -1518) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1075))))) (|HasSignature| |#1| (LIST (QUOTE -2096) (LIST (LIST (QUOTE -583) (QUOTE (-1075))) (|devaluate| |#1|))))))) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) 
 (-290 M) 
 ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) 
 NIL 
@@ -1098,7 +1098,7 @@ NIL
 NIL 
 (-292 S) 
 ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) 
-((-4185 . T) (-4184 . T)) 
+((-4187 . T) (-4186 . T)) 
 ((|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-724)))) 
 (-293 S E) 
 ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
@@ -1114,19 +1114,19 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156)))) 
 (-296 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4184 . T) (-4185 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-297 S) 
 ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-298 S -1724) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-298 S -1725) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-338)))) 
-(-299 -1724) 
+(-299 -1725) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-300) 
 ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,{}contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,{}e,{}f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,{}e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,{}c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,{}c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,{}n,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(f)} returns an object of type OutputForm."))) 
@@ -1144,54 +1144,54 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-304 S -1724 UP UPUP R) 
+(-304 S -1725 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
-(-305 -1724 UP UPUP R) 
+(-305 -1725 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
-(-306 -1724 UP UPUP R) 
+(-306 -1725 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) 
 NIL 
 NIL 
 (-307 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1075)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|)))) 
 (-308 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
 (-309 |basicSymbols| |subscriptedSymbols| R) 
 ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#3| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -953) (QUOTE (-349)))) (|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (LIST (QUOTE -953) (QUOTE (-517))))) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-349)))) (|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (LIST (QUOTE -954) (QUOTE (-517))))) 
 (-310 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
 ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) 
 NIL 
 NIL 
-(-311 S -1724 UP UPUP) 
+(-311 S -1725 UP UPUP) 
 ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-333)))) 
-(-312 -1724 UP UPUP) 
+(-312 -1725 UP UPUP) 
 ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) 
-((-4183 |has| (-377 |#2|) (-333)) (-4188 |has| (-377 |#2|) (-333)) (-4182 |has| (-377 |#2|) (-333)) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 |has| (-377 |#2|) (-333)) (-4190 |has| (-377 |#2|) (-333)) (-4184 |has| (-377 |#2|) (-333)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-313 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-833 |#1|) (QUOTE (-134))) (|HasCategory| (-833 |#1|) (QUOTE (-338))) (|HasCategory| (-833 |#1|) (QUOTE (-132))) (-3745 (|HasCategory| (-833 |#1|) (QUOTE (-132))) (|HasCategory| (-833 |#1|) (QUOTE (-338))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-833 |#1|) (QUOTE (-134))) (|HasCategory| (-833 |#1|) (QUOTE (-338))) (|HasCategory| (-833 |#1|) (QUOTE (-132))) (-3747 (|HasCategory| (-833 |#1|) (QUOTE (-132))) (|HasCategory| (-833 |#1|) (QUOTE (-338))))) 
 (-314 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3745 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
 (-315 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3745 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
 (-316 GF) 
 ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) 
 NIL 
@@ -1206,33 +1206,33 @@ NIL
 NIL 
 (-319) 
 ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-320 R UP -1724) 
+(-320 R UP -1725) 
 ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-321 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-833 |#1|) (QUOTE (-134))) (|HasCategory| (-833 |#1|) (QUOTE (-338))) (|HasCategory| (-833 |#1|) (QUOTE (-132))) (-3745 (|HasCategory| (-833 |#1|) (QUOTE (-132))) (|HasCategory| (-833 |#1|) (QUOTE (-338))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-833 |#1|) (QUOTE (-134))) (|HasCategory| (-833 |#1|) (QUOTE (-338))) (|HasCategory| (-833 |#1|) (QUOTE (-132))) (-3747 (|HasCategory| (-833 |#1|) (QUOTE (-132))) (|HasCategory| (-833 |#1|) (QUOTE (-338))))) 
 (-322 GF |uni|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3745 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
 (-323 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3745 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
 (-324 |p| |n|) 
 ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-833 |#1|) (QUOTE (-134))) (|HasCategory| (-833 |#1|) (QUOTE (-338))) (|HasCategory| (-833 |#1|) (QUOTE (-132))) (-3745 (|HasCategory| (-833 |#1|) (QUOTE (-132))) (|HasCategory| (-833 |#1|) (QUOTE (-338))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-833 |#1|) (QUOTE (-134))) (|HasCategory| (-833 |#1|) (QUOTE (-338))) (|HasCategory| (-833 |#1|) (QUOTE (-132))) (-3747 (|HasCategory| (-833 |#1|) (QUOTE (-132))) (|HasCategory| (-833 |#1|) (QUOTE (-338))))) 
 (-325 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3745 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
-(-326 -1724 GF) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+(-326 -1725 GF) 
 ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
@@ -1240,21 +1240,21 @@ NIL
 ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) 
 NIL 
 NIL 
-(-328 -1724 FP FPP) 
+(-328 -1725 FP FPP) 
 ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
 NIL 
 NIL 
 (-329 GF |n|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3745 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
 (-330 R |ls|) 
 ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) 
 NIL 
 NIL 
 (-331 S) 
 ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-332 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
@@ -1262,7 +1262,7 @@ NIL
 NIL 
 (-333) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-334 |Name| S) 
 ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) 
@@ -1278,7 +1278,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-509)))) 
 (-337 R) 
 ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-4187 |has| |#1| (-509)) (-4185 . T) (-4184 . T)) 
+((-4189 |has| |#1| (-509)) (-4187 . T) (-4186 . T)) 
 NIL 
 (-338) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) 
@@ -1290,7 +1290,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-333)))) 
 (-340 R UP) 
 ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-341 S A R B) 
 ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) 
@@ -1299,14 +1299,14 @@ NIL
 (-342 A S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4191)) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1004)))) 
+((|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005)))) 
 (-343 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
-((-4190 . T) (-2180 . T)) 
+((-4192 . T) (-2181 . T)) 
 NIL 
 (-344 |VarSet| R) 
 ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4185 . T) (-4184 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4187 . T) (-4186 . T)) 
 NIL 
 (-345 S V) 
 ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) 
@@ -1318,7 +1318,7 @@ NIL
 ((|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) 
 (-347 R) 
 ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-348 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) 
@@ -1326,7 +1326,7 @@ NIL
 NIL 
 (-349) 
 ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\^= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-4173 . T) (-4181 . T) (-2202 . T) (-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4175 . T) (-4183 . T) (-2204 . T) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-350 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) 
@@ -1334,23 +1334,23 @@ NIL
 NIL 
 (-351 R S) 
 ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) 
-((-4185 . T) (-4184 . T)) 
+((-4187 . T) (-4186 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156)))) 
 (-352 R |Basis|) 
 ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) 
-((-4185 . T) (-4184 . T)) 
+((-4187 . T) (-4186 . T)) 
 NIL 
 (-353) 
 ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-354) 
 ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-355 R S) 
 ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) 
-((-4185 . T) (-4184 . T)) 
+((-4187 . T) (-4186 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156)))) 
 (-356 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
@@ -1358,7 +1358,7 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-779)))) 
 (-357) 
 ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-358) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
@@ -1370,13 +1370,13 @@ NIL
 NIL 
 (-360 |n| |class| R) 
 ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) 
-((-4185 . T) (-4184 . T)) 
+((-4187 . T) (-4186 . T)) 
 NIL 
 (-361) 
 ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) 
 NIL 
 NIL 
-(-362 -1724 UP UPUP R) 
+(-362 -1725 UP UPUP R) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) 
 NIL 
 NIL 
@@ -1390,27 +1390,27 @@ NIL
 NIL 
 (-365) 
 ((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-366) 
 ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-367) 
 ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-368 -2987 |returnType| |arguments| |symbols|) 
+(-368 -2989 |returnType| |arguments| |symbols|) 
 ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-369 -1724 UP) 
+(-369 -1725 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
 (-370 R) 
 ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-371 S) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
@@ -1418,15 +1418,15 @@ NIL
 NIL 
 (-372) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-373 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4173)) (|HasAttribute| |#1| (QUOTE -4181))) 
+((|HasAttribute| |#1| (QUOTE -4175)) (|HasAttribute| |#1| (QUOTE -4183))) 
 (-374) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
-((-2202 . T) (-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-2204 . T) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-375 R S) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) 
@@ -1438,20 +1438,20 @@ NIL
 NIL 
 (-377 S) 
 ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) 
-((-4177 -12 (|has| |#1| (-6 -4188)) (|has| |#1| (-421)) (|has| |#1| (-6 -4177))) (-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-1075)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1075)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-502))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasAttribute| |#1| (QUOTE -4188)) (|HasAttribute| |#1| (QUOTE -4177)) (|HasCategory| |#1| (QUOTE (-421)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (-3745 (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+((-4179 -12 (|has| |#1| (-6 -4190)) (|has| |#1| (-421)) (|has| |#1| (-6 -4179))) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-502))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasAttribute| |#1| (QUOTE -4190)) (|HasAttribute| |#1| (QUOTE -4179)) (|HasCategory| |#1| (QUOTE (-421)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (-3747 (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-378 S R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
 NIL 
 (-379 R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-380 A S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517))))) 
+((|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) 
 (-381 S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
@@ -1460,14 +1460,14 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-383 R -1724 UP A) 
+(-383 R -1725 UP A) 
 ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
-(-384 R -1724 UP A |ibasis|) 
+(-384 R -1725 UP A |ibasis|) 
 ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,{}...,{}fn])} = the module generated by \\spad{(f1,{}...,{}fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) 
 NIL 
-((|HasCategory| |#4| (LIST (QUOTE -953) (|devaluate| |#2|)))) 
+((|HasCategory| |#4| (LIST (QUOTE -954) (|devaluate| |#2|)))) 
 (-385 AR R AS S) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
@@ -1478,12 +1478,12 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-333)))) 
 (-387 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-4187 |has| |#1| (-509)) (-4185 . T) (-4184 . T)) 
+((-4189 |has| |#1| (-509)) (-4187 . T) (-4186 . T)) 
 NIL 
 (-388 R) 
 ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1075)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -258) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1075)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-421))) (-3745 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-1114))))) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -258) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-1115))))) 
 (-389 R) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) 
 NIL 
@@ -1510,37 +1510,37 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-338)))) 
 (-395 S) 
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-4190 . T) (-4180 . T) (-4191 . T) (-2180 . T)) 
+((-4192 . T) (-4182 . T) (-4193 . T) (-2181 . T)) 
 NIL 
-(-396 R -1724) 
+(-396 R -1725) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) 
 NIL 
 NIL 
 (-397 R E) 
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) 
-((-4177 -12 (|has| |#1| (-6 -4177)) (|has| |#2| (-6 -4177))) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -4177)) (|HasAttribute| |#2| (QUOTE -4177)))) 
-(-398 R -1724) 
+((-4179 -12 (|has| |#1| (-6 -4179)) (|has| |#2| (-6 -4179))) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -4179)) (|HasAttribute| |#2| (QUOTE -4179)))) 
+(-398 R -1725) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) 
 NIL 
 NIL 
 (-399 S R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) 
+((|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) 
 (-400 R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
-((-4187 -3745 (|has| |#1| (-962)) (|has| |#1| (-442))) (-4185 |has| |#1| (-156)) (-4184 |has| |#1| (-156)) ((-4192 "*") |has| |#1| (-509)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-509)) (-4182 |has| |#1| (-509)) (-2180 . T)) 
+((-4189 -3747 (|has| |#1| (-963)) (|has| |#1| (-442))) (-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) ((-4194 "*") |has| |#1| (-509)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-509)) (-4184 |has| |#1| (-509)) (-2181 . T)) 
 NIL 
-(-401 R -1724) 
+(-401 R -1725) 
 ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,{}y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,{}y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,{}y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,{}y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,{}y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,{}y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,{}x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) 
 NIL 
 NIL 
-(-402 R -1724) 
+(-402 R -1725) 
 ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-27)))) 
-(-403 R -1724) 
+(-403 R -1725) 
 ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,{}k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) 
 NIL 
 NIL 
@@ -1548,10 +1548,10 @@ NIL
 ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) 
 NIL 
 NIL 
-(-405 R -1724 UP) 
+(-405 R -1725 UP) 
 ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-47))))) 
+((|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-47))))) 
 (-406) 
 ((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) 
 NIL 
@@ -1566,17 +1566,17 @@ NIL
 NIL 
 (-409) 
 ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-410) 
 ((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-411 UP) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) 
 NIL 
 NIL 
-(-412 R UP -1724) 
+(-412 R UP -1725) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) 
 NIL 
 NIL 
@@ -1614,16 +1614,16 @@ NIL
 NIL 
 (-421) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-422 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,{}b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,{}b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,{}ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,{}v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) 
-((-4187 |has| (-377 (-875 |#1|)) (-509)) (-4185 . T) (-4184 . T)) 
+((-4189 |has| (-377 (-875 |#1|)) (-509)) (-4187 . T) (-4186 . T)) 
 ((|HasCategory| (-377 (-875 |#1|)) (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| (-377 (-875 |#1|)) (QUOTE (-509)))) 
 (-423 |vl| R E) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-4192 "*") |has| |#2| (-156)) (-4183 |has| |#2| (-509)) (-4188 |has| |#2| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3745 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3745 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4188)) (|HasCategory| |#2| (QUOTE (-421))) (-3745 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) 
+(((-4194 "*") |has| |#2| (-156)) (-4185 |has| |#2| (-509)) (-4190 |has| |#2| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3747 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4190)) (|HasCategory| |#2| (QUOTE (-421))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) 
 (-424 R BP) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) 
 NIL 
@@ -1650,7 +1650,7 @@ NIL
 NIL 
 (-430 |vl| R IS E |ff| P) 
 ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,{}e,{}x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,{}i,{}e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,{}x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-4185 . T) (-4184 . T)) 
+((-4187 . T) (-4186 . T)) 
 NIL 
 (-431 E V R P Q) 
 ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
@@ -1658,8 +1658,8 @@ NIL
 NIL 
 (-432 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1004))) (-12 (|HasCategory| |#4| (QUOTE (-1004))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1005))) (-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) 
 (-433 S R E) 
 ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) 
 NIL 
@@ -1688,7 +1688,7 @@ NIL
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-440 |lv| -1724 R) 
+(-440 |lv| -1725 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
@@ -1698,45 +1698,45 @@ NIL
 NIL 
 (-442) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-443 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4182 |has| |#1| (-333)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-333))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2269) (LIST (|devaluate| |#1|) (QUOTE (-1075)))))) (-3745 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1096))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -1518) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1075))))) (|HasSignature| |#1| (LIST (QUOTE -2096) (LIST (LIST (QUOTE -583) (QUOTE (-1075))) (|devaluate| |#1|))))))) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) 
 (-444 |Key| |Entry| |Tbl| |dent|) 
 ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) 
-((-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1004))) (-12 (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (-12 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1860) (|devaluate| |#2|)))))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-1004)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-445 R E V P) 
 ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1004))) (-12 (|HasCategory| |#4| (QUOTE (-1004))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1005))) (-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) 
 (-446) 
 ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-447 |Key| |Entry| |hashfn|) 
 ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (-12 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1860) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1004))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-1004)))) (-12 (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-448) 
 ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) 
 NIL 
 NIL 
 (-449 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
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 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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(QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-963)))) (-3747 (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-156)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-338)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-777)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-963)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-1005))))) (-3747 (-12 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3747 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-1005)))) (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-963)))) (-12 (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076))))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-451 S) 
 ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-452 -1724 UP UPUP R) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-452 -1725 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) 
 NIL 
 NIL 
@@ -1746,15 +1746,15 @@ NIL
 NIL 
 (-454) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -953) (QUOTE (-1075)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-938))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1051))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1075)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3745 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-939))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1052))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3747 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) 
 (-455 A S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4190)) (|HasAttribute| |#1| (QUOTE -4191)) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) 
+((|HasAttribute| |#1| (QUOTE -4192)) (|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) 
 (-456 S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-457 S) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
@@ -1764,34 +1764,34 @@ NIL
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-459 -1724 UP |AlExt| |AlPol|) 
+(-459 -1725 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
 (-460) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,{}y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (LIST (QUOTE -953) (QUOTE (-517))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (LIST (QUOTE -954) (QUOTE (-517))))) 
 (-461 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-462 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-463 K R UP) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) 
 NIL 
 NIL 
-(-464 R UP -1724) 
+(-464 R UP -1725) 
 ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-465 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| (-107) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-107) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-107) (QUOTE (-1004))) (-12 (|HasCategory| (-107) (QUOTE (-1004))) (|HasCategory| (-107) (LIST (QUOTE -280) (QUOTE (-107))))) (|HasCategory| (-107) (LIST (QUOTE -557) (QUOTE (-787))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| (-107) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-107) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-107) (QUOTE (-1005))) (-12 (|HasCategory| (-107) (QUOTE (-1005))) (|HasCategory| (-107) (LIST (QUOTE -280) (QUOTE (-107))))) (|HasCategory| (-107) (LIST (QUOTE -557) (QUOTE (-787))))) 
 (-466 K R UP L) 
 ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) 
 NIL 
@@ -1804,10 +1804,10 @@ NIL
 ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) 
 NIL 
 NIL 
-(-469 -1724 |Expon| |VarSet| |DPoly|) 
+(-469 -1725 |Expon| |VarSet| |DPoly|) 
 ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) 
 NIL 
-((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-1075))))) 
+((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-1076))))) 
 (-470 |vl| |nv|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,{}lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) 
 NIL 
@@ -1850,32 +1850,32 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-724)))) 
 (-480 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-481 |p| |n|) 
 ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-530 |#1|) (QUOTE (-134))) (|HasCategory| (-530 |#1|) (QUOTE (-338))) (|HasCategory| (-530 |#1|) (QUOTE (-132))) (-3745 (|HasCategory| (-530 |#1|) (QUOTE (-132))) (|HasCategory| (-530 |#1|) (QUOTE (-338))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-530 |#1|) (QUOTE (-134))) (|HasCategory| (-530 |#1|) (QUOTE (-338))) (|HasCategory| (-530 |#1|) (QUOTE (-132))) (-3747 (|HasCategory| (-530 |#1|) (QUOTE (-132))) (|HasCategory| (-530 |#1|) (QUOTE (-338))))) 
 (-482 R |mnRow| |mnCol| |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-483 S |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-484 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) 
 NIL 
-((|HasAttribute| |#3| (QUOTE -4191))) 
+((|HasAttribute| |#3| (QUOTE -4193))) 
 (-485 R |Row| |Col| M QF |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) 
 NIL 
-((|HasAttribute| |#7| (QUOTE -4191))) 
+((|HasAttribute| |#7| (QUOTE -4193))) 
 (-486 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4192 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4194 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-487 GF) 
 ((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}."))) 
 NIL 
@@ -1888,7 +1888,7 @@ NIL
 ((|constructor| (NIL "converts entire exponents to OutputForm"))) 
 NIL 
 NIL 
-(-490 K -1724 |Par|) 
+(-490 K -1725 |Par|) 
 ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) 
 NIL 
 NIL 
@@ -1908,7 +1908,7 @@ NIL
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-495 K -1724 |Par|) 
+(-495 K -1725 |Par|) 
 ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,{}lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,{}lden,{}lvar,{}eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,{}eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,{}eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) 
 NIL 
 NIL 
@@ -1938,17 +1938,17 @@ NIL
 NIL 
 (-502) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|hash| (($ $) "\\spad{hash(n)} returns the hash code of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
-((-4188 . T) (-4189 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4190 . T) (-4191 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-503 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (-12 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1860) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1004))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-1004)))) (-12 (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-504 R -1724) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-504 R -1725) 
 ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f,{} x,{} y,{} d)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) 
 NIL 
 NIL 
-(-505 R0 -1724 UP UPUP R) 
+(-505 R0 -1725 UP UPUP R) 
 ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f,{} d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) 
 NIL 
 NIL 
@@ -1958,7 +1958,7 @@ NIL
 NIL 
 (-507 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) 
-((-2202 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-2204 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-508 S) 
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
@@ -1966,9 +1966,9 @@ NIL
 NIL 
 (-509) 
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-510 R -1724) 
+(-510 R -1725) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) 
 NIL 
 NIL 
@@ -1980,7 +1980,7 @@ NIL
 ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) 
 NIL 
 NIL 
-(-513 R -1724 L) 
+(-513 R -1725 L) 
 ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) 
 NIL 
 ((|HasCategory| |#3| (LIST (QUOTE -593) (|devaluate| |#2|)))) 
@@ -1988,31 +1988,31 @@ NIL
 ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ^= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) 
 NIL 
 NIL 
-(-515 -1724 UP UPUP R) 
+(-515 -1725 UP UPUP R) 
 ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} ')} returns \\spad{[g,{}h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) 
 NIL 
 NIL 
-(-516 -1724 UP) 
+(-516 -1725 UP) 
 ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} D)} returns \\spad{[g,{} h,{} s,{} p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) 
 NIL 
 NIL 
 (-517) 
 ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) 
-((-4172 . T) (-4178 . T) (-4182 . T) (-4177 . T) (-4188 . T) (-4189 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4174 . T) (-4180 . T) (-4184 . T) (-4179 . T) (-4190 . T) (-4191 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-518) 
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) 
 NIL 
 NIL 
-(-519 R -1724 L) 
+(-519 R -1725 L) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) 
 NIL 
 ((|HasCategory| |#3| (LIST (QUOTE -593) (|devaluate| |#2|)))) 
-(-520 R -1724) 
+(-520 R -1725) 
 ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1039)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-569))))) 
-(-521 -1724 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1040)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-569))))) 
+(-521 -1725 UP) 
 ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) 
 NIL 
 NIL 
@@ -2020,54 +2020,54 @@ NIL
 ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) 
 NIL 
 NIL 
-(-523 -1724) 
+(-523 -1725) 
 ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) 
 NIL 
 NIL 
 (-524 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) 
-((-2202 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-2204 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-525) 
 ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
 NIL 
 NIL 
-(-526 R -1724) 
+(-526 R -1725) 
 ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-256))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-1075))))) (-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-256)))) (|HasCategory| |#1| (QUOTE (-509)))) 
-(-527 -1724 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-256))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076))))) (-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-256)))) (|HasCategory| |#1| (QUOTE (-509)))) 
+(-527 -1725 UP) 
 ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) 
 NIL 
 NIL 
-(-528 R -1724) 
+(-528 R -1725) 
 ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f,{} s,{} t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) 
 NIL 
 NIL 
 (-529 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-530 |p|) 
 ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 ((|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-132))) (|HasCategory| $ (QUOTE (-338)))) 
 (-531) 
 ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) 
 NIL 
 NIL 
-(-532 R -1724) 
+(-532 R -1725) 
 ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) 
 NIL 
 NIL 
-(-533 E -1724) 
+(-533 E -1725) 
 ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented"))) 
 NIL 
 NIL 
-(-534 -1724) 
+(-534 -1725) 
 ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) 
-((-4185 . T) (-4184 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-1075))))) 
+((-4187 . T) (-4186 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-1076))))) 
 (-535 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) 
 NIL 
@@ -2090,19 +2090,19 @@ NIL
 NIL 
 (-540 |mn|) 
 ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1004))) (-3745 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1004)))) (-12 (|HasCategory| (-131) (QUOTE (-1004))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3745 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1004))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-131) (QUOTE (-1004))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1005))) (-3747 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1005)))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3747 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) 
 (-541 E V R P) 
 ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) 
 NIL 
 NIL 
 (-542 |Coef|) 
 ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|))))) (|HasCategory| (-517) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-333))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2269) (LIST (|devaluate| |#1|) (QUOTE (-1075))))))) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|))))) (|HasCategory| (-517) (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-333))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076))))))) 
 (-543 |Coef|) 
 ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
-((-4185 |has| |#1| (-509)) (-4184 |has| |#1| (-509)) ((-4192 "*") |has| |#1| (-509)) (-4183 |has| |#1| (-509)) (-4187 . T)) 
+((-4187 |has| |#1| (-509)) (-4186 |has| |#1| (-509)) ((-4194 "*") |has| |#1| (-509)) (-4185 |has| |#1| (-509)) (-4189 . T)) 
 ((|HasCategory| |#1| (QUOTE (-509)))) 
 (-544 A B) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) 
@@ -2112,7 +2112,7 @@ NIL
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) 
 NIL 
 NIL 
-(-546 R -1724 FG) 
+(-546 R -1725 FG) 
 ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) 
 NIL 
 NIL 
@@ -2122,31 +2122,31 @@ NIL
 NIL 
 (-548 R |mn|) 
 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-919))) (|HasCategory| |#1| (QUOTE (-962)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-920))) (|HasCategory| |#1| (QUOTE (-963)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-549 S |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4191)) (|HasCategory| |#2| (QUOTE (-779))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#3| (QUOTE (-1004)))) 
+((|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#2| (QUOTE (-779))) (|HasAttribute| |#1| (QUOTE -4192)) (|HasCategory| |#3| (QUOTE (-1005)))) 
 (-550 |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-551 R A) 
 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,{}b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) 
-((-4187 -3745 (-3992 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4185 . T) (-4184 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3745 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) 
+((-4189 -3747 (-3993 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4187 . T) (-4186 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3747 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) 
 (-552 |Entry|) 
 ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| (-1058) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (QUOTE (-1004))) (-12 (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (QUOTE (-1058))) (LIST (QUOTE |:|) (QUOTE -1860) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (LIST (QUOTE -557) (QUOTE (-787))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| (-1059) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (QUOTE (-1059))) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -557) (QUOTE (-787))))) 
 (-553 S |Key| |Entry|) 
 ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) 
 NIL 
 NIL 
 (-554 |Key| |Entry|) 
 ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) 
-((-4191 . T) (-2180 . T)) 
+((-4193 . T) (-2181 . T)) 
 NIL 
 (-555 R S) 
 ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) 
@@ -2164,7 +2164,7 @@ NIL
 ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-559 -1724 UP) 
+(-559 -1725 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) 
 NIL 
 NIL 
@@ -2174,20 +2174,20 @@ NIL
 NIL 
 (-561 R) 
 ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-562 A R S) 
 ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
 ((|HasCategory| |#1| (QUOTE (-777)))) 
-(-563 R -1724) 
+(-563 R -1725) 
 ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f,{} t,{} s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t),{} t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f,{} t,{} s)} if it cannot compute the transform."))) 
 NIL 
 NIL 
 (-564 R UP) 
 ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,{}n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,{}n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) 
-((-4185 . T) (-4184 . T) ((-4192 "*") . T) (-4183 . T) (-4187 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517))))) 
+((-4187 . T) (-4186 . T) ((-4194 "*") . T) (-4185 . T) (-4189 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517))))) 
 (-565 R E V P TS ST) 
 ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) 
 NIL 
@@ -2198,7 +2198,7 @@ NIL
 NIL 
 (-567 |VarSet| R |Order|) 
 ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-568 R |ls|) 
 ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) 
@@ -2208,30 +2208,30 @@ NIL
 ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) 
 NIL 
 NIL 
-(-570 R -1724) 
+(-570 R -1725) 
 ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) 
 NIL 
 NIL 
-(-571 |lv| -1724) 
+(-571 |lv| -1725) 
 ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) 
 NIL 
 NIL 
 (-572) 
 ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) 
-((-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1058) (QUOTE (-779))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1004))) (-12 (|HasCategory| (-51) (QUOTE (-1004))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 (-51))) (QUOTE (-1004))) (-12 (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 (-51))) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (QUOTE (-1058))) (LIST (QUOTE |:|) (QUOTE -1860) (QUOTE (-51))))))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 (-51))) (QUOTE (-1004))) (|HasCategory| (-51) (QUOTE (-1004)))) (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 (-51))) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1004))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1059) (QUOTE (-779))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1005))) (-12 (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (QUOTE (-1059))) (LIST (QUOTE |:|) (QUOTE -1859) (QUOTE (-51))))))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-51) (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-573 S R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-333)))) 
 (-574 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4185 . T) (-4184 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4187 . T) (-4186 . T)) 
 NIL 
 (-575 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) 
-((-4187 -3745 (-3992 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4185 . T) (-4184 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3745 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) 
+((-4189 -3747 (-3993 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4187 . T) (-4186 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3747 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) 
 (-576 R FE) 
 ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) 
 NIL 
@@ -2243,10 +2243,10 @@ NIL
 (-578 S R) 
 ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-333))) (-2477 (|HasCategory| |#1| (QUOTE (-333))))) 
+((|HasCategory| |#1| (QUOTE (-333))) (-2479 (|HasCategory| |#1| (QUOTE (-333))))) 
 (-579 R) 
 ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-580 A B) 
 ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) 
@@ -2262,12 +2262,12 @@ NIL
 NIL 
 (-583 S) 
 ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-584 S) 
 ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-585 R) 
 ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) 
 NIL 
@@ -2279,39 +2279,39 @@ NIL
 (-587 A S) 
 ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4191))) 
+((|HasAttribute| |#1| (QUOTE -4193))) 
 (-588 S) 
 ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
-(-589 R -1724 L) 
+(-589 R -1725 L) 
 ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op,{} g,{} x,{} a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{op y = g,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op,{} g,{} x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) 
 NIL 
 NIL 
 (-590 A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
 (-591 A M) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
 (-592 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-333)))) 
 (-593 A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-594 -1724 UP) 
+(-594 -1725 UP) 
 ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a,{} zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
-(-595 A -3175) 
+(-595 A -2669) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
 (-596 A L) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) 
 NIL 
@@ -2326,7 +2326,7 @@ NIL
 NIL 
 (-599 M R S) 
 ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) 
-((-4185 . T) (-4184 . T)) 
+((-4187 . T) (-4186 . T)) 
 ((|HasCategory| |#1| (QUOTE (-723)))) 
 (-600 R) 
 ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) 
@@ -2334,7 +2334,7 @@ NIL
 NIL 
 (-601 |VarSet| R) 
 ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4185 . T) (-4184 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4187 . T) (-4186 . T)) 
 ((|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-156)))) 
 (-602 A S) 
 ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) 
@@ -2342,13 +2342,13 @@ NIL
 NIL 
 (-603 S) 
 ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
-(-604 -1724) 
+(-604 -1725) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
-(-605 -1724 |Row| |Col| M) 
+(-605 -1725 |Row| |Col| M) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
@@ -2358,8 +2358,8 @@ NIL
 NIL 
 (-607 |n| R) 
 ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) 
-((-4187 . T) (-4190 . T) (-4184 . T) (-4185 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4192 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509))) (-3745 (|HasAttribute| |#2| (QUOTE (-4192 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3745 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1075)))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-156)))) 
+((-4189 . T) (-4192 . T) (-4186 . T) (-4187 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4194 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509))) (-3747 (|HasAttribute| |#2| (QUOTE (-4194 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3747 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-156)))) 
 (-608 |VarSet|) 
 ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
@@ -2370,12 +2370,12 @@ NIL
 NIL 
 (-610 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
 (-611 R) 
 ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-612 |VarSet|) 
 ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) 
 NIL 
@@ -2411,10 +2411,10 @@ NIL
 (-620 S R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) 
 NIL 
-((|HasAttribute| |#2| (QUOTE (-4192 "*"))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509)))) 
+((|HasAttribute| |#2| (QUOTE (-4194 "*"))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509)))) 
 (-621 R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) 
-((-4190 . T) (-4191 . T) (-2180 . T)) 
+((-4192 . T) (-4193 . T) (-2181 . T)) 
 NIL 
 (-622 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{^=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{^=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) 
@@ -2422,13 +2422,13 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509)))) 
 (-623 R) 
 ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4192 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4194 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-624 R) 
 ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) 
 NIL 
 NIL 
-(-625 S -1724 FLAF FLAS) 
+(-625 S -1725 FLAF FLAS) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) 
 NIL 
 NIL 
@@ -2438,11 +2438,11 @@ NIL
 NIL 
 (-627) 
 ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) 
-((-4183 . T) (-4188 |has| (-632) (-333)) (-4182 |has| (-632) (-333)) (-3887 . T) (-4189 |has| (-632) (-6 -4189)) (-4186 |has| (-632) (-6 -4186)) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-632) (QUOTE (-134))) (|HasCategory| (-632) (QUOTE (-132))) (|HasCategory| (-632) (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-338))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-319))) (-3745 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (LIST (QUOTE -258) (QUOTE (-632)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -280) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -478) (QUOTE (-1075)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-632) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-632) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-632) (QUOTE (-938))) (|HasCategory| (-632) (QUOTE (-1096))) (-12 (|HasCategory| (-632) (QUOTE (-919))) (|HasCategory| (-632) (QUOTE (-1096)))) (|HasCategory| (-632) (QUOTE (-502))) (|HasCategory| (-632) (QUOTE (-971))) (-12 (|HasCategory| (-632) (QUOTE (-971))) (|HasCategory| (-632) (QUOTE (-1096)))) (-3745 (|HasCategory| (-632) (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (QUOTE (-278))) (-3745 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (QUOTE (-832))) (-12 (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-333)))) (-12 (|HasCategory| (-632) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-779))) (|HasCategory| (-632) (QUOTE (-509))) (|HasAttribute| (-632) (QUOTE -4189)) (|HasAttribute| (-632) (QUOTE -4186)) (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (-3745 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-333))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-832))))) (-3745 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (-12 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-832)))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-832))))) (-3745 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-333)))) (-3745 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-509)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-132)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-319))))) 
+((-4185 . T) (-4190 |has| (-632) (-333)) (-4184 |has| (-632) (-333)) (-3883 . T) (-4191 |has| (-632) (-6 -4191)) (-4188 |has| (-632) (-6 -4188)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-632) (QUOTE (-134))) (|HasCategory| (-632) (QUOTE (-132))) (|HasCategory| (-632) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-338))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-319))) (-3747 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (LIST (QUOTE -258) (QUOTE (-632)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -280) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-632) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-632) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-632) (QUOTE (-939))) (|HasCategory| (-632) (QUOTE (-1097))) (-12 (|HasCategory| (-632) (QUOTE (-920))) (|HasCategory| (-632) (QUOTE (-1097)))) (|HasCategory| (-632) (QUOTE (-502))) (|HasCategory| (-632) (QUOTE (-972))) (-12 (|HasCategory| (-632) (QUOTE (-972))) (|HasCategory| (-632) (QUOTE (-1097)))) (-3747 (|HasCategory| (-632) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (QUOTE (-278))) (-3747 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (QUOTE (-832))) (-12 (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-333)))) (-12 (|HasCategory| (-632) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-779))) (|HasCategory| (-632) (QUOTE (-509))) (|HasAttribute| (-632) (QUOTE -4191)) (|HasAttribute| (-632) (QUOTE -4188)) (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-333))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-832))))) (-3747 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (-12 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-832)))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-832))))) (-3747 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-333)))) (-3747 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-509)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-132)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-319))))) 
 (-628 S) 
 ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) 
-((-4191 . T) (-2180 . T)) 
+((-4193 . T) (-2181 . T)) 
 NIL 
 (-629 U) 
 ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,{}n,{}g,{}p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl,{} p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,{}p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,{}p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,{}p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,{}f2,{}p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) 
@@ -2452,13 +2452,13 @@ NIL
 ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) 
 NIL 
 NIL 
-(-631 OV E -1724 PG) 
+(-631 OV E -1725 PG) 
 ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) 
 NIL 
 NIL 
 (-632) 
 ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) 
-((-2202 . T) (-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-2204 . T) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-633 R) 
 ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) 
@@ -2466,7 +2466,7 @@ NIL
 NIL 
 (-634) 
 ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) 
-((-4189 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4191 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-635 S D1 D2 I) 
 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,{}x,{}y)} returns a function \\spad{f: (D1,{} D2) -> I} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1,{} D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) 
@@ -2488,7 +2488,7 @@ NIL
 ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) 
 NIL 
 NIL 
-(-640 S -3340 I) 
+(-640 S -3342 I) 
 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) 
 NIL 
 NIL 
@@ -2498,31 +2498,31 @@ NIL
 NIL 
 (-642 R) 
 ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,{}1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i,{} i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\^= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\^= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-643 R1 UP1 UPUP1 R2 UP2 UPUP2) 
 ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f,{} p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) 
 NIL 
 NIL 
-(-644 R |Mod| -3334 -3798 |exactQuo|) 
+(-644 R |Mod| -1769 -2662 |exactQuo|) 
 ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-645 R |Rep|) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4186 |has| |#1| (-333)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-990) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-319))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4188)) (|HasCategory| |#1| (QUOTE (-421))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-991) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-319))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-646 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} \\undocumented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
 (-647 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-4185 |has| |#1| (-156)) (-4184 |has| |#1| (-156)) (-4187 . T)) 
+((-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) (-4189 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134)))) 
-(-648 R |Mod| -3334 -3798 |exactQuo|) 
+(-648 R |Mod| -1769 -2662 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-649 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
@@ -2530,11 +2530,11 @@ NIL
 NIL 
 (-650 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-4185 . T) (-4184 . T)) 
+((-4187 . T) (-4186 . T)) 
 NIL 
-(-651 -1724) 
+(-651 -1725) 
 ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,{}1],{}[1,{}0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,{}h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,{}0],{}[0,{}1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,{}h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,{}k],{}[0,{}1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,{}b,{}c,{}d)} returns \\spad{matrix [[a,{}b],{}[c,{}d]]}."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-652 S) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
@@ -2558,7 +2558,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-338)))) 
 (-657 R UP) 
 ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) 
-((-4183 |has| |#1| (-333)) (-4188 |has| |#1| (-333)) (-4182 |has| |#1| (-333)) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 |has| |#1| (-333)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-658 S) 
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) 
@@ -2568,7 +2568,7 @@ NIL
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-660 -1724 UP) 
+(-660 -1725 UP) 
 ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f,{} D)} returns \\spad{[p,{}n,{}s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f,{} D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p,{} D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m,{} s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p,{} D)} returns \\spad{[n,{}s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
@@ -2586,8 +2586,8 @@ NIL
 NIL 
 (-664 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) 
-(((-4192 "*") |has| |#2| (-156)) (-4183 |has| |#2| (-509)) (-4188 |has| |#2| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3745 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3745 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4188)) (|HasCategory| |#2| (QUOTE (-421))) (-3745 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) 
+(((-4194 "*") |has| |#2| (-156)) (-4185 |has| |#2| (-509)) (-4190 |has| |#2| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3747 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4190)) (|HasCategory| |#2| (QUOTE (-421))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) 
 (-665 E OV R PRF) 
 ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
@@ -2602,16 +2602,16 @@ NIL
 NIL 
 (-668 R M) 
 ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,{}m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}m)} creates a scalar multiple of the basis element \\spad{m}."))) 
-((-4185 |has| |#1| (-156)) (-4184 |has| |#1| (-156)) (-4187 . T)) 
+((-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) (-4189 . T)) 
 ((-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-779)))) 
 (-669 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-4180 . T) (-4191 . T) (-2180 . T)) 
+((-4182 . T) (-4193 . T) (-2181 . T)) 
 NIL 
 (-670 S) 
 ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) 
-((-4190 . T) (-4180 . T) (-4191 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) 
+((-4192 . T) (-4182 . T) (-4193 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) 
 (-671) 
 ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) 
 NIL 
@@ -2622,7 +2622,7 @@ NIL
 NIL 
 (-673 |Coef| |Var|) 
 ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,{}x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,{}x,{}n)} returns \\spad{min(n,{}order(f,{}x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,{}x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,{}x,{}n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4185 . T) (-4184 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4187 . T) (-4186 . T) (-4189 . T)) 
 NIL 
 (-674 OV E R P) 
 ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) 
@@ -2638,7 +2638,7 @@ NIL
 NIL 
 (-677 R) 
 ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,{}n)} is recursively defined to be \\spad{plenaryPower(a,{}n-1)*plenaryPower(a,{}n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) 
-((-4185 . T) (-4184 . T)) 
+((-4187 . T) (-4186 . T)) 
 NIL 
 (-678) 
 ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,{}n,{}scale,{}ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,{}n,{}scale,{}ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) 
@@ -2720,15 +2720,15 @@ NIL
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) 
 NIL 
 NIL 
-(-698 -1724) 
+(-698 -1725) 
 ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) 
 NIL 
 NIL 
-(-699 P -1724) 
+(-699 P -1725) 
 ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) 
 NIL 
 NIL 
-(-700 UP -1724) 
+(-700 UP -1725) 
 ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) 
 NIL 
 NIL 
@@ -2742,9 +2742,9 @@ NIL
 NIL 
 (-703) 
 ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) 
-(((-4192 "*") . T)) 
+(((-4194 "*") . T)) 
 NIL 
-(-704 R -1724) 
+(-704 R -1725) 
 ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,{}y),{} N(x,{}y),{} y,{} x)} returns \\spad{F(x,{}y)} such that \\spad{F(x,{}y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,{}y) dx + N(x,{}y) dy = 0},{} or \"failed\" if no first-integral can be found."))) 
 NIL 
 NIL 
@@ -2764,7 +2764,7 @@ NIL
 ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) 
 NIL 
 NIL 
-(-709 -1724 |ExtF| |SUEx| |ExtP| |n|) 
+(-709 -1725 |ExtF| |SUEx| |ExtP| |n|) 
 ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) 
 NIL 
 NIL 
@@ -2778,28 +2778,28 @@ NIL
 NIL 
 (-712 R |VarSet|) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
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 (-713 R S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
 (-714 R) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4186 |has| |#1| (-333)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
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+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-991) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-715 R) 
 ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) 
 (-716 R E V P) 
 ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
 (-717 S) 
 ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-509))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-156)))) 
+((|HasCategory| |#1| (QUOTE (-509))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (QUOTE (-156)))) 
 (-718) 
 ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) 
 NIL 
@@ -2843,28 +2843,28 @@ NIL
 (-728 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-971))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-338)))) 
+((|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-338)))) 
 (-729 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-730 -3745 R OS S) 
+(-730 -3747 R OS S) 
 ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
 NIL 
 (-731 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1075)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| (-916 |#1|) (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-916 |#1|) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (-3745 (|HasCategory| (-916 |#1|) (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (-3745 (|HasCategory| (-916 |#1|) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))))) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| (-917 |#1|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-917 |#1|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (-3747 (|HasCategory| (-917 |#1|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (-3747 (|HasCategory| (-917 |#1|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))))) 
 (-732) 
 ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-733 R -1724 L) 
+(-733 R -1725 L) 
 ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) 
 NIL 
 NIL 
-(-734 R -1724) 
+(-734 R -1725) 
 ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) 
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@@ -2872,7 +2872,7 @@ NIL
 ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) 
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-(-736 R -1724) 
+(-736 R -1725) 
 ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f,{} x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f,{} x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) 
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@@ -2880,11 +2880,11 @@ NIL
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) 
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-(-738 -1724 UP UPUP R) 
+(-738 -1725 UP UPUP R) 
 ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) 
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-(-739 -1724 UP L LQ) 
+(-739 -1725 UP L LQ) 
 ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) 
 NIL 
 NIL 
@@ -2892,41 +2892,41 @@ NIL
 ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-741 -1724 UP L LQ) 
+(-741 -1725 UP L LQ) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) 
 NIL 
 NIL 
-(-742 -1724 UP) 
+(-742 -1725 UP) 
 ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) 
 NIL 
 NIL 
-(-743 -1724 L UP A LO) 
+(-743 -1725 L UP A LO) 
 ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op,{} g)} returns \\spad{[m,{} v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,{}...,{}z_m) . (b_1,{}...,{}b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) 
 NIL 
 NIL 
-(-744 -1724 UP) 
+(-744 -1725 UP) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
-(-745 -1724 LO) 
+(-745 -1725 LO) 
 ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) 
 NIL 
 NIL 
-(-746 -1724 LODO) 
+(-746 -1725 LODO) 
 ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 
 NIL 
 NIL 
-(-747 -3131 S |f|) 
+(-747 -3136 S |f|) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
-((-4184 |has| |#2| (-962)) (-4185 |has| |#2| (-962)) (-4187 |has| |#2| (-6 -4187)) ((-4192 "*") |has| |#2| (-156)) (-4190 . T)) 
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 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) 
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+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-750 (-1076)) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-750 (-1076)) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-750 (-1076)) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-750 (-1076)) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-750 (-1076)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-749 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) 
-(((-4192 "*") |has| |#2| (-333)) (-4183 |has| |#2| (-333)) (-4188 |has| |#2| (-333)) (-4182 |has| |#2| (-333)) (-4187 . T) (-4185 . T) (-4184 . T)) 
+(((-4194 "*") |has| |#2| (-333)) (-4185 |has| |#2| (-333)) (-4190 |has| |#2| (-333)) (-4184 |has| |#2| (-333)) (-4189 . T) (-4187 . T) (-4186 . T)) 
 ((|HasCategory| |#2| (QUOTE (-333)))) 
 (-750 S) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) 
@@ -2938,7 +2938,7 @@ NIL
 NIL 
 (-752) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-753) 
 ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) 
@@ -2966,7 +2966,7 @@ NIL
 NIL 
 (-759 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
 ((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-207)))) 
 (-760) 
 ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) 
@@ -2978,7 +2978,7 @@ NIL
 NIL 
 (-762 S) 
 ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) 
-((-4190 . T) (-4180 . T) (-4191 . T) (-2180 . T)) 
+((-4192 . T) (-4182 . T) (-4193 . T) (-2181 . T)) 
 NIL 
 (-763) 
 ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) 
@@ -2990,11 +2990,11 @@ NIL
 NIL 
 (-765 R) 
 ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) 
-((-4187 |has| |#1| (-777))) 
-((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3745 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3745 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) 
+((-4189 |has| |#1| (-777))) 
+((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3747 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3747 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) 
 (-766 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-4185 |has| |#1| (-156)) (-4184 |has| |#1| (-156)) (-4187 . T)) 
+((-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) (-4189 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134)))) 
 (-767) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) 
@@ -3018,13 +3018,13 @@ NIL
 NIL 
 (-772 R) 
 ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-4187 |has| |#1| (-777))) 
-((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3745 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3745 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) 
+((-4189 |has| |#1| (-777))) 
+((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3747 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3747 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) 
 (-773) 
 ((|constructor| (NIL "Ordered finite sets."))) 
 NIL 
 NIL 
-(-774 -3131 S) 
+(-774 -3136 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
@@ -3038,7 +3038,7 @@ NIL
 NIL 
 (-777) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-778 S) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) 
@@ -3054,20 +3054,20 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156)))) 
 (-781 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ^= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-782 R C) 
 ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) 
-(-783 R |sigma| -1856) 
+(-783 R |sigma| -1857) 
 ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
-(-784 |x| R |sigma| -1856) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
+(-784 |x| R |sigma| -1857) 
 ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-333)))) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-333)))) 
 (-785 R) 
 ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) 
 NIL 
@@ -3090,7 +3090,7 @@ NIL
 NIL 
 (-790 R |vl| |wl| |wtlevel|) 
 ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(p)} coerces a Polynomial(\\spad{R}) into Weighted form,{} applying weights and ignoring terms") (((|Polynomial| |#1|) $) "\\spad{coerce(p)} converts back into a Polynomial(\\spad{R}),{} ignoring weights"))) 
-((-4185 |has| |#1| (-156)) (-4184 |has| |#1| (-156)) (-4187 . T)) 
+((-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) (-4189 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) 
 (-791 R PS UP) 
 ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) 
@@ -3102,20 +3102,20 @@ NIL
 NIL 
 (-793 |p|) 
 ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-794 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-795 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-794 |#1|) (QUOTE (-832))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -953) (QUOTE (-1075)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-134))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-794 |#1|) (QUOTE (-938))) (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-1051))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-207))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -478) (QUOTE (-1075)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -794) (|devaluate| |#1|)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (QUOTE (-278))) (|HasCategory| (-794 |#1|) (QUOTE (-502))) (|HasCategory| (-794 |#1|) (QUOTE (-779))) (-3745 (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-832)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-794 |#1|) (QUOTE (-832))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-134))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-794 |#1|) (QUOTE (-939))) (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-1052))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-207))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -478) (QUOTE (-1076)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -794) (|devaluate| |#1|)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (QUOTE (-278))) (|HasCategory| (-794 |#1|) (QUOTE (-502))) (|HasCategory| (-794 |#1|) (QUOTE (-779))) (-3747 (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-832)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))))) 
 (-796 |p| PADIC) 
 ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-1075)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1075)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-779))) (-3745 (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-779))) (-3747 (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) 
 (-797) 
 ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) 
 NIL 
@@ -3171,7 +3171,7 @@ NIL
 (-810 |Base| |Subject| |Pat|) 
 ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-1075)))) (-12 (-2477 (|HasCategory| |#2| (QUOTE (-962)))) (-2477 (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-1075)))))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (-2477 (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-1075))))))) 
+((|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076)))) (-12 (-2479 (|HasCategory| |#2| (QUOTE (-963)))) (-2479 (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076)))))) (-12 (|HasCategory| |#2| (QUOTE (-963))) (-2479 (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076))))))) 
 (-811 R A B) 
 ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) 
 NIL 
@@ -3180,7 +3180,7 @@ NIL
 ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) 
 NIL 
 NIL 
-(-813 R -3340) 
+(-813 R -3342) 
 ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) 
 NIL 
 NIL 
@@ -3204,7 +3204,7 @@ NIL
 ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-819 UP -1724) 
+(-819 UP -1725) 
 ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,{}n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,{}q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,{}m,{}n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) 
 NIL 
 NIL 
@@ -3222,19 +3222,19 @@ NIL
 NIL 
 (-823 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-824 S) 
 ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-825 |n| R) 
 ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ^= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) 
 NIL 
 NIL 
 (-826 S) 
 ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
 (-827 S) 
 ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) 
@@ -3242,8 +3242,8 @@ NIL
 NIL 
 (-828 S) 
 ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
-((-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))) (-3745 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))))) 
+((-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))) (-3747 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))))) 
 (-829 R E |VarSet| S) 
 ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) 
 NIL 
@@ -3258,13 +3258,13 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-132)))) 
 (-832) 
 ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-833 |p|) 
 ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 ((|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-132))) (|HasCategory| $ (QUOTE (-338)))) 
-(-834 R0 -1724 UP UPUP R) 
+(-834 R0 -1725 UP UPUP R) 
 ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) 
 NIL 
 NIL 
@@ -3278,7 +3278,7 @@ NIL
 NIL 
 (-837 R) 
 ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,{}denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,{}x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,{}n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-838 R) 
 ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num,{} facdenom,{} var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf,{} var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) 
@@ -3292,7 +3292,7 @@ NIL
 ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube:   +-----+ +-- B   where: marks Side # :               / U   /|/              /     / |         F(ront)    <->    1      L -->  +-----+ R|         R(ight)    <->    2             |     |  +         U(p)       <->    3             |  F  | /          D(own)     <->    4             |     |/           L(eft)     <->    5             +-----+            B(ack)     <->    6                ^                |                DThe Cube's surface:                               The pieces on each side            +---+              (except the unmoveable center            |567|              piece) are clockwise numbered            |4U8|              from 1 to 8 starting with the            |321|              piece in the upper left        +---+---+---+          corner (see figure on the        |781|123|345|          left).  The moves of the cube        |6L2|8F4|2R6|          are represented as        |543|765|187|          permutations on these pieces.        +---+---+---+          Each of the pieces is            |123|              represented as a two digit            |8D4|              integer ij where i is the            |765|              # of the side ( 1 to 6 for            +---+              F to B (see table above ))            |567|              and j is the # of the piece.            |4B8|            |321|            +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) 
 NIL 
 NIL 
-(-841 -1724) 
+(-841 -1725) 
 ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) 
 NIL 
 NIL 
@@ -3302,17 +3302,17 @@ NIL
 NIL 
 (-843) 
 ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,{}...,{}fn],{}h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 (-844) 
 ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) 
-(((-4192 "*") . T)) 
+(((-4194 "*") . T)) 
 NIL 
-(-845 -1724 P) 
+(-845 -1725 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-846 |xx| -1724) 
+(-846 |xx| -1725) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) 
 NIL 
 NIL 
@@ -3336,7 +3336,7 @@ NIL
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-852 R -1724) 
+(-852 R -1725) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
@@ -3348,7 +3348,7 @@ NIL
 ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) 
 NIL 
 NIL 
-(-855 S R -1724) 
+(-855 S R -1725) 
 ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
@@ -3368,11 +3368,11 @@ NIL
 ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) 
 NIL 
 ((|HasCategory| |#3| (LIST (QUOTE -809) (|devaluate| |#1|)))) 
-(-860 R -1724 -3340) 
+(-860 R -1725 -3342) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-861 -3340) 
+(-861 -3342) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) 
 NIL 
 NIL 
@@ -3394,8 +3394,8 @@ NIL
 NIL 
 (-866 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-919))) (|HasCategory| |#1| (QUOTE (-962)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-920))) (|HasCategory| |#1| (QUOTE (-963)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-867 |lv| R) 
 ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) 
 NIL 
@@ -3415,12 +3415,12 @@ NIL
 (-871 S R E |VarSet|) 
 ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-832))) (|HasAttribute| |#2| (QUOTE -4188)) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#4| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#4| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-779)))) 
+((|HasCategory| |#2| (QUOTE (-832))) (|HasAttribute| |#2| (QUOTE -4190)) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#4| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#4| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-779)))) 
 (-872 R E |VarSet|) 
 ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
 NIL 
-(-873 E V R P -1724) 
+(-873 E V R P -1725) 
 ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
@@ -3430,9 +3430,9 @@ NIL
 NIL 
 (-875 R) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4188)) (|HasCategory| |#1| (QUOTE (-421))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
-(-876 E V R P -1724) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(-876 E V R P -1725) 
 ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-421)))) 
@@ -3450,13 +3450,13 @@ NIL
 NIL 
 (-880 S) 
 ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-881) 
 ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) 
 NIL 
 NIL 
-(-882 -1724) 
+(-882 -1725) 
 ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) 
 NIL 
 NIL 
@@ -3470,1195 +3470,1199 @@ NIL
 NIL 
 (-885 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-6 -4188)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-123)))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4188))) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-123)))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4190))) 
 (-886 A B) 
 ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) 
-((-4187 -12 (|has| |#2| (-442)) (|has| |#1| (-442)))) 
-((-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))))) 
-(-887 S) 
+((-4189 -12 (|has| |#2| (-442)) (|has| |#1| (-442)))) 
+((-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))))) 
+(-887) 
+((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,{}q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,{}q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}."))) 
+NIL 
+NIL 
+(-888 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,{}q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) 
-((-4190 . T) (-4191 . T) (-2180 . T)) 
+((-4192 . T) (-4193 . T) (-2181 . T)) 
 NIL 
-(-888 R |polR|) 
+(-889 R |polR|) 
 ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-421)))) 
-(-889) 
+(-890) 
 ((|constructor| (NIL "\\indented{1}{Partition is an OrderedCancellationAbelianMonoid which is used} as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|coerce| (((|List| (|Integer|)) $) "\\spad{coerce(p)} coerces a partition into a list of integers")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(\\spad{li})} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(\\spad{li})} converts a list of integers \\spad{li} to a partition"))) 
 NIL 
 NIL 
-(-890 S |Coef| |Expon| |Var|) 
+(-891 S |Coef| |Expon| |Var|) 
 ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) 
 NIL 
 NIL 
-(-891 |Coef| |Expon| |Var|) 
+(-892 |Coef| |Expon| |Var|) 
 ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4184 . T) (-4185 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-892) 
+(-893) 
 ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-893 S R E |VarSet| P) 
+(-894 S R E |VarSet| P) 
 ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-509)))) 
-(-894 R E |VarSet| P) 
+(-895 R E |VarSet| P) 
 ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
-((-4190 . T) (-2180 . T)) 
+((-4192 . T) (-2181 . T)) 
 NIL 
-(-895 R E V P) 
+(-896 R E V P) 
 ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) 
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 ((-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-278)))) (|HasCategory| |#1| (QUOTE (-421)))) 
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 ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m,{} v)} returns \\spad{[[C_1,{} g_1],{}...,{}[C_k,{} g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,{}...,{}C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M,{} A,{} sig,{} der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M,{} sig,{} der)} returns \\spad{[R,{} A,{} A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) 
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-(-897 |VarSet| E RC P) 
+(-898 |VarSet| E RC P) 
 ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{gcd} domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) 
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-(-898 R) 
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 ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
-(-899 R1 R2) 
+(-900 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) 
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-(-900 R) 
+(-901 R) 
 ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) 
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-(-901 K) 
+(-902 K) 
 ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns \\spad{csc}(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,{}n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-902 R E OV PPR) 
+(-903 R E OV PPR) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-903 K R UP -1724) 
+(-904 K R UP -1725) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) 
 NIL 
 NIL 
-(-904 |vl| |nv|) 
+(-905 |vl| |nv|) 
 ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) 
 NIL 
 NIL 
-(-905 R |Var| |Expon| |Dpoly|) 
+(-906 R |Var| |Expon| |Dpoly|) 
 ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{^=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-278))))) 
-(-906 R E V P TS) 
+(-907 R E V P TS) 
 ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-907) 
+(-908) 
 ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,{}\"a\")} creates a new equation."))) 
 NIL 
 NIL 
-(-908 A B R S) 
+(-909 A B R S) 
 ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) 
 NIL 
 NIL 
-(-909 A S) 
+(-910 A S) 
 ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-1075)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1051)))) 
-(-910 S) 
+((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1052)))) 
+(-911 S) 
 ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) 
-((-2180 . T) (-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-2181 . T) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-911 |n| K) 
+(-912 |n| K) 
 ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-912 S) 
+(-913 S) 
 ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) 
-((-4190 . T) (-4191 . T) (-2180 . T)) 
+((-4192 . T) (-4193 . T) (-2181 . T)) 
 NIL 
-(-913 S R) 
+(-914 S R) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-971))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-262)))) 
-(-914 R) 
+((|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-262)))) 
+(-915 R) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
-((-4183 |has| |#1| (-262)) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 |has| |#1| (-262)) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-915 QR R QS S) 
+(-916 QR R QS S) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) 
 NIL 
 NIL 
-(-916 R) 
+(-917 R) 
 ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) 
-((-4183 |has| |#1| (-262)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-262))) (-3745 (|HasCategory| |#1| (QUOTE (-262))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1075)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-502))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))))) 
-(-917 S) 
-((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4185 |has| |#1| (-262)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-262))) (-3747 (|HasCategory| |#1| (QUOTE (-262))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-502))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))))) 
 (-918 S) 
+((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-919 S) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-919) 
+(-920) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-920 -1724 UP UPUP |radicnd| |n|) 
+(-921 -1725 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
-((-4183 |has| (-377 |#2|) (-333)) (-4188 |has| (-377 |#2|) (-333)) (-4182 |has| (-377 |#2|) (-333)) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3745 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3745 (|HasCategory| (-377 |#2|) (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3745 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3745 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) 
-(-921 |bb|) 
+((-4185 |has| (-377 |#2|) (-333)) (-4190 |has| (-377 |#2|) (-333)) (-4184 |has| (-377 |#2|) (-333)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3747 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3747 (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3747 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3747 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) 
+(-922 |bb|) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -953) (QUOTE (-1075)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-938))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1051))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1075)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3745 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) 
-(-922) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-939))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1052))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3747 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) 
+(-923) 
 ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) 
 NIL 
 NIL 
-(-923) 
+(-924) 
 ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) 
 NIL 
 NIL 
-(-924 RP) 
+(-925 RP) 
 ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) 
 NIL 
 NIL 
-(-925 S) 
+(-926 S) 
 ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) 
 NIL 
 NIL 
-(-926 A S) 
+(-927 A S) 
 ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4191)) (|HasCategory| |#2| (QUOTE (-1004)))) 
-(-927 S) 
+((|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#2| (QUOTE (-1005)))) 
+(-928 S) 
 ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
-(-928 S) 
+(-929 S) 
 ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) 
 NIL 
 NIL 
-(-929) 
+(-930) 
 ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) 
-((-4183 . T) (-4188 . T) (-4182 . T) (-4185 . T) (-4184 . T) ((-4192 "*") . T) (-4187 . T)) 
+((-4185 . T) (-4190 . T) (-4184 . T) (-4187 . T) (-4186 . T) ((-4194 "*") . T) (-4189 . T)) 
 NIL 
-(-930 R -1724) 
+(-931 R -1725) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n,{} f,{} g,{} x,{} lim,{} ext)} returns \\spad{[y,{} h,{} b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) 
 NIL 
 NIL 
-(-931 R -1724) 
+(-932 R -1725) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n,{} f,{} g_1,{} g_2,{} x,{}lim,{}ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,{}dy2/dx) + ((0,{} - n df/dx),{}(n df/dx,{}0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) 
 NIL 
 NIL 
-(-932 -1724 UP) 
+(-933 -1725 UP) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a,{} B,{} C,{} n,{} D)} returns either: 1. \\spad{[Q,{} b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1,{} C1,{} m,{} \\alpha,{} \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f,{} g)} returns a \\spad{[y,{} b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,{}g,{}D)} returns \\spad{[A,{} B,{} C,{} T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-933 -1724 UP) 
+(-934 -1725 UP) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f,{} g1,{} g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,{}g1,{}g2,{}D)} returns \\spad{[A,{} B,{} H,{} C1,{} C2,{} T]} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} has a solution if and only if \\spad{y1 = Q1 / T,{} y2 = Q2 / T},{} where \\spad{B,{}C1,{}C2,{}Q1,{}Q2} have no normal poles and satisfy A \\spad{(Q1',{} Q2') + ((H,{} -B),{} (B,{} H)) (Q1,{}Q2) = (C1,{}C2)} \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-934 S) 
+(-935 S) 
 ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,{}u,{}n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) 
 NIL 
 NIL 
-(-935 F1 UP UPUP R F2) 
+(-936 F1 UP UPUP R F2) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,{}u,{}g)} \\undocumented"))) 
 NIL 
 NIL 
-(-936 |Pol|) 
+(-937 |Pol|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) 
 NIL 
 NIL 
-(-937 |Pol|) 
+(-938 |Pol|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) 
 NIL 
 NIL 
-(-938) 
+(-939) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-939) 
+(-940) 
 ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,{}lv,{}eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) 
 NIL 
 NIL 
-(-940 |TheField|) 
+(-941 |TheField|) 
 ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) 
-((-4183 . T) (-4188 . T) (-4182 . T) (-4185 . T) (-4184 . T) ((-4192 "*") . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -953) (QUOTE (-517)))) (-3745 (|HasCategory| (-377 (-517)) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))))) 
-(-941 -1724 L) 
+((-4185 . T) (-4190 . T) (-4184 . T) (-4187 . T) (-4186 . T) ((-4194 "*") . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -954) (QUOTE (-517)))) (-3747 (|HasCategory| (-377 (-517)) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))))) 
+(-942 -1725 L) 
 ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) 
 NIL 
 NIL 
-(-942 S) 
+(-943 S) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,{}m)} same as \\spad{setelt(n,{}m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,{}m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1004)))) 
-(-943 R E V P) 
+((|HasCategory| |#1| (QUOTE (-1005)))) 
+(-944 R E V P) 
 ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1004))) (-12 (|HasCategory| |#4| (QUOTE (-1004))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) 
-(-944 R) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1005))) (-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) 
+(-945 R) 
 ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE (-4192 "*")))) 
-(-945 R) 
+((|HasAttribute| |#1| (QUOTE (-4194 "*")))) 
+(-946 R) 
 ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-278)))) 
-(-946 S) 
+(-947 S) 
 ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i,{} r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-947) 
+(-948) 
 ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) 
 NIL 
 NIL 
-(-948 S) 
+(-949 S) 
 ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r,{} i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-949 S) 
+(-950 S) 
 ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) 
 NIL 
 NIL 
-(-950 -1724 |Expon| |VarSet| |FPol| |LFPol|) 
+(-951 -1725 |Expon| |VarSet| |FPol| |LFPol|) 
 ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) 
-(((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+(((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-951) 
+(-952) 
 ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (QUOTE (-1004))) (-12 (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (QUOTE (-1075))) (LIST (QUOTE |:|) (QUOTE -1860) (QUOTE (-51))))))) (|HasCategory| (-1075) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1004))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (QUOTE (-1004))) (|HasCategory| (-51) (QUOTE (-1004)))) (-12 (|HasCategory| (-51) (QUOTE (-1004))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1004))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-952 A S) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (QUOTE (-1076))) (LIST (QUOTE |:|) (QUOTE -1859) (QUOTE (-51))))))) (|HasCategory| (-1076) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-51) (QUOTE (-1005)))) (-12 (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-953 A S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%."))) 
 NIL 
 NIL 
-(-953 S) 
+(-954 S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#1|) "\\spad{coerce(a)} transforms a into an element of \\%."))) 
 NIL 
 NIL 
-(-954 Q R) 
+(-955 Q R) 
 ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) 
 NIL 
 NIL 
-(-955) 
+(-956) 
 ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,{}m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,{}m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,{}g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,{}g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) 
 NIL 
 NIL 
-(-956 UP) 
+(-957 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-957 R) 
+(-958 R) 
 ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) 
 NIL 
 NIL 
-(-958 R) 
+(-959 R) 
 ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
-(-959 R |ls|) 
+(-960 R |ls|) 
 ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-712 |#1| (-789 |#2|)) (QUOTE (-1004))) (-12 (|HasCategory| (-712 |#1| (-789 |#2|)) (QUOTE (-1004))) (|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -712) (|devaluate| |#1|) (LIST (QUOTE -789) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| (-789 |#2|) (QUOTE (-338))) (|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -557) (QUOTE (-787))))) 
-(-960) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-712 |#1| (-789 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-712 |#1| (-789 |#2|)) (QUOTE (-1005))) (|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -712) (|devaluate| |#1|) (LIST (QUOTE -789) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| (-789 |#2|) (QUOTE (-338))) (|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -557) (QUOTE (-787))))) 
+(-961) 
 ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) 
 NIL 
 NIL 
-(-961 S) 
+(-962 S) 
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) 
 NIL 
 NIL 
-(-962) 
+(-963) 
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) 
-((-4187 . T)) 
+((-4189 . T)) 
 NIL 
-(-963 |xx| -1724) 
+(-964 |xx| -1725) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-964 S |m| |n| R |Row| |Col|) 
+(-965 S |m| |n| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) 
 NIL 
 ((|HasCategory| |#4| (QUOTE (-278))) (|HasCategory| |#4| (QUOTE (-333))) (|HasCategory| |#4| (QUOTE (-509))) (|HasCategory| |#4| (QUOTE (-156)))) 
-(-965 |m| |n| R |Row| |Col|) 
+(-966 |m| |n| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) 
-((-4190 . T) (-2180 . T) (-4185 . T) (-4184 . T)) 
+((-4192 . T) (-2181 . T) (-4187 . T) (-4186 . T)) 
 NIL 
-(-966 |m| |n| R) 
+(-967 |m| |n| R) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) 
-((-4190 . T) (-4185 . T) (-4184 . T)) 
-((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-1004))) (|HasCategory| |#3| (QUOTE (-278))) (|HasCategory| |#3| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-156))) (-3745 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-333)))) (|HasCategory| |#3| (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| |#3| (QUOTE (-1004))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3745 (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1004))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))))) 
-(-967 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-4192 . T) (-4187 . T) (-4186 . T)) 
+((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (QUOTE (-278))) (|HasCategory| |#3| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-156))) (-3747 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-333)))) (|HasCategory| |#3| (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3747 (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))))) 
+(-968 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-968 R) 
+(-969 R) 
 ((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ $ |#1|) "\\spad{x*r} returns the right multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) 
 NIL 
 NIL 
-(-969) 
+(-970) 
 ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline"))) 
 NIL 
 NIL 
-(-970 S) 
+(-971 S) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-971) 
+(-972) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-972 |TheField| |ThePolDom|) 
+(-973 |TheField| |ThePolDom|) 
 ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-973) 
+(-974) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|convert| (($ (|Symbol|)) "\\spad{convert(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) 
-((-4178 . T) (-4182 . T) (-4177 . T) (-4188 . T) (-4189 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4180 . T) (-4184 . T) (-4179 . T) (-4190 . T) (-4191 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-974) 
+(-975) 
 ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (QUOTE (-1004))) (-12 (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (QUOTE (-1075))) (LIST (QUOTE |:|) (QUOTE -1860) (QUOTE (-51))))))) (|HasCategory| (-1075) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1004))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (QUOTE (-1004))) (|HasCategory| (-51) (QUOTE (-1004)))) (-12 (|HasCategory| (-51) (QUOTE (-1004))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1004))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1075)) (|:| -1860 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-975 S R E V) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (QUOTE (-1076))) (LIST (QUOTE |:|) (QUOTE -1859) (QUOTE (-51))))))) (|HasCategory| (-1076) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-51) (QUOTE (-1005)))) (-12 (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-976 S R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (LIST (QUOTE -37) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-1075))))) 
-(-976 R E V) 
+((|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (LIST (QUOTE -37) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-1076))))) 
+(-977 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
 NIL 
-(-977 S |TheField| |ThePols|) 
+(-978 S |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) 
 NIL 
 NIL 
-(-978 |TheField| |ThePols|) 
+(-979 |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) 
 NIL 
 NIL 
-(-979 R E V P TS) 
+(-980 R E V P TS) 
 ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{gcd} need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-980 S R E V P) 
+(-981 S R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#5| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) 
 NIL 
 NIL 
-(-981 R E V P) 
+(-982 R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
-(-982 R E V P TS) 
+(-983 R E V P TS) 
 ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-983 |f|) 
+(-984 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-984 |Base| R -1724) 
+(-985 |Base| R -1725) 
 ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) 
 NIL 
 NIL 
-(-985 |Base| R -1724) 
+(-986 |Base| R -1725) 
 ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,{}...,{}rn])} creates the rule set \\spad{{r1,{}...,{}rn}}."))) 
 NIL 
 NIL 
-(-986 R |ls|) 
+(-987 R |ls|) 
 ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,{}univ?,{}check?)} returns the same as \\spad{rur(lp,{}true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,{}true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,{}univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,{}univ?)} returns a list of items \\spad{[u,{}lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,{}lc]} in \\spad{rur(lp,{}univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) 
 NIL 
 NIL 
-(-987 UP SAE UPA) 
+(-988 UP SAE UPA) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-988 R UP M) 
+(-989 R UP M) 
 ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) 
-((-4183 |has| |#1| (-333)) (-4188 |has| |#1| (-333)) (-4182 |has| |#1| (-333)) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
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-(-989 UP SAE UPA) 
+((-4185 |has| |#1| (-333)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076))))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-319))))) 
+(-990 UP SAE UPA) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-990) 
+(-991) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-991 S) 
+(-992 S) 
 ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(x,{} y)} to determine whether \\spad{x < y (f(x,{}y) < 0),{} x = y (f(x,{}y) = 0)},{} or \\spad{x > y (f(x,{}y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) 
 NIL 
 NIL 
-(-992 R) 
+(-993 R) 
 ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) 
 NIL 
 NIL 
-(-993 R) 
+(-994 R) 
 ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-994 (-1075)) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-994 (-1075)) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-994 (-1075)) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-994 (-1075)) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-994 (-1075)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#1| (QUOTE (-333))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4188)) (|HasCategory| |#1| (QUOTE (-421))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
-(-994 S) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-995 (-1076)) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-995 (-1076)) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-995 (-1076)) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-995 (-1076)) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-995 (-1076)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(-995 S) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) 
 NIL 
 NIL 
-(-995 R S) 
+(-996 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l),{} f(l+k),{}...,{} f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}l..h)} returns a new segment \\spad{f(l)..f(h)}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-777)))) 
-(-996 R S) 
+(-997 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-997 S) 
+(-998 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions.")) (|segment| (((|Segment| |#1|) $) "\\spad{segment(segb)} returns the segment from the right hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{segment(segb)} returns \\spad{a..b}.")) (|variable| (((|Symbol|) $) "\\spad{variable(segb)} returns the variable from the left hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{variable(segb)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) (|Segment| |#1|)) "\\spad{equation(v,{}a..b)} creates a segment binding value with variable \\spad{v} and segment \\spad{a..b}. Note that the interpreter parses \\spad{v=a..b} to this form."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1004)))) 
-(-998 S) 
+((|HasCategory| |#1| (QUOTE (-1005)))) 
+(-999 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
-(-999 S) 
+(-1000 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1004)))) 
-(-1000 S L) 
+((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1005)))) 
+(-1001 S L) 
 ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l),{} f(l+k),{} ...,{} f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l,{} l+k,{} ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,{}3,{}5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
-(-1001 A S) 
+(-1002 A S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1002 S) 
+(-1003 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
-((-4180 . T) (-2180 . T)) 
+((-4182 . T) (-2181 . T)) 
 NIL 
-(-1003 S) 
+(-1004 S) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1004) 
+(-1005) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1005 |m| |n|) 
+(-1006 |m| |n|) 
 ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) 
 NIL 
 NIL 
-(-1006 S) 
+(-1007 S) 
 ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) 
-((-4190 . T) (-4180 . T) (-4191 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) 
-(-1007 |Str| |Sym| |Int| |Flt| |Expr|) 
+((-4192 . T) (-4182 . T) (-4193 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) 
+(-1008 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) 
 NIL 
 NIL 
-(-1008) 
+(-1009) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1009 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1010 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) 
 NIL 
 NIL 
-(-1010 R FS) 
+(-1011 R FS) 
 ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,{}ftype,{}body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program."))) 
 NIL 
 NIL 
-(-1011 R E V P TS) 
+(-1012 R E V P TS) 
 ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(\\spad{ts},{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-1012 R E V P TS) 
+(-1013 R E V P TS) 
 ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1013 R E V P) 
+(-1014 R E V P) 
 ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,{}mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
-(-1014) 
+(-1015) 
 ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) 
 NIL 
 NIL 
-(-1015 S) 
+(-1016 S) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (^ (($ $ (|PositiveInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1016) 
+(-1017) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (^ (($ $ (|PositiveInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1017 |dimtot| |dim1| S) 
+(-1018 |dimtot| |dim1| S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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-(-1018 R |x|) 
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(QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-963)))) (-3747 (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -823) (QUOTE (-1076))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-25)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-123)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-156)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-207)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-333)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-338)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-725)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-777)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-963)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-1005))))) (-3747 (-12 (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-777))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-963))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517)))))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3747 (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-777))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-963))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -823) (QUOTE (-1076)))))) (|HasCategory| |#3| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#3| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-1005)))) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (QUOTE (-963)))) (-12 (|HasCategory| |#3| (QUOTE (-963))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-963))) (|HasCategory| |#3| (LIST (QUOTE -823) (QUOTE (-1076))))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-1019 R |x|) 
 ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-421)))) 
-(-1019 R -1724) 
+(-1020 R -1725) 
 ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1020 R) 
+(-1021 R) 
 ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1021) 
+(-1022) 
 ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) 
 NIL 
 NIL 
-(-1022) 
+(-1023) 
 ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (~ (($ $) "\\spad{~ n} returns the bit-by-bit logical {\\em not } of the single integer \\spad{n}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|min| (($) "\\spad{min()} returns the smallest single integer.")) (|max| (($) "\\spad{max()} returns the largest single integer.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) 
-((-4178 . T) (-4182 . T) (-4177 . T) (-4188 . T) (-4189 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4180 . T) (-4184 . T) (-4179 . T) (-4190 . T) (-4191 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-1023 S) 
+(-1024 S) 
 ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-4190 . T) (-4191 . T) (-2180 . T)) 
+((-4192 . T) (-4193 . T) (-2181 . T)) 
 NIL 
-(-1024 S |ndim| R |Row| |Col|) 
+(-1025 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-333))) (|HasAttribute| |#3| (QUOTE (-4192 "*"))) (|HasCategory| |#3| (QUOTE (-156)))) 
-(-1025 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-333))) (|HasAttribute| |#3| (QUOTE (-4194 "*"))) (|HasCategory| |#3| (QUOTE (-156)))) 
+(-1026 |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) 
-((-2180 . T) (-4190 . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-2181 . T) (-4192 . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-1026 R |Row| |Col| M) 
+(-1027 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,{}B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-1027 R |VarSet|) 
+(-1028 R |VarSet|) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4188)) (|HasCategory| |#1| (QUOTE (-421))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
-(-1028 |Coef| |Var| SMP) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(-1029 |Coef| |Var| SMP) 
 ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) 
-(-1029 R E V P) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) 
+(-1030 R E V P) 
 ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
-(-1030 UP -1724) 
+(-1031 UP -1725) 
 ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,{}g,{}h,{}i,{}k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,{}g,{}h,{}j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,{}g,{}h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,{}g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,{}g,{}h,{}i,{}j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,{}g,{}h,{}i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,{}g,{}h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,{}g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,{}f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) 
 NIL 
 NIL 
-(-1031 R) 
+(-1032 R) 
 ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,{}lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,{}x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) 
 NIL 
 NIL 
-(-1032 R) 
+(-1033 R) 
 ((|constructor| (NIL "This package finds the function func3 where func1 and func2 \\indented{1}{are given and\\space{2}func1 = func3(func2) .\\space{2}If there is no solution then} \\indented{1}{function func1 will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect,{} var,{} n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1,{} func2,{} newvar)} returns a function func3 where \\spad{func1} = func3(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) 
 NIL 
 NIL 
-(-1033 R) 
+(-1034 R) 
 ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs,{} lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,{}x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,{}x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) 
 NIL 
 NIL 
-(-1034 S A) 
+(-1035 S A) 
 ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,{}f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,{}f)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-779)))) 
-(-1035 R) 
+(-1036 R) 
 ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) 
 NIL 
 NIL 
-(-1036 R) 
+(-1037 R) 
 ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} creates a surface defined over a list of curves,{} \\spad{p0} through \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); close2 set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through \\spad{pn},{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if close2 is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and close2 indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument close2 equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} [props],{} prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{}[props],{}prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,{}p1,{}...,{}pn])} creates a polygon defined by a list of points,{} \\spad{p0} through \\spad{pn},{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,{}[[r0],{}[r1],{}...,{}[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,{}[p0,{}p1,{}...,{}pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,{}R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,{}[[lr0],{}[lr1],{}...,{}[lrn],{}[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,{}[p0,{}p1,{}...,{}pn,{}p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,{}p1,{}p2,{}...,{}pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,{}[[p0],{}[p1],{}...,{}[pn]])} adds a space curve which is a list of points \\spad{p0} through \\spad{pn} defined by lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,{}[p0,{}p1,{}...,{}pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,{}i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,{}[x,{}y,{}z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,{}p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,{}i,{}p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,{}[p0,{}p1,{}...,{}pn])} adds a list of points from \\spad{p0} through \\spad{pn} to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,{}s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) 
 NIL 
 NIL 
-(-1037) 
+(-1038) 
 ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) 
 NIL 
 NIL 
-(-1038) 
+(-1039) 
 ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,{}o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) 
 NIL 
 NIL 
-(-1039) 
+(-1040) 
 ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,{}z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,{}z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,{}z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,{}z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,{}x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,{}x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,{}x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) 
 NIL 
 NIL 
-(-1040 V C) 
+(-1041 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}o2)} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}o1,{}o2)} returns \\spad{true} iff \\axiom{o1(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{vt}.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) 
 NIL 
 NIL 
-(-1041 V C) 
+(-1042 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| (-1040 |#1| |#2|) (QUOTE (-1004))) (-12 (|HasCategory| (-1040 |#1| |#2|) (LIST (QUOTE -280) (LIST (QUOTE -1040) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1040 |#1| |#2|) (QUOTE (-1004)))) (|HasCategory| (-1040 |#1| |#2|) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-1040 |#1| |#2|) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-1040 |#1| |#2|) (LIST (QUOTE -280) (LIST (QUOTE -1040) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1040 |#1| |#2|) (QUOTE (-1004)))))) 
-(-1042 |ndim| R) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| (-1041 |#1| |#2|) (QUOTE (-1005))) (-12 (|HasCategory| (-1041 |#1| |#2|) (LIST (QUOTE -280) (LIST (QUOTE -1041) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1041 |#1| |#2|) (QUOTE (-1005)))) (|HasCategory| (-1041 |#1| |#2|) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-1041 |#1| |#2|) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-1041 |#1| |#2|) (LIST (QUOTE -280) (LIST (QUOTE -1041) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1041 |#1| |#2|) (QUOTE (-1005)))))) 
+(-1043 |ndim| R) 
 ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|coerce| (((|Matrix| |#2|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{SquareMatrix} to a matrix of type \\spadtype{Matrix}.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}."))) 
-((-4187 . T) (-4179 |has| |#2| (-6 (-4192 "*"))) (-4190 . T) (-4184 . T) (-4185 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4192 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-333))) (-3745 (|HasAttribute| |#2| (QUOTE (-4192 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3745 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1075)))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-156)))) 
-(-1043 S) 
+((-4189 . T) (-4181 |has| |#2| (-6 (-4194 "*"))) (-4192 . T) (-4186 . T) (-4187 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4194 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-333))) (-3747 (|HasAttribute| |#2| (QUOTE (-4194 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3747 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-156)))) 
+(-1044 S) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1044) 
+(-1045) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
-(-1045 R E V P TS) 
+(-1046 R E V P TS) 
 ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1046 R E V P) 
+(-1047 R E V P) 
 ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1004))) (-12 (|HasCategory| |#4| (QUOTE (-1004))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) 
-(-1047 S) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1005))) (-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) 
+(-1048 S) 
 ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-1048 A S) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-1049 A S) 
 ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) 
 NIL 
 NIL 
-(-1049 S) 
+(-1050 S) 
 ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
-(-1050 |Key| |Ent| |dent|) 
+(-1051 |Key| |Ent| |dent|) 
 ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) 
-((-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1004))) (-12 (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (-12 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1860) (|devaluate| |#2|)))))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-1004)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-1051) 
+((-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-1052) 
 ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) 
 NIL 
 NIL 
-(-1052 |Coef|) 
+(-1053 |Coef|) 
 ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-1053 S) 
+(-1054 S) 
 ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,{}u)}."))) 
 NIL 
 NIL 
-(-1054 A B) 
+(-1055 A B) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,{}f,{}u)},{} where \\spad{u} is a finite stream \\spad{[x0,{}x1,{}...,{}xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,{}b),{} r1 = f(x1,{}r0),{}...,{} r(n) = f(xn,{}r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,{}h,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[y0,{}y1,{}y2,{}...]},{} where \\spad{y0 = h(x0,{}b)},{} \\spad{y1 = h(x1,{}y0)},{}\\spad{...} \\spad{yn = h(xn,{}y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,{}s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}...]) = [f(x0),{}f(x1),{}f(x2),{}..]}."))) 
 NIL 
 NIL 
-(-1055 A B C) 
+(-1056 A B C) 
 ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}st1,{}st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}..],{}[y0,{}y1,{}y2,{}..]) = [f(x0,{}y0),{}f(x1,{}y1),{}..]}."))) 
 NIL 
 NIL 
-(-1056 S) 
+(-1057 S) 
 ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) 
-((-4191 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-1057) 
+((-4193 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-1058) 
 ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
-(-1058) 
+(-1059) 
 NIL 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1004))) (-12 (|HasCategory| (-131) (QUOTE (-1004))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3745 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1004))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787))))) 
-(-1059 |Entry|) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1005))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3747 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787))))) 
+(-1060 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (QUOTE (-1004))) (-12 (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (QUOTE (-1058))) (LIST (QUOTE |:|) (QUOTE -1860) (|devaluate| |#1|)))))) (|HasCategory| (-1058) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-1004)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) (-3745 (|HasCategory| (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-1060 A) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (QUOTE (-1059))) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#1|)))))) (|HasCategory| (-1059) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-1061 A) 
 ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) 
-(-1061 |Coef|) 
+(-1062 |Coef|) 
 ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) 
 NIL 
 NIL 
-(-1062 |Coef|) 
+(-1063 |Coef|) 
 ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) 
 NIL 
 NIL 
-(-1063 R UP) 
+(-1064 R UP) 
 ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p,{} q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p,{} q)} returns \\spad{[p0,{}...,{}pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p,{} q)}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-278)))) 
-(-1064 |n| R) 
+(-1065 |n| R) 
 ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,{}\\spad{li})} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,{}\\spad{li},{}p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,{}\\spad{li},{}b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,{}ind,{}p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,{}\\spad{li},{}i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,{}\\spad{li},{}p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,{}s2,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,{}p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,{}\\spad{li},{}i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,{}s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,{}n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-1065 S1 S2) 
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 ((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} makes a form \\spad{s:t}"))) 
 NIL 
 NIL 
-(-1066 |Coef| |var| |cen|) 
+(-1067 |Coef| |var| |cen|) 
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(QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-156)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-333)))) (-3747 (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-333))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-3747 (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-939))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (LIST (QUOTE -258) (LIST (QUOTE -1074) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1074) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (LIST (QUOTE -280) (LIST (QUOTE -1074) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 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-37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|)))))) (-3747 (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-333)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1074 |#1| |#2| |#3|) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(-1068 R -1725) 
 ((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n),{} n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) 
 NIL 
 NIL 
-(-1068 R) 
+(-1069 R) 
 ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) 
 NIL 
 NIL 
-(-1069 R S) 
+(-1070 R S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-1070 E OV R P) 
+(-1071 E OV R P) 
 ((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) 
 NIL 
 NIL 
-(-1071 R) 
+(-1072 R) 
 ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{}var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4186 |has| |#1| (-333)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-990) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4188)) (|HasCategory| |#1| (QUOTE (-421))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
-(-1072 |Coef| |var| |cen|) 
-((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4182 |has| |#1| (-333)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-333))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2269) (LIST (|devaluate| |#1|) (QUOTE (-1075)))))) (-3745 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1096))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -1518) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1075))))) (|HasSignature| |#1| (LIST (QUOTE -2096) (LIST (LIST (QUOTE -583) (QUOTE (-1075))) (|devaluate| |#1|))))))) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-991) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-1073 |Coef| |var| |cen|) 
+((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) 
+(-1074 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1016))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2269) (LIST (|devaluate| |#1|) (QUOTE (-1075)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3745 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1096))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -1518) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1075))))) (|HasSignature| |#1| (LIST (QUOTE -2096) (LIST (LIST (QUOTE -583) (QUOTE (-1075))) (|devaluate| |#1|))))))) 
-(-1074) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1017))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) 
+(-1075) 
 ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-1075) 
+(-1076) 
 ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,{}[a1,{}...,{}an])} or \\spad{s}([a1,{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s,{} [a1,{}...,{}an])} returns \\spad{s} arg-scripted by \\spad{[a1,{}...,{}an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s,{} [a1,{}...,{}an])} returns \\spad{s} superscripted by \\spad{[a1,{}...,{}an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s,{} [a1,{}...,{}an])} returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s,{} [a,{}b,{}c])} is equivalent to \\spad{script(s,{}[a,{}b,{}c,{}[],{}[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts the string \\spad{s} to a symbol.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) 
 NIL 
 NIL 
-(-1076 R) 
+(-1077 R) 
 ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r,{} n)} returns the vector of the elementary symmetric functions in \\spad{[r,{}r,{}...,{}r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,{}...,{}rn])} returns the vector of the elementary symmetric functions in the \\spad{\\spad{ri}'s}: \\spad{[r1 + ... + rn,{} r1 r2 + ... + r(n-1) rn,{} ...,{} r1 r2 ... rn]}."))) 
 NIL 
 NIL 
-(-1077 R) 
+(-1078 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-6 -4188)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| (-889) (QUOTE (-123))) (|HasCategory| |#1| (QUOTE (-509)))) (-3745 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4188))) 
-(-1078) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| (-890) (QUOTE (-123))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4190))) 
+(-1079) 
 ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) 
 NIL 
 NIL 
-(-1079) 
+(-1080) 
 ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,{}tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,{}tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,{}t,{}tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,{}t,{}tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) 
 NIL 
 NIL 
-(-1080) 
-((|constructor| (NIL "\\indented{1}{This domain provides a simple,{} general,{} and arguably} complete representation of Spad programs as objects of a term algebra built from ground terms of type boolean,{} integers,{} foats,{} symbols,{} and strings. This domain differs from InputForm in that it represents any entity from a Spad program,{} not just expressions. Related Constructors: Boolean,{} Integer,{} Float,{} symbol,{} String,{} SExpression. See Also: SExpression.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} is \\spad{x} really is a String") (((|Boolean|) $ (|[\|\|]| (|Symbol|))) "\\spad{x case Symbol} is \\spad{true} is \\spad{x} really is a Symbol") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} is \\spad{x} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} is \\spad{x} really is an Integer")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Symbol|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The return value is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Symbol|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extract the string value \\spad{`s'} from the syntax domain") (((|Symbol|) $) "\\spad{coerce(s)} extracts the symbol \\spad{`s'} from the Syntax domain.") (((|DoubleFloat|) $) "\\spad{coerce(f)} extracts the float value \\spad{`f'} from the Syntax domain") (((|Integer|) $) "\\spad{coerce(i)} extracts the integer value `i' from the Syntax domain")) (|autoCoerce| (($ (|String|)) "\\spad{autoCoerce(s)} injects the string value \\spad{`s'} into the syntax domain") (($ (|Symbol|)) "\\spad{autoCoerce(s)} injects the symbol \\spad{`s'} into the Syntax domain.") (($ (|DoubleFloat|)) "\\spad{autoCoerce(f)} injects the float value \\spad{`f'} into the Syntax domain") (($ (|Integer|)) "\\spad{autoCoerce(i)} injects the integer value `i' into the Syntax domain")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cell ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
+(-1081) 
+((|constructor| (NIL "\\indented{1}{This domain provides a simple,{} general,{} and arguably} complete representation of Spad programs as objects of a term algebra built from ground terms of type boolean,{} integers,{} foats,{} symbols,{} and strings. This domain differs from InputForm in that it represents any entity from a Spad program,{} not just expressions. Related Constructors: Boolean,{} Integer,{} Float,{} symbol,{} String,{} SExpression. See Also: SExpression.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} is \\spad{x} really is a String") (((|Boolean|) $ (|[\|\|]| (|Symbol|))) "\\spad{x case Symbol} is \\spad{true} is \\spad{x} really is a Symbol") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} is \\spad{x} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} is \\spad{x} really is an Integer")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Symbol|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The return value is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Symbol|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Symbol|) $) "\\spad{autoCoerce(s)} forcibly extracts a symbo from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (($ (|String|)) "\\spad{coerce(s)} injects the string value \\spad{`s'} into the syntax domain") (((|Symbol|) $) "\\spad{coerce(s)} extracts a symbol from the syntax \\spad{`s'}.") (($ (|Symbol|)) "\\spad{coerce(s)} injects the symbol \\spad{`s'} into the Syntax domain.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (($ (|DoubleFloat|)) "\\spad{coerce(f)} injects the float value \\spad{`f'} into the Syntax domain") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}") (($ (|Integer|)) "\\spad{coerce(i)} injects the integer value `i' into the Syntax domain")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cell ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1081 R) 
+(-1082 R) 
 ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,{}lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,{}v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,{}v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,{}lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) 
 NIL 
 NIL 
-(-1082 S) 
+(-1083 S) 
 ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,{}b,{}c,{}d,{}e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,{}llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,{}pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,{}pr,{}r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) 
 NIL 
 NIL 
-(-1083 S) 
+(-1084 S) 
 ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) 
 NIL 
 NIL 
-(-1084 |Key| |Entry|) 
+(-1085 |Key| |Entry|) 
 ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) 
-((-4190 . T) (-4191 . T)) 
-((|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (-12 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2581) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1860) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1004))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-1004)))) (-12 (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (QUOTE (-1004))) (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3745 (|HasCategory| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-1085 R) 
+((-4192 . T) (-4193 . T)) 
+((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-1086 R) 
 ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) 
 NIL 
 NIL 
-(-1086 S |Key| |Entry|) 
+(-1087 S |Key| |Entry|) 
 ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
 NIL 
 NIL 
-(-1087 |Key| |Entry|) 
+(-1088 |Key| |Entry|) 
 ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
-((-4191 . T) (-2180 . T)) 
+((-4193 . T) (-2181 . T)) 
 NIL 
-(-1088 |Key| |Entry|) 
+(-1089 |Key| |Entry|) 
 ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) 
 NIL 
 NIL 
-(-1089) 
+(-1090) 
 ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) 
 NIL 
 NIL 
-(-1090 S) 
+(-1091 S) 
 ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) 
 NIL 
 NIL 
-(-1091) 
+(-1092) 
 ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) 
 NIL 
 NIL 
-(-1092) 
+(-1093) 
 ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,{}\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,{}s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) 
 NIL 
 NIL 
-(-1093 R) 
+(-1094 R) 
 ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) 
 NIL 
 NIL 
-(-1094) 
+(-1095) 
 ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) 
 NIL 
 NIL 
-(-1095 S) 
+(-1096 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1096) 
+(-1097) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1097 S) 
-((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (QUOTE (-1004))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-1098 S) 
+((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-1099 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1099) 
+(-1100) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1100 R -1724) 
+(-1101 R -1725) 
 ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
-(-1101 R |Row| |Col| M) 
+(-1102 R |Row| |Col| M) 
 ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) 
 NIL 
 NIL 
-(-1102 R -1724) 
+(-1103 R -1725) 
 ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) 
 NIL 
 ((-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -809) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -809) (|devaluate| |#1|))))) 
-(-1103 S R E V P) 
+(-1104 S R E V P) 
 ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
 NIL 
 ((|HasCategory| |#4| (QUOTE (-338)))) 
-(-1104 R E V P) 
+(-1105 R E V P) 
 ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
-(-1105 |Coef|) 
+(-1106 |Coef|) 
 ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) 
-(-1106 |Curve|) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) 
+(-1107 |Curve|) 
 ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) 
 NIL 
 NIL 
-(-1107) 
+(-1108) 
 ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,{}n,{}b,{}r,{}lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,{}sin(n - 1) a],{}...,{}[cos 2 a,{}sin 2 a],{}[cos a,{}sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,{}q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,{}x2,{}x3,{}c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) 
 NIL 
 NIL 
-(-1108 S) 
+(-1109 S) 
 ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) 
-(-1109 -1724) 
+((|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) 
+(-1110 -1725) 
 ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,{}n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) 
 NIL 
 NIL 
-(-1110) 
+(-1111) 
 ((|constructor| (NIL "The fundamental Type."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
-(-1111 S) 
+(-1112 S) 
 ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l,{} fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a,{} b,{} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a,{} b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,{}...,{}bm],{}[a1,{}...,{}an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < \\spad{ai}}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,{}d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < \\spad{ai}\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b,{} c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-779)))) 
-(-1112) 
+(-1113) 
 ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,{}...,{}an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) 
 NIL 
 NIL 
-(-1113 S) 
+(-1114 S) 
 ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
 NIL 
 NIL 
-(-1114) 
+(-1115) 
 ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-1115 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1116 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1116 |Coef|) 
+(-1117 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,{}k1,{}k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,{}k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = n0..infinity,{}a[n] * x**n)) = sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
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 NIL 
-(-1117 S |Coef| UTS) 
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 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-333)))) 
-(-1118 |Coef| UTS) 
+(-1119 |Coef| UTS) 
 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) 
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 NIL 
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 ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) 
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 ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
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 ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) 
 NIL 
 NIL 
-(-1122 R S) 
+(-1123 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-777)))) 
-(-1123 S) 
+(-1124 S) 
 ((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1004)))) 
-(-1124 |x| R |y| S) 
+((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1005)))) 
+(-1125 |x| R |y| S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-1125 R Q UP) 
+(-1126 R Q UP) 
 ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) 
 NIL 
 NIL 
-(-1126 R UP) 
+(-1127 R UP) 
 ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,{}h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,{}d,{}c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,{}d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) 
 NIL 
 NIL 
-(-1127 R UP) 
+(-1128 R UP) 
 ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,{}g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) 
 NIL 
 NIL 
-(-1128 R U) 
+(-1129 R U) 
 ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,{}b,{}l,{}k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,{}b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,{}b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) 
 NIL 
 NIL 
-(-1129 |x| R) 
+(-1130 |x| R) 
 ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) 
-(((-4192 "*") |has| |#2| (-156)) (-4183 |has| |#2| (-509)) (-4186 |has| |#2| (-333)) (-4188 |has| |#2| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3745 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-990) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-990) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1075)))) (-3745 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE -4188)) (|HasCategory| |#2| (QUOTE (-421))) (-3745 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3745 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) 
-(-1130 R PR S PS) 
+(((-4194 "*") |has| |#2| (-156)) (-4185 |has| |#2| (-509)) (-4188 |has| |#2| (-333)) (-4190 |has| |#2| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-991) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (-3747 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE -4190)) (|HasCategory| |#2| (QUOTE (-421))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) 
+(-1131 R PR S PS) 
 ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) 
 NIL 
 NIL 
-(-1131 S R) 
+(-1132 S R) 
 ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-1051)))) 
-(-1132 R) 
+((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-1052)))) 
+(-1133 R) 
 ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4186 |has| |#1| (-333)) (-4188 |has| |#1| (-6 -4188)) (-4185 . T) (-4184 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) 
 NIL 
-(-1133 S |Coef| |Expon|) 
+(-1134 S |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1016))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2269) (LIST (|devaluate| |#2|) (QUOTE (-1075)))))) 
-(-1134 |Coef| |Expon|) 
+((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1017))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2271) (LIST (|devaluate| |#2|) (QUOTE (-1076)))))) 
+(-1135 |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4184 . T) (-4185 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-1135 RC P) 
+(-1136 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1136 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1137 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1137 |Coef|) 
+(-1138 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,{}r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,{}st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4182 |has| |#1| (-333)) (-4184 . T) (-4185 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-1138 S |Coef| ULS) 
+(-1139 S |Coef| ULS) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) 
 NIL 
 NIL 
-(-1139 |Coef| ULS) 
+(-1140 |Coef| ULS) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4182 |has| |#1| (-333)) (-4184 . T) (-4185 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-1140 |Coef| ULS) 
+(-1141 |Coef| ULS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4182 |has| |#1| (-333)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-333))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2269) (LIST (|devaluate| |#1|) (QUOTE (-1075)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-3745 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1096))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -1518) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1075))))) (|HasSignature| |#1| (LIST (QUOTE -2096) (LIST (LIST (QUOTE -583) (QUOTE (-1075))) (|devaluate| |#1|))))))) 
-(-1141 |Coef| |var| |cen|) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) 
+(-1142 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4182 |has| |#1| (-333)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-333))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3745 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2269) (LIST (|devaluate| |#1|) (QUOTE (-1075)))))) (-3745 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1096))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -1518) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1075))))) (|HasSignature| |#1| (LIST (QUOTE -2096) (LIST (LIST (QUOTE -583) (QUOTE (-1075))) (|devaluate| |#1|))))))) 
-(-1142 R FE |var| |cen|) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) 
+(-1143 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) 
-(((-4192 "*") |has| (-1141 |#2| |#3| |#4|) (-156)) (-4183 |has| (-1141 |#2| |#3| |#4|) (-509)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| (-1141 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1141 |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1141 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1141 |#2| |#3| |#4|) (QUOTE (-156))) (|HasCategory| (-1141 |#2| |#3| |#4|) (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1141 |#2| |#3| |#4|) (LIST (QUOTE -953) (QUOTE (-517)))) (|HasCategory| (-1141 |#2| |#3| |#4|) (QUOTE (-333))) (|HasCategory| (-1141 |#2| |#3| |#4|) (QUOTE (-421))) (-3745 (|HasCategory| (-1141 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1141 |#2| |#3| |#4|) (LIST (QUOTE -953) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| (-1141 |#2| |#3| |#4|) (QUOTE (-509)))) 
-(-1143 A S) 
+(((-4194 "*") |has| (-1142 |#2| |#3| |#4|) (-156)) (-4185 |has| (-1142 |#2| |#3| |#4|) (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| (-1142 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-156))) (|HasCategory| (-1142 |#2| |#3| |#4|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1142 |#2| |#3| |#4|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-333))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-421))) (-3747 (|HasCategory| (-1142 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1142 |#2| |#3| |#4|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-509)))) 
+(-1144 A S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4191))) 
-(-1144 S) 
+((|HasAttribute| |#1| (QUOTE -4193))) 
+(-1145 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
-(-1145 |Coef1| |Coef2| UTS1 UTS2) 
+(-1146 |Coef1| |Coef2| UTS1 UTS2) 
 ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) 
 NIL 
 NIL 
-(-1146 S |Coef|) 
+(-1147 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| |#2| (QUOTE (-1096))) (|HasSignature| |#2| (LIST (QUOTE -2096) (LIST (LIST (QUOTE -583) (QUOTE (-1075))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1518) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1075))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333)))) 
-(-1147 |Coef|) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasSignature| |#2| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2356) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1076))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333)))) 
+(-1148 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4184 . T) (-4185 . T) (-4187 . T)) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-1148 |Coef| |var| |cen|) 
+(-1149 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
-(((-4192 "*") |has| |#1| (-156)) (-4183 |has| |#1| (-509)) (-4184 . T) (-4185 . T) (-4187 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3745 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1075)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1016))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2269) (LIST (|devaluate| |#1|) (QUOTE (-1075)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3745 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1096))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -1518) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1075))))) (|HasSignature| |#1| (LIST (QUOTE -2096) (LIST (LIST (QUOTE -583) (QUOTE (-1075))) (|devaluate| |#1|))))))) 
-(-1149 |Coef| UTS) 
+(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1017))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) 
+(-1150 |Coef| UTS) 
 ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y<n>=f(y,{}y',{}..,{}y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) 
 NIL 
 NIL 
-(-1150 -1724 UP L UTS) 
+(-1151 -1725 UP L UTS) 
 ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-509)))) 
-(-1151) 
+(-1152) 
 ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) 
-((-2180 . T)) 
+((-2181 . T)) 
 NIL 
-(-1152 |sym|) 
+(-1153 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1153 S R) 
+(-1154 S R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-919))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1154 R) 
+((|HasCategory| |#2| (QUOTE (-920))) (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
+(-1155 R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-4191 . T) (-4190 . T) (-2180 . T)) 
+((-4193 . T) (-4192 . T) (-2181 . T)) 
 NIL 
-(-1155 A B) 
+(-1156 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
-(-1156 R) 
+(-1157 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004))) (-3745 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1004)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-919))) (|HasCategory| |#1| (QUOTE (-962)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3745 (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-1157) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-920))) (|HasCategory| |#1| (QUOTE (-963)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-1158) 
 ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) 
 NIL 
 NIL 
-(-1158) 
+(-1159) 
 ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) 
 NIL 
 NIL 
-(-1159) 
+(-1160) 
 ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) 
 NIL 
 NIL 
-(-1160) 
+(-1161) 
 ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) 
 NIL 
 NIL 
-(-1161) 
+(-1162) 
 ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} coerces void object to outputForm.")) (|void| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1162 A S) 
+(-1163 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1163 S) 
+(-1164 S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
-((-4185 . T) (-4184 . T)) 
+((-4187 . T) (-4186 . T)) 
 NIL 
-(-1164 R) 
+(-1165 R) 
 ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) 
 NIL 
 NIL 
-(-1165 K R UP -1724) 
+(-1166 K R UP -1725) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) 
 NIL 
 NIL 
-(-1166 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1167 R |VarSet| E P |vl| |wl| |wtlevel|) 
 ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ |#4|) "\\spad{coerce(p)} coerces \\spad{p} into Weighted form,{} applying weights and ignoring terms") ((|#4| $) "convert back into a \\spad{\"P\"},{} ignoring weights"))) 
-((-4185 |has| |#1| (-156)) (-4184 |has| |#1| (-156)) (-4187 . T)) 
+((-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) (-4189 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) 
-(-1167 R E V P) 
+(-1168 R E V P) 
 ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) 
-((-4191 . T) (-4190 . T)) 
-((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1004))) (-12 (|HasCategory| |#4| (QUOTE (-1004))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) 
-(-1168 R) 
+((-4193 . T) (-4192 . T)) 
+((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1005))) (-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) 
+(-1169 R) 
 ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}."))) 
-((-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-1169 |vl| R) 
+(-1170 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) 
-((-4187 . T) (-4183 |has| |#2| (-6 -4183)) (-4185 . T) (-4184 . T)) 
-((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4183))) 
-(-1170 R |VarSet| XPOLY) 
+((-4189 . T) (-4185 |has| |#2| (-6 -4185)) (-4187 . T) (-4186 . T)) 
+((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4185))) 
+(-1171 R |VarSet| XPOLY) 
 ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) 
 NIL 
 NIL 
-(-1171 |vl| R) 
+(-1172 |vl| R) 
 ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-4183 |has| |#2| (-6 -4183)) (-4185 . T) (-4184 . T) (-4187 . T)) 
+((-4185 |has| |#2| (-6 -4185)) (-4187 . T) (-4186 . T) (-4189 . T)) 
 NIL 
-(-1172 S -1724) 
+(-1173 S -1725) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134)))) 
-(-1173 -1724) 
+(-1174 -1725) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
-((-4182 . T) (-4188 . T) (-4183 . T) ((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
-(-1174 |VarSet| R) 
+(-1175 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) 
-((-4183 |has| |#2| (-6 -4183)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -650) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasAttribute| |#2| (QUOTE -4183))) 
-(-1175 |vl| R) 
+((-4185 |has| |#2| (-6 -4185)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -650) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasAttribute| |#2| (QUOTE -4185))) 
+(-1176 |vl| R) 
 ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,{}n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-4183 |has| |#2| (-6 -4183)) (-4185 . T) (-4184 . T) (-4187 . T)) 
+((-4185 |has| |#2| (-6 -4185)) (-4187 . T) (-4186 . T) (-4189 . T)) 
 NIL 
-(-1176 R) 
+(-1177 R) 
 ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) 
-((-4183 |has| |#1| (-6 -4183)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#1| (QUOTE (-156))) (|HasAttribute| |#1| (QUOTE -4183))) 
-(-1177 R E) 
+((-4185 |has| |#1| (-6 -4185)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#1| (QUOTE (-156))) (|HasAttribute| |#1| (QUOTE -4185))) 
+(-1178 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) 
-((-4187 . T) (-4188 |has| |#1| (-6 -4188)) (-4183 |has| |#1| (-6 -4183)) (-4185 . T) (-4184 . T)) 
-((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasAttribute| |#1| (QUOTE -4187)) (|HasAttribute| |#1| (QUOTE -4188)) (|HasAttribute| |#1| (QUOTE -4183))) 
-(-1178 |VarSet| R) 
+((-4189 . T) (-4190 |has| |#1| (-6 -4190)) (-4185 |has| |#1| (-6 -4185)) (-4187 . T) (-4186 . T)) 
+((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasAttribute| |#1| (QUOTE -4189)) (|HasAttribute| |#1| (QUOTE -4190)) (|HasAttribute| |#1| (QUOTE -4185))) 
+(-1179 |VarSet| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) 
-((-4183 |has| |#2| (-6 -4183)) (-4185 . T) (-4184 . T) (-4187 . T)) 
-((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4183))) 
-(-1179 A) 
+((-4185 |has| |#2| (-6 -4185)) (-4187 . T) (-4186 . T) (-4189 . T)) 
+((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4185))) 
+(-1180 A) 
 ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,{}n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) 
 NIL 
 NIL 
-(-1180 R |ls| |ls2|) 
+(-1181 R |ls| |ls2|) 
 ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,{}s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}info?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,{}info?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,{}info?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,{}false,{}false,{}false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,{}info?)} returns the same as \\spad{realSolve(ts,{}info?,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?)} returns the same as \\spad{realSolve(ts,{}info?,{}check?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,{}false,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}check?,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?,{}lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,{}false,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,{}info?)} returns the same as \\spad{triangSolve(lp,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,{}info?,{}lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) 
 NIL 
 NIL 
-(-1181 R) 
+(-1182 R) 
 ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) 
 NIL 
 NIL 
-(-1182 |p|) 
+(-1183 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-4192 "*") . T) (-4184 . T) (-4185 . T) (-4187 . T)) 
+(((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) 
 NIL 
 NIL 
 NIL 
@@ -4680,4 +4684,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-1187 NIL 2224425 2224430 2224435 2224440) (-3 NIL 2224405 2224410 2224415 2224420) (-2 NIL 2224385 2224390 2224395 2224400) (-1 NIL 2224365 2224370 2224375 2224380) (0 NIL 2224345 2224350 2224355 2224360) (-1182 "ZMOD.spad" 2224154 2224167 2224283 2224340) (-1181 "ZLINDEP.spad" 2223198 2223209 2224144 2224149) (-1180 "ZDSOLVE.spad" 2213047 2213069 2223188 2223193) (-1179 "YSTREAM.spad" 2212540 2212551 2213037 2213042) (-1178 "XRPOLY.spad" 2211760 2211780 2212396 2212465) (-1177 "XPR.spad" 2209489 2209502 2211478 2211577) (-1176 "XPOLY.spad" 2209044 2209055 2209345 2209414) (-1175 "XPOLYC.spad" 2208361 2208377 2208970 2209039) (-1174 "XPBWPOLY.spad" 2206798 2206818 2208141 2208210) (-1173 "XF.spad" 2205259 2205274 2206700 2206793) (-1172 "XF.spad" 2203700 2203717 2205143 2205148) (-1171 "XFALG.spad" 2200724 2200740 2203626 2203695) (-1170 "XEXPPKG.spad" 2199975 2200001 2200714 2200719) (-1169 "XDPOLY.spad" 2199589 2199605 2199831 2199900) (-1168 "XALG.spad" 2199187 2199198 2199545 2199584) (-1167 "WUTSET.spad" 2195026 2195043 2198833 2198860) (-1166 "WP.spad" 2194040 2194084 2194884 2194951) (-1165 "WFFINTBS.spad" 2191603 2191625 2194030 2194035) (-1164 "WEIER.spad" 2189817 2189828 2191593 2191598) (-1163 "VSPACE.spad" 2189490 2189501 2189785 2189812) (-1162 "VSPACE.spad" 2189183 2189196 2189480 2189485) (-1161 "VOID.spad" 2188773 2188782 2189173 2189178) (-1160 "VIEW.spad" 2186395 2186404 2188763 2188768) (-1159 "VIEWDEF.spad" 2181592 2181601 2186385 2186390) (-1158 "VIEW3D.spad" 2165427 2165436 2181582 2181587) (-1157 "VIEW2D.spad" 2153164 2153173 2165417 2165422) (-1156 "VECTOR.spad" 2151841 2151852 2152092 2152119) (-1155 "VECTOR2.spad" 2150468 2150481 2151831 2151836) (-1154 "VECTCAT.spad" 2148356 2148367 2150424 2150463) (-1153 "VECTCAT.spad" 2146065 2146078 2148135 2148140) (-1152 "VARIABLE.spad" 2145845 2145860 2146055 2146060) (-1151 "UTYPE.spad" 2145479 2145488 2145825 2145840) (-1150 "UTSODETL.spad" 2144772 2144796 2145435 2145440) (-1149 "UTSODE.spad" 2142960 2142980 2144762 2144767) (-1148 "UTS.spad" 2137749 2137777 2141427 2141524) (-1147 "UTSCAT.spad" 2135200 2135216 2137647 2137744) (-1146 "UTSCAT.spad" 2132295 2132313 2134744 2134749) (-1145 "UTS2.spad" 2131888 2131923 2132285 2132290) (-1144 "URAGG.spad" 2126510 2126521 2131868 2131883) (-1143 "URAGG.spad" 2121106 2121119 2126466 2126471) (-1142 "UPXSSING.spad" 2118752 2118778 2120190 2120323) (-1141 "UPXS.spad" 2115779 2115807 2116884 2117033) (-1140 "UPXSCONS.spad" 2113536 2113556 2113911 2114060) (-1139 "UPXSCCA.spad" 2111994 2112014 2113382 2113531) (-1138 "UPXSCCA.spad" 2110594 2110616 2111984 2111989) (-1137 "UPXSCAT.spad" 2109175 2109191 2110440 2110589) (-1136 "UPXS2.spad" 2108716 2108769 2109165 2109170) (-1135 "UPSQFREE.spad" 2107128 2107142 2108706 2108711) (-1134 "UPSCAT.spad" 2104721 2104745 2107026 2107123) (-1133 "UPSCAT.spad" 2102020 2102046 2104327 2104332) (-1132 "UPOLYC.spad" 2096998 2097009 2101862 2102015) (-1131 "UPOLYC.spad" 2091868 2091881 2096734 2096739) (-1130 "UPOLYC2.spad" 2091337 2091356 2091858 2091863) (-1129 "UP.spad" 2088387 2088402 2088895 2089048) (-1128 "UPMP.spad" 2087277 2087290 2088377 2088382) (-1127 "UPDIVP.spad" 2086840 2086854 2087267 2087272) (-1126 "UPDECOMP.spad" 2085077 2085091 2086830 2086835) (-1125 "UPCDEN.spad" 2084284 2084300 2085067 2085072) (-1124 "UP2.spad" 2083646 2083667 2084274 2084279) (-1123 "UNISEG.spad" 2082999 2083010 2083565 2083570) (-1122 "UNISEG2.spad" 2082492 2082505 2082955 2082960) (-1121 "UNIFACT.spad" 2081593 2081605 2082482 2082487) (-1120 "ULS.spad" 2072152 2072180 2073245 2073674) (-1119 "ULSCONS.spad" 2066195 2066215 2066567 2066716) (-1118 "ULSCCAT.spad" 2063792 2063812 2066015 2066190) (-1117 "ULSCCAT.spad" 2061523 2061545 2063748 2063753) (-1116 "ULSCAT.spad" 2059739 2059755 2061369 2061518) (-1115 "ULS2.spad" 2059251 2059304 2059729 2059734) (-1114 "UFD.spad" 2058316 2058325 2059177 2059246) (-1113 "UFD.spad" 2057443 2057454 2058306 2058311) (-1112 "UDVO.spad" 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2009060) (-1093 "TOOLSIGN.spad" 2008402 2008413 2008729 2008734) (-1092 "TEXTFILE.spad" 2006959 2006968 2008392 2008397) (-1091 "TEX.spad" 2003976 2003985 2006949 2006954) (-1090 "TEX1.spad" 2003532 2003543 2003966 2003971) (-1089 "TEMUTL.spad" 2003087 2003096 2003522 2003527) (-1088 "TBCMPPK.spad" 2001180 2001203 2003077 2003082) (-1087 "TBAGG.spad" 2000204 2000227 2001148 2001175) (-1086 "TBAGG.spad" 1999248 1999273 2000194 2000199) (-1085 "TANEXP.spad" 1998624 1998635 1999238 1999243) (-1084 "TABLE.spad" 1997035 1997058 1997305 1997332) (-1083 "TABLEAU.spad" 1996516 1996527 1997025 1997030) (-1082 "TABLBUMP.spad" 1993299 1993310 1996506 1996511) (-1081 "SYSSOLP.spad" 1990772 1990783 1993289 1993294) (-1080 "syntax.spad" 1987828 1987837 1990762 1990767) (-1079 "SYMTAB.spad" 1985884 1985893 1987818 1987823) (-1078 "SYMS.spad" 1981869 1981878 1985874 1985879) (-1077 "SYMPOLY.spad" 1980879 1980890 1980961 1981088) (-1076 "SYMFUNC.spad" 1980354 1980365 1980869 1980874) (-1075 "SYMBOL.spad" 1977690 1977699 1980344 1980349) (-1074 "SWITCH.spad" 1974447 1974456 1977680 1977685) (-1073 "SUTS.spad" 1971346 1971374 1972914 1973011) (-1072 "SUPXS.spad" 1968360 1968388 1969478 1969627) (-1071 "SUP.spad" 1965137 1965148 1965918 1966071) (-1070 "SUPFRACF.spad" 1964242 1964260 1965127 1965132) (-1069 "SUP2.spad" 1963632 1963645 1964232 1964237) (-1068 "SUMRF.spad" 1962598 1962609 1963622 1963627) (-1067 "SUMFS.spad" 1962231 1962248 1962588 1962593) (-1066 "SULS.spad" 1952777 1952805 1953883 1954312) (-1065 "SUCH.spad" 1952457 1952472 1952767 1952772) (-1064 "SUBSPACE.spad" 1944464 1944479 1952447 1952452) (-1063 "SUBRESP.spad" 1943624 1943638 1944420 1944425) (-1062 "STTF.spad" 1939723 1939739 1943614 1943619) (-1061 "STTFNC.spad" 1936191 1936207 1939713 1939718) (-1060 "STTAYLOR.spad" 1928589 1928600 1936072 1936077) (-1059 "STRTBL.spad" 1927094 1927111 1927243 1927270) (-1058 "STRING.spad" 1926503 1926512 1926517 1926544) (-1057 "STRICAT.spad" 1926279 1926288 1926459 1926498) (-1056 "STREAM.spad" 1923047 1923058 1925804 1925819) (-1055 "STREAM3.spad" 1922592 1922607 1923037 1923042) (-1054 "STREAM2.spad" 1921660 1921673 1922582 1922587) (-1053 "STREAM1.spad" 1921364 1921375 1921650 1921655) (-1052 "STINPROD.spad" 1920270 1920286 1921354 1921359) (-1051 "STEP.spad" 1919471 1919480 1920260 1920265) (-1050 "STBL.spad" 1917997 1918025 1918164 1918179) (-1049 "STAGG.spad" 1917062 1917073 1917977 1917992) (-1048 "STAGG.spad" 1916135 1916148 1917052 1917057) (-1047 "STACK.spad" 1915486 1915497 1915742 1915769) (-1046 "SREGSET.spad" 1913190 1913207 1915132 1915159) (-1045 "SRDCMPK.spad" 1911735 1911755 1913180 1913185) (-1044 "SRAGG.spad" 1906820 1906829 1911691 1911730) (-1043 "SRAGG.spad" 1901937 1901948 1906810 1906815) (-1042 "SQMATRIX.spad" 1899563 1899581 1900471 1900558) (-1041 "SPLTREE.spad" 1894115 1894128 1898999 1899026) (-1040 "SPLNODE.spad" 1890703 1890716 1894105 1894110) (-1039 "SPFCAT.spad" 1889480 1889489 1890693 1890698) (-1038 "SPECOUT.spad" 1888030 1888039 1889470 1889475) (-1037 "spad-parser.spad" 1887495 1887504 1888020 1888025) (-1036 "SPACEC.spad" 1871508 1871519 1887485 1887490) (-1035 "SPACE3.spad" 1871284 1871295 1871498 1871503) (-1034 "SORTPAK.spad" 1870829 1870842 1871240 1871245) (-1033 "SOLVETRA.spad" 1868586 1868597 1870819 1870824) (-1032 "SOLVESER.spad" 1867106 1867117 1868576 1868581) (-1031 "SOLVERAD.spad" 1863116 1863127 1867096 1867101) (-1030 "SOLVEFOR.spad" 1861536 1861554 1863106 1863111) (-1029 "SNTSCAT.spad" 1861124 1861141 1861492 1861531) (-1028 "SMTS.spad" 1859384 1859410 1860689 1860786) (-1027 "SMP.spad" 1856826 1856846 1857216 1857343) (-1026 "SMITH.spad" 1855669 1855694 1856816 1856821) (-1025 "SMATCAT.spad" 1853767 1853797 1855601 1855664) (-1024 "SMATCAT.spad" 1851809 1851841 1853645 1853650) (-1023 "SKAGG.spad" 1850758 1850769 1851765 1851804) (-1022 "SINT.spad" 1849066 1849075 1850624 1850753) (-1021 "SIMPAN.spad" 1848794 1848803 1849056 1849061) (-1020 "SIGNRF.spad" 1847902 1847913 1848784 1848789) (-1019 "SIGNEF.spad" 1847171 1847188 1847892 1847897) (-1018 "SHP.spad" 1845089 1845104 1847127 1847132) (-1017 "SHDP.spad" 1836479 1836506 1836988 1837117) (-1016 "SGROUP.spad" 1835945 1835954 1836469 1836474) (-1015 "SGROUP.spad" 1835409 1835420 1835935 1835940) (-1014 "SGCF.spad" 1828290 1828299 1835399 1835404) (-1013 "SFRTCAT.spad" 1827206 1827223 1828246 1828285) (-1012 "SFRGCD.spad" 1826269 1826289 1827196 1827201) (-1011 "SFQCMPK.spad" 1820906 1820926 1826259 1826264) (-1010 "SFORT.spad" 1820341 1820355 1820896 1820901) (-1009 "SEXOF.spad" 1820184 1820224 1820331 1820336) (-1008 "SEX.spad" 1820076 1820085 1820174 1820179) (-1007 "SEXCAT.spad" 1817180 1817220 1820066 1820071) (-1006 "SET.spad" 1815480 1815491 1816601 1816640) (-1005 "SETMN.spad" 1813914 1813931 1815470 1815475) (-1004 "SETCAT.spad" 1813399 1813408 1813904 1813909) (-1003 "SETCAT.spad" 1812882 1812893 1813389 1813394) (-1002 "SETAGG.spad" 1809405 1809416 1812850 1812877) (-1001 "SETAGG.spad" 1805948 1805961 1809395 1809400) (-1000 "SEGXCAT.spad" 1805060 1805073 1805928 1805943) (-999 "SEG.spad" 1804874 1804884 1804979 1804984) (-998 "SEGCAT.spad" 1803694 1803704 1804854 1804869) (-997 "SEGBIND.spad" 1802767 1802777 1803649 1803654) (-996 "SEGBIND2.spad" 1802464 1802476 1802757 1802762) (-995 "SEG2.spad" 1801890 1801902 1802420 1802425) (-994 "SDVAR.spad" 1801167 1801177 1801880 1801885) (-993 "SDPOL.spad" 1798566 1798576 1798856 1798983) (-992 "SCPKG.spad" 1796646 1796656 1798556 1798561) (-991 "SCACHE.spad" 1795329 1795339 1796636 1796641) (-990 "SAOS.spad" 1795202 1795210 1795319 1795324) (-989 "SAERFFC.spad" 1794916 1794935 1795192 1795197) (-988 "SAE.spad" 1793095 1793110 1793705 1793840) (-987 "SAEFACT.spad" 1792797 1792816 1793085 1793090) (-986 "RURPK.spad" 1790439 1790454 1792787 1792792) (-985 "RULESET.spad" 1789881 1789904 1790429 1790434) (-984 "RULE.spad" 1788086 1788109 1789871 1789876) (-983 "RULECOLD.spad" 1787939 1787951 1788076 1788081) (-982 "RSETGCD.spad" 1784318 1784337 1787929 1787934) (-981 "RSETCAT.spad" 1774091 1774107 1784274 1784313) (-980 "RSETCAT.spad" 1763896 1763914 1774081 1774086) (-979 "RSDCMPK.spad" 1762349 1762368 1763886 1763891) (-978 "RRCC.spad" 1760734 1760763 1762339 1762344) (-977 "RRCC.spad" 1759117 1759148 1760724 1760729) (-976 "RPOLCAT.spad" 1738478 1738492 1758985 1759112) (-975 "RPOLCAT.spad" 1717554 1717570 1738063 1738068) (-974 "ROUTINE.spad" 1713418 1713426 1716201 1716228) (-973 "ROMAN.spad" 1712651 1712659 1713284 1713413) (-972 "ROIRC.spad" 1711732 1711763 1712641 1712646) (-971 "RNS.spad" 1710636 1710644 1711634 1711727) (-970 "RNS.spad" 1709626 1709636 1710626 1710631) (-969 "RNG.spad" 1709362 1709370 1709616 1709621) (-968 "RMODULE.spad" 1709001 1709011 1709352 1709357) (-967 "RMCAT2.spad" 1708410 1708466 1708991 1708996) (-966 "RMATRIX.spad" 1707090 1707108 1707577 1707616) (-965 "RMATCAT.spad" 1702612 1702642 1707034 1707085) (-964 "RMATCAT.spad" 1698036 1698068 1702460 1702465) (-963 "RINTERP.spad" 1697925 1697944 1698026 1698031) (-962 "RING.spad" 1697283 1697291 1697905 1697920) (-961 "RING.spad" 1696649 1696659 1697273 1697278) (-960 "RIDIST.spad" 1696034 1696042 1696639 1696644) (-959 "RGCHAIN.spad" 1694614 1694629 1695519 1695546) (-958 "RF.spad" 1692229 1692239 1694604 1694609) (-957 "RFFACTOR.spad" 1691692 1691702 1692219 1692224) (-956 "RFFACT.spad" 1691428 1691439 1691682 1691687) (-955 "RFDIST.spad" 1690417 1690425 1691418 1691423) (-954 "RETSOL.spad" 1689835 1689847 1690407 1690412) (-953 "RETRACT.spad" 1689185 1689195 1689825 1689830) (-952 "RETRACT.spad" 1688533 1688545 1689175 1689180) (-951 "RESULT.spad" 1686594 1686602 1687180 1687207) (-950 "RESRING.spad" 1685942 1685988 1686532 1686589) (-949 "RESLATC.spad" 1685267 1685277 1685932 1685937) (-948 "REPSQ.spad" 1684997 1685007 1685257 1685262) (-947 "REP.spad" 1682550 1682558 1684987 1684992) (-946 "REPDB.spad" 1682256 1682266 1682540 1682545) (-945 "REP2.spad" 1671829 1671839 1682098 1682103) (-944 "REP1.spad" 1665820 1665830 1671779 1671784) (-943 "REGSET.spad" 1663618 1663634 1665466 1665493) (-942 "REF.spad" 1662948 1662958 1663573 1663578) (-941 "REDORDER.spad" 1662125 1662141 1662938 1662943) (-940 "RECLOS.spad" 1660915 1660934 1661618 1661711) (-939 "REALSOLV.spad" 1660048 1660056 1660905 1660910) (-938 "REAL.spad" 1659921 1659929 1660038 1660043) (-937 "REAL0Q.spad" 1657204 1657218 1659911 1659916) (-936 "REAL0.spad" 1654033 1654047 1657194 1657199) (-935 "RDIV.spad" 1653685 1653709 1654023 1654028) (-934 "RDIST.spad" 1653249 1653259 1653675 1653680) (-933 "RDETRS.spad" 1652046 1652063 1653239 1653244) (-932 "RDETR.spad" 1650154 1650171 1652036 1652041) (-931 "RDEEFS.spad" 1649228 1649244 1650144 1650149) (-930 "RDEEF.spad" 1648225 1648241 1649218 1649223) (-929 "RCFIELD.spad" 1645409 1645417 1648127 1648220) (-928 "RCFIELD.spad" 1642679 1642689 1645399 1645404) (-927 "RCAGG.spad" 1640582 1640592 1642659 1642674) (-926 "RCAGG.spad" 1638422 1638434 1640501 1640506) (-925 "RATRET.spad" 1637783 1637793 1638412 1638417) (-924 "RATFACT.spad" 1637476 1637487 1637773 1637778) (-923 "RANDSRC.spad" 1636796 1636804 1637466 1637471) (-922 "RADUTIL.spad" 1636551 1636559 1636786 1636791) (-921 "RADIX.spad" 1633344 1633357 1635021 1635114) (-920 "RADFF.spad" 1631761 1631797 1631879 1632035) (-919 "RADCAT.spad" 1631355 1631363 1631751 1631756) (-918 "RADCAT.spad" 1630947 1630957 1631345 1631350) (-917 "QUEUE.spad" 1630290 1630300 1630554 1630581) (-916 "QUAT.spad" 1628876 1628886 1629218 1629283) (-915 "QUATCT2.spad" 1628495 1628513 1628866 1628871) (-914 "QUATCAT.spad" 1626660 1626670 1628425 1628490) (-913 "QUATCAT.spad" 1624577 1624589 1626344 1626349) (-912 "QUAGG.spad" 1623391 1623401 1624533 1624572) (-911 "QFORM.spad" 1622854 1622868 1623381 1623386) (-910 "QFCAT.spad" 1621545 1621555 1622744 1622849) (-909 "QFCAT.spad" 1619842 1619854 1621043 1621048) (-908 "QFCAT2.spad" 1619533 1619549 1619832 1619837) (-907 "QEQUAT.spad" 1619090 1619098 1619523 1619528) (-906 "QCMPACK.spad" 1613837 1613856 1619080 1619085) (-905 "QALGSET.spad" 1609912 1609944 1613751 1613756) (-904 "QALGSET2.spad" 1607908 1607926 1609902 1609907) (-903 "PWFFINTB.spad" 1605218 1605239 1607898 1607903) (-902 "PUSHVAR.spad" 1604547 1604566 1605208 1605213) (-901 "PTRANFN.spad" 1600673 1600683 1604537 1604542) (-900 "PTPACK.spad" 1597761 1597771 1600663 1600668) (-899 "PTFUNC2.spad" 1597582 1597596 1597751 1597756) (-898 "PTCAT.spad" 1596664 1596674 1597538 1597577) (-897 "PSQFR.spad" 1595971 1595995 1596654 1596659) (-896 "PSEUDLIN.spad" 1594829 1594839 1595961 1595966) (-895 "PSETPK.spad" 1580262 1580278 1594707 1594712) (-894 "PSETCAT.spad" 1574170 1574193 1580230 1580257) (-893 "PSETCAT.spad" 1568064 1568089 1574126 1574131) (-892 "PSCURVE.spad" 1567047 1567055 1568054 1568059) (-891 "PSCAT.spad" 1565814 1565843 1566945 1567042) (-890 "PSCAT.spad" 1564671 1564702 1565804 1565809) (-889 "PRTITION.spad" 1563514 1563522 1564661 1564666) (-888 "PRS.spad" 1553076 1553093 1563470 1563475) (-887 "PRQAGG.spad" 1552495 1552505 1553032 1553071) (-886 "PRODUCT.spad" 1550175 1550187 1550461 1550516) (-885 "PR.spad" 1548564 1548576 1549269 1549396) (-884 "PRINT.spad" 1548316 1548324 1548554 1548559) (-883 "PRIMES.spad" 1546567 1546577 1548306 1548311) (-882 "PRIMELT.spad" 1544548 1544562 1546557 1546562) (-881 "PRIMCAT.spad" 1544171 1544179 1544538 1544543) (-880 "PRIMARR.spad" 1543176 1543186 1543354 1543381) (-879 "PRIMARR2.spad" 1541899 1541911 1543166 1543171) (-878 "PREASSOC.spad" 1541271 1541283 1541889 1541894) (-877 "PPCURVE.spad" 1540408 1540416 1541261 1541266) (-876 "POLYROOT.spad" 1539180 1539202 1540364 1540369) (-875 "POLY.spad" 1536480 1536490 1536997 1537124) (-874 "POLYLIFT.spad" 1535741 1535764 1536470 1536475) (-873 "POLYCATQ.spad" 1533843 1533865 1535731 1535736) (-872 "POLYCAT.spad" 1527249 1527270 1533711 1533838) (-871 "POLYCAT.spad" 1519957 1519980 1526421 1526426) (-870 "POLY2UP.spad" 1519405 1519419 1519947 1519952) (-869 "POLY2.spad" 1519000 1519012 1519395 1519400) (-868 "POLUTIL.spad" 1517941 1517970 1518956 1518961) (-867 "POLTOPOL.spad" 1516689 1516704 1517931 1517936) (-866 "POINT.spad" 1515530 1515540 1515617 1515644) (-865 "PNTHEORY.spad" 1512196 1512204 1515520 1515525) (-864 "PMTOOLS.spad" 1510953 1510967 1512186 1512191) (-863 "PMSYM.spad" 1510498 1510508 1510943 1510948) (-862 "PMQFCAT.spad" 1510085 1510099 1510488 1510493) (-861 "PMPRED.spad" 1509554 1509568 1510075 1510080) (-860 "PMPREDFS.spad" 1508998 1509020 1509544 1509549) (-859 "PMPLCAT.spad" 1508068 1508086 1508930 1508935) (-858 "PMLSAGG.spad" 1507649 1507663 1508058 1508063) (-857 "PMKERNEL.spad" 1507216 1507228 1507639 1507644) (-856 "PMINS.spad" 1506792 1506802 1507206 1507211) (-855 "PMFS.spad" 1506365 1506383 1506782 1506787) (-854 "PMDOWN.spad" 1505651 1505665 1506355 1506360) (-853 "PMASS.spad" 1504663 1504671 1505641 1505646) (-852 "PMASSFS.spad" 1503632 1503648 1504653 1504658) (-851 "PLOTTOOL.spad" 1503412 1503420 1503622 1503627) (-850 "PLOT.spad" 1498243 1498251 1503402 1503407) (-849 "PLOT3D.spad" 1494663 1494671 1498233 1498238) (-848 "PLOT1.spad" 1493804 1493814 1494653 1494658) (-847 "PLEQN.spad" 1481020 1481047 1493794 1493799) (-846 "PINTERP.spad" 1480636 1480655 1481010 1481015) (-845 "PINTERPA.spad" 1480418 1480434 1480626 1480631) (-844 "PI.spad" 1480025 1480033 1480392 1480413) (-843 "PID.spad" 1478981 1478989 1479951 1480020) (-842 "PICOERCE.spad" 1478638 1478648 1478971 1478976) (-841 "PGROEB.spad" 1477235 1477249 1478628 1478633) (-840 "PGE.spad" 1468488 1468496 1477225 1477230) (-839 "PGCD.spad" 1467370 1467387 1468478 1468483) (-838 "PFRPAC.spad" 1466513 1466523 1467360 1467365) (-837 "PFR.spad" 1463170 1463180 1466415 1466508) (-836 "PFOTOOLS.spad" 1462428 1462444 1463160 1463165) (-835 "PFOQ.spad" 1461798 1461816 1462418 1462423) (-834 "PFO.spad" 1461217 1461244 1461788 1461793) (-833 "PF.spad" 1460791 1460803 1461022 1461115) (-832 "PFECAT.spad" 1458457 1458465 1460717 1460786) (-831 "PFECAT.spad" 1456151 1456161 1458413 1458418) (-830 "PFBRU.spad" 1454021 1454033 1456141 1456146) (-829 "PFBR.spad" 1451559 1451582 1454011 1454016) (-828 "PERM.spad" 1447240 1447250 1451389 1451404) (-827 "PERMGRP.spad" 1441976 1441986 1447230 1447235) (-826 "PERMCAT.spad" 1440528 1440538 1441956 1441971) (-825 "PERMAN.spad" 1439060 1439074 1440518 1440523) (-824 "PENDTREE.spad" 1438333 1438343 1438689 1438694) (-823 "PDRING.spad" 1436824 1436834 1438313 1438328) (-822 "PDRING.spad" 1435323 1435335 1436814 1436819) (-821 "PDEPROB.spad" 1434280 1434288 1435313 1435318) (-820 "PDEPACK.spad" 1428282 1428290 1434270 1434275) (-819 "PDECOMP.spad" 1427744 1427761 1428272 1428277) (-818 "PDECAT.spad" 1426098 1426106 1427734 1427739) (-817 "PCOMP.spad" 1425949 1425962 1426088 1426093) (-816 "PBWLB.spad" 1424531 1424548 1425939 1425944) (-815 "PATTERN.spad" 1418962 1418972 1424521 1424526) (-814 "PATTERN2.spad" 1418698 1418710 1418952 1418957) (-813 "PATTERN1.spad" 1417000 1417016 1418688 1418693) (-812 "PATRES.spad" 1414547 1414559 1416990 1416995) (-811 "PATRES2.spad" 1414209 1414223 1414537 1414542) (-810 "PATMATCH.spad" 1412371 1412402 1413922 1413927) (-809 "PATMAB.spad" 1411796 1411806 1412361 1412366) (-808 "PATLRES.spad" 1410880 1410894 1411786 1411791) (-807 "PATAB.spad" 1410644 1410654 1410870 1410875) (-806 "PARTPERM.spad" 1408006 1408014 1410634 1410639) (-805 "PARSURF.spad" 1407434 1407462 1407996 1408001) (-804 "PARSU2.spad" 1407229 1407245 1407424 1407429) (-803 "script-parser.spad" 1406749 1406757 1407219 1407224) (-802 "PARSCURV.spad" 1406177 1406205 1406739 1406744) (-801 "PARSC2.spad" 1405966 1405982 1406167 1406172) (-800 "PARPCURV.spad" 1405424 1405452 1405956 1405961) (-799 "PARPC2.spad" 1405213 1405229 1405414 1405419) (-798 "PAN2EXPR.spad" 1404625 1404633 1405203 1405208) (-797 "PALETTE.spad" 1403595 1403603 1404615 1404620) (-796 "PADICRC.spad" 1400928 1400946 1402103 1402196) (-795 "PADICRAT.spad" 1398946 1398958 1399167 1399260) (-794 "PADIC.spad" 1398641 1398653 1398872 1398941) (-793 "PADICCT.spad" 1397182 1397194 1398567 1398636) (-792 "PADEPAC.spad" 1395861 1395880 1397172 1397177) (-791 "PADE.spad" 1394601 1394617 1395851 1395856) (-790 "OWP.spad" 1393585 1393615 1394459 1394526) (-789 "OVAR.spad" 1393366 1393389 1393575 1393580) (-788 "OUT.spad" 1392450 1392458 1393356 1393361) (-787 "OUTFORM.spad" 1381864 1381872 1392440 1392445) (-786 "OSI.spad" 1381339 1381347 1381854 1381859) (-785 "ORTHPOL.spad" 1379800 1379810 1381256 1381261) (-784 "OREUP.spad" 1379160 1379188 1379482 1379521) (-783 "ORESUP.spad" 1378461 1378485 1378842 1378881) (-782 "OREPCTO.spad" 1376280 1376292 1378381 1378386) (-781 "OREPCAT.spad" 1370337 1370347 1376236 1376275) (-780 "OREPCAT.spad" 1364284 1364296 1370185 1370190) (-779 "ORDSET.spad" 1363450 1363458 1364274 1364279) (-778 "ORDSET.spad" 1362614 1362624 1363440 1363445) (-777 "ORDRING.spad" 1362004 1362012 1362594 1362609) (-776 "ORDRING.spad" 1361402 1361412 1361994 1361999) (-775 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(-423 "GDMP.spad" 747692 747709 748468 748595) (-422 "GCNAALG.spad" 741587 741614 747486 747553) (-421 "GCDDOM.spad" 740759 740767 741513 741582) (-420 "GCDDOM.spad" 739993 740003 740749 740754) (-419 "GB.spad" 737511 737549 739949 739954) (-418 "GBINTERN.spad" 733531 733569 737501 737506) (-417 "GBF.spad" 729288 729326 733521 733526) (-416 "GBEUCLID.spad" 727162 727200 729278 729283) (-415 "GAUSSFAC.spad" 726459 726467 727152 727157) (-414 "GALUTIL.spad" 724781 724791 726415 726420) (-413 "GALPOLYU.spad" 723227 723240 724771 724776) (-412 "GALFACTU.spad" 721392 721411 723217 723222) (-411 "GALFACT.spad" 711525 711536 721382 721387) (-410 "FVFUN.spad" 708538 708546 711505 711520) (-409 "FVC.spad" 707580 707588 708518 708533) (-408 "FUNCTION.spad" 707429 707441 707570 707575) (-407 "FT.spad" 705641 705649 707419 707424) (-406 "FTEM.spad" 704804 704812 705631 705636) (-405 "FSUPFACT.spad" 703705 703724 704741 704746) (-404 "FST.spad" 701791 701799 703695 703700) (-403 "FSRED.spad" 701269 701285 701781 701786) (-402 "FSPRMELT.spad" 700093 700109 701226 701231) (-401 "FSPECF.spad" 698170 698186 700083 700088) (-400 "FS.spad" 692221 692231 697934 698165) (-399 "FS.spad" 686063 686075 691778 691783) (-398 "FSINT.spad" 685721 685737 686053 686058) (-397 "FSERIES.spad" 684908 684920 685541 685640) (-396 "FSCINT.spad" 684221 684237 684898 684903) (-395 "FSAGG.spad" 683326 683336 684165 684216) (-394 "FSAGG.spad" 682405 682417 683246 683251) (-393 "FSAGG2.spad" 681104 681120 682395 682400) (-392 "FS2UPS.spad" 675493 675527 681094 681099) (-391 "FS2.spad" 675138 675154 675483 675488) (-390 "FS2EXPXP.spad" 674261 674284 675128 675133) (-389 "FRUTIL.spad" 673203 673213 674251 674256) (-388 "FR.spad" 666900 666910 672230 672299) (-387 "FRNAALG.spad" 661987 661997 666842 666895) (-386 "FRNAALG.spad" 657086 657098 661943 661948) (-385 "FRNAAF2.spad" 656540 656558 657076 657081) (-384 "FRMOD.spad" 655935 655965 656472 656477) (-383 "FRIDEAL.spad" 655130 655151 655915 655930) (-382 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"D01GBFA.spad" 224596 224604 225064 225069) (-177 "D01FCFA.spad" 224118 224126 224586 224591) (-176 "D01ASFA.spad" 223586 223594 224108 224113) (-175 "D01AQFA.spad" 223032 223040 223576 223581) (-174 "D01APFA.spad" 222456 222464 223022 223027) (-173 "D01ANFA.spad" 221950 221958 222446 222451) (-172 "D01AMFA.spad" 221460 221468 221940 221945) (-171 "D01ALFA.spad" 221000 221008 221450 221455) (-170 "D01AKFA.spad" 220526 220534 220990 220995) (-169 "D01AJFA.spad" 220049 220057 220516 220521) (-168 "D01AGNT.spad" 216108 216116 220039 220044) (-167 "CYCLOTOM.spad" 215614 215622 216098 216103) (-166 "CYCLES.spad" 212446 212454 215604 215609) (-165 "CVMP.spad" 211863 211873 212436 212441) (-164 "CTRIGMNP.spad" 210353 210369 211853 211858) (-163 "CSTTOOLS.spad" 209596 209609 210343 210348) (-162 "CRFP.spad" 203300 203313 209586 209591) (-161 "CRAPACK.spad" 202343 202353 203290 203295) (-160 "CPMATCH.spad" 201843 201858 202268 202273) (-159 "CPIMA.spad" 201548 201567 201833 201838) (-158 "COORDSYS.spad" 196441 196451 201538 201543) (-157 "CONTFRAC.spad" 192053 192063 196343 196436) (-156 "COMRING.spad" 191727 191735 191991 192048) (-155 "COMPPROP.spad" 191241 191249 191717 191722) (-154 "COMPLPAT.spad" 191008 191023 191231 191236) (-153 "COMPLEX.spad" 185041 185051 185285 185546) (-152 "COMPLEX2.spad" 184754 184766 185031 185036) (-151 "COMPFACT.spad" 184356 184370 184744 184749) (-150 "COMPCAT.spad" 182412 182422 184078 184351) (-149 "COMPCAT.spad" 180175 180187 181843 181848) (-148 "COMMUPC.spad" 179921 179939 180165 180170) (-147 "COMMONOP.spad" 179454 179462 179911 179916) (-146 "COMM.spad" 179263 179271 179444 179449) (-145 "COMBOPC.spad" 178168 178176 179253 179258) (-144 "COMBINAT.spad" 176913 176923 178158 178163) (-143 "COMBF.spad" 174281 174297 176903 176908) (-142 "COLOR.spad" 173118 173126 174271 174276) (-141 "CMPLXRT.spad" 172827 172844 173108 173113) (-140 "CLIP.spad" 168919 168927 172817 172822) (-139 "CLIF.spad" 167558 167574 168875 168914) (-138 "CLAGG.spad" 164033 164043 167538 167553) (-137 "CLAGG.spad" 160389 160401 163896 163901) (-136 "CINTSLPE.spad" 159714 159727 160379 160384) (-135 "CHVAR.spad" 157792 157814 159704 159709) (-134 "CHARZ.spad" 157707 157715 157772 157787) (-133 "CHARPOL.spad" 157215 157225 157697 157702) (-132 "CHARNZ.spad" 156968 156976 157195 157210) (-131 "CHAR.spad" 154858 154866 156958 156963) (-130 "CFCAT.spad" 154174 154182 154848 154853) (-129 "CDEN.spad" 153332 153346 154164 154169) (-128 "CCLASS.spad" 151481 151489 152743 152782) (-127 "CARTEN.spad" 146584 146608 151471 151476) (-126 "CARTEN2.spad" 145970 145997 146574 146579) (-125 "CARD.spad" 143259 143267 145944 145965) (-124 "CACHSET.spad" 142881 142889 143249 143254) (-123 "CABMON.spad" 142434 142442 142871 142876) (-122 "BTREE.spad" 141503 141513 142041 142068) (-121 "BTOURN.spad" 140506 140516 141110 141137) (-120 "BTCAT.spad" 139882 139892 140462 140501) (-119 "BTCAT.spad" 139290 139302 139872 139877) (-118 "BTAGG.spad" 138306 138314 139246 139285) (-117 "BTAGG.spad" 137354 137364 138296 138301) (-116 "BSTREE.spad" 136089 136099 136961 136988) (-115 "BRILL.spad" 134284 134295 136079 136084) (-114 "BRAGG.spad" 133198 133208 134264 134279) (-113 "BRAGG.spad" 132086 132098 133154 133159) (-112 "BPADICRT.spad" 130070 130082 130325 130418) (-111 "BPADIC.spad" 129734 129746 129996 130065) (-110 "BOUNDZRO.spad" 129390 129407 129724 129729) (-109 "BOP.spad" 124854 124862 129380 129385) (-108 "BOP1.spad" 122240 122250 124810 124815) (-107 "BOOLEAN.spad" 121098 121106 122230 122235) (-106 "BMODULE.spad" 120810 120822 121066 121093) (-105 "BITS.spad" 120229 120237 120446 120473) (-104 "BINFILE.spad" 119572 119580 120219 120224) (-103 "BINARY.spad" 117465 117473 118042 118135) (-102 "BGAGG.spad" 116650 116660 117433 117460) (-101 "BGAGG.spad" 115855 115867 116640 116645) (-100 "BFUNCT.spad" 115419 115427 115835 115850) (-99 "BEZOUT.spad" 114554 114580 115369 115374) (-98 "BBTREE.spad" 111374 111383 114161 114188) (-97 "BASTYPE.spad" 111047 111054 111364 111369) (-96 "BASTYPE.spad" 110718 110727 111037 111042) (-95 "BALFACT.spad" 110158 110170 110708 110713) (-94 "AUTOMOR.spad" 109605 109614 110138 110153) (-93 "ATTREG.spad" 106324 106331 109357 109600) (-92 "ATTRBUT.spad" 102347 102354 106304 106319) (-91 "ATRIG.spad" 101817 101824 102337 102342) (-90 "ATRIG.spad" 101285 101294 101807 101812) (-89 "ASTACK.spad" 100618 100627 100892 100919) (-88 "ASSOCEQ.spad" 99418 99429 100574 100579) (-87 "ASP9.spad" 98499 98512 99408 99413) (-86 "ASP8.spad" 97542 97555 98489 98494) (-85 "ASP80.spad" 96864 96877 97532 97537) (-84 "ASP7.spad" 96024 96037 96854 96859) (-83 "ASP78.spad" 95475 95488 96014 96019) (-82 "ASP77.spad" 94844 94857 95465 95470) (-81 "ASP74.spad" 93936 93949 94834 94839) (-80 "ASP73.spad" 93207 93220 93926 93931) (-79 "ASP6.spad" 91839 91852 93197 93202) (-78 "ASP55.spad" 90348 90361 91829 91834) (-77 "ASP50.spad" 88165 88178 90338 90343) (-76 "ASP4.spad" 87460 87473 88155 88160) (-75 "ASP49.spad" 86459 86472 87450 87455) (-74 "ASP42.spad" 84866 84905 86449 86454) (-73 "ASP41.spad" 83445 83484 84856 84861) (-72 "ASP35.spad" 82433 82446 83435 83440) (-71 "ASP34.spad" 81734 81747 82423 82428) (-70 "ASP33.spad" 81294 81307 81724 81729) (-69 "ASP31.spad" 80434 80447 81284 81289) (-68 "ASP30.spad" 79326 79339 80424 80429) (-67 "ASP29.spad" 78792 78805 79316 79321) (-66 "ASP28.spad" 70065 70078 78782 78787) (-65 "ASP27.spad" 68962 68975 70055 70060) (-64 "ASP24.spad" 68049 68062 68952 68957) (-63 "ASP20.spad" 67265 67278 68039 68044) (-62 "ASP1.spad" 66646 66659 67255 67260) (-61 "ASP19.spad" 61332 61345 66636 66641) (-60 "ASP12.spad" 60746 60759 61322 61327) (-59 "ASP10.spad" 60017 60030 60736 60741) (-58 "ARRAY2.spad" 59377 59386 59624 59651) (-57 "ARRAY1.spad" 58212 58221 58560 58587) (-56 "ARRAY12.spad" 56881 56892 58202 58207) (-55 "ARR2CAT.spad" 52531 52552 56837 56876) (-54 "ARR2CAT.spad" 48213 48236 52521 52526) (-53 "APPRULE.spad" 47457 47479 48203 48208) (-52 "APPLYORE.spad" 47072 47085 47447 47452) (-51 "ANY.spad" 45414 45421 47062 47067) (-50 "ANY1.spad" 44485 44494 45404 45409) (-49 "ANTISYM.spad" 42924 42940 44465 44480) (-48 "ANON.spad" 42837 42844 42914 42919) (-47 "AN.spad" 41140 41147 42655 42748) (-46 "AMR.spad" 39319 39330 41038 41135) (-45 "AMR.spad" 37335 37348 39056 39061) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865)) 
\ No newline at end of file
+((-1188 NIL 2225697 2225702 2225707 2225712) (-3 NIL 2225677 2225682 2225687 2225692) (-2 NIL 2225657 2225662 2225667 2225672) (-1 NIL 2225637 2225642 2225647 2225652) (0 NIL 2225617 2225622 2225627 2225632) (-1183 "ZMOD.spad" 2225426 2225439 2225555 2225612) (-1182 "ZLINDEP.spad" 2224470 2224481 2225416 2225421) (-1181 "ZDSOLVE.spad" 2214319 2214341 2224460 2224465) (-1180 "YSTREAM.spad" 2213812 2213823 2214309 2214314) (-1179 "XRPOLY.spad" 2213032 2213052 2213668 2213737) (-1178 "XPR.spad" 2210761 2210774 2212750 2212849) (-1177 "XPOLY.spad" 2210316 2210327 2210617 2210686) (-1176 "XPOLYC.spad" 2209633 2209649 2210242 2210311) (-1175 "XPBWPOLY.spad" 2208070 2208090 2209413 2209482) (-1174 "XF.spad" 2206531 2206546 2207972 2208065) (-1173 "XF.spad" 2204972 2204989 2206415 2206420) (-1172 "XFALG.spad" 2201996 2202012 2204898 2204967) (-1171 "XEXPPKG.spad" 2201247 2201273 2201986 2201991) (-1170 "XDPOLY.spad" 2200861 2200877 2201103 2201172) (-1169 "XALG.spad" 2200459 2200470 2200817 2200856) (-1168 "WUTSET.spad" 2196298 2196315 2200105 2200132) (-1167 "WP.spad" 2195312 2195356 2196156 2196223) (-1166 "WFFINTBS.spad" 2192875 2192897 2195302 2195307) (-1165 "WEIER.spad" 2191089 2191100 2192865 2192870) (-1164 "VSPACE.spad" 2190762 2190773 2191057 2191084) (-1163 "VSPACE.spad" 2190455 2190468 2190752 2190757) (-1162 "VOID.spad" 2190045 2190054 2190445 2190450) (-1161 "VIEW.spad" 2187667 2187676 2190035 2190040) (-1160 "VIEWDEF.spad" 2182864 2182873 2187657 2187662) (-1159 "VIEW3D.spad" 2166699 2166708 2182854 2182859) (-1158 "VIEW2D.spad" 2154436 2154445 2166689 2166694) (-1157 "VECTOR.spad" 2153113 2153124 2153364 2153391) (-1156 "VECTOR2.spad" 2151740 2151753 2153103 2153108) (-1155 "VECTCAT.spad" 2149628 2149639 2151696 2151735) (-1154 "VECTCAT.spad" 2147337 2147350 2149407 2149412) (-1153 "VARIABLE.spad" 2147117 2147132 2147327 2147332) (-1152 "UTYPE.spad" 2146751 2146760 2147097 2147112) (-1151 "UTSODETL.spad" 2146044 2146068 2146707 2146712) (-1150 "UTSODE.spad" 2144232 2144252 2146034 2146039) (-1149 "UTS.spad" 2139021 2139049 2142699 2142796) (-1148 "UTSCAT.spad" 2136472 2136488 2138919 2139016) (-1147 "UTSCAT.spad" 2133567 2133585 2136016 2136021) (-1146 "UTS2.spad" 2133160 2133195 2133557 2133562) (-1145 "URAGG.spad" 2127782 2127793 2133140 2133155) (-1144 "URAGG.spad" 2122378 2122391 2127738 2127743) (-1143 "UPXSSING.spad" 2120024 2120050 2121462 2121595) (-1142 "UPXS.spad" 2117051 2117079 2118156 2118305) (-1141 "UPXSCONS.spad" 2114808 2114828 2115183 2115332) (-1140 "UPXSCCA.spad" 2113266 2113286 2114654 2114803) (-1139 "UPXSCCA.spad" 2111866 2111888 2113256 2113261) (-1138 "UPXSCAT.spad" 2110447 2110463 2111712 2111861) (-1137 "UPXS2.spad" 2109988 2110041 2110437 2110442) (-1136 "UPSQFREE.spad" 2108400 2108414 2109978 2109983) (-1135 "UPSCAT.spad" 2105993 2106017 2108298 2108395) (-1134 "UPSCAT.spad" 2103292 2103318 2105599 2105604) (-1133 "UPOLYC.spad" 2098270 2098281 2103134 2103287) (-1132 "UPOLYC.spad" 2093140 2093153 2098006 2098011) (-1131 "UPOLYC2.spad" 2092609 2092628 2093130 2093135) (-1130 "UP.spad" 2089659 2089674 2090167 2090320) (-1129 "UPMP.spad" 2088549 2088562 2089649 2089654) (-1128 "UPDIVP.spad" 2088112 2088126 2088539 2088544) (-1127 "UPDECOMP.spad" 2086349 2086363 2088102 2088107) (-1126 "UPCDEN.spad" 2085556 2085572 2086339 2086344) (-1125 "UP2.spad" 2084918 2084939 2085546 2085551) (-1124 "UNISEG.spad" 2084271 2084282 2084837 2084842) (-1123 "UNISEG2.spad" 2083764 2083777 2084227 2084232) (-1122 "UNIFACT.spad" 2082865 2082877 2083754 2083759) (-1121 "ULS.spad" 2073424 2073452 2074517 2074946) (-1120 "ULSCONS.spad" 2067467 2067487 2067839 2067988) (-1119 "ULSCCAT.spad" 2065064 2065084 2067287 2067462) (-1118 "ULSCCAT.spad" 2062795 2062817 2065020 2065025) (-1117 "ULSCAT.spad" 2061011 2061027 2062641 2062790) (-1116 "ULS2.spad" 2060523 2060576 2061001 2061006) (-1115 "UFD.spad" 2059588 2059597 2060449 2060518) (-1114 "UFD.spad" 2058715 2058726 2059578 2059583) (-1113 "UDVO.spad" 2057562 2057571 2058705 2058710) (-1112 "UDPO.spad" 2054989 2055000 2057518 2057523) (-1111 "TYPE.spad" 2054911 2054920 2054969 2054984) (-1110 "TWOFACT.spad" 2053561 2053576 2054901 2054906) (-1109 "TUPLE.spad" 2052947 2052958 2053460 2053465) (-1108 "TUBETOOL.spad" 2049784 2049793 2052937 2052942) (-1107 "TUBE.spad" 2048425 2048442 2049774 2049779) (-1106 "TS.spad" 2047014 2047030 2047990 2048087) (-1105 "TSETCAT.spad" 2034129 2034146 2046970 2047009) (-1104 "TSETCAT.spad" 2021242 2021261 2034085 2034090) (-1103 "TRMANIP.spad" 2015608 2015625 2020948 2020953) (-1102 "TRIMAT.spad" 2014567 2014592 2015598 2015603) (-1101 "TRIGMNIP.spad" 2013084 2013101 2014557 2014562) (-1100 "TRIGCAT.spad" 2012596 2012605 2013074 2013079) (-1099 "TRIGCAT.spad" 2012106 2012117 2012586 2012591) (-1098 "TREE.spad" 2010677 2010688 2011713 2011740) (-1097 "TRANFUN.spad" 2010508 2010517 2010667 2010672) (-1096 "TRANFUN.spad" 2010337 2010348 2010498 2010503) (-1095 "TOPSP.spad" 2010011 2010020 2010327 2010332) (-1094 "TOOLSIGN.spad" 2009674 2009685 2010001 2010006) (-1093 "TEXTFILE.spad" 2008231 2008240 2009664 2009669) (-1092 "TEX.spad" 2005248 2005257 2008221 2008226) (-1091 "TEX1.spad" 2004804 2004815 2005238 2005243) (-1090 "TEMUTL.spad" 2004359 2004368 2004794 2004799) (-1089 "TBCMPPK.spad" 2002452 2002475 2004349 2004354) (-1088 "TBAGG.spad" 2001476 2001499 2002420 2002447) (-1087 "TBAGG.spad" 2000520 2000545 2001466 2001471) (-1086 "TANEXP.spad" 1999896 1999907 2000510 2000515) (-1085 "TABLE.spad" 1998307 1998330 1998577 1998604) (-1084 "TABLEAU.spad" 1997788 1997799 1998297 1998302) (-1083 "TABLBUMP.spad" 1994571 1994582 1997778 1997783) (-1082 "SYSSOLP.spad" 1992044 1992055 1994561 1994566) (-1081 "syntax.spad" 1988426 1988435 1992034 1992039) (-1080 "SYMTAB.spad" 1986482 1986491 1988416 1988421) (-1079 "SYMS.spad" 1982467 1982476 1986472 1986477) (-1078 "SYMPOLY.spad" 1981477 1981488 1981559 1981686) (-1077 "SYMFUNC.spad" 1980952 1980963 1981467 1981472) (-1076 "SYMBOL.spad" 1978288 1978297 1980942 1980947) (-1075 "SWITCH.spad" 1975045 1975054 1978278 1978283) (-1074 "SUTS.spad" 1971944 1971972 1973512 1973609) (-1073 "SUPXS.spad" 1968958 1968986 1970076 1970225) (-1072 "SUP.spad" 1965735 1965746 1966516 1966669) (-1071 "SUPFRACF.spad" 1964840 1964858 1965725 1965730) (-1070 "SUP2.spad" 1964230 1964243 1964830 1964835) (-1069 "SUMRF.spad" 1963196 1963207 1964220 1964225) (-1068 "SUMFS.spad" 1962829 1962846 1963186 1963191) (-1067 "SULS.spad" 1953375 1953403 1954481 1954910) (-1066 "SUCH.spad" 1953055 1953070 1953365 1953370) (-1065 "SUBSPACE.spad" 1945062 1945077 1953045 1953050) (-1064 "SUBRESP.spad" 1944222 1944236 1945018 1945023) (-1063 "STTF.spad" 1940321 1940337 1944212 1944217) (-1062 "STTFNC.spad" 1936789 1936805 1940311 1940316) (-1061 "STTAYLOR.spad" 1929187 1929198 1936670 1936675) (-1060 "STRTBL.spad" 1927692 1927709 1927841 1927868) (-1059 "STRING.spad" 1927101 1927110 1927115 1927142) (-1058 "STRICAT.spad" 1926877 1926886 1927057 1927096) (-1057 "STREAM.spad" 1923645 1923656 1926402 1926417) (-1056 "STREAM3.spad" 1923190 1923205 1923635 1923640) (-1055 "STREAM2.spad" 1922258 1922271 1923180 1923185) (-1054 "STREAM1.spad" 1921962 1921973 1922248 1922253) (-1053 "STINPROD.spad" 1920868 1920884 1921952 1921957) (-1052 "STEP.spad" 1920069 1920078 1920858 1920863) (-1051 "STBL.spad" 1918595 1918623 1918762 1918777) (-1050 "STAGG.spad" 1917660 1917671 1918575 1918590) (-1049 "STAGG.spad" 1916733 1916746 1917650 1917655) (-1048 "STACK.spad" 1916084 1916095 1916340 1916367) (-1047 "SREGSET.spad" 1913788 1913805 1915730 1915757) (-1046 "SRDCMPK.spad" 1912333 1912353 1913778 1913783) (-1045 "SRAGG.spad" 1907418 1907427 1912289 1912328) (-1044 "SRAGG.spad" 1902535 1902546 1907408 1907413) (-1043 "SQMATRIX.spad" 1900161 1900179 1901069 1901156) (-1042 "SPLTREE.spad" 1894713 1894726 1899597 1899624) (-1041 "SPLNODE.spad" 1891301 1891314 1894703 1894708) (-1040 "SPFCAT.spad" 1890078 1890087 1891291 1891296) (-1039 "SPECOUT.spad" 1888628 1888637 1890068 1890073) (-1038 "spad-parser.spad" 1888093 1888102 1888618 1888623) (-1037 "SPACEC.spad" 1872106 1872117 1888083 1888088) (-1036 "SPACE3.spad" 1871882 1871893 1872096 1872101) (-1035 "SORTPAK.spad" 1871427 1871440 1871838 1871843) (-1034 "SOLVETRA.spad" 1869184 1869195 1871417 1871422) (-1033 "SOLVESER.spad" 1867704 1867715 1869174 1869179) (-1032 "SOLVERAD.spad" 1863714 1863725 1867694 1867699) (-1031 "SOLVEFOR.spad" 1862134 1862152 1863704 1863709) (-1030 "SNTSCAT.spad" 1861722 1861739 1862090 1862129) (-1029 "SMTS.spad" 1859982 1860008 1861287 1861384) (-1028 "SMP.spad" 1857424 1857444 1857814 1857941) (-1027 "SMITH.spad" 1856267 1856292 1857414 1857419) (-1026 "SMATCAT.spad" 1854365 1854395 1856199 1856262) (-1025 "SMATCAT.spad" 1852407 1852439 1854243 1854248) (-1024 "SKAGG.spad" 1851356 1851367 1852363 1852402) (-1023 "SINT.spad" 1849664 1849673 1851222 1851351) (-1022 "SIMPAN.spad" 1849392 1849401 1849654 1849659) (-1021 "SIGNRF.spad" 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"SETAGG.spad" 1806546 1806559 1809993 1809998) (-1001 "SEGXCAT.spad" 1805658 1805671 1806526 1806541) (-1000 "SEG.spad" 1805471 1805482 1805577 1805582) (-999 "SEGCAT.spad" 1804291 1804301 1805451 1805466) (-998 "SEGBIND.spad" 1803364 1803374 1804246 1804251) (-997 "SEGBIND2.spad" 1803061 1803073 1803354 1803359) (-996 "SEG2.spad" 1802487 1802499 1803017 1803022) (-995 "SDVAR.spad" 1801764 1801774 1802477 1802482) (-994 "SDPOL.spad" 1799163 1799173 1799453 1799580) (-993 "SCPKG.spad" 1797243 1797253 1799153 1799158) (-992 "SCACHE.spad" 1795926 1795936 1797233 1797238) (-991 "SAOS.spad" 1795799 1795807 1795916 1795921) (-990 "SAERFFC.spad" 1795513 1795532 1795789 1795794) (-989 "SAE.spad" 1793692 1793707 1794302 1794437) (-988 "SAEFACT.spad" 1793394 1793413 1793682 1793687) (-987 "RURPK.spad" 1791036 1791051 1793384 1793389) (-986 "RULESET.spad" 1790478 1790501 1791026 1791031) (-985 "RULE.spad" 1788683 1788706 1790468 1790473) (-984 "RULECOLD.spad" 1788536 1788548 1788673 1788678) 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704746) (-404 "FST.spad" 701791 701799 703695 703700) (-403 "FSRED.spad" 701269 701285 701781 701786) (-402 "FSPRMELT.spad" 700093 700109 701226 701231) (-401 "FSPECF.spad" 698170 698186 700083 700088) (-400 "FS.spad" 692221 692231 697934 698165) (-399 "FS.spad" 686063 686075 691778 691783) (-398 "FSINT.spad" 685721 685737 686053 686058) (-397 "FSERIES.spad" 684908 684920 685541 685640) (-396 "FSCINT.spad" 684221 684237 684898 684903) (-395 "FSAGG.spad" 683326 683336 684165 684216) (-394 "FSAGG.spad" 682405 682417 683246 683251) (-393 "FSAGG2.spad" 681104 681120 682395 682400) (-392 "FS2UPS.spad" 675493 675527 681094 681099) (-391 "FS2.spad" 675138 675154 675483 675488) (-390 "FS2EXPXP.spad" 674261 674284 675128 675133) (-389 "FRUTIL.spad" 673203 673213 674251 674256) (-388 "FR.spad" 666900 666910 672230 672299) (-387 "FRNAALG.spad" 661987 661997 666842 666895) (-386 "FRNAALG.spad" 657086 657098 661943 661948) (-385 "FRNAAF2.spad" 656540 656558 657076 657081) (-384 "FRMOD.spad" 655935 655965 656472 656477) (-383 "FRIDEAL.spad" 655130 655151 655915 655930) (-382 "FRIDEAL2.spad" 654732 654764 655120 655125) (-381 "FRETRCT.spad" 654243 654253 654722 654727) (-380 "FRETRCT.spad" 653622 653634 654103 654108) (-379 "FRAMALG.spad" 651950 651963 653578 653617) (-378 "FRAMALG.spad" 650310 650325 651940 651945) (-377 "FRAC.spad" 647413 647423 647816 647989) (-376 "FRAC2.spad" 647016 647028 647403 647408) (-375 "FR2.spad" 646350 646362 647006 647011) (-374 "FPS.spad" 643159 643167 646240 646345) (-373 "FPS.spad" 639996 640006 643079 643084) (-372 "FPC.spad" 639038 639046 639898 639991) (-371 "FPC.spad" 638166 638176 639028 639033) (-370 "FPATMAB.spad" 637918 637928 638146 638161) (-369 "FPARFRAC.spad" 636391 636408 637908 637913) (-368 "FORTRAN.spad" 634891 634940 636381 636386) (-367 "FORT.spad" 633820 633828 634881 634886) (-366 "FORTFN.spad" 630980 630988 633800 633815) (-365 "FORTCAT.spad" 630654 630662 630960 630975) (-364 "FORMULA.spad" 627992 628000 630644 630649) (-363 "FORMULA1.spad" 627471 627481 627982 627987) (-362 "FORDER.spad" 627162 627186 627461 627466) (-361 "FOP.spad" 626363 626371 627152 627157) (-360 "FNLA.spad" 625787 625809 626331 626358) (-359 "FNCAT.spad" 624115 624123 625777 625782) (-358 "FNAME.spad" 624007 624015 624105 624110) (-357 "FMTC.spad" 623805 623813 623933 624002) (-356 "FMONOID.spad" 620860 620870 623761 623766) (-355 "FM.spad" 620555 620567 620794 620821) (-354 "FMFUN.spad" 617575 617583 620535 620550) (-353 "FMC.spad" 616617 616625 617555 617570) (-352 "FMCAT.spad" 614271 614289 616585 616612) (-351 "FM1.spad" 613628 613640 614205 614232) (-350 "FLOATRP.spad" 611349 611363 613618 613623) (-349 "FLOAT.spad" 604513 604521 611215 611344) (-348 "FLOATCP.spad" 601930 601944 604503 604508) (-347 "FLINEXP.spad" 601642 601652 601910 601925) (-346 "FLINEXP.spad" 601308 601320 601578 601583) (-345 "FLASORT.spad" 600628 600640 601298 601303) (-344 "FLALG.spad" 598274 598293 600554 600623) (-343 "FLAGG.spad" 595280 595290 598242 598269) (-342 "FLAGG.spad" 592199 592211 595163 595168) (-341 "FLAGG2.spad" 590880 590896 592189 592194) (-340 "FINRALG.spad" 588909 588922 590836 590875) (-339 "FINRALG.spad" 586864 586879 588793 588798) (-338 "FINITE.spad" 586016 586024 586854 586859) (-337 "FINAALG.spad" 574997 575007 585958 586011) (-336 "FINAALG.spad" 563990 564002 574953 574958) (-335 "FILE.spad" 563573 563583 563980 563985) (-334 "FILECAT.spad" 562091 562108 563563 563568) (-333 "FIELD.spad" 561497 561505 561993 562086) (-332 "FIELD.spad" 560989 560999 561487 561492) (-331 "FGROUP.spad" 559598 559608 560969 560984) (-330 "FGLMICPK.spad" 558385 558400 559588 559593) (-329 "FFX.spad" 557760 557775 558101 558194) (-328 "FFSLPE.spad" 557249 557270 557750 557755) (-327 "FFPOLY.spad" 548501 548512 557239 557244) (-326 "FFPOLY2.spad" 547561 547578 548491 548496) (-325 "FFP.spad" 546958 546978 547277 547370) (-324 "FF.spad" 546406 546422 546639 546732) (-323 "FFNBX.spad" 544918 544938 546122 546215) (-322 "FFNBP.spad" 543431 543448 544634 544727) (-321 "FFNB.spad" 541896 541917 543112 543205) (-320 "FFINTBAS.spad" 539310 539329 541886 541891) (-319 "FFIELDC.spad" 536885 536893 539212 539305) (-318 "FFIELDC.spad" 534546 534556 536875 536880) (-317 "FFHOM.spad" 533294 533311 534536 534541) (-316 "FFF.spad" 530729 530740 533284 533289) (-315 "FFCGX.spad" 529576 529596 530445 530538) (-314 "FFCGP.spad" 528465 528485 529292 529385) (-313 "FFCG.spad" 527257 527278 528146 528239) (-312 "FFCAT.spad" 520158 520180 527096 527252) (-311 "FFCAT.spad" 513138 513162 520078 520083) (-310 "FFCAT2.spad" 512883 512923 513128 513133) (-309 "FEXPR.spad" 504596 504642 512643 512682) (-308 "FEVALAB.spad" 504302 504312 504586 504591) (-307 "FEVALAB.spad" 503793 503805 504079 504084) (-306 "FDIV.spad" 503235 503259 503783 503788) (-305 "FDIVCAT.spad" 501277 501301 503225 503230) (-304 "FDIVCAT.spad" 499317 499343 501267 501272) (-303 "FDIV2.spad" 498971 499011 499307 499312) (-302 "FCPAK1.spad" 497524 497532 498961 498966) (-301 "FCOMP.spad" 496903 496913 497514 497519) (-300 "FC.spad" 486728 486736 496893 496898) (-299 "FAXF.spad" 479663 479677 486630 486723) (-298 "FAXF.spad" 472650 472666 479619 479624) (-297 "FARRAY.spad" 470796 470806 471833 471860) (-296 "FAMR.spad" 468916 468928 470694 470791) (-295 "FAMR.spad" 467020 467034 468800 468805) (-294 "FAMONOID.spad" 466670 466680 466974 466979) (-293 "FAMONC.spad" 464892 464904 466660 466665) (-292 "FAGROUP.spad" 464498 464508 464788 464815) (-291 "FACUTIL.spad" 462694 462711 464488 464493) (-290 "FACTFUNC.spad" 461870 461880 462684 462689) (-289 "EXPUPXS.spad" 458703 458726 460002 460151) (-288 "EXPRTUBE.spad" 455931 455939 458693 458698) (-287 "EXPRODE.spad" 452803 452819 455921 455926) (-286 "EXPR.spad" 448105 448115 448819 449222) (-285 "EXPR2UPS.spad" 444197 444210 448095 448100) (-284 "EXPR2.spad" 443900 443912 444187 444192) (-283 "EXPEXPAN.spad" 440841 440866 441475 441568) (-282 "EXIT.spad" 440512 440520 440831 440836) (-281 "EVALCYC.spad" 439970 439984 440502 440507) (-280 "EVALAB.spad" 439534 439544 439960 439965) (-279 "EVALAB.spad" 439096 439108 439524 439529) (-278 "EUCDOM.spad" 436638 436646 439022 439091) (-277 "EUCDOM.spad" 434242 434252 436628 436633) (-276 "ESTOOLS.spad" 426082 426090 434232 434237) (-275 "ESTOOLS2.spad" 425683 425697 426072 426077) (-274 "ESTOOLS1.spad" 425368 425379 425673 425678) (-273 "ES.spad" 417915 417923 425358 425363) (-272 "ES.spad" 410370 410380 417815 417820) (-271 "ESCONT.spad" 407143 407151 410360 410365) (-270 "ESCONT1.spad" 406892 406904 407133 407138) (-269 "ES2.spad" 406387 406403 406882 406887) (-268 "ES1.spad" 405953 405969 406377 406382) (-267 "ERROR.spad" 403274 403282 405943 405948) (-266 "EQTBL.spad" 401746 401768 401955 401982) (-265 "EQ.spad" 396630 396640 399429 399538) (-264 "EQ2.spad" 396346 396358 396620 396625) (-263 "EP.spad" 392660 392670 396336 396341) (-262 "ENTIRER.spad" 392328 392336 392604 392655) (-261 "EMR.spad" 391529 391570 392254 392323) (-260 "ELTAGG.spad" 389769 389788 391519 391524) (-259 "ELTAGG.spad" 387973 387994 389725 389730) (-258 "ELTAB.spad" 387420 387438 387963 387968) (-257 "ELFUTS.spad" 386799 386818 387410 387415) (-256 "ELEMFUN.spad" 386488 386496 386789 386794) (-255 "ELEMFUN.spad" 386175 386185 386478 386483) (-254 "ELAGG.spad" 384106 384116 386143 386170) (-253 "ELAGG.spad" 381986 381998 384025 384030) (-252 "EFUPXS.spad" 378762 378792 381942 381947) (-251 "EFULS.spad" 375598 375621 378718 378723) (-250 "EFSTRUC.spad" 373553 373569 375588 375593) (-249 "EF.spad" 368319 368335 373543 373548) (-248 "EAB.spad" 366595 366603 368309 368314) (-247 "E04UCFA.spad" 366131 366139 366585 366590) (-246 "E04NAFA.spad" 365708 365716 366121 366126) (-245 "E04MBFA.spad" 365288 365296 365698 365703) (-244 "E04JAFA.spad" 364824 364832 365278 365283) (-243 "E04GCFA.spad" 364360 364368 364814 364819) (-242 "E04FDFA.spad" 363896 363904 364350 364355) (-241 "E04DGFA.spad" 363432 363440 363886 363891) (-240 "E04AGNT.spad" 359274 359282 363422 363427) (-239 "DVARCAT.spad" 355959 355969 359264 359269) (-238 "DVARCAT.spad" 352642 352654 355949 355954) (-237 "DSMP.spad" 350076 350090 350381 350508) (-236 "DROPT.spad" 344021 344029 350066 350071) (-235 "DROPT1.spad" 343684 343694 344011 344016) (-234 "DROPT0.spad" 338511 338519 343674 343679) (-233 "DRAWPT.spad" 336666 336674 338501 338506) (-232 "DRAW.spad" 329266 329279 336656 336661) (-231 "DRAWHACK.spad" 328574 328584 329256 329261) (-230 "DRAWCX.spad" 326016 326024 328564 328569) (-229 "DRAWCURV.spad" 325553 325568 326006 326011) (-228 "DRAWCFUN.spad" 314725 314733 325543 325548) (-227 "DQAGG.spad" 312881 312891 314681 314720) (-226 "DPOLCAT.spad" 308222 308238 312749 312876) (-225 "DPOLCAT.spad" 303649 303667 308178 308183) (-224 "DPMO.spad" 297636 297652 297774 298070) (-223 "DPMM.spad" 291636 291654 291761 292057) (-222 "domain.spad" 291152 291160 291626 291631) (-221 "DMP.spad" 288377 288392 288949 289076) (-220 "DLP.spad" 287725 287735 288367 288372) (-219 "DLIST.spad" 286137 286147 286908 286935) (-218 "DLAGG.spad" 284538 284548 286117 286132) (-217 "DIVRING.spad" 283985 283993 284482 284533) (-216 "DIVRING.spad" 283476 283486 283975 283980) (-215 "DISPLAY.spad" 281656 281664 283466 283471) (-214 "DIRPROD.spad" 272915 272931 273555 273684) (-213 "DIRPROD2.spad" 271723 271741 272905 272910) (-212 "DIRPCAT.spad" 270655 270671 271577 271718) (-211 "DIRPCAT.spad" 269327 269345 270251 270256) (-210 "DIOSP.spad" 268152 268160 269317 269322) (-209 "DIOPS.spad" 267124 267134 268120 268147) (-208 "DIOPS.spad" 266082 266094 267080 267085) (-207 "DIFRING.spad" 265374 265382 266062 266077) (-206 "DIFRING.spad" 264674 264684 265364 265369) (-205 "DIFEXT.spad" 263833 263843 264654 264669) (-204 "DIFEXT.spad" 262909 262921 263732 263737) (-203 "DIAGG.spad" 262527 262537 262877 262904) (-202 "DIAGG.spad" 262165 262177 262517 262522) (-201 "DHMATRIX.spad" 260469 260479 261622 261649) (-200 "DFSFUN.spad" 253877 253885 260459 260464) (-199 "DFLOAT.spad" 250400 250408 253767 253872) (-198 "DFINTTLS.spad" 248609 248625 250390 250395) (-197 "DERHAM.spad" 246519 246551 248589 248604) (-196 "DEQUEUE.spad" 245837 245847 246126 246153) (-195 "DEGRED.spad" 245452 245466 245827 245832) (-194 "DEFINTRF.spad" 242977 242987 245442 245447) (-193 "DEFINTEF.spad" 241473 241489 242967 242972) (-192 "DECIMAL.spad" 239357 239365 239943 240036) (-191 "DDFACT.spad" 237156 237173 239347 239352) (-190 "DBLRESP.spad" 236754 236778 237146 237151) (-189 "DBASE.spad" 235326 235336 236744 236749) (-188 "D03FAFA.spad" 235154 235162 235316 235321) (-187 "D03EEFA.spad" 234974 234982 235144 235149) (-186 "D03AGNT.spad" 234054 234062 234964 234969) (-185 "D02EJFA.spad" 233516 233524 234044 234049) (-184 "D02CJFA.spad" 232994 233002 233506 233511) (-183 "D02BHFA.spad" 232484 232492 232984 232989) (-182 "D02BBFA.spad" 231974 231982 232474 232479) (-181 "D02AGNT.spad" 226778 226786 231964 231969) (-180 "D01WGTS.spad" 225097 225105 226768 226773) (-179 "D01TRNS.spad" 225074 225082 225087 225092) (-178 "D01GBFA.spad" 224596 224604 225064 225069) (-177 "D01FCFA.spad" 224118 224126 224586 224591) (-176 "D01ASFA.spad" 223586 223594 224108 224113) (-175 "D01AQFA.spad" 223032 223040 223576 223581) (-174 "D01APFA.spad" 222456 222464 223022 223027) (-173 "D01ANFA.spad" 221950 221958 222446 222451) (-172 "D01AMFA.spad" 221460 221468 221940 221945) (-171 "D01ALFA.spad" 221000 221008 221450 221455) (-170 "D01AKFA.spad" 220526 220534 220990 220995) (-169 "D01AJFA.spad" 220049 220057 220516 220521) (-168 "D01AGNT.spad" 216108 216116 220039 220044) (-167 "CYCLOTOM.spad" 215614 215622 216098 216103) (-166 "CYCLES.spad" 212446 212454 215604 215609) (-165 "CVMP.spad" 211863 211873 212436 212441) (-164 "CTRIGMNP.spad" 210353 210369 211853 211858) (-163 "CSTTOOLS.spad" 209596 209609 210343 210348) (-162 "CRFP.spad" 203300 203313 209586 209591) (-161 "CRAPACK.spad" 202343 202353 203290 203295) (-160 "CPMATCH.spad" 201843 201858 202268 202273) (-159 "CPIMA.spad" 201548 201567 201833 201838) (-158 "COORDSYS.spad" 196441 196451 201538 201543) (-157 "CONTFRAC.spad" 192053 192063 196343 196436) (-156 "COMRING.spad" 191727 191735 191991 192048) (-155 "COMPPROP.spad" 191241 191249 191717 191722) (-154 "COMPLPAT.spad" 191008 191023 191231 191236) (-153 "COMPLEX.spad" 185041 185051 185285 185546) (-152 "COMPLEX2.spad" 184754 184766 185031 185036) (-151 "COMPFACT.spad" 184356 184370 184744 184749) (-150 "COMPCAT.spad" 182412 182422 184078 184351) (-149 "COMPCAT.spad" 180175 180187 181843 181848) (-148 "COMMUPC.spad" 179921 179939 180165 180170) (-147 "COMMONOP.spad" 179454 179462 179911 179916) (-146 "COMM.spad" 179263 179271 179444 179449) (-145 "COMBOPC.spad" 178168 178176 179253 179258) (-144 "COMBINAT.spad" 176913 176923 178158 178163) (-143 "COMBF.spad" 174281 174297 176903 176908) (-142 "COLOR.spad" 173118 173126 174271 174276) (-141 "CMPLXRT.spad" 172827 172844 173108 173113) (-140 "CLIP.spad" 168919 168927 172817 172822) (-139 "CLIF.spad" 167558 167574 168875 168914) (-138 "CLAGG.spad" 164033 164043 167538 167553) (-137 "CLAGG.spad" 160389 160401 163896 163901) (-136 "CINTSLPE.spad" 159714 159727 160379 160384) (-135 "CHVAR.spad" 157792 157814 159704 159709) (-134 "CHARZ.spad" 157707 157715 157772 157787) (-133 "CHARPOL.spad" 157215 157225 157697 157702) (-132 "CHARNZ.spad" 156968 156976 157195 157210) (-131 "CHAR.spad" 154858 154866 156958 156963) (-130 "CFCAT.spad" 154174 154182 154848 154853) (-129 "CDEN.spad" 153332 153346 154164 154169) (-128 "CCLASS.spad" 151481 151489 152743 152782) (-127 "CARTEN.spad" 146584 146608 151471 151476) (-126 "CARTEN2.spad" 145970 145997 146574 146579) (-125 "CARD.spad" 143259 143267 145944 145965) (-124 "CACHSET.spad" 142881 142889 143249 143254) (-123 "CABMON.spad" 142434 142442 142871 142876) (-122 "BTREE.spad" 141503 141513 142041 142068) (-121 "BTOURN.spad" 140506 140516 141110 141137) (-120 "BTCAT.spad" 139882 139892 140462 140501) (-119 "BTCAT.spad" 139290 139302 139872 139877) (-118 "BTAGG.spad" 138306 138314 139246 139285) (-117 "BTAGG.spad" 137354 137364 138296 138301) (-116 "BSTREE.spad" 136089 136099 136961 136988) (-115 "BRILL.spad" 134284 134295 136079 136084) (-114 "BRAGG.spad" 133198 133208 134264 134279) (-113 "BRAGG.spad" 132086 132098 133154 133159) (-112 "BPADICRT.spad" 130070 130082 130325 130418) (-111 "BPADIC.spad" 129734 129746 129996 130065) (-110 "BOUNDZRO.spad" 129390 129407 129724 129729) (-109 "BOP.spad" 124854 124862 129380 129385) (-108 "BOP1.spad" 122240 122250 124810 124815) (-107 "BOOLEAN.spad" 121098 121106 122230 122235) (-106 "BMODULE.spad" 120810 120822 121066 121093) (-105 "BITS.spad" 120229 120237 120446 120473) (-104 "BINFILE.spad" 119572 119580 120219 120224) (-103 "BINARY.spad" 117465 117473 118042 118135) (-102 "BGAGG.spad" 116650 116660 117433 117460) (-101 "BGAGG.spad" 115855 115867 116640 116645) (-100 "BFUNCT.spad" 115419 115427 115835 115850) (-99 "BEZOUT.spad" 114554 114580 115369 115374) (-98 "BBTREE.spad" 111374 111383 114161 114188) (-97 "BASTYPE.spad" 111047 111054 111364 111369) (-96 "BASTYPE.spad" 110718 110727 111037 111042) (-95 "BALFACT.spad" 110158 110170 110708 110713) (-94 "AUTOMOR.spad" 109605 109614 110138 110153) (-93 "ATTREG.spad" 106324 106331 109357 109600) (-92 "ATTRBUT.spad" 102347 102354 106304 106319) (-91 "ATRIG.spad" 101817 101824 102337 102342) (-90 "ATRIG.spad" 101285 101294 101807 101812) (-89 "ASTACK.spad" 100618 100627 100892 100919) (-88 "ASSOCEQ.spad" 99418 99429 100574 100579) (-87 "ASP9.spad" 98499 98512 99408 99413) (-86 "ASP8.spad" 97542 97555 98489 98494) (-85 "ASP80.spad" 96864 96877 97532 97537) (-84 "ASP7.spad" 96024 96037 96854 96859) (-83 "ASP78.spad" 95475 95488 96014 96019) (-82 "ASP77.spad" 94844 94857 95465 95470) (-81 "ASP74.spad" 93936 93949 94834 94839) (-80 "ASP73.spad" 93207 93220 93926 93931) (-79 "ASP6.spad" 91839 91852 93197 93202) (-78 "ASP55.spad" 90348 90361 91829 91834) (-77 "ASP50.spad" 88165 88178 90338 90343) (-76 "ASP4.spad" 87460 87473 88155 88160) (-75 "ASP49.spad" 86459 86472 87450 87455) (-74 "ASP42.spad" 84866 84905 86449 86454) (-73 "ASP41.spad" 83445 83484 84856 84861) (-72 "ASP35.spad" 82433 82446 83435 83440) (-71 "ASP34.spad" 81734 81747 82423 82428) (-70 "ASP33.spad" 81294 81307 81724 81729) (-69 "ASP31.spad" 80434 80447 81284 81289) (-68 "ASP30.spad" 79326 79339 80424 80429) (-67 "ASP29.spad" 78792 78805 79316 79321) (-66 "ASP28.spad" 70065 70078 78782 78787) (-65 "ASP27.spad" 68962 68975 70055 70060) (-64 "ASP24.spad" 68049 68062 68952 68957) (-63 "ASP20.spad" 67265 67278 68039 68044) (-62 "ASP1.spad" 66646 66659 67255 67260) (-61 "ASP19.spad" 61332 61345 66636 66641) (-60 "ASP12.spad" 60746 60759 61322 61327) (-59 "ASP10.spad" 60017 60030 60736 60741) (-58 "ARRAY2.spad" 59377 59386 59624 59651) (-57 "ARRAY1.spad" 58212 58221 58560 58587) (-56 "ARRAY12.spad" 56881 56892 58202 58207) (-55 "ARR2CAT.spad" 52531 52552 56837 56876) (-54 "ARR2CAT.spad" 48213 48236 52521 52526) (-53 "APPRULE.spad" 47457 47479 48203 48208) (-52 "APPLYORE.spad" 47072 47085 47447 47452) (-51 "ANY.spad" 45414 45421 47062 47067) (-50 "ANY1.spad" 44485 44494 45404 45409) (-49 "ANTISYM.spad" 42924 42940 44465 44480) (-48 "ANON.spad" 42837 42844 42914 42919) (-47 "AN.spad" 41140 41147 42655 42748) (-46 "AMR.spad" 39319 39330 41038 41135) (-45 "AMR.spad" 37335 37348 39056 39061) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865)) 
\ No newline at end of file
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index cdc42401..37cf87c3 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,14 +1,14 @@
 
-(142085 . 3409262770)        
-(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1004))) ((#0=(-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) #0#) |has| (-2 (|:| -2581 |#1|) (|:| -1860 |#2|)) (-280 (-2 (|:| -2581 |#1|) (|:| -1860 |#2|))))) 
+(142085 . 3409435995)        
+(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1005))) ((#0=(-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) #0#) |has| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-280 (-2 (|:| -2585 |#1|) (|:| -1859 |#2|))))) 
 (((|#2| |#2|) . T)) 
 ((((-517)) . T)) 
-((($ $) -3745 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-832))) ((|#2| |#2|) . T) ((#0=(-377 (-517)) #0#) |has| |#2| (-37 (-377 (-517))))) 
+((($ $) -3747 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-832))) ((|#2| |#2|) . T) ((#0=(-377 (-517)) #0#) |has| |#2| (-37 (-377 (-517))))) 
 ((($) . T)) 
 (((|#1|) . T)) 
 ((($) . T) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
 (((|#2|) . T)) 
-((($) -3745 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-832))) ((|#2|) . T) (((-377 (-517))) |has| |#2| (-37 (-377 (-517))))) 
+((($) -3747 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-832))) ((|#2|) . T) (((-377 (-517))) |has| |#2| (-37 (-377 (-517))))) 
 (|has| |#1| (-832)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
@@ -18,33 +18,33 @@
 ((($) . T)) 
 (((|#2| |#2|) . T)) 
 ((((-131)) . T)) 
-((((-493)) . T) (((-1058)) . T) (((-199)) . T) (((-349)) . T) (((-815 (-349))) . T)) 
+((((-493)) . T) (((-1059)) . T) (((-199)) . T) (((-349)) . T) (((-815 (-349))) . T)) 
 (((|#1|) . T)) 
 ((((-199)) . T) (((-787)) . T)) 
-(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) 
+(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1005)))) 
 (((|#1|) . T)) 
-(-3745 (|has| |#1| (-21)) (|has| |#1| (-777))) 
-((($ $) . T) ((#0=(-377 (-517)) #0#) -3745 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1| |#1|) . T)) 
-(-3745 (|has| |#1| (-752)) (|has| |#1| (-779))) 
-((((-377 (-517))) |has| |#1| (-953 (-377 (-517)))) (((-517)) |has| |#1| (-953 (-517))) ((|#1|) . T)) 
+(-3747 (|has| |#1| (-21)) (|has| |#1| (-777))) 
+((($ $) . T) ((#0=(-377 (-517)) #0#) -3747 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1| |#1|) . T)) 
+(-3747 (|has| |#1| (-752)) (|has| |#1| (-779))) 
+((((-377 (-517))) |has| |#1| (-954 (-377 (-517)))) (((-517)) |has| |#1| (-954 (-517))) ((|#1|) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
-(-3745 (|has| |#1| (-333)) (|has| |#1| (-509))) 
+(-3747 (|has| |#1| (-333)) (|has| |#1| (-509))) 
 (|has| |#1| (-777)) 
-(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) 
+(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1005)))) 
 (((|#1| |#2| |#3|) . T)) 
 (((|#4|) . T)) 
-((($) . T) (((-377 (-517))) -3745 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) 
+((($) . T) (((-377 (-517))) -3747 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) 
 ((((-787)) . T)) 
-((((-787)) |has| |#1| (-1004))) 
+((((-787)) |has| |#1| (-1005))) 
 (((|#1|) . T) ((|#2|) . T)) 
-(((|#1|) . T) (((-517)) |has| |#1| (-953 (-517))) (((-377 (-517))) |has| |#1| (-953 (-377 (-517))))) 
-(-3745 (|has| |#2| (-156)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-832))) 
-(-3745 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-832))) 
-(((|#2| (-450 (-3533 |#1|) (-703))) . T)) 
-(((|#1| (-489 (-1075))) . T)) 
+(((|#1|) . T) (((-517)) |has| |#1| (-954 (-517))) (((-377 (-517))) |has| |#1| (-954 (-377 (-517))))) 
+(-3747 (|has| |#2| (-156)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-832))) 
+(-3747 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-832))) 
+(((|#2| (-450 (-3535 |#1|) (-703))) . T)) 
+(((|#1| (-489 (-1076))) . T)) 
 (((#0=(-794 |#1|) #0#) . T) ((#1=(-377 (-517)) #1#) . T) (($ $) . T)) 
-((((-2 (|:| -2581 |#1|) (|:| -1860 |#2|))) . T)) 
+((((-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) . T)) 
 (|has| |#4| (-338)) 
 (|has| |#3| (-338)) 
 (((|#1|) . T)) 
@@ -54,76 +54,76 @@
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 (|has| |#1| (-134)) 
 (|has| |#1| (-509)) 
-(-3745 (|has| |#1| (-333)) (|has| |#1| (-509))) 
-(-3745 (|has| |#1| (-333)) (|has| |#1| (-509))) 
+(-3747 (|has| |#1| (-333)) (|has| |#1| (-509))) 
+(-3747 (|has| |#1| (-333)) (|has| |#1| (-509))) 
 ((($) . T)) 
-((((-787)) -3745 (|has| |#1| (-557 (-787))) (|has| |#1| (-779)) (|has| |#1| (-1004)))) 
+((((-787)) -3747 (|has| |#1| (-557 (-787))) (|has| |#1| (-779)) (|has| |#1| (-1005)))) 
 ((((-493)) |has| |#1| (-558 (-493)))) 
 ((($) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) . T)) 
 ((($) . T)) 
-(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) 
-(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) 
+(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1005)))) 
+(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1005)))) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 ((((-377 (-517))) . T) (($) . T)) 
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+((((-377 (-517))) -3747 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (((-1149 |#1| |#2| |#3|)) |has| |#1| (-333)) (($) . T) ((|#1|) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 (((|#1|) . T)) 
-(((|#1|) . T) (((-377 (-517))) -3745 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) . T)) 
+(((|#1|) . T) (((-377 (-517))) -3747 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) . T)) 
 (((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) (($) . T)) 
-(-3745 (|has| |#1| (-779)) (|has| |#1| (-1004))) 
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 (((|#1| |#2|) . T)) 
 ((((-787)) . T)) 
 (((|#1|) . T)) 
-(((#0=(-377 (-517)) #0#) |has| |#2| (-37 (-377 (-517)))) ((|#2| |#2|) . T) (($ $) -3745 (|has| |#2| (-156)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-832)))) 
+(((#0=(-377 (-517)) #0#) |has| |#2| (-37 (-377 (-517)))) ((|#2| |#2|) . T) (($ $) -3747 (|has| |#2| (-156)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-832)))) 
 (((|#1|) . T)) 
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 (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) 
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+(((#0=(-377 (-517)) #0#) |has| |#1| (-37 (-377 (-517)))) ((|#1| |#1|) . T) (($ $) -3747 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-832)))) 
 ((($ $) . T)) 
 (((|#2|) . T)) 
-((((-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2|) . T) (($) -3745 (|has| |#2| (-156)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-832)))) 
-((((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) . T) (($) -3745 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-832)))) 
+((((-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2|) . T) (($) -3747 (|has| |#2| (-156)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-832)))) 
+((((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) . T) (($) -3747 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-832)))) 
 ((($) . T)) 
 (|has| |#1| (-338)) 
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-((((-2 (|:| -2581 |#1|) (|:| -1860 |#2|))) . T)) 
-(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) 
+((((-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) . T)) 
+(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1005)))) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 (((|#1| |#2|) . T)) 
-(-3745 (|has| |#1| (-21)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-823 (-1075))) (|has| |#1| (-962))) 
-(-3745 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-823 (-1075))) (|has| |#1| (-962))) 
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 (((|#1| |#1|) . T)) 
 (|has| |#1| (-509)) 
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 ((((-377 |#2|)) . T) (((-377 (-517))) . T) (($) . T)) 
-(-3745 (|has| |#1| (-21)) (|has| |#1| (-777))) 
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 ((($ $) . T) ((#0=(-377 (-517)) #0#) . T)) 
-(-3745 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) 
-(-3745 (|has| |#1| (-779)) (|has| |#1| (-1004))) 
-(|has| |#1| (-1004)) 
-(-3745 (|has| |#1| (-779)) (|has| |#1| (-1004))) 
-(|has| |#1| (-1004)) 
-(-3745 (|has| |#1| (-779)) (|has| |#1| (-1004))) 
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+(|has| |#1| (-1005)) 
+(-3747 (|has| |#1| (-779)) (|has| |#1| (-1005))) 
 (|has| |#1| (-777)) 
 ((($) . T) (((-377 (-517))) . T)) 
 (((|#1|) . T)) 
-(-3745 (|has| |#1| (-333)) (|has| |#1| (-319))) 
-(-3745 (|has| |#4| (-725)) (|has| |#4| (-777))) 
-(-3745 (|has| |#4| (-725)) (|has| |#4| (-777))) 
-(-3745 (|has| |#3| (-725)) (|has| |#3| (-777))) 
-(-3745 (|has| |#3| (-725)) (|has| |#3| (-777))) 
+(-3747 (|has| |#1| (-333)) (|has| |#1| (-319))) 
+(-3747 (|has| |#4| (-725)) (|has| |#4| (-777))) 
+(-3747 (|has| |#4| (-725)) (|has| |#4| (-777))) 
+(-3747 (|has| |#3| (-725)) (|has| |#3| (-777))) 
+(-3747 (|has| |#3| (-725)) (|has| |#3| (-777))) 
 (((|#1| |#2|) . T)) 
 (((|#1| |#2|) . T)) 
-(|has| |#1| (-1004)) 
-(|has| |#1| (-1004)) 
-(((|#1| (-1075) (-994 (-1075)) (-489 (-994 (-1075)))) . T)) 
+(|has| |#1| (-1005)) 
+(|has| |#1| (-1005)) 
+(((|#1| (-1076) (-995 (-1076)) (-489 (-995 (-1076)))) . T)) 
 ((((-517) |#1|) . T)) 
 ((((-517)) . T)) 
 ((((-517)) . T)) 
@@ -132,32 +132,32 @@
 ((((-517)) . T)) 
 ((((-517)) . T)) 
 (((|#1|) . T)) 
-(-3745 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-962))) 
+(-3747 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-963))) 
 (((|#1| (-703)) . T)) 
 (|has| |#2| (-725)) 
-(-3745 (|has| |#2| (-725)) (|has| |#2| (-777))) 
+(-3747 (|has| |#2| (-725)) (|has| |#2| (-777))) 
 (|has| |#2| (-777)) 
 (((|#1| |#2| |#3| |#4|) . T)) 
 (((|#1| |#2|) . T)) 
-((((-1058) |#1|) . T)) 
-((((-787)) -3745 (|has| |#1| (-557 (-787))) (|has| |#1| (-1004)))) 
+((((-1059) |#1|) . T)) 
+((((-787)) -3747 (|has| |#1| (-557 (-787))) (|has| |#1| (-1005)))) 
 (((|#1|) . T)) 
 (((|#3| (-703)) . T)) 
 (|has| |#1| (-134)) 
 (|has| |#1| (-132)) 
-(-3745 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) 
-(-3745 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) 
-(|has| |#1| (-1004)) 
+(-3747 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) 
+(-3747 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) 
+(|has| |#1| (-1005)) 
 ((((-377 (-517))) . T) (((-517)) . T)) 
-((((-1075) |#2|) |has| |#2| (-478 (-1075) |#2|)) ((|#2| |#2|) |has| |#2| (-280 |#2|))) 
+((((-1076) |#2|) |has| |#2| (-478 (-1076) |#2|)) ((|#2| |#2|) |has| |#2| (-280 |#2|))) 
 ((((-377 (-517))) . T) (((-517)) . T)) 
 (((|#1|) . T) (($) . T)) 
 ((((-517)) . T)) 
 ((((-517)) . T)) 
-((($) -3745 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-377 (-517))) -3745 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) |has| |#1| (-156))) 
+((($) -3747 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-377 (-517))) -3747 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) |has| |#1| (-156))) 
 ((((-517)) . T)) 
 ((((-517)) . T)) 
-(((#0=(-632) (-1071 #0#)) . T)) 
+(((#0=(-632) (-1072 #0#)) . T)) 
 ((((-377 (-517))) . T) (($) . T)) 
 (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) 
 ((((-517) |#1|) . T)) 
@@ -167,18 +167,18 @@
 (((|#1|) . T)) 
 (((|#1| |#2|) . T)) 
 ((((-787)) . T)) 
-(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) 
-((((-1058) |#1|) . T)) 
+(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1005)))) 
+((((-1059) |#1|) . T)) 
 (((|#3| |#3|) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 (((|#1| |#1|) . T)) 
-(((#0=(-377 (-517)) #0#) |has| |#1| (-37 (-377 (-517)))) ((|#1| |#1|) . T) (($ $) -3745 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-832)))) 
-((($ $) -3745 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-832))) ((|#1| |#1|) . T) ((#0=(-377 (-517)) #0#) |has| |#1| (-37 (-377 (-517))))) 
+(((#0=(-377 (-517)) #0#) |has| |#1| (-37 (-377 (-517)))) ((|#1| |#1|) . T) (($ $) -3747 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-832)))) 
+((($ $) -3747 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-832))) ((|#1| |#1|) . T) ((#0=(-377 (-517)) #0#) |has| |#1| (-37 (-377 (-517))))) 
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+((((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) . T) (($) -3747 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-832)))) 
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@@ -253,73 +253,73 @@
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@@ -677,26 +677,26 @@
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 (|has| |#1| (-37 (-377 (-517)))) 
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+((((-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) . T)) 
 ((((-787)) . T)) 
-((((-2 (|:| -2581 (-1058)) (|:| -1860 |#1|))) . T)) 
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 (|has| |#1| (-37 (-377 (-517)))) 
-((((-358) (-2 (|:| -2581 (-1058)) (|:| -1860 |#1|))) . T)) 
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 (|has| |#1| (-37 (-377 (-517)))) 
-(|has| |#2| (-1051)) 
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 (((|#1|) . T)) 
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 (|has| |#1| (-509)) 
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 ((((-517) |#1|) . T)) 
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 (((|#2|) . T)) 
 ((((-787)) . T)) 
 ((((-751 |#1|)) . T)) 
 (((|#2|) |has| |#2| (-156))) 
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+((((-1076) (-51)) . T)) 
 (((|#1|) . T)) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
@@ -704,17 +704,17 @@
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 ((((-787)) . T)) 
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+(-3747 (|has| |#1| (-779)) (|has| |#1| (-1005))) 
 (((|#2|) |has| |#2| (-280 |#2|))) 
 (((#0=(-517) #0#) . T) ((#1=(-377 (-517)) #1#) . T) (($ $) . T)) 
 (((|#1|) . T)) 
-(((|#1| (-1071 |#1|)) . T)) 
+(((|#1| (-1072 |#1|)) . T)) 
 (|has| $ (-134)) 
 (((|#2|) . T)) 
 (((#0=(-517) #0#) . T) ((#1=(-377 (-517)) #1#) . T) (($ $) . T)) 
 ((($) . T) (((-517)) . T) (((-377 (-517))) . T)) 
 (|has| |#2| (-338)) 
-(-3745 (|has| |#1| (-779)) (|has| |#1| (-1004))) 
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 (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) 
 (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) 
 (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) 
@@ -722,67 +722,67 @@
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+((((-1074 |#1| |#2| |#3|) $) -12 (|has| (-1074 |#1| |#2| |#3|) (-258 (-1074 |#1| |#2| |#3|) (-1074 |#1| |#2| |#3|))) (|has| |#1| (-333))) (($ $) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
-((($) . T) (((-377 (-517))) -3745 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) 
+((($) . T) (((-377 (-517))) -3747 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) 
 ((((-493)) |has| |#1| (-558 (-493)))) 
-((((-787)) -3745 (|has| |#1| (-557 (-787))) (|has| |#1| (-1004)))) 
+((((-787)) -3747 (|has| |#1| (-557 (-787))) (|has| |#1| (-1005)))) 
 ((($ $) . T)) 
 ((($ $) . T)) 
 ((((-787)) . T)) 
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 (((|#1|) . T)) 
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 (((|#1|) . T)) 
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 ((((-787)) . T)) 
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 ((((-517) (-131)) . T)) 
 ((($) . T)) 
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 ((((-787)) . T)) 
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 (((|#1| |#1|) . T)) 
 ((($) . T)) 
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 (-12 (|has| |#1| (-442)) (|has| |#2| (-442))) 
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 (((|#1|) . T)) 
 (|has| |#2| (-725)) 
-(-3745 (|has| |#2| (-725)) (|has| |#2| (-777))) 
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 (((|#1| |#2|) . T)) 
-(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) 
+(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1005)))) 
 (|has| |#2| (-777)) 
 (-12 (|has| |#1| (-725)) (|has| |#2| (-725))) 
 (-12 (|has| |#1| (-725)) (|has| |#2| (-725))) 
@@ -795,19 +795,19 @@
 (((|#1|) . T)) 
 (((|#1|) . T)) 
 ((((-377 (-517))) . T) (($) . T)) 
-((($) . T) (((-377 (-517))) -3745 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) . T)) 
+((($) . T) (((-377 (-517))) -3747 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) . T)) 
 (|has| |#1| (-760)) 
-((((-377 (-517))) |has| |#1| (-953 (-377 (-517)))) (((-517)) |has| |#1| (-953 (-517))) ((|#1|) . T)) 
-(|has| |#1| (-1004)) 
+((((-377 (-517))) |has| |#1| (-954 (-377 (-517)))) (((-517)) |has| |#1| (-954 (-517))) ((|#1|) . T)) 
+(|has| |#1| (-1005)) 
 (((|#1| $) |has| |#1| (-258 |#1| |#1|))) 
 ((((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) |has| |#1| (-156)) (($) |has| |#1| (-509))) 
 ((($) |has| |#1| (-509))) 
-(((|#4|) |has| |#4| (-1004))) 
-(((|#3|) |has| |#3| (-1004))) 
+(((|#4|) |has| |#4| (-1005))) 
+(((|#3|) |has| |#3| (-1005))) 
 (|has| |#3| (-338)) 
 (((|#1|) . T) (((-787)) . T)) 
-((((-377 (-517))) -3745 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3745 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-1148 |#1| |#2| |#3|)) |has| |#1| (-333)) ((|#1|) |has| |#1| (-156))) 
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 ((((-787)) . T)) 
 ((($) |has| |#1| (-509)) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
 (((|#2|) . T)) 
@@ -817,30 +817,30 @@
 (((|#1|) . T)) 
 (((|#1|) |has| |#1| (-156))) 
 ((((-377 (-517))) . T) (((-517)) . T)) 
-((($ $) -3745 (|has| |#1| (-156)) (|has| |#1| (-509))) ((|#1| |#1|) . T) ((#0=(-377 (-517)) #0#) |has| |#1| (-37 (-377 (-517))))) 
-((($) -3745 (|has| |#1| (-156)) (|has| |#1| (-509))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
-(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1004)))) 
+((($ $) -3747 (|has| |#1| (-156)) (|has| |#1| (-509))) ((|#1| |#1|) . T) ((#0=(-377 (-517)) #0#) |has| |#1| (-37 (-377 (-517))))) 
+((($) -3747 (|has| |#1| (-156)) (|has| |#1| (-509))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
+(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1005)))) 
 ((((-131)) . T)) 
 (((|#1|) . T)) 
 ((((-131)) . T)) 
-((($) -3745 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-962))) ((|#2|) -3745 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-962)))) 
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 ((((-131)) . T)) 
 (((|#1| |#2| |#3|) . T)) 
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 (|has| $ (-134)) 
 (|has| $ (-134)) 
-(|has| |#1| (-1004)) 
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 ((((-787)) . T)) 
 (|has| |#1| (-37 (-377 (-517)))) 
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 ((($ $) |has| |#1| (-258 $ $)) ((|#1| $) |has| |#1| (-258 |#1| |#1|))) 
 (((|#1| (-377 (-517))) . T)) 
 (((|#1|) . T)) 
-((((-1075)) . T)) 
+((((-1076)) . T)) 
 (|has| |#1| (-509)) 
-(-3745 (|has| |#1| (-333)) (|has| |#1| (-509))) 
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 (|has| |#1| (-509)) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
@@ -851,7 +851,7 @@
 (|has| |#1| (-134)) 
 (|has| |#1| (-132)) 
 (|has| |#4| (-777)) 
-(((|#2| (-214 (-3533 |#1|) (-703)) (-789 |#1|)) . T)) 
+(((|#2| (-214 (-3535 |#1|) (-703)) (-789 |#1|)) . T)) 
 (|has| |#3| (-777)) 
 (((|#1| (-489 |#3|) |#3|) . T)) 
 (|has| |#1| (-134)) 
@@ -864,22 +864,22 @@
 (|has| |#1| (-338)) 
 (|has| |#1| (-132)) 
 ((((-377 (-517))) |has| |#2| (-333)) (($) . T)) 
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-(-3745 (|has| |#1| (-319)) (|has| |#1| (-338))) 
-((((-1042 |#2| |#1|)) . T) ((|#1|) . T)) 
+(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1005)))) 
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+(-3747 (|has| |#1| (-319)) (|has| |#1| (-338))) 
+((((-1043 |#2| |#1|)) . T) ((|#1|) . T)) 
 (|has| |#2| (-156)) 
 (((|#1| |#2|) . T)) 
-(-12 (|has| |#2| (-207)) (|has| |#2| (-962))) 
-(((|#2|) . T) (((-2 (|:| -2581 |#1|) (|:| -1860 |#2|))) . T)) 
-(-3745 (|has| |#3| (-725)) (|has| |#3| (-777))) 
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+(-12 (|has| |#2| (-207)) (|has| |#2| (-963))) 
+(((|#2|) . T) (((-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) . T)) 
+(-3747 (|has| |#3| (-725)) (|has| |#3| (-777))) 
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 ((((-787)) . T)) 
 (((|#1|) . T)) 
 (((|#2|) . T) (($) . T)) 
 (((|#1|) . T) (($) . T)) 
 ((((-632)) . T)) 
-(-3745 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-962))) 
+(-3747 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-963))) 
 (|has| |#1| (-509)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
@@ -887,7 +887,7 @@
 (((|#1|) . T)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
-((((-1075) (-51)) . T)) 
+((((-1076) (-51)) . T)) 
 ((((-787)) . T)) 
 ((((-493)) . T) (((-815 (-517))) . T) (((-349)) . T) (((-199)) . T)) 
 (((|#1|) . T)) 
@@ -901,38 +901,38 @@
 (((|#1| (-377 (-517))) . T)) 
 (((|#3|) . T) (((-556 $)) . T)) 
 (((|#1| |#2|) . T)) 
-((((-2 (|:| -2581 |#1|) (|:| -1860 |#2|))) . T)) 
+((((-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) . T)) 
 (((|#1|) . T)) 
-(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) 
-((((-2 (|:| -2581 |#1|) (|:| -1860 |#2|))) . T)) 
+(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1005)))) 
+((((-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) . T)) 
 ((($ $) . T) ((|#2| $) . T)) 
 (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) 
-(((#0=(-1073 |#1| |#2| |#3|) #0#) -12 (|has| (-1073 |#1| |#2| |#3|) (-280 (-1073 |#1| |#2| |#3|))) (|has| |#1| (-333))) (((-1075) #0#) -12 (|has| (-1073 |#1| |#2| |#3|) (-478 (-1075) (-1073 |#1| |#2| |#3|))) (|has| |#1| (-333)))) 
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 ((((-517)) . T) (($) . T) (((-377 (-517))) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
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@@ -1138,21 +1138,21 @@
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@@ -1184,11 +1184,11 @@
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@@ -1196,19 +1196,19 @@
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@@ -1228,40 +1228,40 @@
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@@ -1273,7 +1273,7 @@
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@@ -1281,62 +1281,62 @@
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@@ -1345,18 +1345,18 @@
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@@ -1374,45 +1374,45 @@
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@@ -1686,13 +1686,13 @@
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@@ -1707,25 +1707,25 @@
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@@ -1735,15 +1735,15 @@
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@@ -1762,41 +1762,41 @@
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 ((((-349)) . T)) 
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+((((-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) . T)) 
 ((((-377 (-517))) . T) (($) . T)) 
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@@ -1817,17 +1817,17 @@
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-((((-2 (|:| -2581 (-1058)) (|:| -1860 |#1|))) . T)) 
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 (((|#1| |#2|) . T)) 
 (|has| |#1| (-134)) 
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 (((|#2|) . T)) 
 (((|#3|) . T)) 
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@@ -1836,44 +1836,44 @@
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 (((|#1|) |has| |#1| (-333))) 
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-((((-2 (|:| -2581 |#1|) (|:| -1860 |#2|))) . T)) 
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 ((($ $) . T) (((-556 $) $) . T)) 
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@@ -2147,37 +2147,37 @@
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@@ -2209,16 +2209,16 @@
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@@ -2318,10 +2318,10 @@
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 ((($) . T)) 
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 ((($) . T)) 
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@@ -2329,24 +2329,24 @@
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 ((($) . T) (((-377 (-517))) . T)) 
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 ((((-153 (-349))) . T) (((-199)) . T) (((-349)) . T)) 
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@@ -2363,13 +2363,13 @@
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 ((((-377 (-517))) . T) (($) . T)) 
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@@ -2377,54 +2377,54 @@
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 (((|#1|) . T)) 
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 (((|#2|) . T)) 
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 (((|#2|) . T)) 
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+((((-2 (|:| -2585 (-1059)) (|:| -1859 |#1|))) . T)) 
+((((-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) . T)) 
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 (((|#1| |#2|) . T)) 
 (|has| |#1| (-37 (-377 (-517)))) 
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-((((-1058) |#1|) . T)) 
-(-3745 (|has| |#1| (-132)) (|has| |#1| (-338))) 
+((((-1059) |#1|) . T)) 
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 ((($) . T)) 
@@ -2432,13 +2432,13 @@
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 ((((-787)) . T)) 
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 (((#0=(-377 |#2|) #0#) . T) ((#1=(-377 (-517)) #1#) . T) (($ $) . T)) 
-((((-1040 |#1| |#2|)) . T)) 
+((((-1041 |#1| |#2|)) . T)) 
 (((|#1| (-517)) . T)) 
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 ((((-517)) |has| |#2| (-809 (-517))) (((-349)) |has| |#2| (-809 (-349)))) 
@@ -2448,22 +2448,22 @@
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-(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) 
-((((-1075) (-51)) . T)) 
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 (((|#1|) . T)) 
-(|has| |#1| (-1004)) 
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+((((-1143 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-377 (-517))) . T)) 
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@@ -2476,22 +2476,22 @@
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 ((((-787)) . T)) 
 ((((-787)) . T)) 
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+((($) . T) ((#0=(-1142 |#2| |#3| |#4|)) |has| #0# (-156)) (((-377 (-517))) |has| #0# (-37 (-377 (-517))))) 
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 (((#0=(-111 |#1|) $) |has| #0# (-258 #0# #0#))) 
@@ -2500,7 +2500,7 @@
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@@ -2508,17 +2508,17 @@
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 ((((-349)) . T)) 
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@@ -2526,14 +2526,14 @@
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 ((((-787)) . T)) 
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@@ -2542,99 +2542,99 @@
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 (((|#1|) |has| |#1| (-156))) 
-(((|#1| (-1156 |#1|) (-1156 |#1|)) . T)) 
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 ((((-530 |#1|)) . T) (($) . T) (((-377 (-517))) . T)) 
 ((($) . T) (((-377 (-517))) . T)) 
 ((($) . T) (((-377 (-517))) . T)) 
-(((|#2|) |has| |#2| (-6 (-4192 "*")))) 
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 (((|#1|) . T)) 
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 (((|#2| |#2|) . T) ((|#6| |#6|) . T)) 
 ((($) . T) (((-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2|) . T)) 
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 (((|#2|) . T)) 
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@@ -2963,35 +2963,35 @@
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@@ -2999,23 +2999,23 @@
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@@ -3023,43 +3023,43 @@
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@@ -3074,21 +3074,21 @@
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@@ -3096,76 +3096,76 @@
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 ((($) . T)) 
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 ((($ $) . T)) 
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-((((-2 (|:| -2581 |#1|) (|:| -1860 |#2|))) . T)) 
+((((-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) . T)) 
 (|has| |#1| (-509)) 
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 ((($) . T) ((|#2|) . T)) 
@@ -3173,26 +3173,26 @@
 (((|#1| |#2|) . T)) 
 (((|#2| $) |has| |#2| (-258 |#2| |#2|))) 
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. -421) 82846) ((-1066 . -421) 82825) ((-300 . -97) T) ((-796 . -1016) T) ((-286 . -585) 82647) ((-283 . -585) 82576) ((-443 . -509) 82527) ((-309 . -478) 82493) ((-503 . -138) 82443) ((-39 . -278) T) ((-772 . -557) 82425) ((-634 . -262) T) ((-796 . -23) T) ((-349 . -458) T) ((-988 . -205) 82395) ((-476 . -97) T) ((-377 . -558) 82203) ((-377 . -557) 82185) ((-236 . -557) 82167) ((-111 . -262) T) ((-1142 . -659) T) ((-1140 . -333) 82146) ((-1119 . -333) 82125) ((-1167 . -33) T) ((-112 . -1110) T) ((-103 . -205) 82107) ((-1077 . -97) T) ((-446 . -1004) T) ((-486 . -456) 82091) ((-670 . -33) T) ((-450 . -37) 82061) ((-128 . -33) T) ((-112 . -807) 82038) ((-112 . -809) NIL) ((-564 . -953) 81923) ((-583 . -779) 81902) ((-1166 . -97) T) ((-266 . -97) T) ((-645 . -338) 81881) ((-112 . -953) 81858) ((-360 . -650) 81842) ((-562 . -650) 81826) ((-44 . -280) 81630) ((-748 . -132) 81609) ((-748 . -134) 81588) ((-1177 . -352) 81567) ((-751 . -779) T) ((-1158 . -1004) T) ((-1059 . -203) 81514) 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. -209) 22543) ((-214 . -106) 22434) ((-1129 . -650) 22263) ((-47 . -134) T) ((-795 . -156) T) ((-784 . -650) 22233) ((-451 . -1110) T) ((-875 . -478) 22180) ((-590 . -659) T) ((-524 . -650) 22167) ((-950 . -969) T) ((-449 . -478) 22110) ((-866 . -19) 22094) ((-866 . -550) 22071) ((-748 . -558) NIL) ((-748 . -557) 22053) ((-921 . -968) 22003) ((-383 . -557) 21985) ((-224 . -258) 21962) ((-223 . -258) 21939) ((-454 . -832) NIL) ((-286 . -29) 21909) ((-103 . -1110) T) ((-920 . -1016) T) ((-192 . -832) NIL) ((-837 . -968) 21861) ((-988 . -953) 21759) ((-921 . -106) 21693) ((-237 . -205) 21677) ((-670 . -628) 21661) ((-397 . -968) 21645) ((-349 . -969) T) ((-920 . -23) T) ((-837 . -106) 21583) ((-627 . -1099) NIL) ((-454 . -585) 21533) ((-103 . -807) 21515) ((-103 . -809) 21497) ((-627 . -1096) NIL) ((-192 . -585) 21447) ((-329 . -953) 21431) ((-323 . -953) 21415) ((-297 . -280) 21353) ((-315 . -953) 21337) ((-199 . -262) T) ((-397 . -106) 21316) ((-58 . -557) 21248) ((-153 . -156) T) 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\ No newline at end of file
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. -954) 92150) ((-712 . -954) 92009) ((-112 . -585) 91954) ((-423 . -954) 91832) ((-586 . -954) 91816) ((-567 . -97) T) ((-196 . -456) 91800) ((-1157 . -33) T) ((-575 . -650) 91784) ((-551 . -650) 91768) ((-607 . -37) 91728) ((-289 . -97) T) ((-83 . -557) 91710) ((-49 . -954) 91694) ((-1023 . -969) 91681) ((-994 . -347) 91665) ((-58 . -55) 91627) ((-632 . -726) T) ((-632 . -723) T) ((-530 . -954) 91614) ((-481 . -954) 91591) ((-632 . -659) T) ((-286 . -963) 91482) ((-294 . -123) T) ((-283 . -963) T) ((-153 . -1017) T) ((-714 . -347) 91466) ((-712 . -347) 91450) ((-44 . -138) 91400) ((-922 . -911) 91382) ((-423 . -347) 91366) ((-377 . -156) T) ((-286 . -217) 91345) ((-283 . -217) T) ((-283 . -207) NIL) ((-265 . -1005) 91128) ((-199 . -123) T) ((-1023 . -106) 91113) ((-153 . -23) T) ((-731 . -134) 91092) ((-731 . -132) 91071) ((-224 . -579) 90979) ((-223 . -579) 90887) ((-289 . -256) 90853) ((-1057 . -478) 90786) ((-1036 . -1005) T) ((-199 . -972) T) ((-747 . -280) 90724) ((-994 . -823) 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. -91) 87101) ((-524 . -458) T) ((-1073 . -34) 87067) ((-1067 . -1097) 87033) ((-1067 . -1100) 86999) ((-1067 . -91) 86965) ((-331 . -1017) T) ((-329 . -1052) 86944) ((-323 . -1052) 86923) ((-315 . -1052) 86902) ((-1067 . -34) 86868) ((-1029 . -34) 86834) ((-1029 . -91) 86800) ((-103 . -1052) T) ((-1029 . -1100) 86766) ((-765 . -970) 86745) ((-584 . -280) 86683) ((-572 . -280) 86534) ((-1029 . -1097) 86500) ((-645 . -963) T) ((-974 . -579) 86482) ((-989 . -37) 86350) ((-875 . -579) 86298) ((-922 . -134) T) ((-922 . -132) NIL) ((-349 . -1017) T) ((-294 . -25) T) ((-292 . -23) T) ((-866 . -779) 86277) ((-645 . -296) 86254) ((-449 . -579) 86202) ((-39 . -954) 86092) ((-634 . -650) 86079) ((-645 . -207) T) ((-309 . -1005) T) ((-157 . -1005) T) ((-301 . -779) T) ((-388 . -421) 86029) ((-349 . -23) T) ((-329 . -37) 85994) ((-323 . -37) 85959) ((-315 . -37) 85924) ((-78 . -410) T) ((-78 . -365) T) ((-199 . -25) T) ((-199 . -21) T) ((-766 . -1017) T) ((-103 . -37) 85874) ((-759 . -1017) T) 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. -421) 82846) ((-1067 . -421) 82825) ((-300 . -97) T) ((-796 . -1017) T) ((-286 . -585) 82647) ((-283 . -585) 82576) ((-443 . -509) 82527) ((-309 . -478) 82493) ((-503 . -138) 82443) ((-39 . -278) T) ((-772 . -557) 82425) ((-634 . -262) T) ((-796 . -23) T) ((-349 . -458) T) ((-989 . -205) 82395) ((-476 . -97) T) ((-377 . -558) 82203) ((-377 . -557) 82185) ((-236 . -557) 82167) ((-111 . -262) T) ((-1143 . -659) T) ((-1141 . -333) 82146) ((-1120 . -333) 82125) ((-1168 . -33) T) ((-112 . -1111) T) ((-103 . -205) 82107) ((-1078 . -97) T) ((-446 . -1005) T) ((-486 . -456) 82091) ((-670 . -33) T) ((-450 . -37) 82061) ((-128 . -33) T) ((-112 . -807) 82038) ((-112 . -809) NIL) ((-564 . -954) 81923) ((-583 . -779) 81902) ((-1167 . -97) T) ((-266 . -97) T) ((-645 . -338) 81881) ((-112 . -954) 81858) ((-360 . -650) 81842) ((-562 . -650) 81826) ((-44 . -280) 81630) ((-748 . -132) 81609) ((-748 . -134) 81588) ((-1178 . -352) 81567) ((-751 . -779) T) ((-1159 . -1005) T) ((-1060 . -203) 81514) 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. -280) 55357) ((-112 . -1017) T) ((-751 . -97) T) ((-564 . -23) T) ((-1051 . -478) 55149) ((-356 . -97) T) ((-294 . -97) T) ((-921 . -823) 55101) ((-885 . -1005) T) ((-139 . -963) T) ((-112 . -23) T) ((-664 . -381) 55085) ((-668 . -1005) T) ((-648 . -1005) T) ((-636 . -124) T) ((-422 . -1005) T) ((-286 . -400) 55069) ((-377 . -1111) T) ((-944 . -558) 55030) ((-941 . -1115) T) ((-199 . -97) T) ((-944 . -557) 54992) ((-748 . -205) 54976) ((-941 . -509) T) ((-765 . -585) 54949) ((-324 . -1115) T) ((-445 . -557) 54911) ((-445 . -558) 54872) ((-432 . -558) 54833) ((-432 . -557) 54795) ((-377 . -807) 54779) ((-289 . -969) 54614) ((-377 . -809) 54539) ((-772 . -954) 54437) ((-454 . -478) NIL) ((-450 . -550) 54414) ((-324 . -509) T) ((-192 . -478) NIL) ((-796 . -421) T) ((-388 . -1005) T) ((-377 . -954) 54281) ((-289 . -106) 54102) ((-627 . -333) T) ((-199 . -256) T) ((-47 . -1115) T) ((-747 . -963) 54033) ((-529 . -123) T) ((-517 . -123) T) ((-460 . -123) T) ((-47 . -509) T) ((-1060 . -260) 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. -97) T) ((-286 . -881) 10327) ((-125 . -1017) T) ((-111 . -1017) T) ((-548 . -1155) 10311) ((-634 . -23) T) ((-548 . -1005) 10261) ((-89 . -478) 10194) ((-157 . -333) T) ((-286 . -91) 10173) ((-286 . -34) 10152) ((-552 . -456) 10086) ((-125 . -23) T) ((-111 . -23) T) ((-651 . -1005) T) ((-444 . -456) 10023) ((-377 . -579) 9971) ((-590 . -954) 9869) ((-880 . -456) 9853) ((-325 . -970) T) ((-322 . -970) T) ((-314 . -970) T) ((-237 . -970) T) ((-221 . -970) T) ((-795 . -558) NIL) ((-795 . -557) 9835) ((-1178 . -21) T) ((-524 . -920) T) ((-664 . -659) T) ((-1178 . -25) T) ((-224 . -963) 9766) ((-223 . -963) 9697) ((-70 . -1111) T) ((-224 . -207) 9650) ((-223 . -207) 9603) ((-39 . -97) T) ((-833 . -970) T) ((-1074 . -659) T) ((-1073 . -659) T) ((-1067 . -659) T) ((-1067 . -723) NIL) ((-1067 . -726) NIL) ((-844 . -97) T) ((-1029 . -659) T) ((-703 . -97) T) ((-608 . -97) T) ((-443 . -1005) T) ((-309 . -1017) T) ((-157 . -1017) T) ((-289 . -843) 9582) ((-1141 . -650) 9423) ((-796 . -156) T) ((-1120 . -650) 9237) ((-772 . -21) 9189) ((-772 . -25) 9141) ((-219 . -1050) 9125) ((-121 . -478) 9058) ((-377 . -25) T) ((-377 . -21) T) ((-309 . -23) T) ((-153 . -558) 8826) ((-153 . -557) 8808) ((-157 . -23) T) ((-583 . -260) 8785) ((-483 . -33) T) ((-821 . -557) 8767) ((-87 . -1111) T) ((-770 . -557) 8749) ((-740 . -557) 8731) ((-701 . -557) 8713) ((-612 . -557) 8695) ((-214 . -585) 8545) ((-1076 . -1005) T) ((-1072 . -969) 8368) ((-1051 . -1111) T) ((-1028 . -969) 8211) ((-783 . -969) 8195) ((-1072 . -106) 8004) ((-1028 . -106) 7833) ((-783 . -106) 7812) ((-1130 . -558) NIL) ((-1130 . -557) 7794) ((-313 . -1052) T) ((-784 . -557) 7776) ((-985 . -258) 7755) ((-78 . -1111) T) ((-922 . -832) NIL) ((-552 . -258) 7731) ((-1098 . -478) 7664) ((-454 . -1111) T) ((-524 . -557) 7646) ((-444 . -258) 7625) ((-192 . -1111) T) ((-994 . -205) 7609) ((-261 . -843) T) ((-749 . -278) 7588) ((-794 . -97) T) ((-714 . -205) 7572) ((-922 . -585) 7522) ((-880 . -258) 7499) ((-837 . -585) 7451) ((-575 . -21) T) ((-575 . -25) T) ((-551 . -21) T) ((-313 . -37) 7416) ((-627 . -657) 7383) ((-454 . -807) 7365) ((-454 . -809) 7347) ((-443 . -650) 7188) ((-192 . -807) 7170) ((-62 . -1111) T) ((-192 . -809) 7152) ((-551 . -25) T) ((-397 . -585) 7126) ((-454 . -954) 7086) ((-796 . -478) 6998) ((-192 . -954) 6958) ((-214 . -33) T) ((-918 . -1005) 6936) ((-1141 . -156) 6867) ((-1120 . -156) 6798) ((-645 . -132) 6777) ((-645 . -134) 6756) ((-634 . -123) T) ((-127 . -434) 6733) ((-595 . -593) 6717) ((-1048 . -557) 6649) ((-111 . -123) T) ((-446 . -1115) T) ((-552 . -550) 6625) ((-444 . -550) 6604) ((-306 . -305) 6573) ((-493 . -1005) T) ((-446 . -509) T) ((-1072 . -963) T) ((-1028 . -963) T) ((-783 . -963) T) ((-214 . -723) 6552) ((-214 . -726) 6503) ((-214 . -725) 6482) ((-1072 . -296) 6459) ((-214 . -659) 6390) ((-880 . -19) 6374) ((-454 . -347) 6356) ((-454 . -308) 6338) ((-1028 . -296) 6310) ((-324 . -1164) 6287) ((-192 . -347) 6269) ((-192 . -308) 6251) ((-880 . -550) 6228) ((-1072 . -207) T) ((-601 . -1005) T) ((-1153 . -1005) T) ((-1085 . -1005) T) ((-994 . -226) 6167) ((-325 . -1005) T) ((-322 . -1005) T) ((-314 . -1005) T) ((-237 . -1005) T) ((-221 . -1005) T) ((-82 . -1111) T) ((-122 . -97) 6145) ((-116 . -97) 6123) ((-1085 . -554) 6102) ((-447 . -1005) T) ((-1042 . -1005) T) ((-447 . -554) 6081) ((-224 . -727) 6032) ((-224 . -724) 5983) ((-223 . -727) 5934) ((-39 . -1052) NIL) ((-223 . -724) 5885) ((-989 . -843) 5836) ((-922 . -726) T) ((-922 . -723) T) ((-922 . -659) T) ((-890 . -726) T) ((-837 . -659) T) ((-89 . -456) 5820) ((-454 . -823) NIL) ((-833 . -1005) T) ((-199 . -969) 5785) ((-796 . -262) T) ((-192 . -823) NIL) ((-765 . -1017) 5764) ((-57 . -1005) 5714) ((-482 . -1005) 5692) ((-480 . -1005) 5642) ((-462 . -1005) 5620) ((-461 . -1005) 5570) ((-529 . -97) T) ((-517 . -97) T) ((-460 . -97) T) ((-443 . -156) 5501) ((-329 . -843) T) ((-323 . -843) T) ((-315 . -843) T) ((-199 . -106) 5457) ((-765 . -23) 5409) ((-397 . -659) T) ((-103 . -843) T) ((-39 . -37) 5354) ((-103 . -752) T) ((-530 . -319) T) ((-481 . -319) T) ((-1120 . -478) 5214) ((-286 . -421) 5193) ((-283 . -421) T) ((-766 . -258) 5172) ((-309 . -123) T) ((-157 . -123) T) ((-265 . -25) 5037) ((-265 . -21) 4921) ((-44 . -1088) 4900) ((-64 . -557) 4882) ((-815 . -557) 4864) ((-548 . -478) 4797) ((-44 . -102) 4747) ((-1007 . -395) 4731) ((-1007 . -338) 4710) ((-975 . -1111) T) ((-974 . -969) 4697) ((-875 . -969) 4540) ((-449 . -969) 4383) ((-601 . -650) 4367) ((-974 . -106) 4352) ((-875 . -106) 4181) ((-446 . -333) T) ((-325 . -650) 4133) ((-322 . -650) 4085) ((-314 . -650) 4037) ((-237 . -650) 3886) ((-221 . -650) 3735) ((-866 . -588) 3719) ((-449 . -106) 3548) ((-1158 . -97) T) ((-866 . -343) 3532) ((-1121 . -832) NIL) ((-72 . -557) 3514) ((-885 . -46) 3493) ((-562 . -1017) T) ((-1 . -1005) T) ((-632 . -97) T) ((-1157 . -97) 3443) ((-1149 . -585) 3368) ((-1142 . -585) 3265) ((-121 . -456) 3249) ((-1093 . -557) 3231) ((-995 . -557) 3213) ((-360 . -23) T) ((-985 . -557) 3195) ((-85 . -1111) T) ((-1121 . -585) 3047) ((-833 . -650) 3012) ((-562 . -23) T) ((-552 . -557) 2994) ((-552 . -558) NIL) ((-444 . -558) NIL) ((-444 . -557) 2976) ((-475 . -1005) T) ((-471 . -1005) T) ((-321 . -25) T) ((-321 . -21) T) ((-122 . -280) 2914) ((-116 . -280) 2852) ((-543 . -585) 2839) ((-199 . -963) T) ((-542 . -585) 2764) ((-349 . -920) T) ((-199 . -217) T) ((-199 . -207) T) ((-880 . -558) 2725) ((-880 . -557) 2637) ((-794 . -37) 2624) ((-1141 . -262) 2575) ((-1120 . -262) 2526) ((-1023 . -421) T) ((-467 . -779) T) ((-286 . -1040) 2505) ((-917 . -134) 2484) ((-917 . -132) 2463) ((-460 . -280) 2450) ((-266 . -1088) 2429) ((-446 . -1017) T) ((-795 . -969) 2374) ((-564 . -97) T) ((-1098 . -456) 2358) ((-224 . -338) 2337) ((-223 . -338) 2316) ((-266 . -102) 2266) ((-974 . -963) T) ((-112 . -97) T) ((-875 . -963) T) ((-795 . -106) 2195) ((-446 . -23) T) ((-449 . -963) T) ((-974 . -207) T) ((-875 . -296) 2164) ((-449 . -296) 2121) ((-325 . -156) T) ((-322 . -156) T) ((-314 . -156) T) ((-237 . -156) 2032) ((-221 . -156) 1943) ((-885 . -954) 1841) ((-668 . -954) 1812) ((-1010 . -97) T) ((-998 . -557) 1779) ((-951 . -557) 1761) ((-1149 . -659) T) ((-1142 . -659) T) ((-1121 . -723) NIL) ((-153 . -969) 1671) ((-1121 . -726) NIL) ((-833 . -156) T) ((-1121 . -659) T) ((-1168 . -138) 1655) ((-921 . -312) 1629) ((-918 . -478) 1562) ((-772 . -779) 1541) ((-517 . -1052) T) ((-443 . -262) 1492) ((-543 . -659) T) ((-331 . -557) 1474) ((-292 . -557) 1456) ((-388 . -954) 1354) ((-542 . -659) T) ((-377 . -779) 1305) ((-153 . -106) 1201) ((-765 . -123) 1153) ((-670 . -138) 1137) ((-1157 . -280) 1075) ((-454 . -278) T) ((-349 . -557) 1042) ((-483 . -928) 1026) ((-349 . -558) 940) ((-192 . -278) T) ((-128 . -138) 922) ((-647 . -258) 901) ((-454 . -939) T) ((-529 . -37) 888) ((-517 . -37) 875) ((-460 . -37) 840) ((-192 . -939) T) ((-795 . -963) T) ((-766 . -557) 822) ((-759 . -557) 804) ((-757 . -557) 786) ((-748 . -832) 765) ((-1179 . -1017) T) ((-1130 . -969) 588) ((-784 . -969) 572) ((-795 . -217) T) ((-795 . -207) NIL) ((-623 . -1111) T) ((-1179 . -23) T) ((-748 . -585) 497) ((-503 . -1111) T) ((-388 . -308) 481) ((-524 . -969) 468) ((-1130 . -106) 277) ((-634 . -579) 259) ((-784 . -106) 238) ((-351 . -23) T) ((-1085 . -478) 30)) 
\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index db08e4dc..9c88271d 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3409262763)            
-(4193 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3409435989)            
+(4195 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup|
@@ -337,18 +337,18 @@
  |PlottablePlaneCurveCategory| |PrecomputedAssociatedEquations|
  |PrimitiveArrayFunctions2| |PrimitiveArray|
  |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage|
- |PrintPackage| |PolynomialRing| |Product| |PriorityQueueAggregate|
- |PseudoRemainderSequence| |Partition| |PowerSeriesCategory&|
- |PowerSeriesCategory| |PlottableSpaceCurveCategory|
- |PolynomialSetCategory&| |PolynomialSetCategory|
- |PolynomialSetUtilitiesPackage| |PseudoLinearNormalForm|
- |PolynomialSquareFree| |PointCategory| |PointFunctions2|
- |PointPackage| |PartialTranscendentalFunctions| |PushVariables|
- |PAdicWildFunctionFieldIntegralBasis| |QuasiAlgebraicSet2|
- |QuasiAlgebraicSet| |QuasiComponentPackage| |QueryEquation|
- |QuotientFieldCategoryFunctions2| |QuotientFieldCategory&|
- |QuotientFieldCategory| |QuadraticForm| |QueueAggregate|
- |QuaternionCategory&| |QuaternionCategory|
+ |PrintPackage| |PolynomialRing| |Product| |PropositionalLogic|
+ |PriorityQueueAggregate| |PseudoRemainderSequence| |Partition|
+ |PowerSeriesCategory&| |PowerSeriesCategory|
+ |PlottableSpaceCurveCategory| |PolynomialSetCategory&|
+ |PolynomialSetCategory| |PolynomialSetUtilitiesPackage|
+ |PseudoLinearNormalForm| |PolynomialSquareFree| |PointCategory|
+ |PointFunctions2| |PointPackage| |PartialTranscendentalFunctions|
+ |PushVariables| |PAdicWildFunctionFieldIntegralBasis|
+ |QuasiAlgebraicSet2| |QuasiAlgebraicSet| |QuasiComponentPackage|
+ |QueryEquation| |QuotientFieldCategoryFunctions2|
+ |QuotientFieldCategory&| |QuotientFieldCategory| |QuadraticForm|
+ |QueueAggregate| |QuaternionCategory&| |QuaternionCategory|
  |QuaternionCategoryFunctions2| |Quaternion| |Queue| |RadicalCategory&|
  |RadicalCategory| |RadicalFunctionField| |RadixExpansion|
  |RadixUtilities| |RandomNumberSource| |RationalFactorize|
@@ -458,642 +458,639 @@
  |XPolynomialRing| |XRecursivePolynomial|
  |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage|
  |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping|
- |Record| |Union| |Category| |rectangularMatrix|
- |removeSuperfluousCases| |realEigenvectors| |changeNameToObjf|
- |subSet| |rootSplit| |combineFeatureCompatibility| |groebner|
- |areEquivalent?| |f01qef| |sortConstraints| |linearAssociatedLog|
- |birth| |csch2sinh| |closeComponent| |quadraticNorm| |cAsec| |imagE|
- |seed| |OMopenString| |aQuartic| |rename| |e01bhf| |position|
- |axesColorDefault| |mirror| |inGroundField?| |setAttributeButtonStep|
- |logGamma| |integral| |saturate| |roughBase?|
- |degreeSubResultantEuclidean| |realElementary| |cPower|
- |OMlistSymbols| |separateDegrees| |log| |subHeight| |rightNorm|
- |create3Space| |testModulus| |polygon?| |numberOfChildren|
- |setLabelValue| |subPolSet?| |mainVariable?| |commaSeparate| |tree|
- |ignore?| |cyclicGroup| |complexExpand| |OMencodingUnknown|
- |printHeader| |objectOf| |outputFixed| |taylorIfCan| |shuffle|
- |doubleFloatFormat| |iiacoth| |specialTrigs| |e04fdf| |subtractIfCan|
- |finiteBasis| |tab| |quote| |makingStats?| |differentialVariables|
- |LowTriBddDenomInv| |e02ahf| |numberOfFractionalTerms| |hexDigit?|
- |complexEigenvectors| |palgLODE0| |twist| |antiCommutator|
- |showSummary| |generalizedEigenvectors| |OMputEndBVar|
- |selectPolynomials| |null?| |startTable!| |setright!| |d01anf|
- |rightZero| |groebnerIdeal| |basisOfMiddleNucleus| |unitNormalize|
- |acschIfCan| |clearTheSymbolTable| |tubePlot| |d01aqf|
- |resultantEuclidean| |getGraph| |algintegrate| |factorsOfDegree|
- |showAttributes| |sylvesterMatrix| |alternative?| |leftMult|
- |fractionPart| |setleft!| |is?| |swapRows!| |getExplanations|
- |rightGcd| |sumOfKthPowerDivisors| |Nul| |leadingTerm| |drawStyle|
- |permutation| |expandPower| |prindINFO| |univariatePolynomial|
- |countable?| |infLex?| |listBranches| |ran| |ratpart| |mapUp!|
- |wordsForStrongGenerators| |univariatePolynomialsGcds| |mainVariables|
- |qfactor| |setfirst!| |irreducibleRepresentation| |ord| |addPoint2|
- |changeWeightLevel| |generator| |permutationGroup| |changeMeasure|
- |insertBottom!| |zag| |pdf2df| |sign| |directory| |rischDE| BY |gethi|
- |randomLC| |cyclePartition| |clipWithRanges| |singRicDE|
- |antiCommutative?| |cosIfCan| |extendedEuclidean| |resultantnaif|
- |rowEchelonLocal| |yCoordinates| |constantLeft| |fractRagits|
- |pattern| |rootKerSimp| |semiSubResultantGcdEuclidean2| |d01bbf|
- |rombergo| |nodes| |mindeg| |mr| |duplicates?| |mindegTerm| |Gamma|
- |bat| |pseudoRemainder| |numberOfImproperPartitions| |OMputEndError|
- |lfintegrate| |normalise| |maxPoints3D| |removeZero| |zeroVector|
- |matrixDimensions| |systemCommand| |debug| |lazyPrem| |formula|
- |bracket| |wholeRadix| |minus!| |inverse| |s15aef| |loopPoints|
- |iFTable| |connect| |ideal| |setchildren!| |internalInfRittWu?|
- |createMultiplicationTable| |mkAnswer| |arity| |subQuasiComponent?|
- |number?| |extendedResultant| |dioSolve| |splitDenominator| |constant|
- |nthExponent| |normal| |euclideanGroebner| |rationalFunction|
- |inverseIntegralMatrix| |setTopPredicate| |sPol| |lfextlimint|
- |bezoutDiscriminant| |ksec| |noLinearFactor?| |kernel| |d02gbf|
- |lastSubResultantElseSplit| |SturmHabichtSequence| |complexNumeric|
- |createGenericMatrix| |structuralConstants| |subNode?| |getCurve|
- |karatsubaDivide| |op| |reverse!| |OMputError|
- |stiffnessAndStabilityFactor| |mapCoef| |solveLinear| |roughBasicSet|
- |atanhIfCan| |integralLastSubResultant| |innerint|
- |regularRepresentation| |unvectorise| |int| |e02bcf| |nrows| |erf|
- |remove| |kernels| |fortranComplex| |prepareDecompose| |push!|
- |setelt!| |multiple?| |exprToUPS| |primextintfrac| |mulmod| |nonQsign|
- |nextPrime| |ncols| |partialQuotients| |packageCall| |notelem|
- |selectODEIVPRoutines| |lazyPseudoQuotient| |univariate| |s19acf|
- |resetBadValues| |inf| |matrixConcat3D| |last| |true| |safeCeiling|
- |submod| |match?| |listLoops| |remainder| |transcendentalDecompose|
- |algSplitSimple| |integers| |csubst| |expressIdealMember|
- |cycleSplit!| |assoc| |dilog| |e01baf| |getOperands| |controlPanel|
- |weight| |zerosOf| |createLowComplexityTable| |approxSqrt|
- |rubiksGroup| |times!| |negative?| |sin| |iroot| |iicsc|
- |fortranInteger| |powers| |edf2efi| |stop| |rotatex| |swap!| |f02axf|
- |testDim| |univariate?| |cos| |s17aff| |nthRoot| |viewpoint| |genus|
- |closed?| |socf2socdf| |credPol| |setVariableOrder| |sn| |check| |tan|
- |dictionary| |lieAlgebra?| |discreteLog| |children| |draw|
- |rightMinimalPolynomial| |makeSketch| |numberOfHues| |makeSeries|
- |limit| |rightUnit| |weighted| |cot| |morphism| |lift| |e01saf|
- |factorSquareFreePolynomial| |parametric?| |mainVariable| |close!|
- |f01qcf| |f02fjf| |viewSizeDefault| |string| |integrate| |sec|
- |HenselLift| |reduce| |monicCompleteDecompose| |leftQuotient|
- |setnext!| |palgextint0| |linearAssociatedExp| |separant| |node?|
- |empty| |OMsupportsSymbol?| |numberOfCycles| |csc| |setButtonValue|
- |approximants| |parts| |plus!| |rightPower| |sturmVariationsOf|
- |signAround| |tail| |quoted?| |insertRoot!| |innerSolve1|
- |unprotectedRemoveRedundantFactors| |jacobian| |patternMatchTimes|
- |asin| |listOfLists| |makeObject| |outputGeneral| |totalGroebner|
- |middle| |elRow2!| |polyRicDE| |splitConstant| |indiceSubResultant|
- |slash| UP2UTS |exponential| |nthRootIfCan| |acos| |domainOf|
- |doublyTransitive?| |createIrreduciblePoly| |setsubMatrix!| |c05pbf|
- |mapdiv| |f02bbf| |status| |sizeMultiplication| |coefChoose|
- |symmetric?| |contains?| |pureLex| |atan| |integralAtInfinity?|
- |e02bef| |sin2csc| |thetaCoord| |coef| |squareFree| |Aleph| =
- |unravel| |univariatePolynomials| |numberOfPrimitivePoly|
- |flexibleArray| |acot| |nextIrreduciblePoly| |bombieriNorm|
- |mainValue| |parabolicCylindrical| |style| |critB| |OMconnInDevice|
- |divideExponents| |genericLeftMinimalPolynomial| |difference| |asec|
- |genericPosition| |trueEqual| |slex| |leastMonomial| |insertionSort!|
- SEGMENT |exteriorDifferential| < |divisors| |viewWriteDefault|
- |pushdown| |upperCase| |acsc| |acoshIfCan| |tanSum| |rotatez|
- |fixPredicate| > |pdf2ef| |incrementKthElement| |var1Steps|
- |drawCurves| |sinh| |odd?| |lowerCase?| |factorSquareFree|
- |factorGroebnerBasis| |sub| |ipow| <= |lfextendedint|
- |primPartElseUnitCanonical| |cosh| |evenlambert| |imagi|
- |numFunEvals3D| |multiEuclideanTree| |lowerCase!|
- |lazyPseudoRemainder| |normalForm| |polarCoordinates| >=
- |OMencodingXML| |optional?| |critMonD1| |OMputSymbol| |tanh| |primes|
- |reset| |realEigenvalues| |viewport2D| |outputSpacing| |c06fqf|
- |updatF| |rational?| |possiblyInfinite?| |coth| |cyclic?| |bat1|
- |coHeight| |meshPar1Var| |extractSplittingLeaf| |flagFactor| |llprop|
- |normalizeAtInfinity| |flexible?| |torsionIfCan| |degreeSubResultant|
- |currentSubProgram| |sech| |transpose| |write| |primitiveElement|
- |asinIfCan| |presub| |removeZeroes| |cSec| + |lyndonIfCan| |curve?|
- |rowEchelon| |sample| |csch| |adjoint| |save| |copies| |SturmHabicht|
- |hdmpToDmp| |lambert| |predicate| |leftRankPolynomial| -
- |trigs2explogs| |badValues| |exptMod| |asinh| |leftDivide|
- |ParCondList| |validExponential| |OMcloseConn| |constantOpIfCan|
- |complexSolve| |tryFunctionalDecomposition?| / |subCase?|
- |buildSyntax| |f01rcf| |OMgetVariable| |acosh| |deepCopy| |safeFloor|
- |critBonD| |t| |pol| |quoByVar| |log2| |d03faf| |overset?| |concat!|
- |rightExactQuotient| |showAll?| |atanh| |showTheSymbolTable| |close| F
- |probablyZeroDim?| |besselI| |mightHaveRoots| |monic?| |setFormula!|
- |polCase| |SturmHabichtCoefficients| |symmetricRemainder| |palgint0|
- |groebSolve| |acoth| |secIfCan| |tubeRadiusDefault| |changeBase|
- |Frobenius| |setleaves!| |s13adf| |OMputEndObject| |linSolve|
- |resultantReduitEuclidean| |insert| |quadraticForm|
- |viewDeltaYDefault| |deriv| |viewZoomDefault| |logical?| |cTanh|
- |belong?| |linear?| |d01akf| |isQuotient| |display| |df2ef|
- |explimitedint| |stronglyReduced?| |transform| |sturmSequence|
- |cyclic| |selectfirst| |nodeOf?| |genericRightDiscriminant|
- |diophantineSystem| |cap| |hconcat| UTS2UP |localAbs| |generators|
- |raisePolynomial| |addiag| |hasHi| |solveRetract| |addPoint|
- |fullPartialFraction| |fortranLogical| |s19adf| |relationsIdeal|
- |over| |hyperelliptic| GF2FG |subResultantGcd| |extract!|
- |userOrdered?| |minGbasis| |adaptive?| |scripted?| |hermiteH| |prem|
- |changeName| |square?| |besselJ| |GospersMethod| |LiePolyIfCan|
- |checkForZero| |normal?| |unitNormal| |subResultantGcdEuclidean|
- |revert| |basisOfCommutingElements| |computeInt|
- |setLegalFortranSourceExtensions| |compBound| |e04ucf| |height|
- |reduceByQuasiMonic| |input| |summation| |movedPoints| |isExpt|
- |iicosh| |cothIfCan| |solid| |varselect| |diag|
- |getSyntaxFormsFromFile| |d02bbf| |nextsubResultant2| |library|
- |zeroDim?| |blankSeparate| |symmetricGroup|
- |rewriteIdealWithHeadRemainder| |symmetricDifference|
- |HermiteIntegrate| |OMgetAtp| |wholeRagits| |hitherPlane| |entries|
- |postfix| |rangePascalTriangle| |s13acf| |ScanRoman| |sup|
- |infRittWu?| |alphabetic| |rk4qc| |firstDenom| |polygamma| |expandLog|
- |trunc| |symbolTable| |leftRank| |applyRules| |infiniteProduct|
- |numberOfFactors| |unexpand| |uncouplingMatrices| |setProperties|
- |doubleResultant| |rename!| |iiacos| |seriesToOutputForm| |delta|
- |basisOfNucleus| |swap| |singularAtInfinity?| |entry| |traverse|
- |separate| |startPolynomial| |sumOfSquares| |one?| |d01amf|
- |purelyAlgebraic?| |pushFortranOutputStack| |pleskenSplit|
- |factorByRecursion| |linearlyDependentOverZ?| |vark|
- |scanOneDimSubspaces| |separateFactors| |unit| |arg1| |OMputApp|
- |factors| |mainCoefficients| |dimension| |keys|
- |popFortranOutputStack| |set| |ldf2vmf| |cond| |irreducibleFactor|
- |e02zaf| |leftRecip| |subresultantVector| |withPredicates| |bfKeys|
- |rootBound| |arg2| |curve| |latex| |lquo| |outputAsFortran| |say|
- |measure2Result| |characteristicPolynomial| |simpson| |enterInCache|
- |tanAn| |symbolTableOf| |reverse| |fixedPoint| |toseSquareFreePart|
- |KrullNumber| |pointSizeDefault| |RemainderList| |declare| |coerceP|
- |drawToScale| |froot| |f02ajf| |OMbindTCP| |integerBound|
- |balancedBinaryTree| |imaginary| |fixedDivisor| |untab| |point?|
- |conditions| |interpretString| |iicot| |numberOfComposites|
- |outputForm| |PollardSmallFactor| |lowerCase| |lazy?| |modTree|
- |integralMatrix| |cCsc| |simplify| |match| |cot2trig| |normFactors|
- |leaves| |iicos| |leftCharacteristicPolynomial| |matrixGcd|
- |numberOfMonomials| |startStats!| |factorList|
- |nextPrimitiveNormalPoly| |leftDiscriminant| |startTableGcd!| |s20adf|
- |indicialEquationAtInfinity| |lambda| |cyclicEqual?| |jordanAlgebra?|
- |represents| |mapGen| |perfectSqrt| |positiveSolve| |mainMonomial|
- |UP2ifCan| |atoms| |monomial?| |rightOne| |fortranCompilerName|
- |repSq| |OMwrite| |resetVariableOrder| |putGraph| |identity| |e02def|
- |singularitiesOf| |abelianGroup| |chiSquare| |rightScalarTimes!|
- |ridHack1| |merge!| |move| |operators| |maxRowIndex| |s17ahf|
- |cyclicEntries| |makeGraphImage| |pack!| |leftExactQuotient| |dfRange|
- |poisson| |show| |linearPolynomials| |besselK| |laplace| |lex|
- |primintegrate| |s17aef| |getGoodPrime| |setValue!| |basicSet|
- |charClass| |clipBoolean| |newTypeLists| |makeSUP| |iprint|
- |goodnessOfFit| |critMTonD1| |putColorInfo| |zeroDimPrimary?|
- |extendedSubResultantGcd| |build| |normalize| |subResultantChain|
- |trace| |symmetricPower| Y |topFortranOutputStack| |numberOfVariables|
- |bits| |aromberg| |e01daf| |s18aef| |simplifyLog|
- |associatedEquations| |leftZero| |shallowExpand| |numberOfDivisors|
- |setScreenResolution| |iomode| |directSum| |s17agf| |coerceImages|
- |pomopo!| |goto| |makeSin| |oblateSpheroidal| |lookup| |s17acf|
- |zero?| |newReduc| |content| |node| |f02aaf| |rule| |bivariateSLPEBR|
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- |differentiate| |ptFunc| |f01ref| |basis| |partialFraction| |solve|
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- |f04atf| |toScale| |pastel| |semiResultantReduitEuclidean|
- |divideIfCan| |divergence| |monomial| |rightRankPolynomial| |cAsinh|
- |constantOperator| |representationType| |prefixRagits| |choosemon|
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- |variables| |denom| |pole?| |vectorise| |divideIfCan!|
- |particularSolution| |rootSimp| |OMgetInteger| |subset?|
- |extractProperty| |linkToFortran| |minset| |cycleRagits|
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- |pToHdmp| |e02bdf| |iisqrt2| |isList| |f04mbf| |rroot| |complexZeros|
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- |commutativeEquality| |taylor| |rowEch| |e01sff| |hasPredicate?|
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- |possiblyNewVariety?| |LyndonWordsList1| |cExp| |sort| |sechIfCan|
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- |recoverAfterFail| |powmod| |expenseOfEvaluationIF| |exactQuotient|
- |hi| |iteratedInitials| |OMputString| |finiteBound| |baseRDE| |li|
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- |primitivePart| |anticoord| |headRemainder| |printCode| |returns|
- |setRealSteps| |range| |normalizedDivide| |stosePrepareSubResAlgo|
- |s18acf| |rotate!| |someBasis| |child?| |npcoef| |random|
- |FormatRoman| |approximate| |fortranReal| |expint|
- |halfExtendedSubResultantGcd1| |divisorCascade| |digits| |c06gqf|
- |segment| |minimumDegree| |partialDenominators| |upperCase!| |s14baf|
- |ramified?| |bubbleSort!| |repeating| |strongGenerators| |bipolar|
- |vertConcat| |pow| |OMgetFloat| |commonDenominator| |sin?| |s21bbf|
- |function| |computeBasis| |stirling2| |realRoots| |decreasePrecision|
- |linearDependence| |showTheIFTable| |OMgetEndApp| |argscript|
- |lazyEvaluate| |dmpToP| |retractable?| |setImagSteps| |mix| |ref|
- |createPrimitivePoly| |exponential1| |PDESolve| |Ci| |xn| |critT|
- |squareFreeLexTriangular| |expt| |datalist| |meshPar2Var| |symbol|
- |fractionFreeGauss!| |normalizedAssociate| |rationalIfCan|
- |repeatUntilLoop| |dmpToHdmp| |leftAlternative?| |e04ycf|
- |nonSingularModel| |rewriteIdealWithRemainder| |extractTop!|
- |createNormalPoly| |jacobi| |output| |generate| |integer| |overlabel|
- |f07aef| |imagK| |coerce| |OMputFloat| |minrank| |resultant| |case|
- |outputAsScript| |getBadValues| |rewriteSetWithReduction|
- |OMgetEndBind| |implies| |po| |assign| |incrementBy|
- |initializeGroupForWordProblem| |zeroSetSplit| |innerEigenvectors|
- |smith| |construct| |clearCache| |permanent| |OMreadFile| |prevPrime|
- |sinhIfCan| |xor| |curryRight| |expand| |oneDimensionalArray|
- |semiResultantEuclidean1| |limitPlus| |inv| |OMserve|
- |zeroDimensional?| |hclf| |elements| |univcase| |filterWhile|
- |fracPart| |reducedSystem| |phiCoord| |ground?| |floor|
- |clearFortranOutputStack| |adaptive| |high| |filterUntil|
- |tubePointsDefault| |createRandomElement| |c02aff|
- |subresultantSequence| |increase| |ground| |cCos| |OMgetType| |list|
- |root?| |select| |trace2PowMod| |sumSquares| |exquo|
- |leftMinimalPolynomial| |coordinate| |lcm| |plus| |d02kef|
- |leadingMonomial| |setDifference| |binaryFunction| |quotedOperators|
- |lastSubResultant| |derivative| |abs| |div| |aLinear| |subMatrix|
- |printTypes| |numberOfOperations| |leadingCoefficient| |interpret|
- |setIntersection| |e02agf| |reducedDiscriminant| |prepareSubResAlgo|
- |unaryFunction| |univariateSolve| |f02akf| |quo| |reify| |exponent|
- |safetyMargin| |primitiveMonomials| |rootProduct| |setUnion| |more?|
- |shellSort| |OMputEndBind| |iisech| |linears| |s19abf|
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- |reductum| |prolateSpheroidal| |deepExpand| |apply|
- |rightFactorCandidate| |freeOf?| |scaleRoots| |rem| |OMgetEndAttr|
- |minRowIndex| |complement| |union| |createMultiplicationMatrix|
- |times| |btwFact| |cAcsc| |solveLinearPolynomialEquation|
- |jordanAdmissible?| |condition| |splitLinear| |cCot| |RittWuCompare|
- |f01maf| |false| |rewriteSetByReducingWithParticularGenerators|
- |moebiusMu| |size| |makeRecord| |patternMatch| |lazyResidueClass|
- |lastSubResultantEuclidean| |randnum| |refine| |exactQuotient!|
- |extendedIntegrate| |ptree| |selectsecond| |cosSinInfo| |parabolic|
- |localUnquote| |mpsode| |unitsColorDefault| |lagrange|
- |polynomialZeros| |useEisensteinCriterion| |e02dcf|
- |nextsousResultant2| |heap| |recolor| |LyndonCoordinates|
- |createZechTable| |sincos| |monom| |bivariatePolynomials|
- |monomRDEsys| |selectPDERoutines| |first| |lazyPquo|
- |rightTraceMatrix| |imagI| |inspect| |digit?| |functionIsOscillatory|
- |diagonal?| |getlo| |f02xef| |rest| |powerAssociative?|
- |mainSquareFreePart| |pointColorDefault| |fractRadix| |s17ajf|
- |setelt| |zeroDimPrime?| |property| |substitute| |corrPoly| |Is|
- |deepestInitial| |redmat| |intcompBasis| |setlast!| |removeDuplicates|
- |realZeros| |startTableInvSet!| |minimalPolynomial| |universe|
- |interReduce| |solveid| |copy| |readable?| |exprHasWeightCosWXorSinWX|
- |viewDefaults| |primeFrobenius| |hcrf| |mainKernel| |bitLength|
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- |enterPointData| |unary?| |rspace| |euclideanNormalForm| |not|
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- |diagonals| |iisec| |cTan| |ravel| |iiasech| |upDateBranches|
- |autoCoerce| |countRealRoots| |var2Steps| |brillhartIrreducible?|
- |cCsch| |generalizedContinuumHypothesisAssumed?| |transcendenceDegree|
- |reshape| |mesh| |argumentListOf| |scan| |quatern| |s17akf|
- |lieAdmissible?| |groebnerFactorize| |orbits| |lhs|
- |viewDeltaXDefault| |simpleBounds?| |linearAssociatedOrder|
- |arrayStack| |OMputBVar| |powern| |intPatternMatch| |rhs| |code|
- |psolve| |associator| |compile| |palginfieldint| |nthr| |inrootof|
- |LyndonBasis| |regime| |sdf2lst| |complexForm| |quotient| |checkRur|
- |normalDeriv| |weierstrass| |elementary| |collect| |unitVector|
- |pointColorPalette| |update| |f01brf| |hdmpToP| |pointColor| |nil?|
- |hexDigit| |approxNthRoot| |critpOrder| |rk4f| |splitSquarefree|
- |rootRadius| |semiIndiceSubResultantEuclidean| |light| |alphabetic?|
- |leftTraceMatrix| |wordInStrongGenerators| |suffix?|
- |semiLastSubResultantEuclidean| |top| |showRegion| |mainPrimitivePart|
- |s21bcf| |iiasin| |leftUnits| |cCosh| |quadratic| |option?| |continue|
- |listYoungTableaus| |makeEq| |qelt| |tanh2coth| |symmetricProduct|
- |unit?| |bandedJacobian| |prefix?| |tan2cot| |cAtan| |call|
- |legendreP| |cycleEntry| |second| |cscIfCan| |c06ekf| |invertibleSet|
- |squareMatrix| |cross| |readLine!| |key| |decompose|
- |var2StepsDefault| |third| |init| |nullary?| |elColumn2!|
- |multiplyExponents| |alternatingGroup| |OMencodingSGML| |accuracyIF|
- |limitedint| |iiabs| |options| |f04axf| |paraboloidal| |f07fef|
- |mathieu24| |rationalPower| |setEpilogue!| |logIfCan| |printInfo!|
- |compose| |removeRedundantFactors| |airyAi| |makeCos| |elt| |read!|
- |commutator| |filename| |ODESolve| |flatten| |eulerE|
- |completeEchelonBasis| |printInfo| |noKaratsuba| |mkcomm|
- |exprToGenUPS| |iisin| |doubleComplex?| |repeating?| |subscript|
- |initial| |d01gbf| |moduloP| |infix?| |sech2cosh| |setClipValue|
- |totalDegree| |LazardQuotient| |jacobiIdentity?| |OMputVariable|
- |stoseInternalLastSubResultant| |mask| |characteristicSet| |torsion?|
- |removeSuperfluousQuasiComponents| |generalPosition| |legendre|
- |extend| |degreePartition| |pushuconst| |radicalEigenvectors| |parse|
- |heapSort| |idealiser| |mapUnivariateIfCan| |virtualDegree| |OMgetApp|
- |charthRoot| |ratDsolve| |semicolonSeparate| |rarrow| |collectUpper|
- |hex| |setMinPoints| |c06eaf| |removeRedundantFactorsInPols|
- |composites| |characteristicSerie| |htrigs| |superscript|
- |tryFunctionalDecomposition| |OMputAtp| |setPoly| |rootPoly| |e02daf|
- |reverseLex| |redpps| |size?| |screenResolution3D| |relerror|
- |subspace| |escape| |stronglyReduce| |bernoulli| |critM|
- |derivationCoordinates| |semiDegreeSubResultantEuclidean| |lllp|
- |alternating| |eigenvectors| |tube| |rightTrace| |antiAssociative?|
- |semiDiscriminantEuclidean| |relativeApprox| |outerProduct| |s21baf|
- |crest| |OMreadStr| |isPower| |nary?| |cRationalPower|
- |changeThreshhold| |selectOptimizationRoutines| |basisOfRightNucleus|
- |mapMatrixIfCan| |numericalOptimization| |fortran| |radPoly|
- |removeRoughlyRedundantFactorsInContents| |splitNodeOf!| |insert!|
- |rightDiscriminant| |acscIfCan| |xRange| |column| |groebgen| |delete!|
- |errorInfo| |supersub| |minimize| |fmecg| |stFuncN| |viewPosDefault|
- |module| |preprocess| |yRange| |minPoints3D| |compiledFunction|
- |zeroSquareMatrix| |charpol| |showIntensityFunctions| |skewSFunction|
- |stoseSquareFreePart| |c05adf| |pile| |unitCanonical|
- |radicalEigenvector| |zRange| |removeCoshSq| |simplifyExp|
- |patternVariable| |hasoln| |qroot| |roughUnitIdeal?| |outputFloating|
- |leftRegularRepresentation| |expintegrate| |cycle| |f02agf|
- |OMgetEndError| |map!| LODO2FUN |pushucoef| |getStream| |e04mbf|
- |crushedSet| |getVariableOrder| |component| |coerceListOfPairs|
- |insertMatch| |norm| |palgextint| |internalLastSubResultant|
- |qsetelt!| |resetAttributeButtons| |singleFactorBound| |monicDivide|
- |dominantTerm| |iiasec| |gramschmidt| |s17dhf| |fixedPointExquo|
- |trapezoidalo| |rischDEsys| |list?| |degree| |binaryTournament|
- |inverseIntegralMatrixAtInfinity| |e02akf| |fintegrate| |elem?|
- |factorSFBRlcUnit| |principalIdeal| |quasiMonic?| |deepestTail|
- |aCubic| |mainDefiningPolynomial| |internalZeroSetSplit| |lp|
- |getDatabase| |expenseOfEvaluation| |OMUnknownCD?| |subTriSet?|
- |increasePrecision| |firstUncouplingMatrix| |optimize| |copyInto!|
- |tablePow| |integerIfCan| |gcdPolynomial| |internalIntegrate|
- |selectFiniteRoutines| |reindex| |stoseInvertibleSet| |cSinh| |ode2|
- |f2df| |genericRightTrace| |green| |ldf2lst| |duplicates|
- |fortranTypeOf| |cyclotomic| |open?| |red| |graphState| |index|
- |queue| |initTable!| ^ |f02bjf|
- |solveLinearPolynomialEquationByRecursion| |binaryTree| |expIfCan|
- |iidsum| |roughEqualIdeals?| |edf2ef| |shallowCopy| |acsch| |central?|
- |mkIntegral| |invmod| |failed?| |simplifyPower| |integer?|
- |basisOfRightNucloid| |listConjugateBases| |mat| |multiEuclidean|
- |graeffe| |semiResultantEuclideannaif| |solve1| |stopMusserTrials|
- |stirling1| |janko2| |scalarTypeOf| |gcdPrimitive| |script|
- |external?| |lprop| |shrinkable| |palgRDE0| |rangeIsFinite|
- |totalDifferential| |leftPower| |mapExpon| |space| |f04arf|
- |evenInfiniteProduct| |iiatan| |constantKernel| |palgintegrate|
- |bsolve| |deleteProperty!| |ListOfTerms| |trim| |prologue|
- |constantToUnaryFunction| |fortranLinkerArgs| |elRow1!| |stack|
- |symbolIfCan| |readIfCan!| |polyred| |head| |genericRightNorm|
- |tanhIfCan| |roughSubIdeal?| |sparsityIF| |generalizedInverse|
- |certainlySubVariety?| |isPlus| |tex| |lazyIrreducibleFactors|
- |LyndonWordsList| |lazyPseudoDivide| |lexico| |coleman| |maxint|
- |nilFactor| |OMgetBind| |conjugates| |tableForDiscreteLogarithm|
- |stopTable!| |mapmult| |linear| |karatsubaOnce| |makeMulti| |hspace|
- |generalSqFr| |log10| |linearMatrix| |reorder| |dAndcExp| |members|
- |genericLeftDiscriminant| |explicitEntries?| |elliptic?|
- |useSingleFactorBound?| |lexTriangular| |cycleElt| |rightTrim|
- |B1solve| |coefficients| |createLowComplexityNormalBasis| |qPot|
- |discriminantEuclidean| |chebyshevU| |polynomial| |genericLeftTrace|
- |associates?| |moduleSum| |dec| |complexNumericIfCan| |leftTrim|
- |iiacosh| |outputMeasure| |nsqfree| |basisOfLeftNucleus| |asecIfCan|
- |minordet| |interval| |isOp| |makeUnit| |divide| |inHallBasis?|
- |intensity| |float?| |leftScalarTimes!| |toseLastSubResultant|
- |sinhcosh| |fortranLiteral| |pointData| |curryLeft| |meshFun2Var|
- |printStats!| |restorePrecision| |message| |dom| |supDimElseRittWu?|
- |compdegd| |dmp2rfi| |viewPhiDefault| |makeTerm| |OMgetEndBVar|
- |getMultiplicationTable| |characteristic| |nextPartition| |henselFact|
- |autoReduced?| |mathieu23| |double?| |curry| |radicalOfLeftTraceForm|
- |leadingIndex| |monicDecomposeIfCan| |uniform01| |magnitude|
- |pushdterm| |prime?| |definingEquations| |tanQ| |equation| |ef2edf|
- |redPo| |acosIfCan| |subNodeOf?| |removeSquaresIfCan|
- |stripCommentsAndBlanks| |s17adf| |homogeneous?| |split| |iiGamma|
- |rightRegularRepresentation| |ffactor| |mdeg| |modularGcdPrimitive|
- |monomRDE| |extractClosed| |eisensteinIrreducible?| |updatD| |e02aef|
- |root| |name| |stoseInvertible?| |OMParseError?| |cAcos| |d01alf|
- |selectIntegrationRoutines| |cons| |cyclotomicDecomposition|
- |leftRemainder| |primaryDecomp| |sh| |primlimintfrac| |find|
- |showAllElements| |processTemplate| |binarySearchTree|
- |hasTopPredicate?| |addMatchRestricted| |partitions| |coth2tanh|
- |cyclotomicFactorization| |surface| |d02gaf| |genericRightTraceForm|
- |monomialIntPoly| |factorial| |f07fdf| |bezoutMatrix|
- |initiallyReduced?| |frst| |makeViewport3D| |polyRDE| |midpoint|
- |d02bhf| |algebraicOf| |label| |removeRoughlyRedundantFactorsInPols|
- |conditionP| |geometric| |conjugate| |e02ddf| |viewWriteAvailable| |e|
- |identification| |rightRank| |factorset| |isobaric?| |operator|
- |monomialIntegrate| |overlap| |bitTruth| |f01qdf| |paren|
- |normalElement| |stoseInvertible?sqfreg| |select!|
- |halfExtendedResultant2| |makeResult| |equality|
- |removeIrreducibleRedundantFactors| |colorFunction| |iicoth| |minPoly|
- |chebyshevT| |primeFactor| |pmintegrate| |optpair| |eigenMatrix|
- |complexLimit| |dimensions| |integralBasis| |monicRightFactorIfCan|
- |createPrimitiveNormalPoly| |sinIfCan| |selectSumOfSquaresRoutines|
- |orthonormalBasis| |doubleDisc| |leftLcm| |youngGroup| |tRange|
- |extractPoint| |enqueue!| |normInvertible?| |vedf2vef| |setStatus!|
- |getMultiplicationMatrix| |brace| |cAtanh| |palglimint| |OMputEndAttr|
- |definingInequation| |showArrayValues| |mapDown!|
- |solveLinearPolynomialEquationByFractions| |expPot| |ranges| |bumprow|
- |nlde| |appendPoint| |perfectSquare?| |listOfMonoms| |squareFreePart|
- |continuedFraction| |generalTwoFactor| |normalized?| |title|
- |generateIrredPoly| |distdfact| |leastAffineMultiple| |resetNew|
- |generalizedEigenvector| |pquo| |tensorProduct| |reduced?|
- |positiveRemainder| |Vectorise| |imagJ| |iCompose| |argumentList!|
- |exprHasLogarithmicWeights| |polar| |error| |lintgcd| |idealSimplify|
- |numeric| |unrankImproperPartitions0| |dark| |sqfree|
- |invertibleElseSplit?| |antisymmetricTensors| |cos2sec|
- |fillPascalTriangle| |value| |fprindINFO| |radical| |assert| |s19aaf|
- |radicalRoots| |lepol| |toseInvertibleSet| |Lazard2| |coshIfCan|
- |cot2tan| |rootNormalize| |dim| |allRootsOf| |atrapezoidal|
- |semiResultantEuclidean2| |d02ejf| |rCoord|
- |createNormalPrimitivePoly| |euler| |substring?| |s18def|
- |plusInfinity| |addBadValue| |depth| |eulerPhi| |setPosition|
- |diagonal| |curveColorPalette| |permutationRepresentation| |iiacsch|
- |cosh2sech| |maxdeg| |minusInfinity| |inR?| |properties|
- |setprevious!| |primextendedint| |outputAsTex| |UpTriBddDenomInv|
- |option| |any?| |cCoth| |ScanFloatIgnoreSpaces| |recip| |convergents|
- |newSubProgram| |quadratic?| |exQuo| |lists| |schwerpunkt| |rightLcm|
- |cyclicSubmodule| |df2st| |tab1| |has?| |diff| |rootOfIrreduciblePoly|
- |fullDisplay| |trapezoidal| |nextColeman| |eq?|
- |reducedContinuedFraction| |s17dlf| |stoseLastSubResultant| |id|
- |clearTable!| |makeop| |LazardQuotient2| |factorAndSplit| |translate|
- |leadingBasisTerm| |fill!| |sts2stst| |genericRightMinimalPolynomial|
- |lfunc| |leadingExponent| |Beta| |firstSubsetGray| |color| **
- |mapExponents| |table| |d03eef| |purelyAlgebraicLeadingMonomial?|
- |parametersOf| |c06frf| |SFunction| |leastPower| |failed| |float|
- |orbit| |new| |powerSum| |generic| |bitCoef| |removeCosSq|
- |palglimint0| |makeViewport2D| |redPol| EQ |OMclose| |outputList|
- |principal?| |ParCond| |normal01| |denominators| |retractIfCan|
- |OMgetObject| |omError| |balancedFactorisation| |replace| |zeroMatrix|
- |rdregime| |setColumn!| |printingInfo?| |inconsistent?| |localReal?|
- |rightRecip| |setOfMinN| |quartic| |consnewpol| |cSech|
- |physicalLength!| |Lazard| |screenResolution| |taylorQuoByVar|
- |setEmpty!| |UnVectorise| |plenaryPower| |e01bff| |dflist|
- |normDeriv2| |write!| |partialNumerators| |coth2trigh| |laurentIfCan|
- |integral?| |intersect| |delay| |s18adf| |f02wef| |cylindrical|
- |sncndn| |lazyVariations| GE |squareFreePrim| |wrregime| |prime|
- |curveColor| |completeEval| |empty?| GT |karatsuba| |e01bgf|
- |removeSinhSq| |twoFactor| |identityMatrix| |cycleLength| |level|
- |e01sef| |bringDown| |oddlambert| |iiasinh| |palgRDE| LE |back| |left|
- |bezoutResultant| |cardinality| |diagonalMatrix| |solid?|
- |completeHensel| |graphStates| |car| |lexGroebner| |child| LT
- |wholePart| |right| |reducedForm| |hMonic| |leader|
- |removeDuplicates!| |leftTrace| |createNormalElement| |tanNa|
- |laplacian| |cdr| |map| |superHeight| |iitan| |reduceBasisAtInfinity|
- |binary| |fortranLiteralLine| |computeCycleLength| |palgint|
- |sqfrFactor| |power!| |f01mcf| |schema| |f02abf| |pushup|
- |showTypeInOutput| |OMgetError| |newLine| |routines| |modulus|
- |internalIntegrate0| |coercePreimagesImages| |singular?| |digit|
- |leftUnit| |showFortranOutputStack| |cfirst| |reduction|
- |leftFactorIfCan| |nthFactor| |genericLeftNorm| |diagonalProduct|
- |pointPlot| D |generalizedContinuumHypothesisAssumed|
- |genericLeftTraceForm| |SturmHabichtMultiple| |rightRemainder|
- |collectQuasiMonic| |fortranCharacter| |common| |infieldint| |terms|
- |frobenius| |padicallyExpand| |computePowers| |oddintegers|
- |iflist2Result| |OMgetString| |clip| |convert| |mesh?| |addmod|
- |lazyIntegrate| |basisOfCentroid| |writable?| |cAcosh| |clipSurface|
- |varList| |ode1| |prod| |showTheRoutinesTable| |coordinates|
- |monomials| |nthCoef| |s14aaf| |d01ajf| |operation| |cycles| |iiperm|
- |OMReadError?| |wreath| |integralDerivationMatrix| |setProperty|
- |mapUnivariate| |e04dgf| |scale| |basisOfCenter| |nextPrimitivePoly|
- |defineProperty| |cLog| |retract| |nextSubsetGray| |acotIfCan|
- |primintfldpoly| |explicitlyFinite?| |OMmakeConn| |cAsech|
- |lflimitedint| |irreducibleFactors| |rquo| |kmax| |s21bdf|
- |denomRicDE| |atom?| |addPointLast| |totalfract| |print|
- |infieldIntegrate| |getZechTable| |rischNormalize| |linGenPos|
- |expintfldpoly| |complexNormalize| |stoseIntegralLastSubResultant|
- |constantRight| |FormatArabic| |point| |cschIfCan| |e04naf| |width|
- |argument| |padicFraction| |deref| |dn| |headReduce| |completeHermite|
- |setScreenResolution3D| |stoseInvertible?reg| |imagj|
- |algebraicCoefficients?| |optAttributes| |gcdcofactprim|
- |quasiMonicPolynomials| |series| |solveInField| |att2Result|
- |precision| |sequences| |toroidal| |s17def| |box| |roman|
- |setAdaptive| |quasiAlgebraicSet| |minColIndex| |pseudoQuotient|
- |ramifiedAtInfinity?| |gderiv| |optional| |wronskianMatrix|
- |predicates| |lineColorDefault| |partition| |sinh2csch| |sum|
- |epilogue| |primitive?| |OMputObject| |min| |modularFactor| |zeroOf|
- |largest| |f07adf| |asechIfCan| |next| |listexp| |f04asf|
- |leadingIdeal| |inverseLaplace| |gcdprim| |radicalSimplify|
- |fibonacci| |se2rfi| |rightFactorIfCan| |key?| |e01sbf| |constant?|
- |ceiling| |string?| |leftExtendedGcd| |complete| |iidprod| |every?|
- |integralCoordinates| |semiSubResultantGcdEuclidean1| |An| |coord|
- |checkPrecision| |Hausdorff| |asech| |readLineIfCan!| |c02agf|
- |bright| |s14abf| |leftNorm| |externalList| |trivialIdeal?| |exp1|
- |topPredicate| |decimal| |comp| |setAdaptive3D| FG2F |nextSublist|
- |weights| |e02dff| |multiple| |rur| |yCoord|
- |zeroSetSplitIntoTriangularSystems| |clipPointsDefault| |truncate|
- |binomThmExpt| |applyQuote| |leftFactor| |airyBi| |prinb|
- |antisymmetric?| |laguerre| |meatAxe| |rationalPoint?| |factorials|
- |fortranDoubleComplex| |extendedint| |eval| |positive?|
- |monicLeftDivide| |algebraicSort| |any| |wordInGenerators|
- |makeVariable| |setMinPoints3D| |factor1| |nor| |makeprod| |#|
- |functionIsFracPolynomial?| |symmetricSquare| |index?| |ruleset|
- |chvar| |divisor| |ReduceOrder| |explogs2trigs|
- |resultantEuclideannaif| |lowerPolynomial| |product|
- |nextNormalPrimitivePoly| |f02aff| |bernoulliB| |OMconnOutDevice|
- |BasicMethod| |monicModulo| |invertIfCan| |rk4| |multisect|
- |purelyTranscendental?| |pair?| |suchThat| |algDsolve|
- |indicialEquation| |char| |sorted?| |fTable| |search|
- |makeFloatFunction| |c05nbf| F2FG |dimensionsOf| |center| |df2mf|
- |f04adf| |getMeasure| |aspFilename| |nextItem| |cartesian| |squareTop|
- |graphImage| |OMconnectTCP| |stopTableInvSet!| |alphanumeric?|
- |generalInfiniteProduct| |moreAlgebraic?| |internalSubQuasiComponent?|
- |numericalIntegration| |scalarMatrix| |OMencodingBinary| |s20acf|
- |definingPolynomial| |exprToXXP| |maxrank| |quasiRegular?|
- |compactFraction| |setTex!| |evaluate| |remove!| |lifting1| |d01asf|
- |denominator| |simpsono| |exponents| |rdHack1| |forLoop|
- |rationalPoints| |elliptic| |zoom| |lfinfieldint| |supRittWu?|
- |setMaxPoints3D| |extension| |Zero| |companionBlocks|
- |stiffnessAndStabilityOfODEIF| |extractIndex| |linearlyDependent?|
- |sort!| |cup| |measure| |rightUnits| |One| |distribute| |d01apf|
- |aQuadratic| ~ |internalAugment| |mathieu12| |removeSinSq| |cAcoth|
- |quotientByP| |laurentRep| |cn| |f04maf| |realSolve|
- |sizePascalTriangle| |reciprocalPolynomial| |beauzamyBound|
- |radicalEigenvalues| |factorFraction| |dihedral| |infinityNorm|
- |harmonic| |identitySquareMatrix| |presuper| |algint|
- |hypergeometric0F1| |makeFR| |qinterval| |findCycle| |graphCurves|
- |cSin| |bumptab1| |exprHasAlgebraicWeight| |colorDef| |medialSet|
- |rational| |leadingCoefficientRicDE| |opeval| |nthExpon| |tracePowMod|
- |changeVar| |iilog| |monicRightDivide| |palgLODE|
- |numberOfIrreduciblePoly| |setref| |mkPrim| |power| |badNum|
- |anfactor| |copy!| |chainSubResultants| |entry?| |f04faf|
- |makeYoungTableau| |cAcsch| |unmakeSUP| |open| |ddFact| |xCoord|
- |rk4a| |mainCharacterization| |graphs| |length| |s15adf| |composite|
- |complexEigenvalues| |sayLength| |s17dgf| |physicalLength|
- |subResultantsChain| |complementaryBasis| |updateStatus!| |kovacic|
- |scripts| |iisqrt3| |algebraicVariables| |getPickedPoints| |iibinom|
- |swapColumns!| |mantissa| |tanIfCan| |factorsOfCyclicGroupSize|
- |myDegree| |OMgetEndAtp| |prinpolINFO| |rootPower| |low|
- |brillhartTrials| |integralBasisAtInfinity| |leftOne| |seriesSolve|
- |quasiComponent| |mergeDifference| |expr| |symFunc| |totolex|
- |generalLambert| |mathieu22| |neglist| |iExquo| |fglmIfCan| |append|
- |cyclicCopy| |rationalApproximation| |commutative?| |fortranDouble|
- |rightCharacteristicPolynomial| |const| |delete| |usingTable?|
- |dimensionOfIrreducibleRepresentation| |interpolate| |s18aff| |reseed|
- |bipolarCylindrical| |finite?| NOT |minIndex| |rank|
- |useSingleFactorBound| |branchIfCan| |dihedralGroup| |invmultisect|
- |gradient| |c06fpf| |pr2dmp| |numFunEvals| OR |randomR| |create|
- |completeSmith| |asimpson| |variable| |pop!| |showScalarValues|
- |shiftRight| |problemPoints| |printStatement| AND |rightExtendedGcd|
- |drawComplexVectorField| |polygon| |extendIfCan|
- |halfExtendedSubResultantGcd2| |getRef| |e02bbf| |rightAlternative?|
- |lifting| |row| |doubleRank| |mergeFactors| |cycleTail| |df2fi|
- |removeRedundantFactorsInContents| |rootOf| |perfectNthPower?|
- |complexElementary| |selectOrPolynomials| |decrease| |adaptive3D?|
- |initials| |eq| |e02baf| |OMopenFile| |nextLatticePermutation|
- |OMsend| |invertible?| |iisinh| |exists?| |f02adf| |decomposeFunc|
- |rewriteIdealWithQuasiMonicGenerators| |iter| |OMgetSymbol|
- |setErrorBound| |fi2df| |nullSpace| |typeList| |f04qaf| |calcRanges|
- |merge| |OMputEndApp| |writeLine!| |obj| |bfEntry| |/\\|
- |removeRoughlyRedundantFactorsInPol| |nullity| |top!| |isTimes|
- |ratPoly| |f02awf| |factorOfDegree| |stoseInvertibleSetreg|
- |halfExtendedResultant1| |setRow!| |primlimitedint| |\\/|
- |complexIntegrate| |cache| |isMult| |squareFreeFactors|
- |OMsupportsCD?| |numberOfComponents| |sylvesterSequence| |OMreceive|
- |numer| |transcendent?| |tValues| |normalizeIfCan| |contractSolve|
- |f2st| |lazyGintegrate| |tower| |logpart| |replaceKthElement| |mvar|
- |closedCurve| |recur| |returnTypeOf| |shufflein| |plotPolar|
- |chineseRemainder| |internal?| |tubeRadius| |multiplyCoefficients|
- |idealiserMatrix| |hasSolution?| |constDsolve| |numberOfNormalPoly|
- |isAbsolutelyIrreducible?| |tableau| |conical| |ode| * |iiexp|
- |shiftRoots| |numericIfCan| |evaluateInverse| |tubePoints|
- |oddInfiniteProduct| |rowEchLocal| |fixedPoints| |traceMatrix|
- |nullary| |setPredicates| |chiSquare1| |plot| |factor|
- |trailingCoefficient| |exp| |position!| |minPoints| |c06fuf| |stFunc2|
- |selectNonFiniteRoutines| |declare!| |zero| |showTheFTable|
- |horizConcat| |firstNumer| |sqrt| |setStatus| |blue| |tanintegrate|
- |mapBivariate| |algebraicDecompose| |d01fcf| |ScanArabic| |complex|
- |getCode| |null| |mathieu11| |real| |getOrder|
- |selectMultiDimensionalRoutines| |cAsin| |basisOfRightAnnihilator|
- |upperCase?| |leftGcd| |listRepresentation| |shanksDiscLogAlgorithm|
- |And| |useNagFunctions| |OMread| |asinhIfCan| |imag|
- |expandTrigProducts| |rules| |directProduct| |OMputBind|
- |OMunhandledSymbol| |totalLex| |maxPoints| |radicalSolve| |subst| |Or|
- |cyclicParents| |extractIfCan| |OMsetEncoding| |returnType!| |hue|
- |figureUnits| |e04jaf| |rightDivide| |reducedQPowers| |boundOfCauchy|
- |Not| |knownInfBasis| |goodPoint| |iiatanh| |stopTableGcd!|
- |setCondition!| |outlineRender| |mainMonomials| |triangularSystems|
- |character?| |lyndon| |functionIsContinuousAtEndPoints| |groebner?|
- |backOldPos| |vspace| |destruct| |integralMatrixAtInfinity|
- |indiceSubResultantEuclidean| |lyndon?| |radix| |modularGcd|
- |OMUnknownSymbol?| |ocf2ocdf| |maximumExponent|
- |factorSquareFreeByRecursion| |taylorRep| |conjug| |coefficient|
- |setrest!| |points| |block| |imagk| |spherical|
- |createPrimitiveElement| |mainContent| |setClosed| |modifyPointData|
- |iitanh| |numerators| |nthFlag| |insertTop!| |iiacsc| |numerator|
- |baseRDEsys| |d02raf| |objects| |countRealRootsMultiple| |binomial|
- |trigs| |headReduced?| |bivariate?| |ratDenom| |or| |deleteRoutine!|
- |maxIndex| |algebraic?| |pointLists| |intChoose| |in?| |base|
- |increment| |denomLODE| |region| |showClipRegion| |dot| |double|
- |lSpaceBasis| |and| |d02cjf| |errorKind| |e01bef| |maxColIndex|
- |nonLinearPart| |sizeLess?| |contract| |axes| |e04gcf| |qqq|
- |tanh2trigh| |inc| |lighting| |systemSizeIF| |endOfFile?| |member?|
- |maxrow| |iicsch| |branchPoint?| |bit?| |round| |initiallyReduce|
- |makeCrit| |whatInfinity| |setFieldInfo| |setMaxPoints| |setPrologue!|
- |real?| |unparse| |bandedHessian| |prefix| |stoseInvertibleSetsqfreg|
- |s17dcf| |quasiRegular| |stFunc1| |computeCycleEntry|
- |branchPointAtInfinity?| |prinshINFO| |romberg| |discriminant|
- |clikeUniv| |removeConstantTerm| |f01rdf| |dequeue!| |infinite?|
- RF2UTS |closedCurve?| |comment| |ellipticCylindrical| |OMputAttr|
- |less?| |c06ecf| |uniform| |comparison| |yellow| |pToDmp| |lllip|
- |multMonom| |e02ajf| |solveLinearlyOverQ| |test| |rootsOf| |satisfy?|
- |associatedSystem| |debug3D| |multinomial| |limitedIntegrate| |c06gbf|
- |BumInSepFFE| |triangular?| |primitivePart!| |overbar|
- |standardBasisOfCyclicSubmodule| |cubic| |gcdcofact| |drawComplex|
- |lazyPremWithDefault| |conditionsForIdempotents| |factorPolynomial|
- |eigenvalues| |noncommutativeJordanAlgebra?| |inRadical?| |sec2cos|
- |rst| |OMgetEndObject| |rotate| |extractBottom!|
- |numberOfComputedEntries| |nthFractionalTerm| |max| |edf2df|
- |OMgetAttr| |distFact| |LagrangeInterpolation| |ricDsolve|
- |ScanFloatIgnoreSpacesIfCan| |rightQuotient|
- |primPartElseUnitCanonical!| |fortranCarriageReturn| |complex?|
- |symbol?| |euclideanSize| |clearTheIFTable| |highCommonTerms|
- |components| |droot| |super| |viewport3D| |complexRoots|
- |permutations| |minimumExponent| |rightMult| |c06gsf| |pdct| |front|
- |concat| |inverseColeman| |setOrder| |associatorDependence|
- |useEisensteinCriterion?| |internalSubPolSet?| |getMatch| |cAcot|
- |eyeDistance| |vconcat| |intermediateResultsIF| |LiePoly|
- |pascalTriangle| |indices| |previous| |hash| |perspective| |digamma|
- |determinant| |endSubProgram| |f02aef| |edf2fi| |clearTheFTable|
- |createThreeSpace| |tan2trig| |symmetricTensors| |var1StepsDefault|
- |count| |kroneckerDelta| |split!| |s13aaf| |bumptab| |whileLoop|
- |leaf?| |dequeue| |modifyPoint| |basisOfLeftNucloid| |bottom!|
- |localIntegralBasis| |subscriptedVariables| |nextNormalPoly|
- |innerSolve| |c06gcf| |infix| |exponentialOrder| |d03edf|
- |OMputInteger| |bag| |polyPart| |padecf| |element?| |atanIfCan|
- |variationOfParameters| |linearDependenceOverZ|
- |basisOfLeftAnnihilator| |zCoord| |OMlistCDs| |laguerreL| |iipow|
- |messagePrint| |moebius| |gbasis| |normalDenom| |nil| |infinite|
- |arbitraryExponent| |approximate| |complex| |shallowMutable|
- |canonical| |noetherian| |central| |partiallyOrderedSet|
- |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors|
- |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown|
- |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate|
- |shallowlyMutable| |commutative|) 
\ No newline at end of file
+ |Record| |Union| |Category| |setvalue!| |hermiteH| |generalLambert|
+ |digits| |divideExponents| |operators| |infieldIntegrate|
+ |radicalOfLeftTraceForm| |prinshINFO| |pointColorPalette| |binaryTree|
+ |perfectSquare?| |diagonals| |prem| |mathieu22|
+ |genericLeftMinimalPolynomial| |c06gqf| |getZechTable| |maxRowIndex|
+ |leadingIndex| |romberg| |f01brf| |changeName| |position| |iisec|
+ |listOfMonoms| |neglist| |difference| |rischNormalize| |s17ahf|
+ |monicDecomposeIfCan| |discriminant| |hdmpToP| |cTan| |square?|
+ |squareFreePart| |iExquo| |log| |genericPosition| |linGenPos|
+ |cyclicEntries| |uniform01| |clikeUniv| |pointColor| |iiasech|
+ |continuedFraction| |besselJ| |fglmIfCan| |tree| |makeGraphImage|
+ |expintfldpoly| |removeConstantTerm| |magnitude| |nil?|
+ |GospersMethod| |upDateBranches| |generalTwoFactor| |cyclicCopy|
+ |pack!| |complexNormalize| |pushdterm| |f01rdf| |hexDigit|
+ |countRealRoots| |normalized?| |LiePolyIfCan| |rationalApproximation|
+ |leftExactQuotient| |stoseIntegralLastSubResultant| |dequeue!|
+ |prime?| |approxNthRoot| |d01gbf| |checkForZero| |var2Steps|
+ |generateIrredPoly| |showSummary| |commutative?| |dfRange|
+ |constantRight| |infinite?| |definingEquations| |critpOrder| |moduloP|
+ |brillhartIrreducible?| |fortranDouble| |FormatArabic| |poisson|
+ |tanQ| RF2UTS |sech2cosh| |rk4f| |iiGamma| |currentSubProgram| |cCsch|
+ |rightCharacteristicPolynomial| |showAttributes| |linearPolynomials|
+ |cschIfCan| |ef2edf| |closedCurve?| |setClipValue| |splitSquarefree|
+ |rightRegularRepresentation| |transpose|
+ |generalizedContinuumHypothesisAssumed?| |const| |rectangularMatrix|
+ |e04naf| |besselK| |ellipticCylindrical| |redPo| |rootRadius|
+ |totalDegree| |ffactor| |primitiveElement| |transcendenceDegree|
+ |usingTable?| |removeSuperfluousCases| |OMputAttr| |acosIfCan|
+ |LazardQuotient| |semiIndiceSubResultantEuclidean| |asinIfCan| |mdeg|
+ |dimensionOfIrreducibleRepresentation| |singularAtInfinity?|
+ |completeHensel| |realEigenvectors| |generator| |subNodeOf?| |less?|
+ |jacobiIdentity?| |light| |modularGcdPrimitive| |presub| |directory|
+ |interpolate| BY |changeNameToObjf| |traverse| |graphStates| |c06ecf|
+ |removeSquaresIfCan| |alphabetic?| |OMputVariable| |monomRDE|
+ |removeZeroes| |s18aff| |lexGroebner| |pattern| |separate| |subSet|
+ |uniform| |stripCommentsAndBlanks| |leftTraceMatrix|
+ |stoseInternalLastSubResultant| |cSec| |extractClosed| |mr|
+ |rootSplit| |startPolynomial| |child| |comparison| |s17adf|
+ |characteristicSet| |wordInStrongGenerators| |eisensteinIrreducible?|
+ |lyndonIfCan| |extension| |s18dcf| |combineFeatureCompatibility|
+ |sumOfSquares| |systemCommand| |wholePart| |debug| |yellow|
+ |homogeneous?| |formula| |torsion?| |semiLastSubResultantEuclidean|
+ |updatD| |curve?| |constantCoefficientRicDE| |companionBlocks|
+ |reducedForm| |groebner| |one?| |pToDmp| |split|
+ |removeSuperfluousQuasiComponents| |showRegion| |e02aef| |rowEchelon|
+ |stiffnessAndStabilityOfODEIF| |d01gaf| |constant| |hMonic| |normal|
+ |d01amf| |areEquivalent?| |generalPosition| |mainPrimitivePart| |root|
+ |sample| |extractIndex| |order| |iiatanh| |rightTraceMatrix| |kernel|
+ |removeDuplicates!| |f01qef| |purelyAlgebraic?| |constantKernel|
+ |complexNumeric| |s21bcf| |adjoint| |stoseInvertible?| |op|
+ |linearlyDependent?| |collectUnder| |pleskenSplit| |sortConstraints|
+ |leftTrace| |palgintegrate| |imagI| |stopTableGcd!| |copies| |iiasin|
+ |integralRepresents| |OMParseError?| |sort!| |nrows| |erf| |remove|
+ |kernels| |linearAssociatedLog| |createNormalElement|
+ |factorByRecursion| |bsolve| |setCondition!| |cup| |leftUnits| |cAcos|
+ |SturmHabicht| |triangulate| |ncols| |deleteProperty!| |tanNa|
+ |linearlyDependentOverZ?| |birth| |univariate| |outlineRender|
+ |d01alf| |hdmpToDmp| |rightUnits| |addMatch| |last| |true| |vark|
+ |laplacian| |match?| |csch2sinh| |ListOfTerms| |mainMonomials|
+ |selectIntegrationRoutines| |lambert| |crest| |distribute| |mapSolve|
+ |assoc| |dilog| |superHeight| |scanOneDimSubspaces| |closeComponent|
+ |trim| |triangularSystems| |cyclotomicDecomposition|
+ |leftRankPolynomial| |OMreadStr| |ptFunc| |d01apf| |sin| |iitan|
+ |stop| |quadraticNorm| |separateFactors| |character?| |prologue|
+ |trigs2explogs| |leftRemainder| |isPower| |f01ref| |aQuadratic| |cos|
+ |reduceBasisAtInfinity| |unit| |cAsec| |constantToUnaryFunction|
+ |lyndon| |nary?| |primaryDecomp| |badValues| |basis| |internalAugment|
+ |tan| |functionIsContinuousAtEndPoints| |binary| |OMputApp| |imagE|
+ |draw| |fortranLinkerArgs| |cRationalPower| |exptMod|
+ |partialFraction| |sh| |mathieu12| |mesh| |cot| |fortranLiteralLine|
+ |lift| |factors| |seed| |groebner?| |elRow1!| |primlimintfrac|
+ |string| |solve| |leftDivide| |removeSinSq| |argumentListOf| |sec|
+ |computeCycleLength| |reduce| |mainCoefficients| |OMopenString|
+ |backOldPos| |symbolIfCan| |duplicates| |find| |cAcoth| |ParCondList|
+ |shade| |scan| |csc| |parts| |compiledFunction| |palgint| |dimension|
+ |aQuartic| |vspace| |readIfCan!| |tail| |fortranTypeOf|
+ |validExponential| |musserTrials| |showAllElements| |quotientByP|
+ |quatern| |asin| |zeroSquareMatrix| |makeObject| |ldf2vmf|
+ |sqfrFactor| |rename| |integralMatrixAtInfinity| |polyred|
+ |cyclotomic| |processTemplate| |Si| |OMcloseConn| |s17akf|
+ |laurentRep| |acos| |charpol| |irreducibleFactor| |power!| |e01bhf|
+ |indiceSubResultantEuclidean| |head| |status| |open?|
+ |constantOpIfCan| |binarySearchTree| |lieAdmissible?| |f04maf|
+ |s01eaf| |atan| |genericRightNorm| |e02zaf| |f01mcf|
+ |axesColorDefault| |lyndon?| |coef| |complexSolve| =
+ |groebnerFactorize| |hasTopPredicate?| |indicialEquations| |realSolve|
+ |acot| |leftRecip| |mirror| |schema| |tanhIfCan| |radix|
+ |tryFunctionalDecomposition?| |sizePascalTriangle|
+ |addMatchRestricted| |hessian| |orbits| |asec| |modularGcd| |f02abf|
+ |inGroundField?| |subresultantVector| |roughSubIdeal?| SEGMENT
+ |reciprocalPolynomial| < |partitions| |subCase?| |f04atf|
+ |viewDeltaXDefault| |acsc| |withPredicates| |pushup| |sparsityIF|
+ |OMUnknownSymbol?| > |buildSyntax| |coth2tanh| |toScale|
+ |beauzamyBound| |deepExpand| |sinh| |showTypeInOutput| |bfKeys|
+ |ocf2ocdf| |generalizedInverse| |cyclotomicFactorization| <= |heap|
+ |f01rcf| |pastel| |radicalEigenvalues| |cosh| |rightFactorCandidate|
+ |rootBound| |OMgetError| |maximumExponent| |certainlySubVariety?|
+ |recolor| >= |OMgetVariable| |surface| |semiResultantReduitEuclidean|
+ |factorFraction| |freeOf?| |tanh| |reset| |newLine| |curve|
+ |factorSquareFreeByRecursion| |isPlus| |dihedral| |d02gaf| |deepCopy|
+ |scaleRoots| |divideIfCan| |LyndonCoordinates| |coth| |routines|
+ |latex| |lazyIrreducibleFactors| |taylorRep| |createZechTable|
+ |safeFloor| |genericRightTraceForm| |infinityNorm| |divergence| |sech|
+ |OMgetEndAttr| |write| |modulus| |lquo| |LyndonWordsList| |conjug|
+ |critBonD| + |rightRankPolynomial| |monomialIntPoly| |harmonic| |csch|
+ |minRowIndex| |sincos| |save| |measure2Result| |internalIntegrate0|
+ |lazyPseudoDivide| |coefficient| |predicate| |factorial| -
+ |identitySquareMatrix| |pol| |complement| |cAsinh| |asinh|
+ |bivariatePolynomials| |characteristicPolynomial|
+ |coercePreimagesImages| |lexico| |setrest!| |constantOperator| /
+ |f07fdf| |quoByVar| |createMultiplicationMatrix| |presuper| |acosh|
+ |monomRDEsys| |singular?| |simpson| |t| |coleman| |points|
+ |bezoutMatrix| |representationType| |log2|
+ |removeRedundantFactorsInPols| |btwFact| |algint| |atanh|
+ |selectPDERoutines| |close| F |digit| |enterInCache| |block| |maxint|
+ |d03faf| |composites| |initiallyReduced?| |hypergeometric0F1|
+ |prefixRagits| |acoth| |lazyPquo| |leftUnit| |tanAn| |nilFactor|
+ |imagk| |frst| |overset?| |characteristicSerie| |makeFR| |choosemon|
+ |showFortranOutputStack| |insert| |symbolTableOf| |spherical|
+ |OMgetBind| |qinterval| |htrigs| |concat!| |makeViewport3D| |generic?|
+ |isQuotient| |display| |createPrimitiveElement| |fixedPoint| |cfirst|
+ |conjugates| |principalIdeal| |rightExactQuotient| |polyRDE|
+ |superscript| |even?| |findCycle| |tableForDiscreteLogarithm|
+ |reduction| |toseSquareFreePart| |mainContent| |quasiMonic?|
+ |tryFunctionalDecomposition| |midpoint| |showAll?| |f01bsf|
+ |graphCurves| |deepestTail| |KrullNumber| |leftFactorIfCan|
+ |stopTable!| |setClosed| |d02bhf| |OMputAtp| |showTheSymbolTable|
+ |cSin| |csc2sin| |aCubic| |nthFactor| |pointSizeDefault| |mapmult|
+ |modifyPointData| |setPoly| |probablyZeroDim?| |algebraicOf|
+ |quickSort| |bumptab1| |iitanh| |genericLeftNorm| |RemainderList|
+ |mainDefiningPolynomial| |karatsubaOnce| |inspect| |rootPoly|
+ |exprHasAlgebraicWeight| |removeRoughlyRedundantFactorsInPols|
+ |besselI| |f04jgf| |height| |input| |numerators| |coerceP|
+ |diagonalProduct| |makeMulti| |internalZeroSetSplit|
+ |functionIsOscillatory| |e02daf| |conditionP| |mightHaveRoots|
+ |getOperator| |colorDef| |library| |nthFlag| |drawToScale| |pointPlot|
+ |getDatabase| |hspace| |octon| |reverseLex| |geometric| |monic?|
+ |diagonal?| |medialSet| |generalizedContinuumHypothesisAssumed|
+ |insertTop!| |froot| |expenseOfEvaluation| |generalSqFr| |getlo|
+ |setFormula!| |redpps| |conjugate| |rational| |distance| |symbolTable|
+ |iiacsc| |genericLeftTraceForm| |f02ajf| |log10| |OMUnknownCD?|
+ |size?| |polCase| |e02ddf| |f02xef| |leadingCoefficientRicDE|
+ |augment| |delta| |linearMatrix| |entry| |OMbindTCP|
+ |SturmHabichtMultiple| |numerator| |subTriSet?| |powerAssociative?|
+ |SturmHabichtCoefficients| |viewWriteAvailable| |f04mcf| |opeval|
+ |pushFortranOutputStack| |integerBound| |increasePrecision|
+ |rightRemainder| |reorder| |baseRDEsys| |basisOfMiddleNucleus|
+ |symmetricRemainder| |identification| |arg1| |nthExpon| |pole?|
+ |mainSquareFreePart| |keys| |popFortranOutputStack| |set|
+ |balancedBinaryTree| |cond| |dAndcExp| |collectQuasiMonic| |d02raf|
+ |firstUncouplingMatrix| |unitNormalize| |rightRank| |tracePowMod|
+ |palgint0| |arg2| |vectorise| |pointColorDefault| |outputAsFortran|
+ |imaginary| |say| |copyInto!| |fortranCharacter| |members|
+ |countRealRootsMultiple| |acschIfCan| |groebSolve| |divideIfCan!|
+ |reverse| |factorset| |changeVar| |fractRadix| |declare|
+ |genericLeftDiscriminant| |infieldint| |fixedDivisor| |tablePow|
+ |binomial| |clearTheSymbolTable| |isobaric?| |iilog| |s17ajf|
+ |secIfCan| |particularSolution| |conditions| |rubiksGroup|
+ |integerIfCan| |untab| |terms| |explicitEntries?| |trigs| |tubePlot|
+ |rootSimp| |zeroDimPrime?| |operator| |tubeRadiusDefault|
+ |monicRightDivide| |match| |times!| |leaves| |elliptic?| |frobenius|
+ |point?| |gcdPolynomial| |headReduced?| |d01aqf| |palgLODE|
+ |monomialIntegrate| |changeBase| |corrPoly| |OMgetInteger| |lambda|
+ |negative?| |useSingleFactorBound?| |padicallyExpand|
+ |interpretString| |internalIntegrate| |bivariate?|
+ |resultantEuclidean| |numberOfIrreduciblePoly| |Is| |subset?| |iroot|
+ |setEpilogue!| |iicot| |computePowers| |ratDenom| |lexTriangular|
+ |bipolar| |getGraph| |setref| |deepestInitial| |extractProperty|
+ |iicsc| |logIfCan| |numberOfComposites| |oddintegers| |cycleElt|
+ |deleteRoutine!| |algintegrate| |vertConcat| |linkToFortran| |mkPrim|
+ |redmat| |fortranInteger| |printInfo!| |show| |iflist2Result|
+ |outputForm| |maxIndex| |B1solve| |factorsOfDegree| |pow|
+ |intcompBasis| |minset| |power| |powers| |compose| |coefficients|
+ |algebraic?| |sylvesterMatrix| |OMgetFloat| |balancedFactorisation|
+ |badNum| |cycleRagits| |setlast!| |edf2efi| |cAcsc|
+ |removeRedundantFactors| |trace| |subMatrix| Y
+ |createLowComplexityNormalBasis| |pointLists| |alternative?|
+ |commonDenominator| |anfactor| |pmComplexintegrate| |realZeros|
+ |solveLinearPolynomialEquation| |rotatex| |airyAi| |zeroMatrix|
+ |printTypes| |qPot| |intChoose| |sin?| |leftMult| |clipParametric|
+ |copy!| |startTableInvSet!| |jordanAdmissible?| |expintegrate|
+ |makeCos| |swap!| |numberOfOperations| |rdregime| |node| |in?| |rule|
+ |discriminantEuclidean| |fractionPart| |s21bbf| |splitLinear| |void|
+ |read!| |cycle| |f02axf| |vector| |setColumn!| |e02agf| |increment|
+ |chebyshevU| |setleft!| |computeBasis| |bernoulliB| |testDim| |cCot|
+ |f02agf| |commutator| |differentiate| |reducedDiscriminant|
+ |printingInfo?| |genericLeftTrace| |denomLODE| |stirling2| |is?|
+ |OMconnOutDevice| |OMgetEndError| |RittWuCompare| |univariate?|
+ |inconsistent?| |prepareSubResAlgo| |realRoots| |associates?|
+ |selectFiniteRoutines| |region| |swapRows!| |monomial| |extractTop!|
+ |BasicMethod| |f01maf| LODO2FUN |s17aff| |localReal?| |unaryFunction|
+ |multivariate| |getExplanations| |createNormalPoly| |monicModulo|
+ |pushucoef| |rewriteSetByReducingWithParticularGenerators| |nthRoot|
+ |rightRecip| |univariateSolve| |tubePoints| |rightGcd| |variables|
+ |denom| |jacobi| |invertIfCan| |moebiusMu| |getStream| |viewpoint|
+ |f02akf| |setOfMinN| |oddInfiniteProduct| |sumOfKthPowerDivisors|
+ |rk4| |overlabel| |e04mbf| |genus| |reify| |quartic| |rowEchLocal|
+ |Nul| |pi| |f07aef| |multisect| ~= |closed?| |exponent| |consnewpol|
+ |fixedPoints| |leadingTerm| |infinity| |imagK| |purelyTranscendental?|
+ |cCosh| |messagePrint| |socf2socdf| |safetyMargin| |cSech|
+ |traceMatrix| |drawStyle| |OMputFloat| |pair?| |moebius| |quadratic|
+ |rootProduct| |credPol| |physicalLength!| |shift| |nullary|
+ |permutation| |taylor| |algDsolve| |minrank| |option?| |gbasis|
+ |setVariableOrder| |Lazard| |setPredicates| |expandPower| |laurent|
+ |normalDenom| |indicialEquation| |resultant| |lo| |listYoungTableaus|
+ |sn| |screenResolution| |chiSquare1| |sort| |prindINFO| |puiseux|
+ |sorted?| |makeEq| |incr| |check| |taylorQuoByVar| |plot|
+ |univariatePolynomial| |fTable| |hi| |tanh2coth| |dictionary|
+ |setEmpty!| |trailingCoefficient| |countable?| |li| |nil|
+ |makeFloatFunction| |symmetricProduct| |equiv| |lieAlgebra?|
+ |UnVectorise| |position!| |infLex?| |c05nbf| |unit?| |univcase|
+ |discreteLog| |plenaryPower| |minPoints| |listBranches| F2FG
+ |bandedJacobian| |fracPart| |children| |e01bff| |c06fuf| |random|
+ |ran| |approximate| |dimensionsOf| |tan2cot| |reducedSystem|
+ |rightMinimalPolynomial| |dflist| |stFunc2| |segment| |ratpart|
+ |df2mf| |outputAsScript| |cAtan| |phiCoord| |makeSketch| |normDeriv2|
+ |selectNonFiniteRoutines| |mapUp!| |f04adf| |getBadValues| |legendreP|
+ |numberOfHues| |write!| |showTheFTable| |function|
+ |wordsForStrongGenerators| |getMeasure| |rewriteSetWithReduction|
+ |cycleEntry| |makeSeries| |partialNumerators| |horizConcat|
+ |univariatePolynomialsGcds| |aspFilename| |OMgetEndBind| |limit|
+ |coth2trigh| |firstNumer| |mainVariables| |po| |nextItem| |rightUnit|
+ |laurentIfCan| |setStatus| |qfactor| |cartesian| |assign| |datalist|
+ |symbol| |weighted| |integral?| |blue| |setfirst!| |squareTop|
+ |initializeGroupForWordProblem| |morphism| |intersect| |tanintegrate|
+ |red| |irreducibleRepresentation| |graphImage| |output| |zeroSetSplit|
+ |generate| |e01saf| |integer| |delay| |mapBivariate| |coerce| |ord|
+ |innerEigenvectors| |OMconnectTCP| |case| |factorSquareFreePolynomial|
+ |s18adf| |algebraicDecompose| |addPoint2| |implies| |stopTableInvSet!|
+ |smith| |incrementBy| |cscIfCan| |parametric?| |f02wef| |d01fcf|
+ |construct| |clearCache| |changeWeightLevel| |alphanumeric?|
+ |leftMinimalPolynomial| |permanent| |xor| |c06ekf| |expand|
+ |mainVariable| |cylindrical| |ScanArabic| |inv| |permutationGroup|
+ |OMreadFile| |coordinate| |generalInfiniteProduct| |invertibleSet|
+ |filterWhile| |close!| |sncndn| |getCode| |ground?| |changeMeasure|
+ |d02kef| |prevPrime| |moreAlgebraic?| |squareMatrix| |filterUntil|
+ |f01qcf| |lazyVariations| |mathieu11| |insertBottom!| |ground|
+ |binaryFunction| |internalSubQuasiComponent?| |list| |select| |cross|
+ |shellSort| |f02fjf| |exquo| |squareFreePrim| |getOrder| |lcm| |plus|
+ |zag| |leadingMonomial| |setDifference| |numericalIntegration|
+ |quotedOperators| |readLine!| |OMputEndBind| |div| |ODESolve|
+ |viewSizeDefault| |wrregime| |selectMultiDimensionalRoutines| |pdf2df|
+ |leadingCoefficient| |interpret| |setIntersection| |lastSubResultant|
+ |scalarMatrix| |decompose| |iisech| |quo| |eulerE| |integrate| |prime|
+ |cAsin| |primitiveMonomials| |sign| |derivative| |setUnion|
+ |OMencodingBinary| |var2StepsDefault| |linears| |HenselLift|
+ |completeEchelonBasis| |curveColor| |basisOfRightAnnihilator| |gcd|
+ |matrix| |rischDE| |reductum| |s20acf| |apply| |abs| |nullary?|
+ |s19abf| |rem| |monicCompleteDecompose| |noKaratsuba| |completeEval|
+ |upperCase?| |union| |gethi| |times| |definingPolynomial| |aLinear|
+ |elColumn2!| |unrankImproperPartitions1| |condition| |mkcomm|
+ |leftQuotient| |empty?| |leftGcd| |false| |randomLC| |exprToXXP|
+ |size| |makeRecord| |multiplyExponents| |extensionDegree| |setnext!|
+ |exprToGenUPS| |karatsuba| |listRepresentation| |cyclePartition|
+ |ptree| |maxrank| |sinhIfCan| |alternatingGroup| |prolateSpheroidal|
+ |iisin| |palgextint0| |e01bgf| |shanksDiscLogAlgorithm|
+ |clipWithRanges| |curryRight| |quasiRegular?| |OMencodingSGML|
+ |linearAssociatedExp| |doubleComplex?| |removeSinhSq|
+ |useNagFunctions| |monom| |singRicDE| |oneDimensionalArray|
+ |compactFraction| |first| |accuracyIF| |separant| |repeating?|
+ |twoFactor| |digit?| |OMread| |antiCommutative?|
+ |semiResultantEuclidean1| |setTex!| |rest| |limitedint| |node?|
+ |subscript| |identityMatrix| |asinhIfCan| |setelt| |cosIfCan|
+ |property| |substitute| |evaluate| |limitPlus| |iiabs| |empty|
+ |cycleLength| |expandTrigProducts| |removeDuplicates| |OMserve|
+ |remove!| |f04axf| |OMsupportsSymbol?| |e01sef| |OMputBind| |copy|
+ |setAttributeButtonStep| |zeroDimensional?| |lifting1| |paraboloidal|
+ |critT| |numberOfCycles| |bringDown| |OMunhandledSymbol| |logGamma|
+ |result| |units| |d01asf| |hclf| |squareFreeLexTriangular| |f07fef|
+ |setButtonValue| |not| |oddlambert| |totalLex| ^= |integral|
+ |denominator| |elements| |mathieu24| |expt| |ravel| |iiasinh|
+ |maxPoints| |autoCoerce| |saturate| |simpsono| |meshPar2Var|
+ |rationalPower| |lastSubResultantElseSplit| |more?| |reshape|
+ |palgRDE| |radicalSolve| |roughBase?| |exponents| |fractionFreeGauss!|
+ |SturmHabichtSequence| |back| |cyclicParents|
+ |degreeSubResultantEuclidean| |lhs| |rdHack1| |normalizedAssociate|
+ |createGenericMatrix| |bezoutResultant| |extractIfCan|
+ |realElementary| |rhs| |code| |forLoop| |rationalIfCan| |compile|
+ |structuralConstants| |cardinality| |OMsetEncoding| |cPower|
+ |trueEqual| |rationalPoints| |repeatUntilLoop| |subNode?|
+ |diagonalMatrix| |returnType!| |OMlistSymbols| |slex| |elliptic|
+ |dmpToHdmp| |getCurve| |update| |solid?| |hue| |separateDegrees|
+ |leastMonomial| |zoom| |leftAlternative?| |karatsubaDivide|
+ |figureUnits| |subHeight| |insertionSort!| |lfinfieldint| |e04ycf|
+ |normal?| |reverse!| |ScanFloatIgnoreSpaces| |suffix?| |e04jaf| |top|
+ |rightNorm| |exteriorDifferential| |supRittWu?| |nonSingularModel|
+ |OMputError| |unitNormal| |recip| |continue| |rightDivide|
+ |create3Space| |divisors| |setMaxPoints3D| |qelt|
+ |rewriteIdealWithRemainder| |convergents|
+ |stiffnessAndStabilityFactor| |subResultantGcdEuclidean| |prefix?|
+ |reducedQPowers| |call| |testModulus| |viewWriteDefault| |second|
+ |mapCoef| |newSubProgram| |revert| |boundOfCauchy|
+ |integralCoordinates| |polygon?| |laplace| |pushdown| |key| |third|
+ |init| |solveLinear| |basisOfCommutingElements| |quadratic?|
+ |knownInfBasis| |numberOfChildren| |semiSubResultantGcdEuclidean1|
+ |upperCase| |lex| |options| |roughBasicSet| |computeInt| |exQuo|
+ |goodPoint| |setLabelValue| |acoshIfCan| |primintegrate| |An|
+ |atanhIfCan| |schwerpunkt| |setLegalFortranSourceExtensions|
+ |subPolSet?| |elt| |filename| |tanSum| |coord| |s17aef| |flatten|
+ |compBound| |integralLastSubResultant| |rightLcm| |printInfo|
+ |baseRDE| |nullSpace| |mainVariable?| |rotatez| |getGoodPrime|
+ |Hausdorff| |innerint| |initial| |e04ucf| |infix?| |cyclicSubmodule|
+ |linearPart| |typeList| |commaSeparate| |fixPredicate| |setValue!|
+ |readLineIfCan!| |df2st| |regularRepresentation| |mask|
+ |reduceByQuasiMonic| |alphanumeric| |f04qaf| |ignore?| |pdf2ef|
+ |c02agf| |parse| |basicSet| |unvectorise| |summation| |tab1|
+ |calcRanges| |acothIfCan| |cyclicGroup| |incrementKthElement|
+ |charClass| |s14abf| |front| |has?| |int| |movedPoints| |legendre|
+ |besselY| |merge| |complexExpand| |var1Steps| |clipBoolean| |leftNorm|
+ |inverseColeman| |e02bcf| |diff| |isExpt| |extend| |OMputEndApp|
+ |direction| |OMencodingUnknown| |drawCurves| |newTypeLists|
+ |externalList| |setOrder| |iicosh| |fortranComplex|
+ |rootOfIrreduciblePoly| |degreePartition| |primitivePart| |writeLine!|
+ |printHeader| |odd?| |trivialIdeal?| |makeSUP| |associatorDependence|
+ |outerProduct| |fullDisplay| |prepareDecompose| |pushuconst|
+ |cothIfCan| |bfEntry| |anticoord| |objectOf| |lowerCase?| |exp1|
+ |iprint| |useEisensteinCriterion?| |fortran| |solid| |push!|
+ |trapezoidal| |radicalEigenvectors| |headRemainder|
+ |removeRoughlyRedundantFactorsInPol| |xRange| |outputFixed|
+ |factorSquareFree| |goodnessOfFit| |topPredicate| |internalSubPolSet?|
+ |heapSort| |setelt!| |varselect| |nextColeman| |printCode| |nullity|
+ |yRange| |taylorIfCan| |factorGroebnerBasis| |decimal| |critMTonD1|
+ |getMatch| |eq?| |multiple?| |idealiser| |diag| |top!| |returns|
+ |zRange| |shuffle| |sub| |putColorInfo| |setAdaptive3D| |cAcot|
+ |crushedSet| |reducedContinuedFraction| |exprToUPS|
+ |mapUnivariateIfCan| |getSyntaxFormsFromFile| |setRealSteps| |isTimes|
+ |map!| |doubleFloatFormat| |ipow| |zeroDimPrimary?| FG2F
+ |getVariableOrder| |eyeDistance| |virtualDegree| |primextintfrac|
+ |d02bbf| |s17dlf| |ratPoly| |range| |qsetelt!| |iiacoth|
+ |lfextendedint| |nextSublist| |extendedSubResultantGcd| |component|
+ |vconcat| |minimalPolynomial| |mulmod| |nextsubResultant2|
+ |stoseLastSubResultant| |normalizedDivide| |f02awf| |specialTrigs|
+ |primPartElseUnitCanonical| |weights| |build| |intermediateResultsIF|
+ |coerceListOfPairs| |universe| |nonQsign| |zeroDim?| |clearTable!|
+ |factorOfDegree| |stosePrepareSubResAlgo| |lp| |e04fdf| |evenlambert|
+ |e02dff| |normalize| |LiePoly| |insertMatch| |optimize| |makeop|
+ |nextPrime| |blankSeparate| |interReduce| |s18acf|
+ |stoseInvertibleSetreg| |subtractIfCan| |imagi| |subResultantChain|
+ |rur| |pascalTriangle| |norm| |partialQuotients| |solveid|
+ |symmetricGroup| |LazardQuotient2| |halfExtendedResultant1| |rotate!|
+ |finiteBasis| |symmetricPower| |index| |numFunEvals3D| |yCoord| ^
+ |palgextint| |indices| |factorAndSplit| |packageCall| |readable?|
+ |rewriteIdealWithHeadRemainder| |setRow!| |someBasis| |acsch| |tab|
+ |multiEuclideanTree| |topFortranOutputStack|
+ |zeroSetSplitIntoTriangularSystems| |internalLastSubResultant|
+ |perspective| |exprHasWeightCosWXorSinWX| |notelem| |leadingBasisTerm|
+ |symmetricDifference| |primlimitedint| |child?| |quote| |lowerCase!|
+ |clipPointsDefault| |numberOfVariables| |resetAttributeButtons|
+ |digamma| |script| |HermiteIntegrate| |selectODEIVPRoutines| |fill!|
+ |viewDefaults| |complexIntegrate| |npcoef| |makingStats?|
+ |lazyPseudoRemainder| |bits| |truncate| |determinant| |primeFrobenius|
+ |lazyPseudoQuotient| |OMgetAtp| |sts2stst| |isMult| |FormatRoman|
+ |differentialVariables| |normalForm| |binomThmExpt| |aromberg| |stack|
+ |endSubProgram| |genericRightMinimalPolynomial| |s19acf| |hcrf|
+ |wholeRagits| |squareFreeFactors| |expIfCan| |LowTriBddDenomInv|
+ |polarCoordinates| |e01daf| |leftFactor| |f02aef| |tex|
+ |resetBadValues| |lfunc| |hitherPlane| |iidsum| |OMsupportsCD?|
+ |e02ahf| |OMencodingXML| |s18aef| |airyBi| |edf2fi| |leadingExponent|
+ |inf| |entries| |linear| |roughEqualIdeals?| |numberOfComponents|
+ |numberOfFractionalTerms| |optional?| |prinb| |simplifyLog|
+ |clearTheFTable| |matrixConcat3D| |postfix| |Beta| |edf2ef|
+ |sylvesterSequence| |hexDigit?| |critMonD1| |rightTrim|
+ |associatedEquations| |antisymmetric?| |createThreeSpace|
+ |rangePascalTriangle| |safeCeiling| |firstSubsetGray| |polynomial|
+ |OMreceive| |shallowCopy| |dec| |complexEigenvectors| |OMputSymbol|
+ |leftTrim| |leftZero| |laguerre| |tan2trig| |submod| |s13acf| |color|
+ |central?| |transcendent?| |palgLODE0| |primes| |shallowExpand|
+ |meatAxe| |symmetricTensors| |listLoops| |mapExponents| |ScanRoman|
+ |mkIntegral| |tValues| |twist| |rationalPoint?| |realEigenvalues|
+ |numberOfDivisors| |message| |dom| |var1StepsDefault| |remainder|
+ |d03eef| |sup| |invmod| |normalizeIfCan| |antiCommutator| |viewport2D|
+ |factorials| |setScreenResolution| |kroneckerDelta|
+ |transcendentalDecompose| |purelyAlgebraicLeadingMonomial?|
+ |infRittWu?| |failed?| |contractSolve| |floor|
+ |generalizedEigenvectors| |outputSpacing| |iomode|
+ |fortranDoubleComplex| |split!| |algSplitSimple| |equation|
+ |alphabetic| |parametersOf| |f2st| |simplifyPower|
+ |clearFortranOutputStack| |OMputEndBVar| |c06fqf| |extendedint|
+ |directSum| |s13aaf| |integers| |c06frf| |rk4qc| |integer?|
+ |lazyGintegrate| |adaptive| |selectPolynomials| |updatF| |s17agf|
+ |positive?| |name| |bumptab| |showIntensityFunctions| |SFunction|
+ |csubst| |firstDenom| |cons| |basisOfRightNucloid| |logpart| |high|
+ |null?| |rational?| |monicLeftDivide| |coerceImages| |whileLoop|
+ |skewSFunction| |simpleBounds?| |expressIdealMember| |leastPower|
+ |polygamma| |listConjugateBases| |replaceKthElement|
+ |tubePointsDefault| |startTable!| |possiblyInfinite?| |pomopo!|
+ |algebraicSort| |mat| |leaf?| |linearAssociatedOrder|
+ |stoseSquareFreePart| |cycleSplit!| |label| |orbit| |expandLog| |mvar|
+ |graphState| |createRandomElement| |setright!| |cyclic?| |goto|
+ |wordInGenerators| |e| |dequeue| |arrayStack| |c05adf| |powerSum|
+ |e01baf| |multiEuclidean| |trunc| |closedCurve| |queue| |c02aff|
+ |d01anf| |bat1| |makeVariable| |makeSin| |modifyPoint| |leftRank|
+ |pile| |getOperands| |OMputBVar| |graeffe| |generic| |recur|
+ |initTable!| |subresultantSequence| |rightZero| |coHeight|
+ |oblateSpheroidal| |setMinPoints3D| |basisOfLeftNucloid| |applyRules|
+ |unitCanonical| |controlPanel| |powern| |bitCoef| |f02bjf|
+ |semiResultantEuclideannaif| |returnTypeOf| |increase| |groebnerIdeal|
+ |meshPar1Var| |lookup| |factor1| |bottom!| |brace|
+ |radicalEigenvector| |weight| |intPatternMatch| |infiniteProduct|
+ |removeCosSq| |solve1| |shufflein| |extractSplittingLeaf| |nor|
+ |s17acf| |localIntegralBasis| |zerosOf| |removeCoshSq|
+ |stopMusserTrials| |psolve| |numberOfFactors| |palglimint0|
+ |plotPolar| |title| |flagFactor| |makeprod| |zero?|
+ |subscriptedVariables| |createLowComplexityTable| |associator|
+ |makeViewport2D| |unexpand| |stirling1| |chineseRemainder| |llprop|
+ |functionIsFracPolynomial?| |newReduc| |nextNormalPoly|
+ |uncouplingMatrices| |error| |palginfieldint| |approxSqrt| |redPol|
+ |numeric| |janko2| |internal?| |normalizeAtInfinity| |symmetricSquare|
+ |content| |innerSolve| |value| |setProperties| |assert| |nthr|
+ |radical| |OMclose| |tubeRadius| |scalarTypeOf| |flexible?| |index?|
+ |f02aaf| |c06gcf| |inrootof| |doubleResultant| |principal?| |dim|
+ |gcdPrimitive| |multiplyCoefficients| |chvar| |torsionIfCan|
+ |substring?| |bivariateSLPEBR| |plusInfinity| |infix| |depth|
+ |LyndonBasis| |ParCond| |rename!| |external?| |idealiserMatrix|
+ |degreeSubResultant| |divisor| |leadingSupport| |exponentialOrder|
+ |minusInfinity| |properties| |option| |regime| |iiacos| |normal01|
+ |hasSolution?| |lprop| |ReduceOrder| |internalDecompose| |d03edf|
+ |denominators| |seriesToOutputForm| |shrinkable| |constDsolve| |lists|
+ |nand| |explogs2trigs| |OMputInteger| |basisOfNucleus| |OMgetObject|
+ |numberOfNormalPoly| |palgRDE0| |changeThreshhold| |pade|
+ |resultantEuclideannaif| |bag| |swap| |omError| |rangeIsFinite|
+ |isAbsolutelyIrreducible?| |id| |selectOptimizationRoutines|
+ |lowerPolynomial| |mainForm| |polyPart| |translate|
+ |totalDifferential| |tableau| |basisOfRightNucleus| |shiftLeft|
+ |product| |padecf| |distdfact| |conical| |leftPower| **
+ |mapMatrixIfCan| |table| |nextNormalPrimitivePoly| |outputArgs|
+ |element?| |leastAffineMultiple| |mapExpon| |ode|
+ |numericalOptimization| |float| |failed| |new| |f02aff| |parent|
+ |atanIfCan| |resetNew| |space| |iiexp| |radPoly| EQ
+ |variationOfParameters| |outputList| |generalizedEigenvector|
+ |shiftRoots| |f04arf| |removeRoughlyRedundantFactorsInContents|
+ |retractIfCan| |argument| |linearDependenceOverZ| |pquo| |replace|
+ |numericIfCan| |evenInfiniteProduct| |splitNodeOf!| |padicFraction|
+ |basisOfLeftAnnihilator| |tensorProduct| |iiatan| |evaluateInverse|
+ |insert!| |deref| |zCoord| |reduced?| |rightDiscriminant| |dn|
+ |OMlistCDs| |positiveRemainder| |reduceLODE| |reseed| |acscIfCan|
+ |headReduce| |laguerreL| |Vectorise| |bipolarCylindrical| |OMgetBVar|
+ |cCos| |retractable?| |column| |completeHermite| |iipow| |imagJ|
+ |e02adf| |finite?| |OMgetType| GE |setImagSteps| |groebgen|
+ |setScreenResolution3D| |iCompose| |minIndex| |hermite| |root?| GT
+ |delete!| |mix| |stoseInvertible?reg| |singleFactorBound| |lllip|
+ |level| |argumentList!| |useSingleFactorBound| |cotIfCan|
+ |trace2PowMod| |errorInfo| LE |ref| |left| |imagj| |multMonom|
+ |monicDivide| |exprHasLogarithmicWeights| |branchIfCan| |typeLists|
+ |createPrimitivePoly| |sumSquares| |car| LT |supersub| |right|
+ |leader| |algebraicCoefficients?| |e02ajf| |dominantTerm| |polar|
+ |rotatey| |dihedralGroup| |minimize| |cdr| |map| |exponential1|
+ |optAttributes| |iiasec| |solveLinearlyOverQ| |lintgcd|
+ |expextendedint| |invmultisect| |hasoln| |PDESolve| |fmecg|
+ |gcdcofactprim| |rootsOf| |gramschmidt| |simplifyExp| |idealSimplify|
+ |gradient| |squareFreePolynomial| |qroot| |Ci| |stFuncN|
+ |quasiMonicPolynomials| |s17dhf| |satisfy?| |patternVariable|
+ |unrankImproperPartitions0| |c06fpf| |resultantReduit|
+ |roughUnitIdeal?| |xn| |viewPosDefault| |solveInField| D
+ |associatedSystem| |fixedPointExquo| |dark| |perfectNthRoot| |pr2dmp|
+ |outputFloating| |common| |module| |att2Result| |trapezoidalo|
+ |debug3D| |sdf2lst| |sqfree| |iifact| |numFunEvals|
+ |leftRegularRepresentation| |convert| |preprocess| |sequences|
+ |multinomial| |complexForm| |invertibleElseSplit?| |associative?|
+ |randomR| |varList| |minPoints3D| |toroidal| |limitedIntegrate|
+ |quotient| |antisymmetricTensors| |leviCivitaSymbol| |create| |s17def|
+ |operation| |c06gbf| |checkRur| |cos2sec| |pToHdmp| |completeSmith|
+ |roman| |BumInSepFFE| |normalDeriv| |fillPascalTriangle| |e02bdf|
+ |asimpson| |setAdaptive| |triangular?| |retract| |fprindINFO|
+ |weierstrass| |iisqrt2| |pop!| |quasiAlgebraicSet| |primitivePart!|
+ |s19aaf| |isList| |showScalarValues| |minColIndex| |overbar|
+ |radicalRoots| |f04mbf| |shiftRight| |pseudoQuotient| |print|
+ |standardBasisOfCyclicSubmodule| |lepol| |problemPoints| |rroot|
+ |ramifiedAtInfinity?| |cubic| |toseInvertibleSet| |complexZeros|
+ |printStatement| |point| |gderiv| |gcdcofact| |width| |Lazard2|
+ |rightExtendedGcd| |triangSolve| |wronskianMatrix| |drawComplex|
+ |coshIfCan| |drawComplexVectorField| |minPol| |predicates|
+ |lazyPremWithDefault| |cot2tan| |toseInvertible?| |polygon| |series|
+ |lineColorDefault| |conditionsForIdempotents| |precision|
+ |rootNormalize| |biRank| |extendIfCan| |box| |partition|
+ |factorPolynomial| |allRootsOf| |absolutelyIrreducible?|
+ |halfExtendedSubResultantGcd2| |sinh2csch| |eigenvalues| |optional|
+ |atrapezoidal| |getRef| |resize| |epilogue|
+ |noncommutativeJordanAlgebra?| |sum| |semiResultantEuclidean2|
+ |e02bbf| |selectAndPolynomials| |min| |primitive?| |inRadical?|
+ |d02ejf| |rightAlternative?| |commutativeEquality| |next|
+ |OMputObject| |sec2cos| |parabolic| |rCoord| |rowEch| |lifting|
+ |modularFactor| |rst| |localUnquote| |createNormalPrimitivePoly|
+ |e01sff| |row| |zeroOf| |OMgetEndObject| |mpsode| |euler| |doubleRank|
+ |hasPredicate?| |largest| |rotate| |unitsColorDefault| |mergeFactors|
+ |s18def| |checkPrecision| |asech| |midpoints| |bright| |minimumDegree|
+ |f07adf| |extractBottom!| |lagrange| |addBadValue| |irreducible?|
+ |cycleTail| |partialDenominators| |comp| |asechIfCan|
+ |numberOfComputedEntries| |polynomialZeros| |df2fi| |eulerPhi|
+ |reopen!| |multiple| |upperCase!| |listexp| |nthFractionalTerm|
+ |useEisensteinCriterion| |setPosition| |applyQuote|
+ |removeRedundantFactorsInContents| |enumerate| |s14baf| |f04asf|
+ |edf2df| |e02dcf| |diagonal| |c06ebf| |rootOf| |ramified?| |eval|
+ |leadingIdeal| |OMgetAttr| |nextsousResultant2| |any|
+ |curveColorPalette| |iiacot| |perfectNthPower?| |bubbleSort!|
+ |inverseLaplace| |distFact| |#| |sumOfDivisors|
+ |permutationRepresentation| |ruleset| |complexElementary| |repeating|
+ |gcdprim| |LagrangeInterpolation| |iiacsch| |patternMatch| |e02gaf|
+ |selectOrPolynomials| |radicalSimplify| |ricDsolve| |lazyResidueClass|
+ |cosh2sech| |decrease| |clearDenominator| |strongGenerators|
+ |fibonacci| |ScanFloatIgnoreSpacesIfCan| |lastSubResultantEuclidean|
+ |maxdeg| |suchThat| |adaptive3D?| |possiblyNewVariety?| |char|
+ |se2rfi| |rightQuotient| |search| |inR?| |randnum| |LyndonWordsList1|
+ |initials| |center| |rightFactorIfCan| |primPartElseUnitCanonical!|
+ |extendedEuclidean| |setprevious!| |refine| |cExp| |e02baf| |key?|
+ |fortranCarriageReturn| |resultantnaif| |primextendedint|
+ |exactQuotient!| |OMopenFile| |sechIfCan| |e01sbf| |complex?|
+ |rowEchelonLocal| |extendedIntegrate| |outputAsTex|
+ |nextLatticePermutation| |pseudoDivide| |constant?| |symbol?|
+ |yCoordinates| |selectsecond| |UpTriBddDenomInv| |getButtonValue|
+ |OMsend| |approximants| |ceiling| |euclideanSize| |constantLeft|
+ |any?| |cosSinInfo| |Ei| |invertible?| |plus!| |string?|
+ |clearTheIFTable| |fractRagits| |Zero| |cCoth| |iisinh| |OMputEndAtp|
+ |rightPower| |leftExtendedGcd| |highCommonTerms| |measure|
+ |rootKerSimp| |One| |exists?| |recoverAfterFail| |sturmVariationsOf| ~
+ |complete| |rischDEsys| |components| |semiSubResultantGcdEuclidean2|
+ |overlap| |Frobenius| |cn| |powmod| |f02adf| |signAround| |droot|
+ |iidprod| |reindex| |list?| |d01bbf| |setleaves!| |bitTruth|
+ |expenseOfEvaluationIF| |decomposeFunc| |quoted?| |every?|
+ |stoseInvertibleSet| |super| |degree| |rombergo| |f01qdf| |s13adf|
+ |rewriteIdealWithQuasiMonicGenerators| |exactQuotient| |insertRoot!|
+ |binaryTournament| |cSinh| |viewport3D| |nodes| |OMputEndObject|
+ |paren| |OMgetSymbol| |iteratedInitials| |innerSolve1|
+ |PollardSmallFactor| |OMgetString| |inverseIntegralMatrixAtInfinity|
+ |complexRoots| |ode2| |mindeg| |normalElement| |linSolve|
+ |setErrorBound| |OMputString| |unprotectedRemoveRedundantFactors|
+ |clip| |lowerCase| |open| |e02akf| |permutations| |duplicates?|
+ |resultantReduitEuclidean| |stoseInvertible?sqfreg| |length|
+ |finiteBound| |fi2df| |jacobian| |lazy?| |mesh?| |minimumExponent|
+ |fintegrate| |select!| |mindegTerm| |quadraticForm| |scripts|
+ |patternMatchTimes| |modTree| |addmod| |elem?| |rightMult| |mantissa|
+ |Gamma| |halfExtendedResultant2| |viewDeltaYDefault|
+ |chainSubResultants| |listOfLists| |integralMatrix| |lazyIntegrate|
+ |c06gsf| |factorSFBRlcUnit| |bat| |makeResult| |deriv| |entry?| |expr|
+ |outputGeneral| |basisOfCentroid| |cCsc| |pdct| |equality|
+ |pseudoRemainder| |append| |viewZoomDefault| |f04faf| |totalGroebner|
+ |writable?| |simplify| |logical?| |numberOfImproperPartitions|
+ |delete| |removeIrreducibleRedundantFactors| |makeYoungTableau|
+ |middle| |cAcosh| |cot2trig| |moduleSum| |showClipRegion| NOT |rank|
+ |OMputEndError| |colorFunction| |cTanh| |cAcsch| |elRow2!|
+ |normFactors| |clipSurface| |complexNumericIfCan| |dot| OR
+ |lfintegrate| |iicoth| |belong?| |unmakeSUP| |variable| |polyRicDE|
+ |iicos| |ode1| |iiacosh| |lSpaceBasis| AND |normalise| |minPoly|
+ |linear?| |ddFact| |splitConstant| |leftCharacteristicPolynomial|
+ |prod| |outputMeasure| |d02cjf| |maxPoints3D| |d01akf| |chebyshevT|
+ |xCoord| |indiceSubResultant| |matrixGcd| |showTheRoutinesTable|
+ |nsqfree| |errorKind| |removeZero| |df2ef| |primeFactor| |rk4a| |eq|
+ |slash| |numberOfMonomials| |coordinates| |basisOfLeftNucleus|
+ |e01bef| |zeroVector| |decreasePrecision| |pmintegrate|
+ |explimitedint| |mainCharacterization| |iter| UP2UTS |monomials|
+ |startStats!| |asecIfCan| |maxColIndex| |linearDependence|
+ |matrixDimensions| |optpair| |stronglyReduced?| |graphs| |obj|
+ |exponential| |/\\| |nthCoef| |factorList| |nonLinearPart| |minordet|
+ |transform| |lazyPrem| |eigenMatrix| |showTheIFTable| |s15adf|
+ |nextPrimitiveNormalPoly| |nthRootIfCan| |\\/| |s14aaf| |cache|
+ |sizeLess?| |interval| |complexLimit| |sturmSequence| |bracket|
+ |OMgetEndApp| |numer| |composite| |domainOf| |leftDiscriminant|
+ |d01ajf| |contract| |isOp| |cyclic| |tower| |wholeRadix| |dimensions|
+ |argscript| |complexEigenvalues| |doublyTransitive?| |cycles|
+ |startTableGcd!| |makeUnit| |axes| |lazyEvaluate| |minus!|
+ |selectfirst| |integralBasis| |sayLength| |createIrreduciblePoly|
+ |iiperm| |s20adf| |e04gcf| |divide| * |nodeOf?| |inverse|
+ |monicRightFactorIfCan| |dmpToP| |s17dgf| |setsubMatrix!|
+ |indicialEquationAtInfinity| |OMReadError?| |inHallBasis?| |qqq|
+ |createPrimitiveNormalPoly| |s15aef| |genericRightDiscriminant|
+ |factor| |physicalLength| |exp| |wreath| |c05pbf| |cyclicEqual?|
+ |declare!| |tanh2trigh| |intensity| |zero| |sinIfCan| |loopPoints|
+ |sqrt| |diophantineSystem| |subResultantsChain| |complex| |mapdiv|
+ |integralDerivationMatrix| |jordanAlgebra?| |float?| |lighting| |cap|
+ |null| |screenResolution3D| |iFTable| |selectSumOfSquaresRoutines|
+ |real| |complementaryBasis| |f02bbf| |setProperty| |represents|
+ |systemSizeIF| |leftScalarTimes!| |relerror| |And| |hconcat| |connect|
+ |orthonormalBasis| |imag| |updateStatus!| |rules| |directProduct|
+ |sizeMultiplication| |mapUnivariate| |mapGen| |toseLastSubResultant|
+ |endOfFile?| |subst| |Or| |ideal| |subspace| |doubleDisc| UTS2UP
+ |kovacic| |coefChoose| |perfectSqrt| |e04dgf| |member?| |sinhcosh|
+ |Not| |escape| |setchildren!| |localAbs| |leftLcm| |iisqrt3|
+ |symmetric?| |scale| |positiveSolve| |fortranLiteral| |maxrow|
+ |generators| |stronglyReduce| |internalInfRittWu?| |youngGroup|
+ |destruct| |algebraicVariables| |contains?| |basisOfCenter|
+ |mainMonomial| |iicsch| |pointData| |createMultiplicationTable|
+ |bernoulli| |raisePolynomial| |tRange| |getPickedPoints| |pureLex|
+ |nextPrimitivePoly| |UP2ifCan| |branchPoint?| |curryLeft| |critM|
+ |mkAnswer| |OMgetApp| |addiag| |extractPoint| |iibinom| |arity|
+ |integralAtInfinity?| |atoms| |defineProperty| |bit?| |meshFun2Var|
+ |mainKernel| |objects| |derivationCoordinates| |charthRoot| |enqueue!|
+ |hasHi| |swapColumns!| |bitLength| |e02bef| |or| |cLog| |monomial?|
+ |round| |printStats!| |base| |normInvertible?|
+ |semiDegreeSubResultantEuclidean| |subQuasiComponent?| |ratDsolve|
+ |solveRetract| |tanIfCan| |double| |and| |sin2csc| |rightOne|
+ |nextSubsetGray| |restorePrecision| |initiallyReduce| |vedf2vef|
+ |number?| |viewThetaDefault| |lllp| |semicolonSeparate| |addPoint|
+ |factorsOfCyclicGroupSize| |inc| |thetaCoord| |fortranCompilerName|
+ |acotIfCan| |makeCrit| |supDimElseRittWu?| |alternating|
+ |fullPartialFraction| |extendedResultant| |rarrow| |setStatus!|
+ |myDegree| |squareFree| |repSq| |primintfldpoly| |compdegd|
+ |whatInfinity| |dioSolve| |eigenvectors| |getMultiplicationMatrix|
+ |prefix| |fortranLogical| |collectUpper| |OMgetEndAtp| |Aleph|
+ |setFieldInfo| |OMwrite| |explicitlyFinite?|
+ |solveLinearPolynomialEquationByRecursion| |dmp2rfi| |hex| |tube|
+ |splitDenominator| |cAtanh| |s19adf| |prinpolINFO| |comment| |unravel|
+ |OMmakeConn| |resetVariableOrder| |setMaxPoints| |viewPhiDefault|
+ |f2df| |rightTrace| |nthExponent| |relationsIdeal| |palglimint|
+ |setMinPoints| |rootPower| |test| |antiAssociative?|
+ |univariatePolynomials| |cAsech| |putGraph| |makeTerm| |setPrologue!|
+ |euclideanGroebner| |genericRightTrace| |multiset| |c06eaf|
+ |OMputEndAttr| |over| |low| |numberOfPrimitivePoly| |identity|
+ |lflimitedint| |OMgetEndBVar| |real?| |green| |eigenvector|
+ |semiDiscriminantEuclidean| |rationalFunction| |hyperelliptic|
+ |definingInequation| |brillhartTrials| |flexibleArray| |e02def|
+ |irreducibleFactors| |max| |getMultiplicationTable| |unparse|
+ |ldf2lst| |inverseIntegralMatrix| GF2FG |relativeApprox|
+ |enterPointData| |showArrayValues| |integralBasisAtInfinity|
+ |nextIrreduciblePoly| |fortranReal| |singularitiesOf| |rquo|
+ |bandedHessian| |characteristic| |mapDown!| |s21baf| |setTopPredicate|
+ |unary?| |subResultantGcd| |leftOne| |bombieriNorm| |kmax| |expint|
+ |abelianGroup| |concat| |stoseInvertibleSetsqfreg| |nextPartition|
+ |extract!| |sPol| |solveLinearPolynomialEquationByFractions| |rspace|
+ |seriesSolve| |halfExtendedSubResultantGcd1| |mainValue| |s21bdf|
+ |chiSquare| |s17dcf| |henselFact| |previous| |hash|
+ |euclideanNormalForm| |lfextlimint| |expPot| |userOrdered?|
+ |quasiComponent| |parabolicCylindrical| |divisorCascade|
+ |rightScalarTimes!| |denomRicDE| |autoReduced?| |quasiRegular| |count|
+ |weakBiRank| |bezoutDiscriminant| |minGbasis| |ranges|
+ |mergeDifference| |style| |ridHack1| |atom?| |mathieu23| |stFunc1|
+ |elementary| |ksec| |explicitlyEmpty?| |adaptive?| |bumprow| |symFunc|
+ |critB| |merge!| |addPointLast| |computeCycleEntry| |double?|
+ |collect| |noLinearFactor?| |constantIfCan| |nlde| |scripted?|
+ |totolex| |OMconnInDevice| |totalfract| |move|
+ |branchPointAtInfinity?| |curry| |unitVector| |appendPoint| |d02gbf|
+ |nil| |infinite| |arbitraryExponent| |approximate| |complex|
+ |shallowMutable| |canonical| |noetherian| |central|
+ |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed|
+ |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation|
+ |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation|
+ |finiteAggregate| |shallowlyMutable| |commutative|) 
\ No newline at end of file
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 8e4f9ff5..e76d5921 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,4863 +1,4867 @@
 
-(3125642 . 3409262783)       
-((-3560 (((-107) (-1 (-107) |#2| |#2|) $) 63) (((-107) $) NIL)) (-3613 (($ (-1 (-107) |#2| |#2|) $) 17) (($ $) NIL)) (-2443 ((|#2| $ (-517) |#2|) NIL) ((|#2| $ (-1123 (-517)) |#2|) 34)) (-1407 (($ $) 59)) (-1521 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 41) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-1211 (((-517) (-1 (-107) |#2|) $) 22) (((-517) |#2| $) NIL) (((-517) |#2| $ (-517)) 71)) (-1535 (((-583 |#2|) $) 13)) (-3798 (($ (-1 (-107) |#2| |#2|) $ $) 48) (($ $ $) NIL)) (-2744 (($ (-1 |#2| |#2|) $) 29)) (-3308 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 45)) (-1745 (($ |#2| $ (-517)) NIL) (($ $ $ (-517)) 50)) (-2999 (((-3 |#2| "failed") (-1 (-107) |#2|) $) 24)) (-3480 (((-107) (-1 (-107) |#2|) $) 21)) (-2607 ((|#2| $ (-517) |#2|) NIL) ((|#2| $ (-517)) NIL) (($ $ (-1123 (-517))) 49)) (-3726 (($ $ (-517)) 56) (($ $ (-1123 (-517))) 55)) (-4135 (((-703) (-1 (-107) |#2|) $) 26) (((-703) |#2| $) NIL)) (-2790 (($ $ $ (-517)) 52)) (-2460 (($ $) 51)) (-2286 (($ (-583 |#2|)) 53)) (-4108 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 64) (($ (-583 $)) 62)) (-2269 (((-787) $) 69)) (-3160 (((-107) (-1 (-107) |#2|) $) 20)) (-1583 (((-107) $ $) 70)) (-1607 (((-107) $ $) 73))) 
-(((-18 |#1| |#2|) (-10 -8 (-15 -1583 ((-107) |#1| |#1|)) (-15 -2269 ((-787) |#1|)) (-15 -1607 ((-107) |#1| |#1|)) (-15 -3613 (|#1| |#1|)) (-15 -3613 (|#1| (-1 (-107) |#2| |#2|) |#1|)) (-15 -1407 (|#1| |#1|)) (-15 -2790 (|#1| |#1| |#1| (-517))) (-15 -3560 ((-107) |#1|)) (-15 -3798 (|#1| |#1| |#1|)) (-15 -1211 ((-517) |#2| |#1| (-517))) (-15 -1211 ((-517) |#2| |#1|)) (-15 -1211 ((-517) (-1 (-107) |#2|) |#1|)) (-15 -3560 ((-107) (-1 (-107) |#2| |#2|) |#1|)) (-15 -3798 (|#1| (-1 (-107) |#2| |#2|) |#1| |#1|)) (-15 -2443 (|#2| |#1| (-1123 (-517)) |#2|)) (-15 -1745 (|#1| |#1| |#1| (-517))) (-15 -1745 (|#1| |#2| |#1| (-517))) (-15 -3726 (|#1| |#1| (-1123 (-517)))) (-15 -3726 (|#1| |#1| (-517))) (-15 -2607 (|#1| |#1| (-1123 (-517)))) (-15 -3308 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4108 (|#1| (-583 |#1|))) (-15 -4108 (|#1| |#1| |#1|)) (-15 -4108 (|#1| |#2| |#1|)) (-15 -4108 (|#1| |#1| |#2|)) (-15 -2286 (|#1| (-583 |#2|))) (-15 -2999 ((-3 |#2| "failed") (-1 (-107) |#2|) |#1|)) (-15 -1521 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -1521 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1521 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2607 (|#2| |#1| (-517))) (-15 -2607 (|#2| |#1| (-517) |#2|)) (-15 -2443 (|#2| |#1| (-517) |#2|)) (-15 -4135 ((-703) |#2| |#1|)) (-15 -1535 ((-583 |#2|) |#1|)) (-15 -4135 ((-703) (-1 (-107) |#2|) |#1|)) (-15 -3480 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -3160 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -2744 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3308 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2460 (|#1| |#1|))) (-19 |#2|) (-1110)) (T -18)) 
-NIL 
-(-10 -8 (-15 -1583 ((-107) |#1| |#1|)) (-15 -2269 ((-787) |#1|)) (-15 -1607 ((-107) |#1| |#1|)) (-15 -3613 (|#1| |#1|)) (-15 -3613 (|#1| (-1 (-107) |#2| |#2|) |#1|)) (-15 -1407 (|#1| |#1|)) (-15 -2790 (|#1| |#1| |#1| (-517))) (-15 -3560 ((-107) |#1|)) (-15 -3798 (|#1| |#1| |#1|)) (-15 -1211 ((-517) |#2| |#1| (-517))) (-15 -1211 ((-517) |#2| |#1|)) (-15 -1211 ((-517) (-1 (-107) |#2|) |#1|)) (-15 -3560 ((-107) (-1 (-107) |#2| |#2|) |#1|)) (-15 -3798 (|#1| (-1 (-107) |#2| |#2|) |#1| |#1|)) (-15 -2443 (|#2| |#1| (-1123 (-517)) |#2|)) (-15 -1745 (|#1| |#1| |#1| (-517))) (-15 -1745 (|#1| |#2| |#1| (-517))) (-15 -3726 (|#1| |#1| (-1123 (-517)))) (-15 -3726 (|#1| |#1| (-517))) (-15 -2607 (|#1| |#1| (-1123 (-517)))) (-15 -3308 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4108 (|#1| (-583 |#1|))) (-15 -4108 (|#1| |#1| |#1|)) (-15 -4108 (|#1| |#2| |#1|)) (-15 -4108 (|#1| |#1| |#2|)) (-15 -2286 (|#1| (-583 |#2|))) (-15 -2999 ((-3 |#2| "failed") (-1 (-107) |#2|) |#1|)) (-15 -1521 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -1521 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1521 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2607 (|#2| |#1| (-517))) (-15 -2607 (|#2| |#1| (-517) |#2|)) (-15 -2443 (|#2| |#1| (-517) |#2|)) (-15 -4135 ((-703) |#2| |#1|)) (-15 -1535 ((-583 |#2|) |#1|)) (-15 -4135 ((-703) (-1 (-107) |#2|) |#1|)) (-15 -3480 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -3160 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -2744 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3308 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2460 (|#1| |#1|))) 
-((-2118 (((-107) $ $) 19 (|has| |#1| (-1004)))) (-1478 (((-1161) $ (-517) (-517)) 40 (|has| $ (-6 -4191)))) (-3560 (((-107) (-1 (-107) |#1| |#1|) $) 98) (((-107) $) 92 (|has| |#1| (-779)))) (-3613 (($ (-1 (-107) |#1| |#1|) $) 89 (|has| $ (-6 -4191))) (($ $) 88 (-12 (|has| |#1| (-779)) (|has| $ (-6 -4191))))) (-2162 (($ (-1 (-107) |#1| |#1|) $) 99) (($ $) 93 (|has| |#1| (-779)))) (-2670 (((-107) $ (-703)) 8)) (-2443 ((|#1| $ (-517) |#1|) 52 (|has| $ (-6 -4191))) ((|#1| $ (-1123 (-517)) |#1|) 58 (|has| $ (-6 -4191)))) (-2324 (($ (-1 (-107) |#1|) $) 75 (|has| $ (-6 -4190)))) (-1681 (($) 7 T CONST)) (-1407 (($ $) 90 (|has| $ (-6 -4191)))) (-1905 (($ $) 100)) (-2453 (($ $) 78 (-12 (|has| |#1| (-1004)) (|has| $ (-6 -4190))))) (-1422 (($ |#1| $) 77 (-12 (|has| |#1| (-1004)) (|has| $ (-6 -4190)))) (($ (-1 (-107) |#1|) $) 74 (|has| $ (-6 -4190)))) (-1521 ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) 76 (-12 (|has| |#1| (-1004)) (|has| $ (-6 -4190)))) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) 73 (|has| $ (-6 -4190))) ((|#1| (-1 |#1| |#1| |#1|) $) 72 (|has| $ (-6 -4190)))) (-2757 ((|#1| $ (-517) |#1|) 53 (|has| $ (-6 -4191)))) (-2563 ((|#1| $ (-517)) 51)) (-1211 (((-517) (-1 (-107) |#1|) $) 97) (((-517) |#1| $) 96 (|has| |#1| (-1004))) (((-517) |#1| $ (-517)) 95 (|has| |#1| (-1004)))) (-1535 (((-583 |#1|) $) 30 (|has| $ (-6 -4190)))) (-3211 (($ (-703) |#1|) 69)) (-2361 (((-107) $ (-703)) 9)) (-3735 (((-517) $) 43 (|has| (-517) (-779)))) (-3456 (($ $ $) 87 (|has| |#1| (-779)))) (-3798 (($ (-1 (-107) |#1| |#1|) $ $) 101) (($ $ $) 94 (|has| |#1| (-779)))) (-2898 (((-583 |#1|) $) 29 (|has| $ (-6 -4190)))) (-4008 (((-107) |#1| $) 27 (-12 (|has| |#1| (-1004)) (|has| $ (-6 -4190))))) (-3979 (((-517) $) 44 (|has| (-517) (-779)))) (-4082 (($ $ $) 86 (|has| |#1| (-779)))) (-2744 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4191)))) (-3308 (($ (-1 |#1| |#1|) $) 35) (($ (-1 |#1| |#1| |#1|) $ $) 64)) (-4043 (((-107) $ (-703)) 10)) (-1895 (((-1058) $) 22 (|has| |#1| (-1004)))) (-1745 (($ |#1| $ (-517)) 60) (($ $ $ (-517)) 59)) (-4121 (((-583 (-517)) $) 46)) (-3536 (((-107) (-517) $) 47)) (-4123 (((-1022) $) 21 (|has| |#1| (-1004)))) (-2427 ((|#1| $) 42 (|has| (-517) (-779)))) (-2999 (((-3 |#1| "failed") (-1 (-107) |#1|) $) 71)) (-3191 (($ $ |#1|) 41 (|has| $ (-6 -4191)))) (-3480 (((-107) (-1 (-107) |#1|) $) 32 (|has| $ (-6 -4190)))) (-3522 (($ $ (-583 (-265 |#1|))) 26 (-12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) (($ $ (-265 |#1|)) 25 (-12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) (($ $ |#1| |#1|) 24 (-12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) (($ $ (-583 |#1|) (-583 |#1|)) 23 (-12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004))))) (-3180 (((-107) $ $) 14)) (-3669 (((-107) |#1| $) 45 (-12 (|has| $ (-6 -4190)) (|has| |#1| (-1004))))) (-1831 (((-583 |#1|) $) 48)) (-3270 (((-107) $) 11)) (-1529 (($) 12)) (-2607 ((|#1| $ (-517) |#1|) 50) ((|#1| $ (-517)) 49) (($ $ (-1123 (-517))) 63)) (-3726 (($ $ (-517)) 62) (($ $ (-1123 (-517))) 61)) (-4135 (((-703) (-1 (-107) |#1|) $) 31 (|has| $ (-6 -4190))) (((-703) |#1| $) 28 (-12 (|has| |#1| (-1004)) (|has| $ (-6 -4190))))) (-2790 (($ $ $ (-517)) 91 (|has| $ (-6 -4191)))) (-2460 (($ $) 13)) (-3357 (((-493) $) 79 (|has| |#1| (-558 (-493))))) (-2286 (($ (-583 |#1|)) 70)) (-4108 (($ $ |#1|) 68) (($ |#1| $) 67) (($ $ $) 66) (($ (-583 $)) 65)) (-2269 (((-787) $) 18 (|has| |#1| (-557 (-787))))) (-3160 (((-107) (-1 (-107) |#1|) $) 33 (|has| $ (-6 -4190)))) (-1641 (((-107) $ $) 84 (|has| |#1| (-779)))) (-1617 (((-107) $ $) 83 (|has| |#1| (-779)))) (-1583 (((-107) $ $) 20 (|has| |#1| (-1004)))) (-1629 (((-107) $ $) 85 (|has| |#1| (-779)))) (-1607 (((-107) $ $) 82 (|has| |#1| (-779)))) (-3533 (((-703) $) 6 (|has| $ (-6 -4190))))) 
-(((-19 |#1|) (-1187) (-1110)) (T -19)) 
-NIL 
-(-13 (-343 |t#1|) (-10 -7 (-6 -4191))) 
-(((-33) . T) ((-97) -3745 (|has| |#1| (-1004)) (|has| |#1| (-779))) ((-557 (-787)) -3745 (|has| |#1| (-1004)) (|has| |#1| (-779)) (|has| |#1| (-557 (-787)))) ((-138 |#1|) . T) ((-558 (-493)) |has| |#1| (-558 (-493))) ((-258 #0=(-517) |#1|) . T) ((-260 #0# |#1|) . T) ((-280 |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004))) ((-343 |#1|) . T) ((-456 |#1|) . T) ((-550 #0# |#1|) . T) ((-478 |#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004))) ((-588 |#1|) . T) ((-779) |has| |#1| (-779)) ((-1004) -3745 (|has| |#1| (-1004)) (|has| |#1| (-779))) ((-1110) . T)) 
-((-1250 (((-3 $ "failed") $ $) 12)) (-1691 (($ $) NIL) (($ $ $) 9)) (* (($ (-844) $) NIL) (($ (-703) $) 16) (($ (-517) $) 21))) 
-(((-20 |#1|) (-10 -8 (-15 * (|#1| (-517) |#1|)) (-15 -1691 (|#1| |#1| |#1|)) (-15 -1691 (|#1| |#1|)) (-15 -1250 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-703) |#1|)) (-15 * (|#1| (-844) |#1|))) (-21)) (T -20)) 
-NIL 
-(-10 -8 (-15 * (|#1| (-517) |#1|)) (-15 -1691 (|#1| |#1| |#1|)) (-15 -1691 (|#1| |#1|)) (-15 -1250 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-703) |#1|)) (-15 * (|#1| (-844) |#1|))) 
-((-2118 (((-107) $ $) 7)) (-2033 (((-107) $) 16)) (-1250 (((-3 $ "failed") $ $) 19)) (-1681 (($) 17 T CONST)) (-1895 (((-1058) $) 9)) (-4123 (((-1022) $) 10)) (-2269 (((-787) $) 11)) (-3608 (($) 18 T CONST)) (-1583 (((-107) $ $) 6)) (-1691 (($ $) 22) (($ $ $) 21)) (-1677 (($ $ $) 14)) (* (($ (-844) $) 13) (($ (-703) $) 15) (($ (-517) $) 20))) 
-(((-21) (-1187)) (T -21)) 
-((-1691 (*1 *1 *1) (-4 *1 (-21))) (-1691 (*1 *1 *1 *1) (-4 *1 (-21))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-21)) (-5 *2 (-517))))) 
-(-13 (-123) (-10 -8 (-15 -1691 ($ $)) (-15 -1691 ($ $ $)) (-15 * ($ (-517) $)))) 
-(((-23) . T) ((-25) . T) ((-97) . T) ((-123) . T) ((-557 (-787)) . T) ((-1004) . T)) 
-((-2033 (((-107) $) 10)) (-1681 (($) 15)) (* (($ (-844) $) 14) (($ (-703) $) 18))) 
-(((-22 |#1|) (-10 -8 (-15 * (|#1| (-703) |#1|)) (-15 -2033 ((-107) |#1|)) (-15 -1681 (|#1|)) (-15 * (|#1| (-844) |#1|))) (-23)) (T -22)) 
-NIL 
-(-10 -8 (-15 * (|#1| (-703) |#1|)) (-15 -2033 ((-107) |#1|)) (-15 -1681 (|#1|)) (-15 * (|#1| (-844) |#1|))) 
-((-2118 (((-107) $ $) 7)) (-2033 (((-107) $) 16)) (-1681 (($) 17 T CONST)) (-1895 (((-1058) $) 9)) (-4123 (((-1022) $) 10)) (-2269 (((-787) $) 11)) (-3608 (($) 18 T CONST)) (-1583 (((-107) $ $) 6)) (-1677 (($ $ $) 14)) (* (($ (-844) $) 13) (($ (-703) $) 15))) 
-(((-23) (-1187)) (T -23)) 
-((-3608 (*1 *1) (-4 *1 (-23))) (-1681 (*1 *1) (-4 *1 (-23))) (-2033 (*1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-107)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-703))))) 
-(-13 (-25) (-10 -8 (-15 (-3608) ($) -1384) (-15 -1681 ($) -1384) (-15 -2033 ((-107) $)) (-15 * ($ (-703) $)))) 
-(((-25) . T) ((-97) . T) ((-557 (-787)) . T) ((-1004) . T)) 
+(3127291 . 3409436009)       
+((-2166 (((-107) (-1 (-107) |#2| |#2|) $) 63) (((-107) $) NIL)) (-1420 (($ (-1 (-107) |#2| |#2|) $) 17) (($ $) NIL)) (-2445 ((|#2| $ (-517) |#2|) NIL) ((|#2| $ (-1124 (-517)) |#2|) 34)) (-2549 (($ $) 59)) (-1522 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 41) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-1212 (((-517) (-1 (-107) |#2|) $) 22) (((-517) |#2| $) NIL) (((-517) |#2| $ (-517)) 71)) (-1534 (((-583 |#2|) $) 13)) (-2662 (($ (-1 (-107) |#2| |#2|) $ $) 48) (($ $ $) NIL)) (-2746 (($ (-1 |#2| |#2|) $) 29)) (-3310 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 45)) (-1747 (($ |#2| $ (-517)) NIL) (($ $ $ (-517)) 50)) (-1528 (((-3 |#2| "failed") (-1 (-107) |#2|) $) 24)) (-3644 (((-107) (-1 (-107) |#2|) $) 21)) (-2609 ((|#2| $ (-517) |#2|) NIL) ((|#2| $ (-517)) NIL) (($ $ (-1124 (-517))) 49)) (-3728 (($ $ (-517)) 56) (($ $ (-1124 (-517))) 55)) (-4137 (((-703) (-1 (-107) |#2|) $) 26) (((-703) |#2| $) NIL)) (-1901 (($ $ $ (-517)) 52)) (-2462 (($ $) 51)) (-2288 (($ (-583 |#2|)) 53)) (-4110 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 64) (($ (-583 $)) 62)) (-2271 (((-787) $) 69)) (-3602 (((-107) (-1 (-107) |#2|) $) 20)) (-1584 (((-107) $ $) 70)) (-1608 (((-107) $ $) 73))) 
+(((-18 |#1| |#2|) (-10 -8 (-15 -1584 ((-107) |#1| |#1|)) (-15 -2271 ((-787) |#1|)) (-15 -1608 ((-107) |#1| |#1|)) (-15 -1420 (|#1| |#1|)) (-15 -1420 (|#1| (-1 (-107) |#2| |#2|) |#1|)) (-15 -2549 (|#1| |#1|)) (-15 -1901 (|#1| |#1| |#1| (-517))) (-15 -2166 ((-107) |#1|)) (-15 -2662 (|#1| |#1| |#1|)) (-15 -1212 ((-517) |#2| |#1| (-517))) (-15 -1212 ((-517) |#2| |#1|)) (-15 -1212 ((-517) (-1 (-107) |#2|) |#1|)) (-15 -2166 ((-107) (-1 (-107) |#2| |#2|) |#1|)) (-15 -2662 (|#1| (-1 (-107) |#2| |#2|) |#1| |#1|)) (-15 -2445 (|#2| |#1| (-1124 (-517)) |#2|)) (-15 -1747 (|#1| |#1| |#1| (-517))) (-15 -1747 (|#1| |#2| |#1| (-517))) (-15 -3728 (|#1| |#1| (-1124 (-517)))) (-15 -3728 (|#1| |#1| (-517))) (-15 -2609 (|#1| |#1| (-1124 (-517)))) (-15 -3310 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4110 (|#1| (-583 |#1|))) (-15 -4110 (|#1| |#1| |#1|)) (-15 -4110 (|#1| |#2| |#1|)) (-15 -4110 (|#1| |#1| |#2|)) (-15 -2288 (|#1| (-583 |#2|))) (-15 -1528 ((-3 |#2| "failed") (-1 (-107) |#2|) |#1|)) (-15 -1522 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -1522 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1522 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2609 (|#2| |#1| (-517))) (-15 -2609 (|#2| |#1| (-517) |#2|)) (-15 -2445 (|#2| |#1| (-517) |#2|)) (-15 -4137 ((-703) |#2| |#1|)) (-15 -1534 ((-583 |#2|) |#1|)) (-15 -4137 ((-703) (-1 (-107) |#2|) |#1|)) (-15 -3644 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -3602 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -2746 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3310 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2462 (|#1| |#1|))) (-19 |#2|) (-1111)) (T -18)) 
+NIL 
+(-10 -8 (-15 -1584 ((-107) |#1| |#1|)) (-15 -2271 ((-787) |#1|)) (-15 -1608 ((-107) |#1| |#1|)) (-15 -1420 (|#1| |#1|)) (-15 -1420 (|#1| (-1 (-107) |#2| |#2|) |#1|)) (-15 -2549 (|#1| |#1|)) (-15 -1901 (|#1| |#1| |#1| (-517))) (-15 -2166 ((-107) |#1|)) (-15 -2662 (|#1| |#1| |#1|)) (-15 -1212 ((-517) |#2| |#1| (-517))) (-15 -1212 ((-517) |#2| |#1|)) (-15 -1212 ((-517) (-1 (-107) |#2|) |#1|)) (-15 -2166 ((-107) (-1 (-107) |#2| |#2|) |#1|)) (-15 -2662 (|#1| (-1 (-107) |#2| |#2|) |#1| |#1|)) (-15 -2445 (|#2| |#1| (-1124 (-517)) |#2|)) (-15 -1747 (|#1| |#1| |#1| (-517))) (-15 -1747 (|#1| |#2| |#1| (-517))) (-15 -3728 (|#1| |#1| (-1124 (-517)))) (-15 -3728 (|#1| |#1| (-517))) (-15 -2609 (|#1| |#1| (-1124 (-517)))) (-15 -3310 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4110 (|#1| (-583 |#1|))) (-15 -4110 (|#1| |#1| |#1|)) (-15 -4110 (|#1| |#2| |#1|)) (-15 -4110 (|#1| |#1| |#2|)) (-15 -2288 (|#1| (-583 |#2|))) (-15 -1528 ((-3 |#2| "failed") (-1 (-107) |#2|) |#1|)) (-15 -1522 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -1522 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1522 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2609 (|#2| |#1| (-517))) (-15 -2609 (|#2| |#1| (-517) |#2|)) (-15 -2445 (|#2| |#1| (-517) |#2|)) (-15 -4137 ((-703) |#2| |#1|)) (-15 -1534 ((-583 |#2|) |#1|)) (-15 -4137 ((-703) (-1 (-107) |#2|) |#1|)) (-15 -3644 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -3602 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -2746 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3310 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2462 (|#1| |#1|))) 
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+(((-19 |#1|) (-1188) (-1111)) (T -19)) 
+NIL 
+(-13 (-343 |t#1|) (-10 -7 (-6 -4193))) 
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+NIL 
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+(((-21) (-1188)) (T -21)) 
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+(((-23) . T) ((-25) . T) ((-97) . T) ((-123) . T) ((-557 (-787)) . T) ((-1005) . T)) 
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+NIL 
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 ((* (($ (-844) $) 10))) 
 (((-24 |#1|) (-10 -8 (-15 * (|#1| (-844) |#1|))) (-25)) (T -24)) 
 NIL 
 (-10 -8 (-15 * (|#1| (-844) |#1|))) 
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-(((-25) (-1187)) (T -25)) 
-((-1677 (*1 *1 *1 *1) (-4 *1 (-25))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-844))))) 
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-(((-97) . T) ((-557 (-787)) . T) ((-1004) . T)) 
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-NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-37 #0=(-377 (-517))) . T) ((-37 $) . T) ((-97) . T) ((-106 #0# #0#) . T) ((-106 $ $) . T) ((-123) . T) ((-557 (-787)) . T) ((-156) . T) ((-217) . T) ((-262) . T) ((-278) . T) ((-333) . T) ((-421) . T) ((-509) . T) ((-585 #0#) . T) ((-585 $) . T) ((-650 #0#) . T) ((-650 $) . T) ((-659) . T) ((-843) . T) ((-919) . T) ((-968 #0#) . T) ((-968 $) . T) ((-962) . T) ((-969) . T) ((-1016) . T) ((-1004) . T) ((-1114) . T)) 
-((-1464 (((-583 $) (-875 $)) NIL) (((-583 $) (-1071 $)) NIL) (((-583 $) (-1071 $) (-1075)) 50) (((-583 $) $) 19) (((-583 $) $ (-1075)) 41)) (-3458 (($ (-875 $)) NIL) (($ (-1071 $)) NIL) (($ (-1071 $) (-1075)) 52) (($ $) 17) (($ $ (-1075)) 37)) (-4054 (((-583 $) (-875 $)) NIL) (((-583 $) (-1071 $)) NIL) (((-583 $) (-1071 $) (-1075)) 48) (((-583 $) $) 15) (((-583 $) $ (-1075)) 43)) (-3772 (($ (-875 $)) NIL) (($ (-1071 $)) NIL) (($ (-1071 $) (-1075)) NIL) (($ $) 12) (($ $ (-1075)) 39))) 
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 NIL 
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-NIL 
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-((-2118 (((-107) $ $) NIL)) (-1895 (((-1058) $) NIL)) (-4123 (((-1022) $) NIL)) (-2269 (((-787) $) 7)) (-1583 (((-107) $ $) NIL))) 
-(((-48) (-1004)) (T -48)) 
-NIL 
-(-1004) 
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-NIL 
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+NIL 
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 NIL 
 (-409) 
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-NIL 
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-NIL 
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-NIL 
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 NIL 
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-NIL 
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-NIL 
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 (((-169) (-719)) (T -169)) 
 NIL 
 (-719) 
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 (((-170) (-719)) (T -170)) 
 NIL 
 (-719) 
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 (((-171) (-719)) (T -171)) 
 NIL 
 (-719) 
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 (((-172) (-719)) (T -172)) 
 NIL 
 (-719) 
-((-2118 (((-107) $ $) NIL)) (-3582 (((-951) (-2 (|:| |var| (-1075)) (|:| |fn| (-286 (-199))) (|:| -2192 (-999 (-772 (-199)))) (|:| |abserr| (-199)) (|:| |relerr| (-199))) (-951)) 65) (((-951) (-2 (|:| |fn| (-286 (-199))) (|:| -2192 (-583 (-999 (-772 (-199))))) (|:| |abserr| (-199)) (|:| |relerr| (-199))) (-951)) NIL)) (-3615 (((-2 (|:| -3615 (-349)) (|:| |explanations| (-1058)) (|:| |extra| (-951))) (-974) (-2 (|:| |var| (-1075)) (|:| |fn| (-286 (-199))) (|:| -2192 (-999 (-772 (-199)))) (|:| |abserr| (-199)) (|:| |relerr| (-199)))) 35) (((-2 (|:| -3615 (-349)) (|:| |explanations| (-1058)) (|:| |extra| (-951))) (-974) (-2 (|:| |fn| (-286 (-199))) (|:| -2192 (-583 (-999 (-772 (-199))))) (|:| |abserr| (-199)) (|:| |relerr| (-199)))) NIL)) (-1895 (((-1058) $) NIL)) (-4123 (((-1022) $) NIL)) (-2269 (((-787) $) NIL)) (-1583 (((-107) $ $) NIL))) 
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 (((-173) (-719)) (T -173)) 
 NIL 
 (-719) 
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 (((-174) (-719)) (T -174)) 
 NIL 
 (-719) 
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 (((-175) (-719)) (T -175)) 
 NIL 
 (-719) 
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 (((-176) (-719)) (T -176)) 
 NIL 
 (-719) 
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 (((-177) (-719)) (T -177)) 
 NIL 
 (-719) 
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 (((-178) (-719)) (T -178)) 
 NIL 
 (-719) 
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 (((-179) (-719)) (T -179)) 
 NIL 
 (-719) 
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 (((-182) (-732)) (T -182)) 
 NIL 
 (-732) 
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 (((-183) (-732)) (T -183)) 
 NIL 
 (-732) 
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 (((-184) (-732)) (T -184)) 
 NIL 
 (-732) 
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 (((-185) (-732)) (T -185)) 
 NIL 
 (-732) 
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 (((-187) (-818)) (T -187)) 
 NIL 
 (-818) 
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 (((-188) (-818)) (T -188)) 
 NIL 
 (-818) 
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 NIL 
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-NIL 
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-NIL 
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(-583 (-703))) NIL (-12 (|has| |#2| (-823 (-1075))) (|has| |#2| (-962)))) (($ $ (-1 |#2| |#2|) (-703)) NIL (|has| |#2| (-962))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-962)))) (-1641 (((-107) $ $) NIL (-3745 (|has| |#2| (-725)) (|has| |#2| (-777))))) (-1617 (((-107) $ $) NIL (-3745 (|has| |#2| (-725)) (|has| |#2| (-777))))) (-1583 (((-107) $ $) 26 (|has| |#2| (-1004)))) (-1629 (((-107) $ $) NIL (-3745 (|has| |#2| (-725)) (|has| |#2| (-777))))) (-1607 (((-107) $ $) 58 (-3745 (|has| |#2| (-725)) (|has| |#2| (-777))))) (-1703 (($ $ |#2|) NIL (|has| |#2| (-333)))) (-1691 (($ $ $) NIL (|has| |#2| (-962))) (($ $) NIL (|has| |#2| (-962)))) (-1677 (($ $ $) 33 (|has| |#2| (-25)))) (** (($ $ (-703)) NIL (|has| |#2| (-962))) (($ $ (-844)) NIL (|has| |#2| (-962)))) (* (($ $ $) 49 (|has| |#2| (-962))) (($ (-517) $) NIL (|has| |#2| (-962))) (($ $ |#2|) 42 (|has| |#2| (-659))) (($ |#2| $) 43 (|has| |#2| (-659))) (($ (-703) $) NIL (|has| |#2| (-123))) (($ (-844) $) NIL (|has| |#2| (-25)))) (-3533 (((-703) $) NIL (|has| $ (-6 -4190))))) 
-(((-214 |#1| |#2|) (-212 |#1| |#2|) (-703) (-1110)) (T -214)) 
+(((-33) . T) ((-102 |#1|) . T) ((-97) |has| |#1| (-1005)) ((-557 (-787)) -3747 (|has| |#1| (-1005)) (|has| |#1| (-557 (-787)))) ((-138 |#1|) . T) ((-558 (-493)) |has| |#1| (-558 (-493))) ((-209 |#1|) . T) ((-280 |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1005))) ((-456 |#1|) . T) ((-478 |#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1005))) ((-1005) |has| |#1| (-1005)) ((-1111) . T)) 
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+NIL 
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+((-1532 (((-214 |#1| |#3|) (-1 |#3| |#2| |#3|) (-214 |#1| |#2|) |#3|) 21)) (-1522 ((|#3| (-1 |#3| |#2| |#3|) (-214 |#1| |#2|) |#3|) 23)) (-3310 (((-214 |#1| |#3|) (-1 |#3| |#2|) (-214 |#1| |#2|)) 18))) 
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+((-3310 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-214 *5 *6)) (-14 *5 (-703)) (-4 *6 (-1111)) (-4 *7 (-1111)) (-5 *2 (-214 *5 *7)) (-5 *1 (-213 *5 *6 *7)))) (-1522 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-214 *5 *6)) (-14 *5 (-703)) (-4 *6 (-1111)) (-4 *2 (-1111)) (-5 *1 (-213 *5 *6 *2)))) (-1532 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-214 *6 *7)) (-14 *6 (-703)) (-4 *7 (-1111)) (-4 *5 (-1111)) (-5 *2 (-214 *6 *5)) (-5 *1 (-213 *6 *7 *5))))) 
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(-2271 (((-1157 |#2|) $) 10) (($ (-517)) NIL (-3747 (-12 (|has| |#2| (-954 (-517))) (|has| |#2| (-1005))) (|has| |#2| (-963)))) (($ (-377 (-517))) NIL (-12 (|has| |#2| (-954 (-377 (-517)))) (|has| |#2| (-1005)))) (($ |#2|) 13 (|has| |#2| (-1005))) (((-787) $) NIL (|has| |#2| (-557 (-787))))) (-4099 (((-703)) NIL (|has| |#2| (-963)))) (-3602 (((-107) (-1 (-107) |#2|) $) NIL (|has| $ (-6 -4192)))) (-2376 (($ $) NIL (|has| |#2| (-777)))) (-2815 (($ $ (-703)) NIL (|has| |#2| (-963))) (($ $ (-844)) NIL (|has| |#2| (-963)))) (-3610 (($) 35 (|has| |#2| (-123)) CONST)) (-3619 (($) 38 (|has| |#2| (-963)) CONST)) (-3342 (($ $) NIL (-12 (|has| |#2| (-207)) (|has| |#2| (-963)))) (($ $ (-703)) NIL (-12 (|has| |#2| (-207)) (|has| |#2| (-963)))) (($ $ (-1076)) NIL (-12 (|has| |#2| (-823 (-1076))) (|has| |#2| (-963)))) (($ $ (-583 (-1076))) NIL (-12 (|has| |#2| (-823 (-1076))) (|has| |#2| (-963)))) (($ $ (-1076) (-703)) NIL (-12 (|has| |#2| (-823 (-1076))) (|has| |#2| (-963)))) (($ $ (-583 (-1076)) (-583 (-703))) NIL (-12 (|has| |#2| (-823 (-1076))) (|has| |#2| (-963)))) (($ $ (-1 |#2| |#2|) (-703)) NIL (|has| |#2| (-963))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-963)))) (-1642 (((-107) $ $) NIL (-3747 (|has| |#2| (-725)) (|has| |#2| (-777))))) (-1618 (((-107) $ $) NIL (-3747 (|has| |#2| (-725)) (|has| |#2| (-777))))) (-1584 (((-107) $ $) 26 (|has| |#2| (-1005)))) (-1630 (((-107) $ $) NIL (-3747 (|has| |#2| (-725)) (|has| |#2| (-777))))) (-1608 (((-107) $ $) 58 (-3747 (|has| |#2| (-725)) (|has| |#2| (-777))))) (-1704 (($ $ |#2|) NIL (|has| |#2| (-333)))) (-1692 (($ $ $) NIL (|has| |#2| (-963))) (($ $) NIL (|has| |#2| (-963)))) (-1678 (($ $ $) 33 (|has| |#2| (-25)))) (** (($ $ (-703)) NIL (|has| |#2| (-963))) (($ $ (-844)) NIL (|has| |#2| (-963)))) (* (($ $ $) 49 (|has| |#2| (-963))) (($ (-517) $) NIL (|has| |#2| (-963))) (($ $ |#2|) 42 (|has| |#2| (-659))) (($ |#2| $) 43 (|has| |#2| (-659))) (($ (-703) $) NIL (|has| |#2| (-123))) (($ (-844) $) NIL (|has| |#2| (-25)))) (-3535 (((-703) $) NIL (|has| $ (-6 -4192))))) 
+(((-214 |#1| |#2|) (-212 |#1| |#2|) (-703) (-1111)) (T -214)) 
 NIL 
 (-212 |#1| |#2|) 
-((-3684 (((-517) (-583 (-1058))) 24) (((-517) (-1058)) 19)) (-1898 (((-1161) (-583 (-1058))) 29) (((-1161) (-1058)) 28)) (-3324 (((-1058)) 14)) (-1685 (((-1058) (-517) (-1058)) 16)) (-3567 (((-583 (-1058)) (-583 (-1058)) (-517) (-1058)) 25) (((-1058) (-1058) (-517) (-1058)) 23)) (-3490 (((-583 (-1058)) (-583 (-1058))) 13) (((-583 (-1058)) (-1058)) 11))) 
-(((-215) (-10 -7 (-15 -3490 ((-583 (-1058)) (-1058))) (-15 -3490 ((-583 (-1058)) (-583 (-1058)))) (-15 -3324 ((-1058))) (-15 -1685 ((-1058) (-517) (-1058))) (-15 -3567 ((-1058) (-1058) (-517) (-1058))) (-15 -3567 ((-583 (-1058)) (-583 (-1058)) (-517) (-1058))) (-15 -1898 ((-1161) (-1058))) (-15 -1898 ((-1161) (-583 (-1058)))) (-15 -3684 ((-517) (-1058))) (-15 -3684 ((-517) (-583 (-1058)))))) (T -215)) 
-((-3684 (*1 *2 *3) (-12 (-5 *3 (-583 (-1058))) (-5 *2 (-517)) (-5 *1 (-215)))) (-3684 (*1 *2 *3) (-12 (-5 *3 (-1058)) (-5 *2 (-517)) (-5 *1 (-215)))) (-1898 (*1 *2 *3) (-12 (-5 *3 (-583 (-1058))) (-5 *2 (-1161)) (-5 *1 (-215)))) (-1898 (*1 *2 *3) (-12 (-5 *3 (-1058)) (-5 *2 (-1161)) (-5 *1 (-215)))) (-3567 (*1 *2 *2 *3 *4) (-12 (-5 *2 (-583 (-1058))) (-5 *3 (-517)) (-5 *4 (-1058)) (-5 *1 (-215)))) (-3567 (*1 *2 *2 *3 *2) (-12 (-5 *2 (-1058)) (-5 *3 (-517)) (-5 *1 (-215)))) (-1685 (*1 *2 *3 *2) (-12 (-5 *2 (-1058)) (-5 *3 (-517)) (-5 *1 (-215)))) (-3324 (*1 *2) (-12 (-5 *2 (-1058)) (-5 *1 (-215)))) (-3490 (*1 *2 *2) (-12 (-5 *2 (-583 (-1058))) (-5 *1 (-215)))) (-3490 (*1 *2 *3) (-12 (-5 *2 (-583 (-1058))) (-5 *1 (-215)) (-5 *3 (-1058))))) 
-(-10 -7 (-15 -3490 ((-583 (-1058)) (-1058))) (-15 -3490 ((-583 (-1058)) (-583 (-1058)))) (-15 -3324 ((-1058))) (-15 -1685 ((-1058) (-517) (-1058))) (-15 -3567 ((-1058) (-1058) (-517) (-1058))) (-15 -3567 ((-583 (-1058)) (-583 (-1058)) (-517) (-1058))) (-15 -1898 ((-1161) (-1058))) (-15 -1898 ((-1161) (-583 (-1058)))) (-15 -3684 ((-517) (-1058))) (-15 -3684 ((-517) (-583 (-1058))))) 
-((-2813 (($ $ (-844)) NIL) (($ $ (-703)) NIL) (($ $ (-517)) 9)) (** (($ $ (-844)) NIL) (($ $ (-703)) NIL) (($ $ (-517)) 18)) (* (($ (-844) $) NIL) (($ (-703) $) NIL) (($ (-517) $) NIL) (($ $ $) NIL) (($ (-377 (-517)) $) 25) (($ $ (-377 (-517))) NIL))) 
-(((-216 |#1|) (-10 -8 (-15 -2813 (|#1| |#1| (-517))) (-15 ** (|#1| |#1| (-517))) (-15 * (|#1| |#1| (-377 (-517)))) (-15 * (|#1| (-377 (-517)) |#1|)) (-15 ** (|#1| |#1| (-703))) (-15 -2813 (|#1| |#1| (-703))) (-15 * (|#1| |#1| |#1|)) (-15 ** (|#1| |#1| (-844))) (-15 -2813 (|#1| |#1| (-844))) (-15 * (|#1| (-517) |#1|)) (-15 * (|#1| (-703) |#1|)) (-15 * (|#1| (-844) |#1|))) (-217)) (T -216)) 
-NIL 
-(-10 -8 (-15 -2813 (|#1| |#1| (-517))) (-15 ** (|#1| |#1| (-517))) (-15 * (|#1| |#1| (-377 (-517)))) (-15 * (|#1| (-377 (-517)) |#1|)) (-15 ** (|#1| |#1| (-703))) (-15 -2813 (|#1| |#1| (-703))) (-15 * (|#1| |#1| |#1|)) (-15 ** (|#1| |#1| (-844))) (-15 -2813 (|#1| |#1| (-844))) (-15 * (|#1| (-517) |#1|)) (-15 * (|#1| (-703) |#1|)) (-15 * (|#1| (-844) |#1|))) 
-((-2118 (((-107) $ $) 7)) (-2033 (((-107) $) 16)) (-1250 (((-3 $ "failed") $ $) 19)) (-1681 (($) 17 T CONST)) (-3163 (((-3 $ "failed") $) 34)) (-1865 (((-107) $) 31)) (-1895 (((-1058) $) 9)) (-2298 (($ $) 39)) (-4123 (((-1022) $) 10)) (-2269 (((-787) $) 11) (($ (-517)) 28) (($ (-377 (-517))) 44)) (-2950 (((-703)) 29)) (-2813 (($ $ (-844)) 26) (($ $ (-703)) 33) (($ $ (-517)) 40)) (-3608 (($) 18 T CONST)) (-3617 (($) 30 T CONST)) (-1583 (((-107) $ $) 6)) (-1691 (($ $) 22) (($ $ $) 21)) (-1677 (($ $ $) 14)) (** (($ $ (-844)) 25) (($ $ (-703)) 32) (($ $ (-517)) 41)) (* (($ (-844) $) 13) (($ (-703) $) 15) (($ (-517) $) 20) (($ $ $) 24) (($ (-377 (-517)) $) 43) (($ $ (-377 (-517))) 42))) 
-(((-217) (-1187)) (T -217)) 
-((** (*1 *1 *1 *2) (-12 (-4 *1 (-217)) (-5 *2 (-517)))) (-2813 (*1 *1 *1 *2) (-12 (-4 *1 (-217)) (-5 *2 (-517)))) (-2298 (*1 *1 *1) (-4 *1 (-217)))) 
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-NIL 
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-NIL 
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-(((-239 |#1|) (-1187) (-779)) (T -239)) 
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-(((-97) . T) ((-557 (-787)) . T) ((-779) . T) ((-953 |#1|) . T) ((-1004) . T)) 
-((-2096 (((-583 (-1075)) (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2585 (-583 (-199))))) 40)) (-3365 (((-583 (-1075)) (-286 (-199)) (-703)) 79)) (-1864 (((-3 (-286 (-199)) "failed") (-286 (-199))) 50)) (-2390 (((-286 (-199)) (-286 (-199))) 65)) (-1198 (((-2 (|:| |fn| (-286 (-199))) (|:| -2585 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199))))) (-2 (|:| |fn| (-286 (-199))) (|:| -2585 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199)))))) 26)) (-2507 (((-107) (-583 (-286 (-199)))) 83)) (-3166 (((-107) (-286 (-199))) 24)) (-3428 (((-583 (-1058)) (-3 (|:| |noa| (-2 (|:| |fn| (-286 (-199))) (|:| -2585 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199)))))) (|:| |lsa| (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2585 (-583 (-199))))))) 105)) (-3997 (((-583 (-286 (-199))) (-583 (-286 (-199)))) 87)) (-2181 (((-583 (-286 (-199))) (-583 (-286 (-199)))) 85)) (-2895 (((-623 (-199)) (-583 (-286 (-199))) (-703)) 94)) (-1753 (((-107) (-286 (-199))) 20) (((-107) (-583 (-286 (-199)))) 84)) (-2177 (((-583 (-199)) (-583 (-772 (-199))) (-199)) 14)) (-2784 (((-349) (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2585 (-583 (-199))))) 100)) (-1191 (((-951) (-1075) (-951)) 33))) 
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-((-3428 (*1 *2 *3) (-12 (-5 *3 (-3 (|:| |noa| (-2 (|:| |fn| (-286 (-199))) (|:| -2585 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199)))))) (|:| |lsa| (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2585 (-583 (-199))))))) (-5 *2 (-583 (-1058))) (-5 *1 (-240)))) (-2784 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2585 (-583 (-199))))) (-5 *2 (-349)) (-5 *1 (-240)))) (-1191 (*1 *2 *3 *2) (-12 (-5 *2 (-951)) (-5 *3 (-1075)) (-5 *1 (-240)))) (-3365 (*1 *2 *3 *4) (-12 (-5 *3 (-286 (-199))) (-5 *4 (-703)) (-5 *2 (-583 (-1075))) (-5 *1 (-240)))) (-2096 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2585 (-583 (-199))))) (-5 *2 (-583 (-1075))) (-5 *1 (-240)))) (-3166 (*1 *2 *3) (-12 (-5 *3 (-286 (-199))) (-5 *2 (-107)) (-5 *1 (-240)))) (-3997 (*1 *2 *2) (-12 (-5 *2 (-583 (-286 (-199)))) (-5 *1 (-240)))) (-2181 (*1 *2 *2) (-12 (-5 *2 (-583 (-286 (-199)))) (-5 *1 (-240)))) (-2895 (*1 *2 *3 *4) (-12 (-5 *3 (-583 (-286 (-199)))) (-5 *4 (-703)) (-5 *2 (-623 (-199))) (-5 *1 (-240)))) (-1753 (*1 *2 *3) (-12 (-5 *3 (-286 (-199))) (-5 *2 (-107)) (-5 *1 (-240)))) (-1753 (*1 *2 *3) (-12 (-5 *3 (-583 (-286 (-199)))) (-5 *2 (-107)) (-5 *1 (-240)))) (-2507 (*1 *2 *3) (-12 (-5 *3 (-583 (-286 (-199)))) (-5 *2 (-107)) (-5 *1 (-240)))) (-2390 (*1 *2 *2) (-12 (-5 *2 (-286 (-199))) (-5 *1 (-240)))) (-1864 (*1 *2 *2) (|partial| -12 (-5 *2 (-286 (-199))) (-5 *1 (-240)))) (-1198 (*1 *2 *2) (-12 (-5 *2 (-2 (|:| |fn| (-286 (-199))) (|:| -2585 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199)))))) (-5 *1 (-240)))) (-2177 (*1 *2 *3 *4) (-12 (-5 *3 (-583 (-772 (-199)))) (-5 *4 (-199)) (-5 *2 (-583 *4)) (-5 *1 (-240))))) 
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-((-2118 (((-107) $ $) NIL)) (-2699 (((-951) (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2585 (-583 (-199))))) NIL) (((-951) (-2 (|:| |fn| (-286 (-199))) (|:| -2585 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199)))))) 39)) (-3615 (((-2 (|:| -3615 (-349)) (|:| |explanations| (-1058))) (-974) (-2 (|:| |fn| (-286 (-199))) (|:| -2585 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199)))))) 20) (((-2 (|:| -3615 (-349)) (|:| |explanations| (-1058))) (-974) (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2585 (-583 (-199))))) NIL)) (-1895 (((-1058) $) NIL)) (-4123 (((-1022) $) NIL)) (-2269 (((-787) $) NIL)) (-1583 (((-107) $ $) NIL))) 
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+NIL 
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 (((-241) (-768)) (T -241)) 
 NIL 
 (-768) 
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 (((-242) (-768)) (T -242)) 
 NIL 
 (-768) 
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 (((-243) (-768)) (T -243)) 
 NIL 
 (-768) 
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+((-2119 (((-107) $ $) NIL)) (-3210 (((-952) (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2587 (-583 (-199))))) NIL) (((-952) (-2 (|:| |fn| (-286 (-199))) (|:| -2587 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199)))))) 48)) (-3617 (((-2 (|:| -3617 (-349)) (|:| |explanations| (-1059))) (-975) (-2 (|:| |fn| (-286 (-199))) (|:| -2587 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199)))))) 27) (((-2 (|:| -3617 (-349)) (|:| |explanations| (-1059))) (-975) (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2587 (-583 (-199))))) NIL)) (-1662 (((-1059) $) NIL)) (-4125 (((-1023) $) NIL)) (-2271 (((-787) $) NIL)) (-1584 (((-107) $ $) NIL))) 
 (((-244) (-768)) (T -244)) 
 NIL 
 (-768) 
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 (((-245) (-768)) (T -245)) 
 NIL 
 (-768) 
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 (((-246) (-768)) (T -246)) 
 NIL 
 (-768) 
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 (((-247) (-768)) (T -247)) 
 NIL 
 (-768) 
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+NIL 
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 ((** (($ $ $) 10))) 
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 NIL 
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-NIL 
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-NIL 
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-NIL 
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 NIL 
 (-293 |#1| (-703)) 
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-NIL 
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-NIL 
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+NIL 
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 NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+((-2116 (*1 *1) (-5 *1 (-446)))) 
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(($ (-1 (-107) (-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) $) NIL (|has| $ (-6 -4192)))) (-1522 (((-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-1 (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) $ (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) NIL (-12 (|has| $ (-6 -4192)) (|has| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-1005)))) (((-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-1 (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) $ (-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) NIL (|has| $ (-6 -4192))) (((-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-1 (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) $) NIL (|has| $ (-6 -4192)))) (-2759 ((|#2| $ |#1| |#2|) NIL (|has| $ (-6 -4193)))) (-2566 ((|#2| $ |#1|) NIL)) (-1534 (((-583 (-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) $) NIL (|has| $ 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|#2|)) (|has| |#2| (-1005))))) (-2727 (((-107) $ $) NIL)) (-3712 (((-107) |#2| $) NIL (-12 (|has| $ (-6 -4192)) (|has| |#2| (-1005))))) (-2891 (((-583 |#2|) $) NIL)) (-2394 (((-107) $) NIL)) (-2452 (($) 19)) (-2609 ((|#2| $ |#1|) NIL) ((|#2| $ |#1| |#2|) NIL)) (-2176 (($) NIL) (($ (-583 (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)))) NIL)) (-4137 (((-703) (-1 (-107) (-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) $) NIL (|has| $ (-6 -4192))) (((-703) (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) $) NIL (-12 (|has| $ (-6 -4192)) (|has| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-1005)))) (((-703) |#2| $) NIL (-12 (|has| $ (-6 -4192)) (|has| |#2| (-1005)))) (((-703) (-1 (-107) |#2|) $) NIL (|has| $ (-6 -4192)))) (-2462 (($ $) NIL)) (-3359 (((-493) $) NIL (|has| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-558 (-493))))) (-2288 (($ (-583 (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)))) NIL)) (-2271 (((-787) $) NIL (-3747 (|has| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-557 (-787))) (|has| |#2| (-557 (-787)))))) (-3181 (($ 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+(((-447 |#1| |#2| |#3|) (-13 (-1088 |#1| |#2|) (-10 -7 (-6 -4192))) (-1005) (-1005) (-1059)) (T -447)) 
+NIL 
+(-13 (-1088 |#1| |#2|) (-10 -7 (-6 -4192))) 
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 NIL 
 (-305 |#1| |#2| |#3| |#4|) 
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-NIL 
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-((-1646 (($ $) 15)) (-1622 (($ $) 24)) (-1669 (($ $) 12)) (-1682 (($ $) 10)) (-1656 (($ $) 17)) (-1632 (($ $) 22))) 
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-NIL 
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 NIL 
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 NIL 
 (-55 |#1| (-461 |#1| |#3|) (-461 |#1| |#2|)) 
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 (((-471 |#1| |#2|) (-13 (-21) (-473 |#1| |#2|)) (-21) (-779)) (T -471)) 
 NIL 
 (-13 (-21) (-473 |#1| |#2|)) 
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 (((-472 |#1| |#2|) (-13 (-23) (-473 |#1| |#2|)) (-23) (-779)) (T -472)) 
 NIL 
 (-13 (-23) (-473 |#1| |#2|)) 
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 NIL 
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 NIL 
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 NIL 
 (-473 |#1| |#2|) 
-((-3522 (($ $ (-583 |#2|) (-583 |#3|)) NIL) (($ $ |#2| |#3|) 12))) 
-(((-477 |#1| |#2| |#3|) (-10 -8 (-15 -3522 (|#1| |#1| |#2| |#3|)) (-15 -3522 (|#1| |#1| (-583 |#2|) (-583 |#3|)))) (-478 |#2| |#3|) (-1004) (-1110)) (T -477)) 
+((-3524 (($ $ (-583 |#2|) (-583 |#3|)) NIL) (($ $ |#2| |#3|) 12))) 
+(((-477 |#1| |#2| |#3|) (-10 -8 (-15 -3524 (|#1| |#1| |#2| |#3|)) (-15 -3524 (|#1| |#1| (-583 |#2|) (-583 |#3|)))) (-478 |#2| |#3|) (-1005) (-1111)) (T -477)) 
 NIL 
-(-10 -8 (-15 -3522 (|#1| |#1| |#2| |#3|)) (-15 -3522 (|#1| |#1| (-583 |#2|) (-583 |#3|)))) 
-((-3522 (($ $ (-583 |#1|) (-583 |#2|)) 7) (($ $ |#1| |#2|) 6))) 
-(((-478 |#1| |#2|) (-1187) (-1004) (-1110)) (T -478)) 
-((-3522 (*1 *1 *1 *2 *3) (-12 (-5 *2 (-583 *4)) (-5 *3 (-583 *5)) (-4 *1 (-478 *4 *5)) (-4 *4 (-1004)) (-4 *5 (-1110)))) (-3522 (*1 *1 *1 *2 *3) (-12 (-4 *1 (-478 *2 *3)) (-4 *2 (-1004)) (-4 *3 (-1110))))) 
-(-13 (-10 -8 (-15 -3522 ($ $ |t#1| |t#2|)) (-15 -3522 ($ $ (-583 |t#1|) (-583 |t#2|))))) 
-((-2118 (((-107) $ $) NIL)) (-2033 (((-107) $) 16)) (-3349 (((-583 (-2 (|:| |gen| |#1|) (|:| -3868 |#2|))) $) 18)) (-1250 (((-3 $ "failed") $ $) NIL)) (-2397 (((-703) $) NIL)) (-1681 (($) NIL T CONST)) (-3226 (((-3 |#1| "failed") $) NIL)) (-3388 ((|#1| $) NIL)) (-3336 ((|#1| $ (-517)) 23)) (-3371 ((|#2| $ (-517)) 21)) (-1954 (($ (-1 |#1| |#1|) $) 46)) (-1410 (($ (-1 |#2| |#2|) $) 43)) (-1895 (((-1058) $) NIL)) (-4096 (($ $ $) 53 (|has| |#2| (-724)))) (-4123 (((-1022) $) NIL)) (-2269 (((-787) $) 42) (($ |#1|) NIL)) (-3952 ((|#2| |#1| $) 49)) (-3608 (($) 11 T CONST)) (-1583 (((-107) $ $) 29)) (-1677 (($ $ $) 27) (($ |#1| $) 25)) (* (($ (-844) $) NIL) (($ (-703) $) 36) (($ |#2| |#1|) 31))) 
-(((-479 |#1| |#2| |#3|) (-293 |#1| |#2|) (-1004) (-123) |#2|) (T -479)) 
+(-10 -8 (-15 -3524 (|#1| |#1| |#2| |#3|)) (-15 -3524 (|#1| |#1| (-583 |#2|) (-583 |#3|)))) 
+((-3524 (($ $ (-583 |#1|) (-583 |#2|)) 7) (($ $ |#1| |#2|) 6))) 
+(((-478 |#1| |#2|) (-1188) (-1005) (-1111)) (T -478)) 
+((-3524 (*1 *1 *1 *2 *3) (-12 (-5 *2 (-583 *4)) (-5 *3 (-583 *5)) (-4 *1 (-478 *4 *5)) (-4 *4 (-1005)) (-4 *5 (-1111)))) (-3524 (*1 *1 *1 *2 *3) (-12 (-4 *1 (-478 *2 *3)) (-4 *2 (-1005)) (-4 *3 (-1111))))) 
+(-13 (-10 -8 (-15 -3524 ($ $ |t#1| |t#2|)) (-15 -3524 ($ $ (-583 |t#1|) (-583 |t#2|))))) 
+((-2119 (((-107) $ $) NIL)) (-3097 (((-107) $) 16)) (-1928 (((-583 (-2 (|:| |gen| |#1|) (|:| -3870 |#2|))) $) 18)) (-2798 (((-3 $ "failed") $ $) NIL)) (-2399 (((-703) $) NIL)) (-1393 (($) NIL T CONST)) (-3228 (((-3 |#1| "failed") $) NIL)) (-3390 ((|#1| $) NIL)) (-1789 ((|#1| $ (-517)) 23)) (-3806 ((|#2| $ (-517)) 21)) (-3912 (($ (-1 |#1| |#1|) $) 46)) (-2577 (($ (-1 |#2| |#2|) $) 43)) (-1662 (((-1059) $) NIL)) (-3616 (($ $ $) 53 (|has| |#2| (-724)))) (-4125 (((-1023) $) NIL)) (-2271 (((-787) $) 42) (($ |#1|) NIL)) (-1689 ((|#2| |#1| $) 49)) (-3610 (($) 11 T CONST)) (-1584 (((-107) $ $) 29)) (-1678 (($ $ $) 27) (($ |#1| $) 25)) (* (($ (-844) $) NIL) (($ (-703) $) 36) (($ |#2| |#1|) 31))) 
+(((-479 |#1| |#2| |#3|) (-293 |#1| |#2|) (-1005) (-123) |#2|) (T -479)) 
 NIL 
 (-293 |#1| |#2|) 
-((-2118 (((-107) $ $) NIL (|has| |#1| (-1004)))) (-1478 (((-1161) $ (-517) (-517)) NIL (|has| $ (-6 -4191)))) (-3560 (((-107) (-1 (-107) |#1| |#1|) $) NIL) (((-107) $) NIL (|has| |#1| (-779)))) (-3613 (($ (-1 (-107) |#1| |#1|) $) NIL (|has| $ (-6 -4191))) (($ $) NIL (-12 (|has| $ (-6 -4191)) (|has| |#1| (-779))))) (-2162 (($ (-1 (-107) |#1| |#1|) $) NIL) (($ $) NIL (|has| |#1| (-779)))) (-2670 (((-107) $ (-703)) NIL)) (-2844 (((-107) (-107)) 24)) (-2443 ((|#1| $ (-517) |#1|) 27 (|has| $ (-6 -4191))) ((|#1| $ (-1123 (-517)) |#1|) NIL (|has| $ (-6 -4191)))) (-3042 (($ (-1 (-107) |#1|) $) 51)) (-2324 (($ (-1 (-107) |#1|) $) NIL (|has| $ (-6 -4190)))) (-1681 (($) NIL T CONST)) (-1407 (($ $) NIL (|has| $ (-6 -4191)))) (-1905 (($ $) NIL)) (-3302 (($ $) 55 (|has| |#1| (-1004)))) (-2453 (($ $) NIL (-12 (|has| $ (-6 -4190)) (|has| |#1| (-1004))))) (-3593 (($ |#1| $) NIL (|has| |#1| (-1004))) (($ (-1 (-107) |#1|) $) 43)) (-1422 (($ |#1| $) NIL (-12 (|has| $ (-6 -4190)) (|has| |#1| (-1004)))) (($ (-1 (-107) |#1|) $) NIL (|has| $ (-6 -4190)))) (-1521 ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) NIL (-12 (|has| $ (-6 -4190)) (|has| |#1| (-1004)))) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (-6 -4190))) ((|#1| (-1 |#1| |#1| |#1|) $) NIL (|has| $ (-6 -4190)))) (-2757 ((|#1| $ (-517) |#1|) NIL (|has| $ (-6 -4191)))) (-2563 ((|#1| $ (-517)) NIL)) (-1211 (((-517) (-1 (-107) |#1|) $) NIL) (((-517) |#1| $) NIL (|has| |#1| (-1004))) (((-517) |#1| $ (-517)) NIL (|has| |#1| (-1004)))) (-3242 (($ $ (-517)) 13)) (-3686 (((-703) $) 11)) (-1535 (((-583 |#1|) $) NIL (|has| $ (-6 -4190)))) (-3211 (($ (-703) |#1|) 22)) (-2361 (((-107) $ (-703)) NIL)) (-3735 (((-517) $) 20 (|has| (-517) (-779)))) (-3456 (($ $ $) NIL (|has| |#1| (-779)))) (-1974 (($ $ $) NIL (|has| |#1| (-779))) (($ (-1 (-107) |#1| |#1|) $ $) 34)) (-3798 (($ (-1 (-107) |#1| |#1|) $ $) 35) (($ $ $) NIL (|has| |#1| (-779)))) (-2898 (((-583 |#1|) $) NIL (|has| $ (-6 -4190)))) (-4008 (((-107) |#1| $) NIL (-12 (|has| $ (-6 -4190)) (|has| |#1| (-1004))))) (-3979 (((-517) $) 19 (|has| (-517) (-779)))) (-4082 (($ $ $) NIL (|has| |#1| (-779)))) (-2744 (($ (-1 |#1| |#1|) $) NIL (|has| $ (-6 -4191)))) (-3308 (($ (-1 |#1| |#1|) $) NIL) (($ (-1 |#1| |#1| |#1|) $ $) NIL)) (-4043 (((-107) $ (-703)) NIL)) (-1895 (((-1058) $) NIL (|has| |#1| (-1004)))) (-2704 (($ $ $ (-517)) 50) (($ |#1| $ (-517)) 36)) (-1745 (($ |#1| $ (-517)) NIL) (($ $ $ (-517)) NIL)) (-4121 (((-583 (-517)) $) NIL)) (-3536 (((-107) (-517) $) NIL)) (-4123 (((-1022) $) NIL (|has| |#1| (-1004)))) (-1587 (($ (-583 |#1|)) 28)) (-2427 ((|#1| $) NIL (|has| (-517) (-779)))) (-2999 (((-3 |#1| "failed") (-1 (-107) |#1|) $) NIL)) (-3191 (($ $ |#1|) 18 (|has| $ (-6 -4191)))) (-3480 (((-107) (-1 (-107) |#1|) $) NIL (|has| $ (-6 -4190)))) (-3522 (($ $ (-583 (-265 |#1|))) NIL (-12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) (($ $ (-265 |#1|)) NIL (-12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) (($ $ |#1| |#1|) NIL (-12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004)))) (($ $ (-583 |#1|) (-583 |#1|)) NIL (-12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004))))) (-3180 (((-107) $ $) 39)) (-3669 (((-107) |#1| $) NIL (-12 (|has| $ (-6 -4190)) (|has| |#1| (-1004))))) (-1831 (((-583 |#1|) $) NIL)) (-3270 (((-107) $) NIL)) (-1529 (($) 14)) (-2607 ((|#1| $ (-517) |#1|) NIL) ((|#1| $ (-517)) 32) (($ $ (-1123 (-517))) NIL)) (-2710 (($ $ (-1123 (-517))) 49) (($ $ (-517)) 44)) (-3726 (($ $ (-517)) NIL) (($ $ (-1123 (-517))) NIL)) (-4135 (((-703) (-1 (-107) |#1|) $) NIL (|has| $ (-6 -4190))) (((-703) |#1| $) NIL (-12 (|has| $ (-6 -4190)) (|has| |#1| (-1004))))) (-2790 (($ $ $ (-517)) 40 (|has| $ (-6 -4191)))) (-2460 (($ $) 31)) (-3357 (((-493) $) NIL (|has| |#1| (-558 (-493))))) (-2286 (($ (-583 |#1|)) NIL)) (-1718 (($ $ $) 41) (($ $ |#1|) 38)) (-4108 (($ $ |#1|) NIL) (($ |#1| $) 37) (($ $ $) NIL) (($ (-583 $)) NIL)) (-2269 (((-787) $) NIL (|has| |#1| (-557 (-787))))) (-3160 (((-107) (-1 (-107) |#1|) $) NIL (|has| $ (-6 -4190)))) (-1641 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1617 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1583 (((-107) $ $) NIL (|has| |#1| (-1004)))) (-1629 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1607 (((-107) $ $) NIL (|has| |#1| (-779)))) (-3533 (((-703) $) 15 (|has| $ (-6 -4190))))) 
-(((-480 |#1| |#2|) (-13 (-19 |#1|) (-254 |#1|) (-10 -8 (-15 -1587 ($ (-583 |#1|))) (-15 -3686 ((-703) $)) (-15 -3242 ($ $ (-517))) (-15 -2844 ((-107) (-107))))) (-1110) (-517)) (T -480)) 
-((-1587 (*1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *3 (-1110)) (-5 *1 (-480 *3 *4)) (-14 *4 (-517)))) (-3686 (*1 *2 *1) (-12 (-5 *2 (-703)) (-5 *1 (-480 *3 *4)) (-4 *3 (-1110)) (-14 *4 (-517)))) (-3242 (*1 *1 *1 *2) (-12 (-5 *2 (-517)) (-5 *1 (-480 *3 *4)) (-4 *3 (-1110)) (-14 *4 *2))) (-2844 (*1 *2 *2) (-12 (-5 *2 (-107)) (-5 *1 (-480 *3 *4)) (-4 *3 (-1110)) (-14 *4 (-517))))) 
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 (((-481 |#1| |#2|) (-299 (-530 |#1|)) (-844) (-844)) (T -481)) 
 NIL 
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 NIL 
 (-55 |#1| |#4| |#5|) 
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NIL (|has| $ (-6 -4190)))) (-1641 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1617 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1583 (((-107) $ $) 48 (|has| |#1| (-1004)))) (-1629 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1607 (((-107) $ $) NIL (|has| |#1| (-779)))) (-3533 (((-703) $) 9 (|has| $ (-6 -4190))))) 
-(((-483 |#1| |#2|) (-603 |#1|) (-1110) (-517)) (T -483)) 
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(|has| $ (-6 -4193)))) (-3929 (($ $ (-583 $)) NIL (|has| $ (-6 -4193)))) (-3690 (($ (-1 (-107) |#1|) $) NIL)) (-2325 (($ (-1 (-107) |#1|) $) NIL (|has| $ (-6 -4192)))) (-2576 ((|#1| $) NIL)) (-1393 (($) NIL T CONST)) (-2549 (($ $) 28 (|has| $ (-6 -4193)))) (-1908 (($ $) 29)) (-2439 (($ $) 18) (($ $ (-703)) 32)) (-1399 (($ $) 54 (|has| |#1| (-1005)))) (-2455 (($ $) NIL (-12 (|has| $ (-6 -4192)) (|has| |#1| (-1005))))) (-2457 (($ |#1| $) NIL (|has| |#1| (-1005))) (($ (-1 (-107) |#1|) $) NIL)) (-1423 (($ (-1 (-107) |#1|) $) NIL (|has| $ (-6 -4192))) (($ |#1| $) NIL (-12 (|has| $ (-6 -4192)) (|has| |#1| (-1005))))) (-1522 ((|#1| (-1 |#1| |#1| |#1|) $) NIL (|has| $ (-6 -4192))) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (-6 -4192))) ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) NIL (-12 (|has| $ (-6 -4192)) (|has| |#1| (-1005))))) (-2759 ((|#1| $ (-517) |#1|) NIL (|has| $ (-6 -4193)))) (-2566 ((|#1| $ (-517)) NIL)) (-3013 (((-107) $) NIL)) (-1212 (((-517) |#1| $ (-517)) NIL (|has| |#1| 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NIL (|has| $ (-6 -4192)))) (-1642 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1618 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1584 (((-107) $ $) 48 (|has| |#1| (-1005)))) (-1630 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1608 (((-107) $ $) NIL (|has| |#1| (-779)))) (-3535 (((-703) $) 9 (|has| $ (-6 -4192))))) 
+(((-483 |#1| |#2|) (-603 |#1|) (-1111) (-517)) (T -483)) 
 NIL 
 (-603 |#1|) 
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 NIL 
 (-621 |#1| (-548 |#1| |#3|) (-548 |#1| |#2|)) 
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 (((-489 |#1|) (-13 (-725) (-473 (-703) |#1|)) (-779)) (T -489)) 
 NIL 
 (-13 (-725) (-473 (-703) |#1|)) 
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-((-3141 (((-772 (-517))) 11)) (-3152 (((-772 (-517))) 13)) (-2124 (((-765 (-517))) 8))) 
-(((-491) (-10 -7 (-15 -2124 ((-765 (-517)))) (-15 -3141 ((-772 (-517)))) (-15 -3152 ((-772 (-517)))))) (T -491)) 
-((-3152 (*1 *2) (-12 (-5 *2 (-772 (-517))) (-5 *1 (-491)))) (-3141 (*1 *2) (-12 (-5 *2 (-772 (-517))) (-5 *1 (-491)))) (-2124 (*1 *2) (-12 (-5 *2 (-765 (-517))) (-5 *1 (-491))))) 
-(-10 -7 (-15 -2124 ((-765 (-517)))) (-15 -3141 ((-772 (-517)))) (-15 -3152 ((-772 (-517))))) 
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-NIL 
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 (((-529 |#1| |#2|) (-793 |#1|) (-517) (-107)) (T -529)) 
 NIL 
 (-793 |#1|) 
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 (((-530 |#1|) (-13 (-319) (-299 $) (-558 (-517))) (-844)) (T -530)) 
 NIL 
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 NIL 
 (-593 |#1|) 
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 NIL 
 (-13 (-593 |#1|) (-258 |#2| |#2|)) 
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-NIL 
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 NIL 
 (-593 |#1|) 
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(-1076))) NIL (|has| |#2| (-823 (-1076)))) (($ $ (-1076)) NIL (|has| |#2| (-823 (-1076)))) (($ $ (-703)) NIL (|has| |#2| (-207))) (($ $) NIL (|has| |#2| (-207)))) (-1584 (((-107) $ $) NIL)) (-1704 (($ $ |#2|) NIL (|has| |#2| (-333)))) (-1692 (($ $) NIL) (($ $ $) NIL)) (-1678 (($ $ $) NIL)) (** (($ $ (-844)) NIL) (($ $ (-703)) NIL) (($ $ (-517)) NIL (|has| |#2| (-333)))) (* (($ (-844) $) NIL) (($ (-703) $) NIL) (($ (-517) $) NIL) (($ $ $) NIL) (($ $ |#2|) NIL) (($ |#2| $) NIL) (((-214 |#1| |#2|) $ (-214 |#1| |#2|)) NIL) (((-214 |#1| |#2|) (-214 |#1| |#2|) $) NIL)) (-3535 (((-703) $) NIL (|has| $ (-6 -4192))))) 
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+NIL 
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 ((* (($ (-844) $) NIL) (($ (-703) $) NIL) (($ (-517) $) NIL) (($ |#2| $) NIL) (($ $ |#2|) 9))) 
 (((-649 |#1| |#2|) (-10 -8 (-15 * (|#1| |#1| |#2|)) (-15 * (|#1| |#2| |#1|)) (-15 * (|#1| (-517) |#1|)) (-15 * (|#1| (-703) |#1|)) (-15 * (|#1| (-844) |#1|))) (-650 |#2|) (-156)) (T -649)) 
 NIL 
 (-10 -8 (-15 * (|#1| |#1| |#2|)) (-15 * (|#1| |#2| |#1|)) (-15 * (|#1| (-517) |#1|)) (-15 * (|#1| (-703) |#1|)) (-15 * (|#1| (-844) |#1|))) 
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-(((-650 |#1|) (-1187) (-156)) (T -650)) 
+((-2119 (((-107) $ $) 7)) (-3097 (((-107) $) 16)) (-2798 (((-3 $ "failed") $ $) 19)) (-1393 (($) 17 T CONST)) (-1662 (((-1059) $) 9)) (-4125 (((-1023) $) 10)) (-2271 (((-787) $) 11)) (-3610 (($) 18 T CONST)) (-1584 (((-107) $ $) 6)) (-1692 (($ $) 22) (($ $ $) 21)) (-1678 (($ $ $) 14)) (* (($ (-844) $) 13) (($ (-703) $) 15) (($ (-517) $) 20) (($ |#1| $) 23) (($ $ |#1|) 26))) 
+(((-650 |#1|) (-1188) (-156)) (T -650)) 
 NIL 
 (-13 (-106 |t#1| |t#1|)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-97) . T) ((-106 |#1| |#1|) . T) ((-123) . T) ((-557 (-787)) . T) ((-585 |#1|) . T) ((-968 |#1|) . T) ((-1004) . T)) 
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-((-1537 (($ $ (-844)) 12)) (-2848 (($ $ (-844)) 13)) (** (($ $ (-844)) 10))) 
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-NIL 
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-(((-653) (-1187)) (T -653)) 
-((* (*1 *1 *1 *1) (-4 *1 (-653))) (-1537 (*1 *1 *1 *2) (-12 (-4 *1 (-653)) (-5 *2 (-844)))) (-2848 (*1 *1 *1 *2) (-12 (-4 *1 (-653)) (-5 *2 (-844)))) (** (*1 *1 *1 *2) (-12 (-4 *1 (-653)) (-5 *2 (-844))))) 
-(-13 (-1004) (-10 -8 (-15 * ($ $ $)) (-15 -1537 ($ $ (-844))) (-15 -2848 ($ $ (-844))) (-15 ** ($ $ (-844))))) 
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-NIL 
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 NIL 
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 NIL 
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 NIL 
 (-212 |#1| |#2|) 
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-NIL 
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 (((-750 |#1|) (-239 |#1|) (-779)) (T -750)) 
 NIL 
 (-239 |#1|) 
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 NIL 
 (-13 (-509) (-777)) 
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 NIL 
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 NIL 
 (-13 (-779) (-659)) 
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-NIL 
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-NIL 
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-NIL 
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 NIL 
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-((-4082 (*1 *2 *1) (-12 (-4 *1 (-887 *2)) (-4 *2 (-779)))) (-3798 (*1 *1 *1 *1) (-12 (-4 *1 (-887 *2)) (-4 *2 (-779)))) (-1974 (*1 *1 *1 *1) (-12 (-4 *1 (-887 *2)) (-4 *2 (-779))))) 
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-(((-33) . T) ((-102 |#1|) . T) ((-97) |has| |#1| (-1004)) ((-557 (-787)) -3745 (|has| |#1| (-1004)) (|has| |#1| (-557 (-787)))) ((-280 |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004))) ((-456 |#1|) . T) ((-478 |#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1004))) ((-1004) |has| |#1| (-1004)) ((-1110) . T)) 
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-NIL 
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+((-2119 (((-107) $ $) NIL)) (-3097 (((-107) $) NIL)) (-2798 (((-3 $ "failed") $ $) 27)) (-1393 (($) NIL T CONST)) (-1996 (((-583 (-583 (-517))) (-583 (-517))) 29)) (-3717 (((-517) $) 45)) (-3441 (($ (-583 (-517))) 17)) (-3458 (($ $ $) NIL)) (-4084 (($ $ $) NIL)) (-1662 (((-1059) $) NIL)) (-4125 (((-1023) $) NIL)) (-3359 (((-583 (-517)) $) 11)) (-1842 (($ $) 32)) (-2271 (((-787) $) 43) (((-583 (-517)) $) 9)) (-3610 (($) 7 T CONST)) (-1642 (((-107) $ $) NIL)) (-1618 (((-107) $ $) NIL)) (-1584 (((-107) $ $) 20)) (-1630 (((-107) $ $) NIL)) (-1608 (((-107) $ $) 19)) (-1678 (($ $ $) 21)) (* (($ (-703) $) 25) (($ (-844) $) NIL))) 
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+((-3441 (*1 *1 *2) (-12 (-5 *2 (-583 (-517))) (-5 *1 (-890)))) (-1996 (*1 *2 *3) (-12 (-5 *2 (-583 (-583 (-517)))) (-5 *1 (-890)) (-5 *3 (-583 (-517))))) (-3717 (*1 *2 *1) (-12 (-5 *2 (-517)) (-5 *1 (-890)))) (-1842 (*1 *1 *1) (-5 *1 (-890))) (-2271 (*1 *2 *1) (-12 (-5 *2 (-583 (-517))) (-5 *1 (-890))))) 
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+NIL 
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 (((-557 (-787)) . T)) 
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-NIL 
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 NIL 
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 NIL 
 (-395 |#1|) 
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-(((-97) . T) ((-557 (-787)) . T) ((-1004) . T)) 
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-(((-1008) (-1007 (-1058) (-1075) (-517) (-199) (-787))) (T -1008)) 
-NIL 
-(-1007 (-1058) (-1075) (-517) (-199) (-787)) 
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-NIL 
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-NIL 
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-NIL 
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*7)) (-14 *6 (-583 (-1075))) (-14 *7 (-583 (-1075)))))) 
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-((-4052 (((-3 (-1156 (-377 (-517))) "failed") (-1156 |#1|) |#1|) 17)) (-1871 (((-107) (-1156 |#1|)) 11)) (-4161 (((-3 (-1156 (-517)) "failed") (-1156 |#1|)) 14))) 
-(((-1181 |#1|) (-10 -7 (-15 -1871 ((-107) (-1156 |#1|))) (-15 -4161 ((-3 (-1156 (-517)) "failed") (-1156 |#1|))) (-15 -4052 ((-3 (-1156 (-377 (-517))) "failed") (-1156 |#1|) |#1|))) (-579 (-517))) (T -1181)) 
-((-4052 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1156 *4)) (-4 *4 (-579 (-517))) (-5 *2 (-1156 (-377 (-517)))) (-5 *1 (-1181 *4)))) (-4161 (*1 *2 *3) (|partial| -12 (-5 *3 (-1156 *4)) (-4 *4 (-579 (-517))) (-5 *2 (-1156 (-517))) (-5 *1 (-1181 *4)))) (-1871 (*1 *2 *3) (-12 (-5 *3 (-1156 *4)) (-4 *4 (-579 (-517))) (-5 *2 (-107)) (-5 *1 (-1181 *4))))) 
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-(((-1182 |#1|) (-13 (-156) (-338) (-558 (-517)) (-1051)) (-844)) (T -1182)) 
-NIL 
-(-13 (-156) (-338) (-558 (-517)) (-1051)) 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
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"XPBWPOLY" 3101872 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1173 3094513 3096826 3096869 "XF" 3097490 NIL XF (NIL T) -9 NIL 3097889) (-1172 3094134 3094222 3094391 "XF-" 3094396 NIL XF- (NIL T T) -8 NIL NIL) (-1171 3089513 3090812 3090867 "XFALG" 3093015 NIL XFALG (NIL T T) -9 NIL 3093802) (-1170 3088650 3088754 3088958 "XEXPPKG" 3089405 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1169 3086748 3088501 3088596 "XDPOLY" 3088601 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1168 3085626 3086236 3086279 "XALG" 3086341 NIL XALG (NIL T) -9 NIL 3086460) (-1167 3079102 3083610 3084103 "WUTSET" 3085218 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1166 3076914 3077721 3078072 "WP" 3078884 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1165 3075800 3075998 3076293 "WFFINTBS" 3076711 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1164 3073704 3074131 3074593 "WEIER" 3075372 NIL WEIER (NIL T) -7 NIL NIL) (-1163 3072852 3073276 3073319 "VSPACE" 3073455 NIL VSPACE (NIL T) -9 NIL 3073529) (-1162 3072690 3072717 3072808 "VSPACE-" 3072813 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1161 3072436 3072479 3072550 "VOID" 3072641 T VOID (NIL) -8 NIL NIL) (-1160 3070572 3070931 3071337 "VIEW" 3072052 T VIEW (NIL) -7 NIL NIL) (-1159 3066997 3067635 3068372 "VIEWDEF" 3069857 T VIEWDEF (NIL) -7 NIL NIL) (-1158 3056336 3058545 3060718 "VIEW3D" 3064846 T VIEW3D (NIL) -8 NIL NIL) (-1157 3048618 3050247 3051826 "VIEW2D" 3054779 T VIEW2D (NIL) -8 NIL NIL) (-1156 3044027 3048388 3048480 "VECTOR" 3048561 NIL VECTOR (NIL T) -8 NIL NIL) (-1155 3042604 3042863 3043181 "VECTOR2" 3043757 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1154 3036143 3040395 3040439 "VECTCAT" 3041427 NIL VECTCAT (NIL T) -9 NIL 3042011) (-1153 3035157 3035411 3035801 "VECTCAT-" 3035806 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1152 3034638 3034808 3034928 "VARIABLE" 3035072 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1151 3034570 3034575 3034606 "UTYPE" 3034611 T UTYPE (NIL) -9 NIL NIL) (-1150 3033405 3033559 3033820 "UTSODETL" 3034396 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1149 3030845 3031305 3031829 "UTSODE" 3032946 NIL UTSODE (NIL T T) -7 NIL NIL) (-1148 3022692 3028485 3028973 "UTS" 3030414 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1147 3014040 3019402 3019445 "UTSCAT" 3020546 NIL UTSCAT (NIL T) -9 NIL 3021303) (-1146 3011396 3012111 3013099 "UTSCAT-" 3013104 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1145 3011027 3011070 3011201 "UTS2" 3011347 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1144 3005302 3007867 3007911 "URAGG" 3009981 NIL URAGG (NIL T) -9 NIL 3010703) (-1143 3002241 3003104 3004227 "URAGG-" 3004232 NIL URAGG- (NIL T T) -8 NIL NIL) (-1142 2997927 3000858 3001329 "UPXSSING" 3001905 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1141 2989821 2997048 2997328 "UPXS" 2997704 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1140 2982853 2989726 2989797 "UPXSCONS" 2989802 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1139 2973145 2979972 2980034 "UPXSCCA" 2980683 NIL UPXSCCA (NIL T T) -9 NIL 2980924) (-1138 2972784 2972869 2973042 "UPXSCCA-" 2973047 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1137 2962998 2969598 2969641 "UPXSCAT" 2970284 NIL UPXSCAT (NIL T) -9 NIL 2970892) (-1136 2962432 2962511 2962688 "UPXS2" 2962913 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1135 2961086 2961339 2961690 "UPSQFREE" 2962175 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1134 2954981 2958033 2958088 "UPSCAT" 2959237 NIL UPSCAT (NIL T T) -9 NIL 2960010) (-1133 2954195 2954399 2954722 "UPSCAT-" 2954727 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1132 2940327 2948324 2948367 "UPOLYC" 2950445 NIL UPOLYC (NIL T) -9 NIL 2951665) (-1131 2931720 2934124 2937249 "UPOLYC-" 2937254 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1130 2931351 2931394 2931525 "UPOLYC2" 2931671 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1129 2922810 2930920 2931057 "UP" 2931261 NIL UP (NIL NIL T) -8 NIL NIL) (-1128 2922153 2922260 2922423 "UPMP" 2922699 NIL UPMP (NIL T T) -7 NIL NIL) (-1127 2921706 2921787 2921926 "UPDIVP" 2922066 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1126 2920274 2920523 2920839 "UPDECOMP" 2921455 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1125 2919509 2919621 2919806 "UPCDEN" 2920158 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1124 2919032 2919101 2919248 "UP2" 2919434 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1123 2917555 2918241 2918516 "UNISEG" 2918792 NIL UNISEG (NIL T) -8 NIL NIL) (-1122 2916770 2916897 2917102 "UNISEG2" 2917398 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1121 2915830 2916010 2916236 "UNIFACT" 2916586 NIL UNIFACT (NIL T) -7 NIL NIL) (-1120 2899729 2915011 2915261 "ULS" 2915637 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1119 2887697 2899634 2899705 "ULSCONS" 2899710 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1118 2870450 2882460 2882522 "ULSCCAT" 2883234 NIL ULSCCAT (NIL T T) -9 NIL 2883530) (-1117 2869501 2869746 2870133 "ULSCCAT-" 2870138 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1116 2859494 2866008 2866051 "ULSCAT" 2866907 NIL ULSCAT (NIL T) -9 NIL 2867637) (-1115 2858928 2859007 2859184 "ULS2" 2859409 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1114 2857325 2858292 2858323 "UFD" 2858535 T UFD (NIL) -9 NIL 2858649) (-1113 2857119 2857165 2857260 "UFD-" 2857265 NIL UFD- (NIL T) -8 NIL NIL) (-1112 2856201 2856384 2856600 "UDVO" 2856925 T UDVO (NIL) -7 NIL NIL) (-1111 2854017 2854426 2854897 "UDPO" 2855765 NIL UDPO (NIL T) -7 NIL NIL) (-1110 2853949 2853954 2853985 "TYPE" 2853990 T TYPE (NIL) -9 NIL NIL) (-1109 2852920 2853122 2853362 "TWOFACT" 2853743 NIL TWOFACT (NIL T) -7 NIL NIL) (-1108 2851858 2852195 2852458 "TUPLE" 2852692 NIL TUPLE (NIL T) -8 NIL NIL) (-1107 2849549 2850068 2850607 "TUBETOOL" 2851341 T TUBETOOL (NIL) -7 NIL NIL) (-1106 2848398 2848603 2848844 "TUBE" 2849342 NIL TUBE (NIL T) -8 NIL NIL) (-1105 2843122 2847376 2847658 "TS" 2848150 NIL TS (NIL T) -8 NIL NIL) (-1104 2831825 2835917 2836014 "TSETCAT" 2841248 NIL TSETCAT (NIL T T T T) -9 NIL 2842779) (-1103 2826560 2828158 2830048 "TSETCAT-" 2830053 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1102 2820823 2821669 2822611 "TRMANIP" 2825696 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1101 2820264 2820327 2820490 "TRIMAT" 2820755 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1100 2818070 2818307 2818670 "TRIGMNIP" 2820013 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1099 2817589 2817702 2817733 "TRIGCAT" 2817946 T TRIGCAT (NIL) -9 NIL NIL) (-1098 2817258 2817337 2817478 "TRIGCAT-" 2817483 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1097 2814157 2816118 2816398 "TREE" 2817013 NIL TREE (NIL T) -8 NIL NIL) (-1096 2813430 2813958 2813989 "TRANFUN" 2814024 T TRANFUN (NIL) -9 NIL 2814090) (-1095 2812709 2812900 2813180 "TRANFUN-" 2813185 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1094 2812513 2812545 2812606 "TOPSP" 2812670 T TOPSP (NIL) -7 NIL NIL) (-1093 2811865 2811980 2812133 "TOOLSIGN" 2812394 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1092 2810526 2811042 2811281 "TEXTFILE" 2811648 T TEXTFILE (NIL) -8 NIL NIL) (-1091 2808391 2808905 2809343 "TEX" 2810110 T TEX (NIL) -8 NIL NIL) (-1090 2808172 2808203 2808275 "TEX1" 2808354 NIL TEX1 (NIL T) -7 NIL NIL) (-1089 2807820 2807883 2807973 "TEMUTL" 2808104 T TEMUTL (NIL) -7 NIL NIL) (-1088 2805974 2806254 2806579 "TBCMPPK" 2807543 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1087 2797862 2804134 2804191 "TBAGG" 2804591 NIL TBAGG (NIL T T) -9 NIL 2804802) (-1086 2792932 2794420 2796174 "TBAGG-" 2796179 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1085 2792316 2792423 2792568 "TANEXP" 2792821 NIL TANEXP (NIL T) -7 NIL NIL) (-1084 2785817 2792173 2792266 "TABLE" 2792271 NIL TABLE (NIL T T) -8 NIL NIL) (-1083 2785230 2785328 2785466 "TABLEAU" 2785714 NIL TABLEAU (NIL T) -8 NIL NIL) (-1082 2779838 2781058 2782306 "TABLBUMP" 2784016 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1081 2776301 2776996 2777779 "SYSSOLP" 2779089 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1080 2773291 2773804 2774427 "SYNTAX" 2775700 T SYNTAX (NIL) -8 NIL NIL) (-1079 2770425 2771033 2771671 "SYMTAB" 2772675 T SYMTAB (NIL) -8 NIL NIL) (-1078 2765674 2766576 2767559 "SYMS" 2769464 T SYMS (NIL) -8 NIL NIL) (-1077 2762907 2765134 2765363 "SYMPOLY" 2765479 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1076 2762427 2762502 2762624 "SYMFUNC" 2762819 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1075 2758405 2759664 2760486 "SYMBOL" 2761627 T SYMBOL (NIL) -8 NIL NIL) (-1074 2751944 2753633 2755353 "SWITCH" 2756707 T SWITCH (NIL) -8 NIL NIL) (-1073 2745177 2750771 2751073 "SUTS" 2751699 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1072 2737070 2744298 2744578 "SUPXS" 2744954 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1071 2728602 2736691 2736816 "SUP" 2736979 NIL SUP (NIL T) -8 NIL NIL) (-1070 2727761 2727888 2728105 "SUPFRACF" 2728470 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1069 2727386 2727445 2727556 "SUP2" 2727696 NIL SUP2 (NIL T T) -7 NIL NIL) (-1068 2725812 2726084 2726444 "SUMRF" 2727087 NIL SUMRF (NIL T) -7 NIL NIL) (-1067 2725133 2725198 2725395 "SUMFS" 2725734 NIL SUMFS (NIL T T) -7 NIL NIL) (-1066 2709072 2724314 2724564 "SULS" 2724940 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1065 2708394 2708597 2708737 "SUCH" 2708980 NIL SUCH (NIL T T) -8 NIL NIL) (-1064 2702321 2703333 2704291 "SUBSPACE" 2707482 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1063 2701751 2701841 2702005 "SUBRESP" 2702209 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1062 2695120 2696416 2697727 "STTF" 2700487 NIL STTF (NIL T) -7 NIL NIL) (-1061 2689293 2690413 2691560 "STTFNC" 2694020 NIL STTFNC (NIL T) -7 NIL NIL) (-1060 2680644 2682511 2684304 "STTAYLOR" 2687534 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1059 2673888 2680508 2680591 "STRTBL" 2680596 NIL STRTBL (NIL T) -8 NIL NIL) (-1058 2669279 2673843 2673874 "STRING" 2673879 T STRING (NIL) -8 NIL NIL) (-1057 2664167 2668652 2668683 "STRICAT" 2668742 T STRICAT (NIL) -9 NIL 2668804) (-1056 2656883 2661690 2662310 "STREAM" 2663582 NIL STREAM (NIL T) -8 NIL NIL) (-1055 2656393 2656470 2656614 "STREAM3" 2656800 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1054 2655375 2655558 2655793 "STREAM2" 2656206 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1053 2655063 2655115 2655208 "STREAM1" 2655317 NIL STREAM1 (NIL T) -7 NIL NIL) (-1052 2654079 2654260 2654491 "STINPROD" 2654879 NIL STINPROD (NIL T) -7 NIL NIL) (-1051 2653657 2653841 2653872 "STEP" 2653952 T STEP (NIL) -9 NIL 2654030) (-1050 2647200 2653556 2653633 "STBL" 2653638 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1049 2642375 2646422 2646466 "STAGG" 2646619 NIL STAGG (NIL T) -9 NIL 2646708) (-1048 2640077 2640679 2641551 "STAGG-" 2641556 NIL STAGG- (NIL T T) -8 NIL NIL) (-1047 2638272 2639847 2639939 "STACK" 2640020 NIL STACK (NIL T) -8 NIL NIL) (-1046 2631003 2636419 2636874 "SREGSET" 2637902 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1045 2623443 2624811 2626323 "SRDCMPK" 2629609 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1044 2616410 2620883 2620914 "SRAGG" 2622217 T SRAGG (NIL) -9 NIL 2622825) (-1043 2615427 2615682 2616061 "SRAGG-" 2616066 NIL SRAGG- (NIL T) -8 NIL NIL) (-1042 2609876 2614346 2614773 "SQMATRIX" 2615046 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1041 2603628 2606596 2607322 "SPLTREE" 2609222 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1040 2599618 2600284 2600930 "SPLNODE" 2603054 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1039 2598664 2598897 2598928 "SPFCAT" 2599372 T SPFCAT (NIL) -9 NIL NIL) (-1038 2597401 2597611 2597875 "SPECOUT" 2598422 T SPECOUT (NIL) -7 NIL NIL) (-1037 2597162 2597202 2597271 "SPADPRSR" 2597354 T SPADPRSR (NIL) -7 NIL NIL) (-1036 2589184 2590931 2590974 "SPACEC" 2595297 NIL SPACEC (NIL T) -9 NIL 2597113) (-1035 2587356 2589117 2589165 "SPACE3" 2589170 NIL SPACE3 (NIL T) -8 NIL NIL) (-1034 2586108 2586279 2586570 "SORTPAK" 2587161 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1033 2584164 2584467 2584885 "SOLVETRA" 2585772 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1032 2583175 2583397 2583671 "SOLVESER" 2583937 NIL SOLVESER (NIL T) -7 NIL NIL) (-1031 2578395 2579276 2580278 "SOLVERAD" 2582227 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1030 2574210 2574819 2575548 "SOLVEFOR" 2577762 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1029 2568509 2573561 2573658 "SNTSCAT" 2573663 NIL SNTSCAT (NIL T T T T) -9 NIL 2573733) (-1028 2562614 2566840 2567230 "SMTS" 2568199 NIL SMTS (NIL T T T) -8 NIL NIL) (-1027 2557025 2562503 2562579 "SMP" 2562584 NIL SMP (NIL T T) -8 NIL NIL) (-1026 2555184 2555485 2555883 "SMITH" 2556722 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1025 2548148 2552344 2552447 "SMATCAT" 2553787 NIL SMATCAT (NIL NIL T T T) -9 NIL 2554336) (-1024 2545089 2545912 2547089 "SMATCAT-" 2547094 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1023 2542802 2544325 2544369 "SKAGG" 2544630 NIL SKAGG (NIL T) -9 NIL 2544765) (-1022 2538860 2541906 2542184 "SINT" 2542546 T SINT (NIL) -8 NIL NIL) (-1021 2538632 2538670 2538736 "SIMPAN" 2538816 T SIMPAN (NIL) -7 NIL NIL) (-1020 2537470 2537691 2537966 "SIGNRF" 2538391 NIL SIGNRF (NIL T) -7 NIL NIL) (-1019 2536279 2536430 2536720 "SIGNEF" 2537299 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1018 2533969 2534423 2534929 "SHP" 2535820 NIL SHP (NIL T NIL) -7 NIL NIL) (-1017 2527822 2533870 2533946 "SHDP" 2533951 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1016 2527311 2527503 2527534 "SGROUP" 2527686 T SGROUP (NIL) -9 NIL 2527773) (-1015 2527081 2527133 2527237 "SGROUP-" 2527242 NIL SGROUP- (NIL T) -8 NIL NIL) (-1014 2523917 2524614 2525337 "SGCF" 2526380 T SGCF (NIL) -7 NIL NIL) (-1013 2518315 2523367 2523464 "SFRTCAT" 2523469 NIL SFRTCAT (NIL T T T T) -9 NIL 2523507) (-1012 2511775 2512790 2513924 "SFRGCD" 2517298 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1011 2504941 2506012 2507196 "SFQCMPK" 2510708 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1010 2504563 2504652 2504762 "SFORT" 2504882 NIL SFORT (NIL T T) -8 NIL NIL) (-1009 2503708 2504403 2504524 "SEXOF" 2504529 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1008 2502842 2503589 2503657 "SEX" 2503662 T SEX (NIL) -8 NIL NIL) (-1007 2497618 2498307 2498403 "SEXCAT" 2502174 NIL SEXCAT (NIL T T T T T) -9 NIL 2502793) (-1006 2494798 2497552 2497600 "SET" 2497605 NIL SET (NIL T) -8 NIL NIL) (-1005 2493049 2493511 2493816 "SETMN" 2494539 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1004 2492656 2492782 2492813 "SETCAT" 2492930 T SETCAT (NIL) -9 NIL 2493014) (-1003 2492436 2492488 2492587 "SETCAT-" 2492592 NIL SETCAT- (NIL T) -8 NIL NIL) (-1002 2488823 2490897 2490941 "SETAGG" 2491811 NIL SETAGG (NIL T) -9 NIL 2492151) (-1001 2488281 2488397 2488634 "SETAGG-" 2488639 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1000 2487486 2487779 2487841 "SEGXCAT" 2488127 NIL SEGXCAT (NIL T T) -9 NIL 2488246) (-999 2486546 2487156 2487335 "SEG" 2487340 NIL SEG (NIL T) -8 NIL NIL) (-998 2485463 2485676 2485718 "SEGCAT" 2486291 NIL SEGCAT (NIL T) -9 NIL 2486529) (-997 2484525 2484853 2485049 "SEGBIND" 2485300 NIL SEGBIND (NIL T) -8 NIL NIL) (-996 2484157 2484214 2484323 "SEGBIND2" 2484462 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-995 2483392 2483515 2483714 "SEG2" 2484004 NIL SEG2 (NIL T T) -7 NIL NIL) (-994 2482831 2483329 2483374 "SDVAR" 2483379 NIL SDVAR (NIL T) -8 NIL NIL) (-993 2475137 2482610 2482734 "SDPOL" 2482739 NIL SDPOL (NIL T) -8 NIL NIL) (-992 2473736 2474002 2474319 "SCPKG" 2474852 NIL SCPKG (NIL T) -7 NIL NIL) (-991 2472963 2473096 2473273 "SCACHE" 2473591 NIL SCACHE (NIL T) -7 NIL NIL) (-990 2472406 2472727 2472810 "SAOS" 2472900 T SAOS (NIL) -8 NIL NIL) (-989 2471974 2472009 2472180 "SAERFFC" 2472365 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-988 2465870 2471873 2471951 "SAE" 2471956 NIL SAE (NIL T T NIL) -8 NIL NIL) (-987 2465466 2465501 2465658 "SAEFACT" 2465829 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-986 2463792 2464106 2464505 "RURPK" 2465132 NIL RURPK (NIL T NIL) -7 NIL NIL) (-985 2462445 2462722 2463029 "RULESET" 2463628 NIL RULESET (NIL T T T) -8 NIL NIL) (-984 2459653 2460156 2460617 "RULE" 2462127 NIL RULE (NIL T T T) -8 NIL NIL) (-983 2459295 2459450 2459531 "RULECOLD" 2459605 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-982 2454187 2454981 2455897 "RSETGCD" 2458494 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-981 2443501 2448553 2448648 "RSETCAT" 2452713 NIL RSETCAT (NIL T T T T) -9 NIL 2453810) (-980 2441432 2441971 2442791 "RSETCAT-" 2442796 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-979 2433862 2435237 2436753 "RSDCMPK" 2440031 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-978 2431879 2432320 2432393 "RRCC" 2433469 NIL RRCC (NIL T T) -9 NIL 2433813) (-977 2431233 2431407 2431683 "RRCC-" 2431688 NIL RRCC- (NIL T T T) -8 NIL NIL) (-976 2405599 2415224 2415289 "RPOLCAT" 2425791 NIL RPOLCAT (NIL T T T) -9 NIL 2428949) (-975 2397103 2399441 2402559 "RPOLCAT-" 2402564 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-974 2388169 2395333 2395813 "ROUTINE" 2396643 T ROUTINE (NIL) -8 NIL NIL) (-973 2384874 2387725 2387872 "ROMAN" 2388042 T ROMAN (NIL) -8 NIL NIL) (-972 2383160 2383745 2384002 "ROIRC" 2384680 NIL ROIRC (NIL T T) -8 NIL NIL) (-971 2379564 2381868 2381897 "RNS" 2382193 T RNS (NIL) -9 NIL 2382463) (-970 2378078 2378461 2378992 "RNS-" 2379065 NIL RNS- (NIL T) -8 NIL NIL) (-969 2377503 2377911 2377940 "RNG" 2377945 T RNG (NIL) -9 NIL 2377966) (-968 2376900 2377262 2377303 "RMODULE" 2377363 NIL RMODULE (NIL T) -9 NIL 2377405) (-967 2375752 2375846 2376176 "RMCAT2" 2376801 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-966 2372466 2374935 2375256 "RMATRIX" 2375487 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-965 2365462 2367696 2367809 "RMATCAT" 2371118 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2372100) (-964 2364841 2364988 2365291 "RMATCAT-" 2365296 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-963 2364411 2364486 2364612 "RINTERP" 2364760 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-962 2363461 2364025 2364054 "RING" 2364164 T RING (NIL) -9 NIL 2364258) (-961 2363256 2363300 2363394 "RING-" 2363399 NIL RING- (NIL T) -8 NIL NIL) (-960 2362108 2362344 2362599 "RIDIST" 2363021 T RIDIST (NIL) -7 NIL NIL) (-959 2353430 2361582 2361785 "RGCHAIN" 2361957 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-958 2350435 2351049 2351717 "RF" 2352794 NIL RF (NIL T) -7 NIL NIL) (-957 2350084 2350147 2350248 "RFFACTOR" 2350366 NIL RFFACTOR (NIL T) -7 NIL NIL) (-956 2349812 2349847 2349942 "RFFACT" 2350043 NIL RFFACT (NIL T) -7 NIL NIL) (-955 2347942 2348306 2348686 "RFDIST" 2349452 T RFDIST (NIL) -7 NIL NIL) (-954 2347400 2347492 2347652 "RETSOL" 2347844 NIL RETSOL (NIL T T) -7 NIL NIL) (-953 2346992 2347072 2347114 "RETRACT" 2347304 NIL RETRACT (NIL T) -9 NIL NIL) (-952 2346844 2346869 2346953 "RETRACT-" 2346958 NIL RETRACT- (NIL T T) -8 NIL NIL) (-951 2339702 2346501 2346626 "RESULT" 2346739 T RESULT (NIL) -8 NIL NIL) (-950 2338287 2338976 2339173 "RESRING" 2339605 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-949 2337927 2337976 2338072 "RESLATC" 2338224 NIL RESLATC (NIL T) -7 NIL NIL) (-948 2337636 2337670 2337775 "REPSQ" 2337886 NIL REPSQ (NIL T) -7 NIL NIL) (-947 2335067 2335647 2336247 "REP" 2337056 T REP (NIL) -7 NIL NIL) (-946 2334768 2334802 2334911 "REPDB" 2335026 NIL REPDB (NIL T) -7 NIL NIL) (-945 2328713 2330092 2331312 "REP2" 2333580 NIL REP2 (NIL T) -7 NIL NIL) (-944 2325119 2325800 2326605 "REP1" 2327940 NIL REP1 (NIL T) -7 NIL NIL) (-943 2317865 2323280 2323732 "REGSET" 2324750 NIL REGSET (NIL T T T T) -8 NIL NIL) (-942 2316686 2317021 2317269 "REF" 2317650 NIL REF (NIL T) -8 NIL NIL) (-941 2316067 2316170 2316335 "REDORDER" 2316570 NIL REDORDER (NIL T T) -7 NIL NIL) (-940 2312036 2315301 2315522 "RECLOS" 2315898 NIL RECLOS (NIL T) -8 NIL NIL) (-939 2311093 2311274 2311487 "REALSOLV" 2311843 T REALSOLV (NIL) -7 NIL NIL) (-938 2310940 2310981 2311010 "REAL" 2311015 T REAL (NIL) -9 NIL 2311050) (-937 2307431 2308233 2309115 "REAL0Q" 2310105 NIL REAL0Q (NIL T) -7 NIL NIL) (-936 2303042 2304030 2305089 "REAL0" 2306412 NIL REAL0 (NIL T) -7 NIL NIL) (-935 2302450 2302522 2302727 "RDIV" 2302964 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-934 2301523 2301697 2301908 "RDIST" 2302272 NIL RDIST (NIL T) -7 NIL NIL) (-933 2300127 2300414 2300783 "RDETRS" 2301231 NIL RDETRS (NIL T T) -7 NIL NIL) (-932 2297948 2298402 2298937 "RDETR" 2299669 NIL RDETR (NIL T T) -7 NIL NIL) (-931 2296564 2296842 2297243 "RDEEFS" 2297664 NIL RDEEFS (NIL T T) -7 NIL NIL) (-930 2295064 2295370 2295799 "RDEEF" 2296252 NIL RDEEF (NIL T T) -7 NIL NIL) (-929 2289348 2292280 2292309 "RCFIELD" 2293586 T RCFIELD (NIL) -9 NIL 2294316) (-928 2287417 2287921 2288614 "RCFIELD-" 2288687 NIL RCFIELD- (NIL T) -8 NIL NIL) (-927 2283748 2285533 2285575 "RCAGG" 2286646 NIL RCAGG (NIL T) -9 NIL 2287111) (-926 2283379 2283473 2283633 "RCAGG-" 2283638 NIL RCAGG- (NIL T T) -8 NIL NIL) (-925 2282724 2282835 2282997 "RATRET" 2283263 NIL RATRET (NIL T) -7 NIL NIL) (-924 2282281 2282348 2282467 "RATFACT" 2282652 NIL RATFACT (NIL T) -7 NIL NIL) (-923 2281596 2281716 2281866 "RANDSRC" 2282151 T RANDSRC (NIL) -7 NIL NIL) (-922 2281333 2281377 2281448 "RADUTIL" 2281545 T RADUTIL (NIL) -7 NIL NIL) (-921 2274340 2280076 2280393 "RADIX" 2281048 NIL RADIX (NIL NIL) -8 NIL NIL) (-920 2265910 2274184 2274312 "RADFF" 2274317 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-919 2265561 2265636 2265665 "RADCAT" 2265822 T RADCAT (NIL) -9 NIL NIL) (-918 2265346 2265394 2265491 "RADCAT-" 2265496 NIL RADCAT- (NIL T) -8 NIL NIL) (-917 2263497 2265121 2265210 "QUEUE" 2265290 NIL QUEUE (NIL T) -8 NIL NIL) (-916 2259994 2263434 2263479 "QUAT" 2263484 NIL QUAT (NIL T) -8 NIL NIL) (-915 2259632 2259675 2259802 "QUATCT2" 2259945 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-914 2253425 2256805 2256846 "QUATCAT" 2257625 NIL QUATCAT (NIL T) -9 NIL 2258390) (-913 2249569 2250606 2251993 "QUATCAT-" 2252087 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-912 2247089 2248653 2248695 "QUAGG" 2249070 NIL QUAGG (NIL T) -9 NIL 2249245) (-911 2246014 2246487 2246659 "QFORM" 2246961 NIL QFORM (NIL NIL T) -8 NIL NIL) (-910 2237310 2242568 2242609 "QFCAT" 2243267 NIL QFCAT (NIL T) -9 NIL 2244260) (-909 2232882 2234083 2235674 "QFCAT-" 2235768 NIL QFCAT- (NIL T T) -8 NIL NIL) (-908 2232520 2232563 2232690 "QFCAT2" 2232833 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-907 2231980 2232090 2232220 "QEQUAT" 2232410 T QEQUAT (NIL) -8 NIL NIL) (-906 2225166 2226237 2227419 "QCMPACK" 2230913 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-905 2222742 2223163 2223591 "QALGSET" 2224821 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-904 2221987 2222161 2222393 "QALGSET2" 2222562 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-903 2220678 2220901 2221218 "PWFFINTB" 2221760 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-902 2218866 2219034 2219387 "PUSHVAR" 2220492 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-901 2214783 2215837 2215879 "PTRANFN" 2217763 NIL PTRANFN (NIL T) -9 NIL NIL) (-900 2213195 2213486 2213807 "PTPACK" 2214494 NIL PTPACK (NIL T) -7 NIL NIL) (-899 2212831 2212888 2212995 "PTFUNC2" 2213132 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-898 2207307 2211648 2211689 "PTCAT" 2212057 NIL PTCAT (NIL T) -9 NIL 2212219) (-897 2206965 2207000 2207124 "PSQFR" 2207266 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-896 2205560 2205858 2206192 "PSEUDLIN" 2206663 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-895 2192368 2194732 2197055 "PSETPK" 2203320 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-894 2185454 2188168 2188263 "PSETCAT" 2191244 NIL PSETCAT (NIL T T T T) -9 NIL 2192058) (-893 2183292 2183926 2184745 "PSETCAT-" 2184750 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-892 2182649 2182811 2182840 "PSCURVE" 2183105 T PSCURVE (NIL) -9 NIL 2183269) (-891 2179100 2180626 2180691 "PSCAT" 2181527 NIL PSCAT (NIL T T T) -9 NIL 2181767) (-890 2178164 2178380 2178779 "PSCAT-" 2178784 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-889 2176817 2177449 2177663 "PRTITION" 2177970 T PRTITION (NIL) -8 NIL NIL) (-888 2165915 2168121 2170309 "PRS" 2174679 NIL PRS (NIL T T) -7 NIL NIL) (-887 2163773 2165265 2165306 "PRQAGG" 2165489 NIL PRQAGG (NIL T) -9 NIL 2165591) (-886 2157547 2161939 2162759 "PRODUCT" 2162999 NIL PRODUCT (NIL T T) -8 NIL NIL) (-885 2154823 2157007 2157240 "PR" 2157358 NIL PR (NIL T T) -8 NIL NIL) (-884 2154619 2154651 2154710 "PRINT" 2154784 T PRINT (NIL) -7 NIL NIL) (-883 2153959 2154076 2154228 "PRIMES" 2154499 NIL PRIMES (NIL T) -7 NIL NIL) (-882 2152024 2152425 2152891 "PRIMELT" 2153538 NIL PRIMELT (NIL T) -7 NIL NIL) (-881 2151755 2151803 2151832 "PRIMCAT" 2151955 T PRIMCAT (NIL) -9 NIL NIL) (-880 2147916 2151693 2151738 "PRIMARR" 2151743 NIL PRIMARR (NIL T) -8 NIL NIL) (-879 2146923 2147101 2147329 "PRIMARR2" 2147734 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-878 2146566 2146622 2146733 "PREASSOC" 2146861 NIL PREASSOC (NIL T T) -7 NIL NIL) (-877 2146046 2146177 2146206 "PPCURVE" 2146409 T PPCURVE (NIL) -9 NIL 2146543) (-876 2143405 2143804 2144396 "POLYROOT" 2145627 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-875 2137311 2143011 2143170 "POLY" 2143278 NIL POLY (NIL T) -8 NIL NIL) (-874 2136696 2136754 2136987 "POLYLIFT" 2137247 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-873 2132981 2133430 2134058 "POLYCATQ" 2136241 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-872 2120021 2125418 2125483 "POLYCAT" 2128968 NIL POLYCAT (NIL T T T) -9 NIL 2130895) (-871 2113472 2115333 2117716 "POLYCAT-" 2117721 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-870 2113061 2113129 2113248 "POLY2UP" 2113398 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-869 2112697 2112754 2112861 "POLY2" 2112998 NIL POLY2 (NIL T T) -7 NIL NIL) (-868 2111382 2111621 2111897 "POLUTIL" 2112471 NIL POLUTIL (NIL T T) -7 NIL NIL) (-867 2109744 2110021 2110351 "POLTOPOL" 2111104 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-866 2105267 2109681 2109726 "POINT" 2109731 NIL POINT (NIL T) -8 NIL NIL) (-865 2103454 2103811 2104186 "PNTHEORY" 2104912 T PNTHEORY (NIL) -7 NIL NIL) (-864 2101882 2102179 2102588 "PMTOOLS" 2103152 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-863 2101475 2101553 2101670 "PMSYM" 2101798 NIL PMSYM (NIL T) -7 NIL NIL) (-862 2100985 2101054 2101228 "PMQFCAT" 2101400 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-861 2100340 2100450 2100606 "PMPRED" 2100862 NIL PMPRED (NIL T) -7 NIL NIL) (-860 2099736 2099822 2099983 "PMPREDFS" 2100241 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-859 2098382 2098590 2098974 "PMPLCAT" 2099498 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-858 2097914 2097993 2098145 "PMLSAGG" 2098297 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-857 2097391 2097467 2097647 "PMKERNEL" 2097832 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-856 2097008 2097083 2097196 "PMINS" 2097310 NIL PMINS (NIL T) -7 NIL NIL) (-855 2096438 2096507 2096722 "PMFS" 2096933 NIL PMFS (NIL T T T) -7 NIL NIL) (-854 2095669 2095787 2095991 "PMDOWN" 2096315 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-853 2094832 2094991 2095173 "PMASS" 2095507 T PMASS (NIL) -7 NIL NIL) (-852 2094106 2094217 2094380 "PMASSFS" 2094718 NIL PMASSFS (NIL T T) -7 NIL NIL) (-851 2093765 2093832 2093925 "PLOTTOOL" 2094033 T PLOTTOOL (NIL) -7 NIL NIL) (-850 2088466 2089632 2090759 "PLOT" 2092658 T PLOT (NIL) -8 NIL NIL) (-849 2084339 2085354 2086259 "PLOT3D" 2087581 T PLOT3D (NIL) -8 NIL NIL) (-848 2083263 2083437 2083669 "PLOT1" 2084146 NIL PLOT1 (NIL T) -7 NIL NIL) (-847 2058658 2063329 2068180 "PLEQN" 2078529 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-846 2057976 2058098 2058278 "PINTERP" 2058523 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-845 2057669 2057716 2057819 "PINTERPA" 2057923 NIL PINTERPA (NIL T T) -7 NIL NIL) (-844 2056896 2057463 2057556 "PI" 2057596 T PI (NIL) -8 NIL NIL) (-843 2055287 2056272 2056301 "PID" 2056483 T PID (NIL) -9 NIL 2056617) (-842 2055012 2055049 2055137 "PICOERCE" 2055244 NIL PICOERCE (NIL T) -7 NIL NIL) (-841 2054333 2054471 2054647 "PGROEB" 2054868 NIL PGROEB (NIL T) -7 NIL NIL) (-840 2049920 2050734 2051639 "PGE" 2053448 T PGE (NIL) -7 NIL NIL) (-839 2048044 2048290 2048656 "PGCD" 2049637 NIL PGCD (NIL T T T T) -7 NIL NIL) (-838 2047382 2047485 2047646 "PFRPAC" 2047928 NIL PFRPAC (NIL T) -7 NIL NIL) (-837 2043997 2045930 2046283 "PFR" 2047061 NIL PFR (NIL T) -8 NIL NIL) (-836 2042386 2042630 2042955 "PFOTOOLS" 2043744 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-835 2040919 2041158 2041509 "PFOQ" 2042143 NIL PFOQ (NIL T T T) -7 NIL NIL) (-834 2039396 2039608 2039970 "PFO" 2040703 NIL PFO (NIL T T T T T) -7 NIL NIL) (-833 2035919 2039285 2039354 "PF" 2039359 NIL PF (NIL NIL) -8 NIL NIL) (-832 2033347 2034628 2034657 "PFECAT" 2035242 T PFECAT (NIL) -9 NIL 2035626) (-831 2032792 2032946 2033160 "PFECAT-" 2033165 NIL PFECAT- (NIL T) -8 NIL NIL) (-830 2031396 2031647 2031948 "PFBRU" 2032541 NIL PFBRU (NIL T T) -7 NIL NIL) (-829 2029263 2029614 2030046 "PFBR" 2031047 NIL PFBR (NIL T T T T) -7 NIL NIL) (-828 2025115 2026639 2027315 "PERM" 2028620 NIL PERM (NIL T) -8 NIL NIL) (-827 2020381 2021322 2022192 "PERMGRP" 2024278 NIL PERMGRP (NIL T) -8 NIL NIL) (-826 2018451 2019444 2019486 "PERMCAT" 2019932 NIL PERMCAT (NIL T) -9 NIL 2020237) (-825 2018106 2018147 2018270 "PERMAN" 2018404 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-824 2015546 2017675 2017806 "PENDTREE" 2018008 NIL PENDTREE (NIL T) -8 NIL NIL) (-823 2013618 2014396 2014438 "PDRING" 2015095 NIL PDRING (NIL T) -9 NIL 2015380) (-822 2012721 2012939 2013301 "PDRING-" 2013306 NIL PDRING- (NIL T T) -8 NIL NIL) (-821 2009863 2010613 2011304 "PDEPROB" 2012050 T PDEPROB (NIL) -8 NIL NIL) (-820 2007434 2007930 2008479 "PDEPACK" 2009334 T PDEPACK (NIL) -7 NIL NIL) (-819 2006346 2006536 2006787 "PDECOMP" 2007233 NIL PDECOMP (NIL T T) -7 NIL NIL) (-818 2003957 2004772 2004801 "PDECAT" 2005586 T PDECAT (NIL) -9 NIL 2006297) (-817 2003710 2003743 2003832 "PCOMP" 2003918 NIL PCOMP (NIL T T) -7 NIL NIL) (-816 2001917 2002513 2002809 "PBWLB" 2003440 NIL PBWLB (NIL T) -8 NIL NIL) (-815 1994426 1995994 1997330 "PATTERN" 2000602 NIL PATTERN (NIL T) -8 NIL NIL) (-814 1994058 1994115 1994224 "PATTERN2" 1994363 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-813 1991815 1992203 1992660 "PATTERN1" 1993647 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-812 1989210 1989764 1990245 "PATRES" 1991380 NIL PATRES (NIL T T) -8 NIL NIL) (-811 1988774 1988841 1988973 "PATRES2" 1989137 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-810 1986671 1987071 1987476 "PATMATCH" 1988443 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-809 1986207 1986390 1986432 "PATMAB" 1986539 NIL PATMAB (NIL T) -9 NIL 1986622) (-808 1984752 1985061 1985319 "PATLRES" 1986012 NIL PATLRES (NIL T T T) -8 NIL NIL) (-807 1984297 1984420 1984462 "PATAB" 1984467 NIL PATAB (NIL T) -9 NIL 1984639) (-806 1981778 1982310 1982883 "PARTPERM" 1983744 T PARTPERM (NIL) -7 NIL NIL) (-805 1981399 1981462 1981564 "PARSURF" 1981709 NIL PARSURF (NIL T) -8 NIL NIL) (-804 1981031 1981088 1981197 "PARSU2" 1981336 NIL PARSU2 (NIL T T) -7 NIL NIL) (-803 1980795 1980835 1980902 "PARSER" 1980984 T PARSER (NIL) -7 NIL NIL) (-802 1980416 1980479 1980581 "PARSCURV" 1980726 NIL PARSCURV (NIL T) -8 NIL NIL) (-801 1980048 1980105 1980214 "PARSC2" 1980353 NIL PARSC2 (NIL T T) -7 NIL NIL) (-800 1979687 1979745 1979842 "PARPCURV" 1979984 NIL PARPCURV (NIL T) -8 NIL NIL) (-799 1979319 1979376 1979485 "PARPC2" 1979624 NIL PARPC2 (NIL T T) -7 NIL NIL) (-798 1978839 1978925 1979044 "PAN2EXPR" 1979220 T PAN2EXPR (NIL) -7 NIL NIL) (-797 1977645 1977960 1978188 "PALETTE" 1978631 T PALETTE (NIL) -8 NIL NIL) (-796 1971495 1976904 1977098 "PADICRC" 1977500 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-795 1964703 1970841 1971025 "PADICRAT" 1971343 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-794 1963007 1964640 1964685 "PADIC" 1964690 NIL PADIC (NIL NIL) -8 NIL NIL) (-793 1960211 1961785 1961826 "PADICCT" 1962407 NIL PADICCT (NIL NIL) -9 NIL 1962689) (-792 1959168 1959368 1959636 "PADEPAC" 1959998 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-791 1958380 1958513 1958719 "PADE" 1959030 NIL PADE (NIL T T T) -7 NIL NIL) (-790 1956391 1957223 1957538 "OWP" 1958148 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-789 1955500 1955996 1956168 "OVAR" 1956259 NIL OVAR (NIL NIL) -8 NIL NIL) (-788 1954764 1954885 1955046 "OUT" 1955359 T OUT (NIL) -7 NIL NIL) (-787 1943810 1945989 1948159 "OUTFORM" 1952614 T OUTFORM (NIL) -8 NIL NIL) (-786 1943218 1943539 1943628 "OSI" 1943741 T OSI (NIL) -8 NIL NIL) (-785 1941963 1942190 1942475 "ORTHPOL" 1942965 NIL ORTHPOL (NIL T) -7 NIL NIL) (-784 1939334 1941624 1941762 "OREUP" 1941906 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-783 1936730 1939027 1939153 "ORESUP" 1939276 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-782 1934265 1934765 1935325 "OREPCTO" 1936219 NIL OREPCTO (NIL T T) -7 NIL NIL) (-781 1928174 1930380 1930421 "OREPCAT" 1932742 NIL OREPCAT (NIL T) -9 NIL 1933845) (-780 1925322 1926104 1927161 "OREPCAT-" 1927166 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-779 1924499 1924771 1924800 "ORDSET" 1925109 T ORDSET (NIL) -9 NIL 1925273) (-778 1924018 1924140 1924333 "ORDSET-" 1924338 NIL ORDSET- (NIL T) -8 NIL NIL) (-777 1922631 1923432 1923461 "ORDRING" 1923663 T ORDRING (NIL) -9 NIL 1923787) (-776 1922276 1922370 1922514 "ORDRING-" 1922519 NIL ORDRING- (NIL T) -8 NIL NIL) (-775 1921651 1922132 1922161 "ORDMON" 1922166 T ORDMON (NIL) -9 NIL 1922187) (-774 1920813 1920960 1921155 "ORDFUNS" 1921500 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-773 1920324 1920683 1920712 "ORDFIN" 1920717 T ORDFIN (NIL) -9 NIL 1920738) (-772 1916836 1918910 1919319 "ORDCOMP" 1919948 NIL ORDCOMP (NIL T) -8 NIL NIL) (-771 1916102 1916229 1916415 "ORDCOMP2" 1916696 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-770 1912610 1913492 1914329 "OPTPROB" 1915285 T OPTPROB (NIL) -8 NIL NIL) (-769 1909452 1910081 1910775 "OPTPACK" 1911936 T OPTPACK (NIL) -7 NIL NIL) (-768 1907177 1907913 1907942 "OPTCAT" 1908757 T OPTCAT (NIL) -9 NIL 1909403) (-767 1906945 1906984 1907050 "OPQUERY" 1907131 T OPQUERY (NIL) -7 NIL NIL) (-766 1904081 1905272 1905772 "OP" 1906477 NIL OP (NIL T) -8 NIL NIL) (-765 1900846 1902878 1903247 "ONECOMP" 1903745 NIL ONECOMP (NIL T) -8 NIL NIL) (-764 1900151 1900266 1900440 "ONECOMP2" 1900718 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-763 1899570 1899676 1899806 "OMSERVER" 1900041 T OMSERVER (NIL) -7 NIL NIL) (-762 1896458 1899010 1899051 "OMSAGG" 1899112 NIL OMSAGG (NIL T) -9 NIL 1899176) (-761 1895081 1895344 1895626 "OMPKG" 1896196 T OMPKG (NIL) -7 NIL NIL) (-760 1894510 1894613 1894642 "OM" 1894941 T OM (NIL) -9 NIL NIL) (-759 1893049 1894062 1894230 "OMLO" 1894391 NIL OMLO (NIL T T) -8 NIL NIL) (-758 1891979 1892126 1892352 "OMEXPR" 1892875 NIL OMEXPR (NIL T) -7 NIL NIL) (-757 1891297 1891525 1891661 "OMERR" 1891863 T OMERR (NIL) -8 NIL NIL) (-756 1890475 1890718 1890878 "OMERRK" 1891157 T OMERRK (NIL) -8 NIL NIL) (-755 1889953 1890152 1890260 "OMENC" 1890387 T OMENC (NIL) -8 NIL NIL) (-754 1883848 1885033 1886204 "OMDEV" 1888802 T OMDEV (NIL) -8 NIL NIL) (-753 1882917 1883088 1883282 "OMCONN" 1883674 T OMCONN (NIL) -8 NIL NIL) (-752 1881532 1882518 1882547 "OINTDOM" 1882552 T OINTDOM (NIL) -9 NIL 1882573) (-751 1877294 1878524 1879239 "OFMONOID" 1880849 NIL OFMONOID (NIL T) -8 NIL NIL) (-750 1876732 1877231 1877276 "ODVAR" 1877281 NIL ODVAR (NIL T) -8 NIL NIL) (-749 1873857 1876229 1876414 "ODR" 1876607 NIL ODR (NIL T T NIL) -8 NIL NIL) (-748 1866163 1873636 1873760 "ODPOL" 1873765 NIL ODPOL (NIL T) -8 NIL NIL) (-747 1859986 1866035 1866140 "ODP" 1866145 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-746 1858752 1858967 1859242 "ODETOOLS" 1859760 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-745 1855721 1856377 1857093 "ODESYS" 1858085 NIL ODESYS (NIL T T) -7 NIL NIL) (-744 1850625 1851533 1852556 "ODERTRIC" 1854796 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-743 1850051 1850133 1850327 "ODERED" 1850537 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-742 1846953 1847501 1848176 "ODERAT" 1849474 NIL ODERAT (NIL T T) -7 NIL NIL) (-741 1843921 1844385 1844981 "ODEPRRIC" 1846482 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-740 1841792 1842359 1842868 "ODEPROB" 1843432 T ODEPROB (NIL) -8 NIL NIL) (-739 1838324 1838807 1839453 "ODEPRIM" 1841271 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-738 1837577 1837679 1837937 "ODEPAL" 1838216 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-737 1833779 1834560 1835414 "ODEPACK" 1836743 T ODEPACK (NIL) -7 NIL NIL) (-736 1832816 1832923 1833151 "ODEINT" 1833668 NIL ODEINT (NIL T T) -7 NIL NIL) (-735 1826917 1828342 1829789 "ODEIFTBL" 1831389 T ODEIFTBL (NIL) -8 NIL NIL) (-734 1822261 1823047 1824005 "ODEEF" 1826076 NIL ODEEF (NIL T T) -7 NIL NIL) (-733 1821598 1821687 1821916 "ODECONST" 1822166 NIL ODECONST (NIL T T T) -7 NIL NIL) (-732 1819755 1820388 1820417 "ODECAT" 1821020 T ODECAT (NIL) -9 NIL 1821549) (-731 1816627 1819467 1819586 "OCT" 1819668 NIL OCT (NIL T) -8 NIL NIL) (-730 1816265 1816308 1816435 "OCTCT2" 1816578 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-729 1811098 1813536 1813577 "OC" 1814673 NIL OC (NIL T) -9 NIL 1815530) (-728 1808325 1809073 1810063 "OC-" 1810157 NIL OC- (NIL T T) -8 NIL NIL) (-727 1807703 1808145 1808174 "OCAMON" 1808179 T OCAMON (NIL) -9 NIL 1808200) (-726 1807156 1807563 1807592 "OASGP" 1807597 T OASGP (NIL) -9 NIL 1807617) (-725 1806443 1806906 1806935 "OAMONS" 1806975 T OAMONS (NIL) -9 NIL 1807018) (-724 1805883 1806290 1806319 "OAMON" 1806324 T OAMON (NIL) -9 NIL 1806344) (-723 1805187 1805679 1805708 "OAGROUP" 1805713 T OAGROUP (NIL) -9 NIL 1805733) (-722 1804877 1804927 1805015 "NUMTUBE" 1805131 NIL NUMTUBE (NIL T) -7 NIL NIL) (-721 1798450 1799968 1801504 "NUMQUAD" 1803361 T NUMQUAD (NIL) -7 NIL NIL) (-720 1794206 1795194 1796219 "NUMODE" 1797445 T NUMODE (NIL) -7 NIL NIL) (-719 1791621 1792463 1792492 "NUMINT" 1793405 T NUMINT (NIL) -9 NIL 1794157) (-718 1790569 1790766 1790984 "NUMFMT" 1791423 T NUMFMT (NIL) -7 NIL NIL) (-717 1776951 1779885 1782415 "NUMERIC" 1788078 NIL NUMERIC (NIL T) -7 NIL NIL) (-716 1771351 1776403 1776498 "NTSCAT" 1776503 NIL NTSCAT (NIL T T T T) -9 NIL 1776541) (-715 1770545 1770710 1770903 "NTPOLFN" 1771190 NIL NTPOLFN (NIL T) -7 NIL NIL) (-714 1758401 1767387 1768197 "NSUP" 1769767 NIL NSUP (NIL T) -8 NIL NIL) (-713 1758037 1758094 1758201 "NSUP2" 1758338 NIL NSUP2 (NIL T T) -7 NIL NIL) (-712 1747999 1757816 1757946 "NSMP" 1757951 NIL NSMP (NIL T T) -8 NIL NIL) (-711 1746431 1746732 1747089 "NREP" 1747687 NIL NREP (NIL T) -7 NIL NIL) (-710 1745022 1745274 1745632 "NPCOEF" 1746174 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-709 1744088 1744203 1744419 "NORMRETR" 1744903 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-708 1742141 1742431 1742838 "NORMPK" 1743796 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-707 1741826 1741854 1741978 "NORMMA" 1742107 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-706 1741653 1741783 1741812 "NONE" 1741817 T NONE (NIL) -8 NIL NIL) (-705 1741442 1741471 1741540 "NONE1" 1741617 NIL NONE1 (NIL T) -7 NIL NIL) (-704 1740927 1740989 1741174 "NODE1" 1741374 NIL NODE1 (NIL T T) -7 NIL NIL) (-703 1739220 1740090 1740345 "NNI" 1740692 T NNI (NIL) -8 NIL NIL) (-702 1737640 1737953 1738317 "NLINSOL" 1738888 NIL NLINSOL (NIL T) -7 NIL NIL) (-701 1733832 1734793 1735709 "NIPROB" 1736744 T NIPROB (NIL) -8 NIL NIL) (-700 1732589 1732823 1733125 "NFINTBAS" 1733594 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-699 1731297 1731528 1731809 "NCODIV" 1732357 NIL NCODIV (NIL T T) -7 NIL NIL) (-698 1731059 1731096 1731171 "NCNTFRAC" 1731254 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-697 1729239 1729603 1730023 "NCEP" 1730684 NIL NCEP (NIL T) -7 NIL NIL) (-696 1728150 1728889 1728918 "NASRING" 1729028 T NASRING (NIL) -9 NIL 1729102) (-695 1727945 1727989 1728083 "NASRING-" 1728088 NIL NASRING- (NIL T) -8 NIL NIL) (-694 1727098 1727597 1727626 "NARNG" 1727743 T NARNG (NIL) -9 NIL 1727834) (-693 1726790 1726857 1726991 "NARNG-" 1726996 NIL NARNG- (NIL T) -8 NIL NIL) (-692 1725669 1725876 1726111 "NAGSP" 1726575 T NAGSP (NIL) -7 NIL NIL) (-691 1717093 1718739 1720374 "NAGS" 1724054 T NAGS (NIL) -7 NIL NIL) (-690 1715657 1715961 1716288 "NAGF07" 1716786 T NAGF07 (NIL) -7 NIL NIL) (-689 1710239 1711519 1712815 "NAGF04" 1714381 T NAGF04 (NIL) -7 NIL NIL) (-688 1703271 1704869 1706486 "NAGF02" 1708642 T NAGF02 (NIL) -7 NIL NIL) (-687 1698535 1699625 1700732 "NAGF01" 1702184 T NAGF01 (NIL) -7 NIL NIL) (-686 1692195 1693753 1695330 "NAGE04" 1696978 T NAGE04 (NIL) -7 NIL NIL) (-685 1683436 1685539 1687651 "NAGE02" 1690103 T NAGE02 (NIL) -7 NIL NIL) (-684 1679429 1680366 1681320 "NAGE01" 1682502 T NAGE01 (NIL) -7 NIL NIL) (-683 1677236 1677767 1678322 "NAGD03" 1678894 T NAGD03 (NIL) -7 NIL NIL) (-682 1669022 1670941 1672886 "NAGD02" 1675311 T NAGD02 (NIL) -7 NIL NIL) (-681 1662881 1664294 1665722 "NAGD01" 1667614 T NAGD01 (NIL) -7 NIL NIL) (-680 1659138 1659948 1660773 "NAGC06" 1662076 T NAGC06 (NIL) -7 NIL NIL) (-679 1657615 1657944 1658297 "NAGC05" 1658805 T NAGC05 (NIL) -7 NIL NIL) (-678 1656999 1657116 1657258 "NAGC02" 1657493 T NAGC02 (NIL) -7 NIL NIL) (-677 1656060 1656617 1656658 "NAALG" 1656737 NIL NAALG (NIL T) -9 NIL 1656798) (-676 1655895 1655924 1656014 "NAALG-" 1656019 NIL NAALG- (NIL T T) -8 NIL NIL) (-675 1649845 1650953 1652140 "MULTSQFR" 1654791 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-674 1649164 1649239 1649423 "MULTFACT" 1649757 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-673 1642357 1646268 1646321 "MTSCAT" 1647381 NIL MTSCAT (NIL T T) -9 NIL 1647895) (-672 1642069 1642123 1642215 "MTHING" 1642297 NIL MTHING (NIL T) -7 NIL NIL) (-671 1641861 1641894 1641954 "MSYSCMD" 1642029 T MSYSCMD (NIL) -7 NIL NIL) (-670 1637973 1640616 1640936 "MSET" 1641574 NIL MSET (NIL T) -8 NIL NIL) (-669 1635068 1637534 1637576 "MSETAGG" 1637581 NIL MSETAGG (NIL T) -9 NIL 1637615) (-668 1630924 1632466 1633207 "MRING" 1634371 NIL MRING (NIL T T) -8 NIL NIL) (-667 1630494 1630561 1630690 "MRF2" 1630851 NIL MRF2 (NIL T T T) -7 NIL NIL) (-666 1630112 1630147 1630291 "MRATFAC" 1630453 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-665 1627724 1628019 1628450 "MPRFF" 1629817 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-664 1621744 1627579 1627675 "MPOLY" 1627680 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-663 1621234 1621269 1621477 "MPCPF" 1621703 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-662 1620750 1620793 1620976 "MPC3" 1621185 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-661 1619951 1620032 1620251 "MPC2" 1620665 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-660 1618252 1618589 1618979 "MONOTOOL" 1619611 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-659 1617376 1617711 1617740 "MONOID" 1618017 T MONOID (NIL) -9 NIL 1618189) (-658 1616754 1616917 1617160 "MONOID-" 1617165 NIL MONOID- (NIL T) -8 NIL NIL) (-657 1607734 1613720 1613780 "MONOGEN" 1614454 NIL MONOGEN (NIL T T) -9 NIL 1614910) (-656 1604952 1605687 1606687 "MONOGEN-" 1606806 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-655 1603811 1604231 1604260 "MONADWU" 1604652 T MONADWU (NIL) -9 NIL 1604890) (-654 1603183 1603342 1603590 "MONADWU-" 1603595 NIL MONADWU- (NIL T) -8 NIL NIL) (-653 1602568 1602786 1602815 "MONAD" 1603022 T MONAD (NIL) -9 NIL 1603134) (-652 1602253 1602331 1602463 "MONAD-" 1602468 NIL MONAD- (NIL T) -8 NIL NIL) (-651 1600504 1601166 1601445 "MOEBIUS" 1602006 NIL MOEBIUS (NIL T) -8 NIL NIL) (-650 1599897 1600275 1600316 "MODULE" 1600321 NIL MODULE (NIL T) -9 NIL 1600347) (-649 1599465 1599561 1599751 "MODULE-" 1599756 NIL MODULE- (NIL T T) -8 NIL NIL) (-648 1597136 1597831 1598157 "MODRING" 1599290 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-647 1594092 1595257 1595774 "MODOP" 1596668 NIL MODOP (NIL T T) -8 NIL NIL) (-646 1592279 1592731 1593072 "MODMONOM" 1593891 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-645 1581997 1590483 1590905 "MODMON" 1591907 NIL MODMON (NIL T T) -8 NIL NIL) (-644 1579123 1580841 1581117 "MODFIELD" 1581872 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-643 1578649 1578692 1578871 "MMAP" 1579074 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-642 1576885 1577662 1577703 "MLO" 1578120 NIL MLO (NIL T) -9 NIL 1578361) (-641 1574252 1574767 1575369 "MLIFT" 1576366 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-640 1573643 1573727 1573881 "MKUCFUNC" 1574163 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-639 1573242 1573312 1573435 "MKRECORD" 1573566 NIL MKRECORD (NIL T T) -7 NIL NIL) (-638 1572290 1572451 1572679 "MKFUNC" 1573053 NIL MKFUNC (NIL T) -7 NIL NIL) (-637 1571678 1571782 1571938 "MKFLCFN" 1572173 NIL MKFLCFN (NIL T) -7 NIL NIL) (-636 1571104 1571471 1571560 "MKCHSET" 1571622 NIL MKCHSET (NIL T) -8 NIL NIL) (-635 1570381 1570483 1570668 "MKBCFUNC" 1570997 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-634 1567065 1569935 1570071 "MINT" 1570265 T MINT (NIL) -8 NIL NIL) (-633 1565877 1566120 1566397 "MHROWRED" 1566820 NIL MHROWRED (NIL T) -7 NIL NIL) (-632 1561148 1564322 1564746 "MFLOAT" 1565473 T MFLOAT (NIL) -8 NIL NIL) (-631 1560505 1560581 1560752 "MFINFACT" 1561060 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-630 1556852 1557691 1558566 "MESH" 1559650 T MESH (NIL) -7 NIL NIL) (-629 1555242 1555554 1555907 "MDDFACT" 1556539 NIL MDDFACT (NIL T) -7 NIL NIL) (-628 1552084 1554401 1554443 "MDAGG" 1554698 NIL MDAGG (NIL T) -9 NIL 1554841) (-627 1541782 1551377 1551584 "MCMPLX" 1551897 T MCMPLX (NIL) -8 NIL NIL) (-626 1540923 1541069 1541269 "MCDEN" 1541631 NIL MCDEN (NIL T T) -7 NIL NIL) (-625 1538813 1539083 1539463 "MCALCFN" 1540653 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-624 1536435 1536958 1537519 "MATSTOR" 1538284 NIL MATSTOR (NIL T) -7 NIL NIL) (-623 1532443 1535810 1536057 "MATRIX" 1536220 NIL MATRIX (NIL T) -8 NIL NIL) (-622 1528213 1528916 1529652 "MATLIN" 1531800 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-621 1518410 1521548 1521625 "MATCAT" 1526463 NIL MATCAT (NIL T T T) -9 NIL 1527880) (-620 1514775 1515788 1517143 "MATCAT-" 1517148 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-619 1513377 1513530 1513861 "MATCAT2" 1514610 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-618 1511489 1511813 1512197 "MAPPKG3" 1513052 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-617 1510470 1510643 1510865 "MAPPKG2" 1511313 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-616 1508969 1509253 1509580 "MAPPKG1" 1510176 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-615 1508580 1508638 1508761 "MAPHACK3" 1508905 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-614 1508172 1508233 1508347 "MAPHACK2" 1508512 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-613 1507610 1507713 1507855 "MAPHACK1" 1508063 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-612 1505718 1506312 1506615 "MAGMA" 1507339 NIL MAGMA (NIL T) -8 NIL NIL) (-611 1502192 1503962 1504422 "M3D" 1505291 NIL M3D (NIL T) -8 NIL NIL) (-610 1496347 1500562 1500604 "LZSTAGG" 1501386 NIL LZSTAGG (NIL T) -9 NIL 1501681) (-609 1492320 1493478 1494935 "LZSTAGG-" 1494940 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-608 1489436 1490213 1490699 "LWORD" 1491866 NIL LWORD (NIL T) -8 NIL NIL) (-607 1482596 1489207 1489341 "LSQM" 1489346 NIL LSQM (NIL NIL T) -8 NIL NIL) (-606 1481820 1481959 1482187 "LSPP" 1482451 NIL LSPP (NIL T T T T) -7 NIL NIL) (-605 1479632 1479933 1480389 "LSMP" 1481509 NIL LSMP (NIL T T T T) -7 NIL NIL) (-604 1476411 1477085 1477815 "LSMP1" 1478934 NIL LSMP1 (NIL T) -7 NIL NIL) (-603 1470337 1475579 1475621 "LSAGG" 1475683 NIL LSAGG (NIL T) -9 NIL 1475761) (-602 1467032 1467956 1469169 "LSAGG-" 1469174 NIL LSAGG- (NIL T T) -8 NIL NIL) (-601 1464658 1466176 1466425 "LPOLY" 1466827 NIL LPOLY (NIL T T) -8 NIL NIL) (-600 1464240 1464325 1464448 "LPEFRAC" 1464567 NIL LPEFRAC (NIL T) -7 NIL NIL) (-599 1462587 1463334 1463587 "LO" 1464072 NIL LO (NIL T T T) -8 NIL NIL) (-598 1462240 1462352 1462381 "LOGIC" 1462492 T LOGIC (NIL) -9 NIL 1462572) (-597 1462102 1462125 1462196 "LOGIC-" 1462201 NIL LOGIC- (NIL T) -8 NIL NIL) (-596 1461295 1461435 1461628 "LODOOPS" 1461958 NIL LODOOPS (NIL T T) -7 NIL NIL) (-595 1458713 1461212 1461277 "LODO" 1461282 NIL LODO (NIL T NIL) -8 NIL NIL) (-594 1457259 1457494 1457845 "LODOF" 1458460 NIL LODOF (NIL T T) -7 NIL NIL) (-593 1453678 1456114 1456155 "LODOCAT" 1456587 NIL LODOCAT (NIL T) -9 NIL 1456798) (-592 1453412 1453470 1453596 "LODOCAT-" 1453601 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-591 1450726 1453253 1453371 "LODO2" 1453376 NIL LODO2 (NIL T T) -8 NIL NIL) (-590 1448155 1450663 1450708 "LODO1" 1450713 NIL LODO1 (NIL T) -8 NIL NIL) (-589 1447018 1447183 1447494 "LODEEF" 1447978 NIL LODEEF (NIL T T T) -7 NIL NIL) (-588 1442304 1445148 1445190 "LNAGG" 1446137 NIL LNAGG (NIL T) -9 NIL 1446581) (-587 1441451 1441665 1442007 "LNAGG-" 1442012 NIL LNAGG- (NIL T T) -8 NIL NIL) (-586 1437616 1438378 1439016 "LMOPS" 1440867 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-585 1437013 1437375 1437416 "LMODULE" 1437476 NIL LMODULE (NIL T) -9 NIL 1437518) (-584 1434259 1436658 1436781 "LMDICT" 1436923 NIL LMDICT (NIL T) -8 NIL NIL) (-583 1427486 1433205 1433503 "LIST" 1433994 NIL LIST (NIL T) -8 NIL NIL) (-582 1427011 1427085 1427224 "LIST3" 1427406 NIL LIST3 (NIL T T T) -7 NIL NIL) (-581 1426018 1426196 1426424 "LIST2" 1426829 NIL LIST2 (NIL T T) -7 NIL NIL) (-580 1424152 1424464 1424863 "LIST2MAP" 1425665 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-579 1422864 1423544 1423585 "LINEXP" 1423838 NIL LINEXP (NIL T) -9 NIL 1423986) (-578 1421511 1421771 1422068 "LINDEP" 1422616 NIL LINDEP (NIL T T) -7 NIL NIL) (-577 1418278 1418997 1419774 "LIMITRF" 1420766 NIL LIMITRF (NIL T) -7 NIL NIL) (-576 1416558 1416853 1417268 "LIMITPS" 1417973 NIL LIMITPS (NIL T T) -7 NIL NIL) (-575 1411013 1416069 1416297 "LIE" 1416379 NIL LIE (NIL T T) -8 NIL NIL) (-574 1410063 1410506 1410547 "LIECAT" 1410687 NIL LIECAT (NIL T) -9 NIL 1410838) (-573 1409904 1409931 1410019 "LIECAT-" 1410024 NIL LIECAT- (NIL T T) -8 NIL NIL) (-572 1402516 1409353 1409518 "LIB" 1409759 T LIB (NIL) -8 NIL NIL) (-571 1398153 1399034 1399969 "LGROBP" 1401633 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-570 1396023 1396296 1396657 "LF" 1397875 NIL LF (NIL T T) -7 NIL NIL) (-569 1394863 1395554 1395583 "LFCAT" 1395790 T LFCAT (NIL) -9 NIL 1395929) (-568 1391775 1392401 1393087 "LEXTRIPK" 1394229 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-567 1388481 1389345 1389848 "LEXP" 1391355 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-566 1386879 1387192 1387593 "LEADCDET" 1388163 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-565 1386075 1386149 1386376 "LAZM3PK" 1386800 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-564 1380991 1384154 1384691 "LAUPOL" 1385588 NIL LAUPOL (NIL T T) -8 NIL NIL) (-563 1380558 1380602 1380769 "LAPLACE" 1380941 NIL LAPLACE (NIL T T) -7 NIL NIL) (-562 1378486 1379659 1379910 "LA" 1380391 NIL LA (NIL T T T) -8 NIL NIL) (-561 1377548 1378142 1378183 "LALG" 1378244 NIL LALG (NIL T) -9 NIL 1378302) (-560 1377263 1377322 1377457 "LALG-" 1377462 NIL LALG- (NIL T T) -8 NIL NIL) (-559 1376173 1376360 1376657 "KOVACIC" 1377063 NIL KOVACIC (NIL T T) -7 NIL NIL) (-558 1376007 1376031 1376073 "KONVERT" 1376135 NIL KONVERT (NIL T) -9 NIL NIL) (-557 1375841 1375865 1375907 "KOERCE" 1375969 NIL KOERCE (NIL T) -9 NIL NIL) (-556 1373575 1374335 1374728 "KERNEL" 1375480 NIL KERNEL (NIL T) -8 NIL NIL) (-555 1373077 1373158 1373288 "KERNEL2" 1373489 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-554 1366928 1371616 1371671 "KDAGG" 1372048 NIL KDAGG (NIL T T) -9 NIL 1372254) (-553 1366457 1366581 1366786 "KDAGG-" 1366791 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-552 1359632 1366118 1366273 "KAFILE" 1366335 NIL KAFILE (NIL T) -8 NIL NIL) (-551 1354087 1359143 1359371 "JORDAN" 1359453 NIL JORDAN (NIL T T) -8 NIL NIL) (-550 1350386 1352292 1352347 "IXAGG" 1353276 NIL IXAGG (NIL T T) -9 NIL 1353735) (-549 1349305 1349611 1350030 "IXAGG-" 1350035 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-548 1344890 1349227 1349286 "IVECTOR" 1349291 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-547 1343656 1343893 1344159 "ITUPLE" 1344657 NIL ITUPLE (NIL T) -8 NIL NIL) (-546 1342092 1342269 1342575 "ITRIGMNP" 1343478 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-545 1340837 1341041 1341324 "ITFUN3" 1341868 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-544 1340469 1340526 1340635 "ITFUN2" 1340774 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-543 1338271 1339342 1339639 "ITAYLOR" 1340204 NIL ITAYLOR (NIL T) -8 NIL NIL) (-542 1327262 1332457 1333616 "ISUPS" 1337144 NIL ISUPS (NIL T) -8 NIL NIL) (-541 1326370 1326509 1326744 "ISUMP" 1327110 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-540 1321634 1326171 1326250 "ISTRING" 1326323 NIL ISTRING (NIL NIL) -8 NIL NIL) (-539 1320847 1320928 1321143 "IRURPK" 1321548 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-538 1319783 1319984 1320224 "IRSN" 1320627 T IRSN (NIL) -7 NIL NIL) (-537 1317818 1318173 1318608 "IRRF2F" 1319421 NIL IRRF2F (NIL T) -7 NIL NIL) (-536 1317565 1317603 1317679 "IRREDFFX" 1317774 NIL IRREDFFX (NIL T) -7 NIL NIL) (-535 1316180 1316439 1316738 "IROOT" 1317298 NIL IROOT (NIL T) -7 NIL NIL) (-534 1312818 1313869 1314559 "IR" 1315522 NIL IR (NIL T) -8 NIL NIL) (-533 1310431 1310926 1311492 "IR2" 1312296 NIL IR2 (NIL T T) -7 NIL NIL) (-532 1309507 1309620 1309840 "IR2F" 1310314 NIL IR2F (NIL T T) -7 NIL NIL) (-531 1309298 1309332 1309392 "IPRNTPK" 1309467 T IPRNTPK (NIL) -7 NIL NIL) (-530 1305852 1309187 1309256 "IPF" 1309261 NIL IPF (NIL NIL) -8 NIL NIL) (-529 1304169 1305777 1305834 "IPADIC" 1305839 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-528 1303668 1303726 1303915 "INVLAPLA" 1304105 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-527 1293317 1295670 1298056 "INTTR" 1301332 NIL INTTR (NIL T T) -7 NIL NIL) (-526 1289665 1290406 1291269 "INTTOOLS" 1292503 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-525 1289251 1289342 1289459 "INTSLPE" 1289568 T INTSLPE (NIL) -7 NIL NIL) (-524 1287201 1289174 1289233 "INTRVL" 1289238 NIL INTRVL (NIL T) -8 NIL NIL) (-523 1284808 1285320 1285894 "INTRF" 1286686 NIL INTRF (NIL T) -7 NIL NIL) (-522 1284223 1284320 1284461 "INTRET" 1284706 NIL INTRET (NIL T) -7 NIL NIL) (-521 1282225 1282614 1283083 "INTRAT" 1283831 NIL INTRAT (NIL T T) -7 NIL NIL) (-520 1279458 1280041 1280666 "INTPM" 1281710 NIL INTPM (NIL T T) -7 NIL NIL) (-519 1276167 1276766 1277510 "INTPAF" 1278844 NIL INTPAF (NIL T T T) -7 NIL NIL) (-518 1271450 1272386 1273411 "INTPACK" 1275162 T INTPACK (NIL) -7 NIL NIL) (-517 1268304 1271179 1271306 "INT" 1271343 T INT (NIL) -8 NIL NIL) (-516 1267556 1267708 1267916 "INTHERTR" 1268146 NIL INTHERTR (NIL T T) -7 NIL NIL) (-515 1266995 1267075 1267263 "INTHERAL" 1267470 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-514 1264841 1265284 1265741 "INTHEORY" 1266558 T INTHEORY (NIL) -7 NIL NIL) (-513 1256164 1257784 1259562 "INTG0" 1263193 NIL INTG0 (NIL T T T) -7 NIL NIL) (-512 1236761 1241545 1246349 "INTFTBL" 1251380 T INTFTBL (NIL) -8 NIL NIL) (-511 1236010 1236148 1236321 "INTFACT" 1236620 NIL INTFACT (NIL T) -7 NIL NIL) (-510 1233401 1233847 1234410 "INTEF" 1235564 NIL INTEF (NIL T T) -7 NIL NIL) (-509 1231862 1232611 1232640 "INTDOM" 1232941 T INTDOM (NIL) -9 NIL 1233148) (-508 1231231 1231405 1231647 "INTDOM-" 1231652 NIL INTDOM- (NIL T) -8 NIL NIL) (-507 1227723 1229655 1229710 "INTCAT" 1230509 NIL INTCAT (NIL T) -9 NIL 1230828) (-506 1227196 1227298 1227426 "INTBIT" 1227615 T INTBIT (NIL) -7 NIL NIL) (-505 1225871 1226025 1226338 "INTALG" 1227041 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-504 1225328 1225418 1225588 "INTAF" 1225775 NIL INTAF (NIL T T) -7 NIL NIL) (-503 1218782 1225138 1225278 "INTABL" 1225283 NIL INTABL (NIL T T T) -8 NIL NIL) (-502 1213732 1216461 1216490 "INS" 1217458 T INS (NIL) -9 NIL 1218139) (-501 1210972 1211743 1212717 "INS-" 1212790 NIL INS- (NIL T) -8 NIL NIL) (-500 1209751 1209978 1210275 "INPSIGN" 1210725 NIL INPSIGN (NIL T T) -7 NIL NIL) (-499 1208869 1208986 1209183 "INPRODPF" 1209631 NIL INPRODPF (NIL T T) -7 NIL NIL) (-498 1207763 1207880 1208117 "INPRODFF" 1208749 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-497 1206763 1206915 1207175 "INNMFACT" 1207599 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-496 1205960 1206057 1206245 "INMODGCD" 1206662 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-495 1204469 1204713 1205037 "INFSP" 1205705 NIL INFSP (NIL T T T) -7 NIL NIL) (-494 1203653 1203770 1203953 "INFPROD0" 1204349 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-493 1200663 1201822 1202313 "INFORM" 1203170 T INFORM (NIL) -8 NIL NIL) (-492 1200273 1200333 1200431 "INFORM1" 1200598 NIL INFORM1 (NIL T) -7 NIL NIL) (-491 1199796 1199885 1199999 "INFINITY" 1200179 T INFINITY (NIL) -7 NIL NIL) (-490 1198414 1198662 1198983 "INEP" 1199544 NIL INEP (NIL T T T) -7 NIL NIL) (-489 1197690 1198311 1198376 "INDE" 1198381 NIL INDE (NIL T) -8 NIL NIL) (-488 1197254 1197322 1197439 "INCRMAPS" 1197617 NIL INCRMAPS (NIL T) -7 NIL NIL) (-487 1192565 1193490 1194434 "INBFF" 1196342 NIL INBFF (NIL T) -7 NIL NIL) (-486 1189060 1192410 1192513 "IMATRIX" 1192518 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-485 1187772 1187895 1188210 "IMATQF" 1188916 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-484 1185992 1186219 1186556 "IMATLIN" 1187528 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-483 1180618 1185916 1185974 "ILIST" 1185979 NIL ILIST (NIL T NIL) -8 NIL NIL) (-482 1178571 1180478 1180591 "IIARRAY2" 1180596 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-481 1173939 1178482 1178546 "IFF" 1178551 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-480 1168982 1173231 1173419 "IFARRAY" 1173796 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-479 1168189 1168886 1168959 "IFAMON" 1168964 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-478 1167772 1167837 1167892 "IEVALAB" 1168099 NIL IEVALAB (NIL T T) -9 NIL NIL) (-477 1167447 1167515 1167675 "IEVALAB-" 1167680 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-476 1167105 1167361 1167424 "IDPO" 1167429 NIL IDPO (NIL T T) -8 NIL NIL) (-475 1166382 1166994 1167069 "IDPOAMS" 1167074 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-474 1165716 1166271 1166346 "IDPOAM" 1166351 NIL IDPOAM (NIL T T) -8 NIL NIL) (-473 1164801 1165051 1165105 "IDPC" 1165518 NIL IDPC (NIL T T) -9 NIL 1165667) (-472 1164297 1164693 1164766 "IDPAM" 1164771 NIL IDPAM (NIL T T) -8 NIL NIL) (-471 1163700 1164189 1164262 "IDPAG" 1164267 NIL IDPAG (NIL T T) -8 NIL NIL) (-470 1159955 1160803 1161698 "IDECOMP" 1162857 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-469 1152829 1153878 1154925 "IDEAL" 1158991 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-468 1151993 1152105 1152304 "ICDEN" 1152713 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-467 1151092 1151473 1151620 "ICARD" 1151866 T ICARD (NIL) -8 NIL NIL) (-466 1149164 1149477 1149880 "IBPTOOLS" 1150769 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-465 1144778 1148784 1148897 "IBITS" 1149083 NIL IBITS (NIL NIL) -8 NIL NIL) (-464 1141501 1142077 1142772 "IBATOOL" 1144195 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-463 1139281 1139742 1140275 "IBACHIN" 1141036 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-462 1137158 1139127 1139230 "IARRAY2" 1139235 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-461 1133311 1137084 1137141 "IARRAY1" 1137146 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-460 1127250 1131729 1132207 "IAN" 1132853 T IAN (NIL) -8 NIL NIL) (-459 1126761 1126818 1126991 "IALGFACT" 1127187 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-458 1126288 1126401 1126430 "HYPCAT" 1126637 T HYPCAT (NIL) -9 NIL NIL) (-457 1125826 1125943 1126129 "HYPCAT-" 1126134 NIL HYPCAT- (NIL T) -8 NIL NIL) (-456 1122505 1123836 1123878 "HOAGG" 1124859 NIL HOAGG (NIL T) -9 NIL 1125538) (-455 1121099 1121498 1122024 "HOAGG-" 1122029 NIL HOAGG- (NIL T T) -8 NIL NIL) (-454 1114930 1120540 1120706 "HEXADEC" 1120953 T HEXADEC (NIL) -8 NIL NIL) (-453 1113678 1113900 1114163 "HEUGCD" 1114707 NIL HEUGCD (NIL T) -7 NIL NIL) (-452 1112781 1113515 1113645 "HELLFDIV" 1113650 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-451 1111009 1112558 1112646 "HEAP" 1112725 NIL HEAP (NIL T) -8 NIL NIL) (-450 1104876 1110924 1110986 "HDP" 1110991 NIL HDP (NIL NIL T) -8 NIL NIL) (-449 1098588 1104513 1104664 "HDMP" 1104777 NIL HDMP (NIL NIL T) -8 NIL NIL) (-448 1097913 1098052 1098216 "HB" 1098444 T HB (NIL) -7 NIL NIL) (-447 1091410 1097759 1097863 "HASHTBL" 1097868 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-446 1089163 1091038 1091217 "HACKPI" 1091251 T HACKPI (NIL) -8 NIL NIL) (-445 1084859 1089017 1089129 "GTSET" 1089134 NIL GTSET (NIL T T T T) -8 NIL NIL) (-444 1078385 1084737 1084835 "GSTBL" 1084840 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-443 1070621 1077421 1077685 "GSERIES" 1078176 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-442 1069643 1070096 1070125 "GROUP" 1070386 T GROUP (NIL) -9 NIL 1070545) (-441 1068759 1068982 1069326 "GROUP-" 1069331 NIL GROUP- (NIL T) -8 NIL NIL) (-440 1067128 1067447 1067834 "GROEBSOL" 1068436 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-439 1066068 1066330 1066382 "GRMOD" 1066911 NIL GRMOD (NIL T T) -9 NIL 1067079) (-438 1065836 1065872 1066000 "GRMOD-" 1066005 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-437 1061175 1062198 1063195 "GRIMAGE" 1064859 T GRIMAGE (NIL) -8 NIL NIL) (-436 1059642 1059902 1060226 "GRDEF" 1060871 T GRDEF (NIL) -7 NIL NIL) (-435 1059086 1059202 1059343 "GRAY" 1059521 T GRAY (NIL) -7 NIL NIL) (-434 1058319 1058699 1058751 "GRALG" 1058904 NIL GRALG (NIL T T) -9 NIL 1058996) (-433 1057980 1058053 1058216 "GRALG-" 1058221 NIL GRALG- (NIL T T T) -8 NIL NIL) (-432 1054788 1057569 1057745 "GPOLSET" 1057887 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-431 1054144 1054201 1054458 "GOSPER" 1054725 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-430 1049903 1050582 1051108 "GMODPOL" 1053843 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-429 1048908 1049092 1049330 "GHENSEL" 1049715 NIL GHENSEL (NIL T T) -7 NIL NIL) (-428 1042974 1043817 1044843 "GENUPS" 1047992 NIL GENUPS (NIL T T) -7 NIL NIL) (-427 1042671 1042722 1042811 "GENUFACT" 1042917 NIL GENUFACT (NIL T) -7 NIL NIL) (-426 1042083 1042160 1042325 "GENPGCD" 1042589 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-425 1041557 1041592 1041805 "GENMFACT" 1042042 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-424 1040125 1040380 1040687 "GENEEZ" 1041300 NIL GENEEZ (NIL T T) -7 NIL NIL) (-423 1033999 1039738 1039899 "GDMP" 1040048 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-422 1023381 1027770 1028876 "GCNAALG" 1032982 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-421 1021802 1022674 1022703 "GCDDOM" 1022958 T GCDDOM (NIL) -9 NIL 1023115) (-420 1021272 1021399 1021614 "GCDDOM-" 1021619 NIL GCDDOM- (NIL T) -8 NIL NIL) (-419 1019944 1020129 1020433 "GB" 1021051 NIL GB (NIL T T T T) -7 NIL NIL) (-418 1008564 1010890 1013282 "GBINTERN" 1017635 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-417 1006401 1006693 1007114 "GBF" 1008239 NIL GBF (NIL T T T T) -7 NIL NIL) (-416 1005182 1005347 1005614 "GBEUCLID" 1006217 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-415 1004531 1004656 1004805 "GAUSSFAC" 1005053 T GAUSSFAC (NIL) -7 NIL NIL) (-414 1002908 1003210 1003523 "GALUTIL" 1004250 NIL GALUTIL (NIL T) -7 NIL NIL) (-413 1001225 1001499 1001822 "GALPOLYU" 1002635 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-412 998614 998904 999309 "GALFACTU" 1000922 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-411 990420 991919 993527 "GALFACT" 997046 NIL GALFACT (NIL T) -7 NIL NIL) (-410 987807 988465 988494 "FVFUN" 989650 T FVFUN (NIL) -9 NIL 990370) (-409 987072 987254 987283 "FVC" 987574 T FVC (NIL) -9 NIL 987757) (-408 986714 986869 986950 "FUNCTION" 987024 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-407 984384 984935 985424 "FT" 986245 T FT (NIL) -8 NIL NIL) (-406 983202 983685 983888 "FTEM" 984201 T FTEM (NIL) -8 NIL NIL) (-405 981467 981755 982157 "FSUPFACT" 982894 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-404 979864 980153 980485 "FST" 981155 T FST (NIL) -8 NIL NIL) (-403 979039 979145 979339 "FSRED" 979746 NIL FSRED (NIL T T) -7 NIL NIL) (-402 977718 977973 978327 "FSPRMELT" 978754 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-401 974803 975241 975740 "FSPECF" 977281 NIL FSPECF (NIL T T) -7 NIL NIL) (-400 957176 965733 965774 "FS" 969612 NIL FS (NIL T) -9 NIL 971894) (-399 945826 948816 952872 "FS-" 953169 NIL FS- (NIL T T) -8 NIL NIL) (-398 945342 945396 945572 "FSINT" 945767 NIL FSINT (NIL T T) -7 NIL NIL) (-397 943623 944335 944638 "FSERIES" 945121 NIL FSERIES (NIL T T) -8 NIL NIL) (-396 942641 942757 942987 "FSCINT" 943503 NIL FSCINT (NIL T T) -7 NIL NIL) (-395 938875 941585 941627 "FSAGG" 941997 NIL FSAGG (NIL T) -9 NIL 942256) (-394 936637 937238 938034 "FSAGG-" 938129 NIL FSAGG- (NIL T T) -8 NIL NIL) (-393 935679 935822 936049 "FSAGG2" 936490 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-392 933338 933617 934170 "FS2UPS" 935397 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-391 932924 932967 933120 "FS2" 933289 NIL FS2 (NIL T T T T) -7 NIL NIL) (-390 931784 931955 932263 "FS2EXPXP" 932749 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-389 931210 931325 931477 "FRUTIL" 931664 NIL FRUTIL (NIL T) -7 NIL NIL) (-388 922631 926709 928065 "FR" 929886 NIL FR (NIL T) -8 NIL NIL) (-387 917707 920350 920391 "FRNAALG" 921787 NIL FRNAALG (NIL T) -9 NIL 922394) (-386 913386 914456 915731 "FRNAALG-" 916481 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-385 913024 913067 913194 "FRNAAF2" 913337 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-384 911389 911881 912175 "FRMOD" 912837 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-383 909112 909780 910096 "FRIDEAL" 911180 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-382 908311 908398 908685 "FRIDEAL2" 909019 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-381 907568 907976 908018 "FRETRCT" 908023 NIL FRETRCT (NIL T) -9 NIL 908194) (-380 906680 906911 907262 "FRETRCT-" 907267 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-379 903889 905109 905169 "FRAMALG" 906051 NIL FRAMALG (NIL T T) -9 NIL 906343) (-378 902022 902478 903108 "FRAMALG-" 903331 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-377 895924 901497 901773 "FRAC" 901778 NIL FRAC (NIL T) -8 NIL NIL) (-376 895560 895617 895724 "FRAC2" 895861 NIL FRAC2 (NIL T T) -7 NIL NIL) (-375 895196 895253 895360 "FR2" 895497 NIL FR2 (NIL T T) -7 NIL NIL) (-374 889869 892782 892811 "FPS" 893930 T FPS (NIL) -9 NIL 894486) (-373 889318 889427 889591 "FPS-" 889737 NIL FPS- (NIL T) -8 NIL NIL) (-372 886766 888463 888492 "FPC" 888717 T FPC (NIL) -9 NIL 888859) (-371 886559 886599 886696 "FPC-" 886701 NIL FPC- (NIL T) -8 NIL NIL) (-370 885437 886047 886089 "FPATMAB" 886094 NIL FPATMAB (NIL T) -9 NIL 886246) (-369 883137 883613 884039 "FPARFRAC" 885074 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-368 878532 879029 879711 "FORTRAN" 882569 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-367 876248 876748 877287 "FORT" 878013 T FORT (NIL) -7 NIL NIL) (-366 873923 874485 874514 "FORTFN" 875574 T FORTFN (NIL) -9 NIL 876198) (-365 873686 873736 873765 "FORTCAT" 873824 T FORTCAT (NIL) -9 NIL 873886) (-364 871746 872229 872628 "FORMULA" 873307 T FORMULA (NIL) -8 NIL NIL) (-363 871534 871564 871633 "FORMULA1" 871710 NIL FORMULA1 (NIL T) -7 NIL NIL) (-362 871057 871109 871282 "FORDER" 871476 NIL FORDER (NIL T T T T) -7 NIL NIL) (-361 870153 870317 870510 "FOP" 870884 T FOP (NIL) -7 NIL NIL) (-360 868761 869433 869607 "FNLA" 870035 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-359 867429 867818 867847 "FNCAT" 868419 T FNCAT (NIL) -9 NIL 868712) (-358 866995 867388 867416 "FNAME" 867421 T FNAME (NIL) -8 NIL NIL) (-357 865654 866627 866656 "FMTC" 866661 T FMTC (NIL) -9 NIL 866696) (-356 861972 863179 863807 "FMONOID" 865059 NIL FMONOID (NIL T) -8 NIL NIL) (-355 861192 861715 861863 "FM" 861868 NIL FM (NIL T T) -8 NIL NIL) (-354 858615 859261 859290 "FMFUN" 860434 T FMFUN (NIL) -9 NIL 861142) (-353 857883 858064 858093 "FMC" 858383 T FMC (NIL) -9 NIL 858565) (-352 855112 855946 856000 "FMCAT" 857182 NIL FMCAT (NIL T T) -9 NIL 857676) (-351 854007 854880 854979 "FM1" 855057 NIL FM1 (NIL T T) -8 NIL NIL) (-350 851781 852197 852691 "FLOATRP" 853558 NIL FLOATRP (NIL T) -7 NIL NIL) (-349 845267 849437 850067 "FLOAT" 851171 T FLOAT (NIL) -8 NIL NIL) (-348 842705 843205 843783 "FLOATCP" 844734 NIL FLOATCP (NIL T) -7 NIL NIL) (-347 841493 842341 842382 "FLINEXP" 842387 NIL FLINEXP (NIL T) -9 NIL 842480) (-346 840648 840883 841210 "FLINEXP-" 841215 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-345 839724 839868 840092 "FLASORT" 840500 NIL FLASORT (NIL T T) -7 NIL NIL) (-344 836942 837784 837837 "FLALG" 839064 NIL FLALG (NIL T T) -9 NIL 839531) (-343 830726 834428 834470 "FLAGG" 835732 NIL FLAGG (NIL T) -9 NIL 836384) (-342 829452 829791 830281 "FLAGG-" 830286 NIL FLAGG- (NIL T T) -8 NIL NIL) (-341 828494 828637 828864 "FLAGG2" 829305 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-340 825466 826484 826544 "FINRALG" 827672 NIL FINRALG (NIL T T) -9 NIL 828180) (-339 824626 824855 825194 "FINRALG-" 825199 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-338 824032 824245 824274 "FINITE" 824470 T FINITE (NIL) -9 NIL 824577) (-337 816491 818652 818693 "FINAALG" 822360 NIL FINAALG (NIL T) -9 NIL 823813) (-336 811832 812873 814017 "FINAALG-" 815396 NIL FINAALG- (NIL T T) -8 NIL NIL) (-335 811227 811587 811690 "FILE" 811762 NIL FILE (NIL T) -8 NIL NIL) (-334 809911 810223 810278 "FILECAT" 810962 NIL FILECAT (NIL T T) -9 NIL 811178) (-333 807773 809329 809358 "FIELD" 809398 T FIELD (NIL) -9 NIL 809478) (-332 806393 806778 807289 "FIELD-" 807294 NIL FIELD- (NIL T) -8 NIL NIL) (-331 804208 805030 805376 "FGROUP" 806080 NIL FGROUP (NIL T) -8 NIL NIL) (-330 803298 803462 803682 "FGLMICPK" 804040 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-329 799100 803223 803280 "FFX" 803285 NIL FFX (NIL T NIL) -8 NIL NIL) (-328 798701 798762 798897 "FFSLPE" 799033 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-327 794696 795473 796269 "FFPOLY" 797937 NIL FFPOLY (NIL T) -7 NIL NIL) (-326 794200 794236 794445 "FFPOLY2" 794654 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-325 790022 794119 794182 "FFP" 794187 NIL FFP (NIL T NIL) -8 NIL NIL) (-324 785390 789933 789997 "FF" 790002 NIL FF (NIL NIL NIL) -8 NIL NIL) (-323 780486 784733 784923 "FFNBX" 785244 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-322 775396 779621 779879 "FFNBP" 780340 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-321 769999 774680 774891 "FFNB" 775229 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-320 768831 769029 769344 "FFINTBAS" 769796 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-319 765054 767294 767323 "FFIELDC" 767943 T FFIELDC (NIL) -9 NIL 768319) (-318 763717 764087 764584 "FFIELDC-" 764589 NIL FFIELDC- (NIL T) -8 NIL NIL) (-317 763287 763332 763456 "FFHOM" 763659 NIL FFHOM (NIL T T T) -7 NIL NIL) (-316 760985 761469 761986 "FFF" 762802 NIL FFF (NIL T) -7 NIL NIL) (-315 756573 760727 760828 "FFCGX" 760928 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-314 752175 756305 756412 "FFCGP" 756516 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-313 747328 751902 752010 "FFCG" 752111 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-312 729273 738396 738483 "FFCAT" 743648 NIL FFCAT (NIL T T T) -9 NIL 745135) (-311 724471 725518 726832 "FFCAT-" 728062 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-310 723882 723925 724160 "FFCAT2" 724422 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-309 713082 716872 718089 "FEXPR" 722737 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-308 712081 712516 712558 "FEVALAB" 712642 NIL FEVALAB (NIL T) -9 NIL 712903) (-307 711240 711450 711788 "FEVALAB-" 711793 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-306 709833 710623 710826 "FDIV" 711139 NIL FDIV (NIL T T T T) -8 NIL NIL) (-305 706899 707614 707730 "FDIVCAT" 709298 NIL FDIVCAT (NIL T T T T) -9 NIL 709735) (-304 706661 706688 706858 "FDIVCAT-" 706863 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-303 705881 705968 706245 "FDIV2" 706568 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-302 704574 704831 705118 "FCPAK1" 705614 T FCPAK1 (NIL) -7 NIL NIL) (-301 703702 704074 704215 "FCOMP" 704465 NIL FCOMP (NIL T) -8 NIL NIL) (-300 687342 690754 694314 "FC" 700162 T FC (NIL) -8 NIL NIL) (-299 679937 683983 684024 "FAXF" 685826 NIL FAXF (NIL T) -9 NIL 686517) (-298 677216 677871 678696 "FAXF-" 679161 NIL FAXF- (NIL T T) -8 NIL NIL) (-297 672316 676592 676768 "FARRAY" 677073 NIL FARRAY (NIL T) -8 NIL NIL) (-296 667706 669777 669830 "FAMR" 670842 NIL FAMR (NIL T T) -9 NIL 671302) (-295 666597 666899 667333 "FAMR-" 667338 NIL FAMR- (NIL T T T) -8 NIL NIL) (-294 665793 666519 666572 "FAMONOID" 666577 NIL FAMONOID (NIL T) -8 NIL NIL) (-293 663625 664309 664363 "FAMONC" 665304 NIL FAMONC (NIL T T) -9 NIL 665689) (-292 662317 663379 663516 "FAGROUP" 663521 NIL FAGROUP (NIL T) -8 NIL NIL) (-291 660120 660439 660841 "FACUTIL" 661998 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-290 659219 659404 659626 "FACTFUNC" 659930 NIL FACTFUNC (NIL T) -7 NIL NIL) (-289 651542 658470 658682 "EXPUPXS" 659075 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-288 649041 649577 650159 "EXPRTUBE" 650980 T EXPRTUBE (NIL) -7 NIL NIL) (-287 645235 645827 646564 "EXPRODE" 648380 NIL EXPRODE (NIL T T) -7 NIL NIL) (-286 630397 643894 644320 "EXPR" 644841 NIL EXPR (NIL T) -8 NIL NIL) (-285 624825 625412 626224 "EXPR2UPS" 629695 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-284 624461 624518 624625 "EXPR2" 624762 NIL EXPR2 (NIL T T) -7 NIL NIL) (-283 615815 623598 623893 "EXPEXPAN" 624299 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-282 615642 615772 615801 "EXIT" 615806 T EXIT (NIL) -8 NIL NIL) (-281 615269 615331 615444 "EVALCYC" 615574 NIL EVALCYC (NIL T) -7 NIL NIL) (-280 614809 614927 614969 "EVALAB" 615139 NIL EVALAB (NIL T) -9 NIL 615243) (-279 614290 614412 614633 "EVALAB-" 614638 NIL EVALAB- (NIL T T) -8 NIL NIL) (-278 611752 613064 613093 "EUCDOM" 613648 T EUCDOM (NIL) -9 NIL 613998) (-277 610157 610599 611189 "EUCDOM-" 611194 NIL EUCDOM- (NIL T) -8 NIL NIL) (-276 597770 600509 603240 "ESTOOLS" 607446 T ESTOOLS (NIL) -7 NIL NIL) (-275 597406 597463 597570 "ESTOOLS2" 597707 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-274 597157 597199 597279 "ESTOOLS1" 597358 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-273 591094 592818 592847 "ES" 595611 T ES (NIL) -9 NIL 597017) (-272 586042 587328 589145 "ES-" 589309 NIL ES- (NIL T) -8 NIL NIL) (-271 582449 583201 583973 "ESCONT" 585290 T ESCONT (NIL) -7 NIL NIL) (-270 582194 582226 582308 "ESCONT1" 582411 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-269 581869 581919 582019 "ES2" 582138 NIL ES2 (NIL T T) -7 NIL NIL) (-268 581499 581557 581666 "ES1" 581805 NIL ES1 (NIL T T) -7 NIL NIL) (-267 580715 580844 581020 "ERROR" 581343 T ERROR (NIL) -7 NIL NIL) (-266 574218 580574 580665 "EQTBL" 580670 NIL EQTBL (NIL T T) -8 NIL NIL) (-265 566655 569536 570983 "EQ" 572804 NIL -3219 (NIL T) -8 NIL NIL) (-264 566287 566344 566453 "EQ2" 566592 NIL EQ2 (NIL T T) -7 NIL NIL) (-263 561579 562625 563718 "EP" 565226 NIL EP (NIL T) -7 NIL NIL) (-262 560738 561302 561331 "ENTIRER" 561336 T ENTIRER (NIL) -9 NIL 561381) (-261 557194 558693 559063 "EMR" 560537 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-260 556337 556522 556577 "ELTAGG" 556957 NIL ELTAGG (NIL T T) -9 NIL 557168) (-259 556056 556118 556259 "ELTAGG-" 556264 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-258 555844 555873 555928 "ELTAB" 556012 NIL ELTAB (NIL T T) -9 NIL NIL) (-257 554970 555116 555315 "ELFUTS" 555695 NIL ELFUTS (NIL T T) -7 NIL NIL) (-256 554711 554767 554796 "ELEMFUN" 554901 T ELEMFUN (NIL) -9 NIL NIL) (-255 554581 554602 554670 "ELEMFUN-" 554675 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-254 549472 552681 552723 "ELAGG" 553663 NIL ELAGG (NIL T) -9 NIL 554126) (-253 547757 548191 548854 "ELAGG-" 548859 NIL ELAGG- (NIL T T) -8 NIL NIL) (-252 540625 542424 543251 "EFUPXS" 547033 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-251 534075 535876 536686 "EFULS" 539901 NIL EFULS (NIL T T T) -8 NIL NIL) (-250 531506 531864 532342 "EFSTRUC" 533707 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-249 520578 522143 523703 "EF" 530021 NIL EF (NIL T T) -7 NIL NIL) (-248 519679 520063 520212 "EAB" 520449 T EAB (NIL) -8 NIL NIL) (-247 518892 519638 519666 "E04UCFA" 519671 T E04UCFA (NIL) -8 NIL NIL) (-246 518105 518851 518879 "E04NAFA" 518884 T E04NAFA (NIL) -8 NIL NIL) (-245 517318 518064 518092 "E04MBFA" 518097 T E04MBFA (NIL) -8 NIL NIL) (-244 516531 517277 517305 "E04JAFA" 517310 T E04JAFA (NIL) -8 NIL NIL) (-243 515746 516490 516518 "E04GCFA" 516523 T E04GCFA (NIL) -8 NIL NIL) (-242 514961 515705 515733 "E04FDFA" 515738 T E04FDFA (NIL) -8 NIL NIL) (-241 514174 514920 514948 "E04DGFA" 514953 T E04DGFA (NIL) -8 NIL NIL) (-240 508359 509704 511066 "E04AGNT" 512832 T E04AGNT (NIL) -7 NIL NIL) (-239 507085 507565 507606 "DVARCAT" 508081 NIL DVARCAT (NIL T) -9 NIL 508279) (-238 506289 506501 506815 "DVARCAT-" 506820 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-237 499151 506091 506218 "DSMP" 506223 NIL DSMP (NIL T T T) -8 NIL NIL) (-236 493977 495108 496172 "DROPT" 498107 T DROPT (NIL) -8 NIL NIL) (-235 493642 493701 493799 "DROPT1" 493912 NIL DROPT1 (NIL T) -7 NIL NIL) (-234 488764 489888 491023 "DROPT0" 492527 T DROPT0 (NIL) -7 NIL NIL) (-233 487109 487434 487820 "DRAWPT" 488398 T DRAWPT (NIL) -7 NIL NIL) (-232 481784 482683 483738 "DRAW" 486107 NIL DRAW (NIL T) -7 NIL NIL) (-231 481425 481476 481592 "DRAWHACK" 481727 NIL DRAWHACK (NIL T) -7 NIL NIL) (-230 480170 480435 480722 "DRAWCX" 481158 T DRAWCX (NIL) -7 NIL NIL) (-229 479688 479756 479906 "DRAWCURV" 480096 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-228 470292 472214 474293 "DRAWCFUN" 477629 T DRAWCFUN (NIL) -7 NIL NIL) (-227 467105 468987 469029 "DQAGG" 469658 NIL DQAGG (NIL T) -9 NIL 469931) (-226 455611 462349 462432 "DPOLCAT" 464270 NIL DPOLCAT (NIL T T T T) -9 NIL 464814) (-225 450451 451797 453754 "DPOLCAT-" 453759 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-224 444535 450313 450410 "DPMO" 450415 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-223 438522 444316 444482 "DPMM" 444487 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-222 438155 438231 438329 "DOMAIN" 438444 T DOMAIN (NIL) -8 NIL NIL) (-221 431867 437792 437943 "DMP" 438056 NIL DMP (NIL NIL T) -8 NIL NIL) (-220 431467 431523 431667 "DLP" 431805 NIL DLP (NIL T) -7 NIL NIL) (-219 425111 430568 430795 "DLIST" 431272 NIL DLIST (NIL T) -8 NIL NIL) (-218 421957 423966 424008 "DLAGG" 424558 NIL DLAGG (NIL T) -9 NIL 424787) (-217 420666 421358 421387 "DIVRING" 421537 T DIVRING (NIL) -9 NIL 421645) (-216 419654 419907 420300 "DIVRING-" 420305 NIL DIVRING- (NIL T) -8 NIL NIL) (-215 417756 418113 418519 "DISPLAY" 419268 T DISPLAY (NIL) -7 NIL NIL) (-214 411645 417670 417733 "DIRPROD" 417738 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-213 410493 410696 410961 "DIRPROD2" 411438 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-212 400123 406128 406182 "DIRPCAT" 406590 NIL DIRPCAT (NIL NIL T) -9 NIL 407417) (-211 397449 398091 398972 "DIRPCAT-" 399309 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-210 396736 396896 397082 "DIOSP" 397283 T DIOSP (NIL) -7 NIL NIL) (-209 393438 395648 395690 "DIOPS" 396124 NIL DIOPS (NIL T) -9 NIL 396353) (-208 392987 393101 393292 "DIOPS-" 393297 NIL DIOPS- (NIL T T) -8 NIL NIL) (-207 391858 392496 392525 "DIFRING" 392712 T DIFRING (NIL) -9 NIL 392821) (-206 391504 391581 391733 "DIFRING-" 391738 NIL DIFRING- (NIL T) -8 NIL NIL) (-205 389293 390575 390616 "DIFEXT" 390975 NIL DIFEXT (NIL T) -9 NIL 391268) (-204 387579 388007 388672 "DIFEXT-" 388677 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-203 384901 387111 387153 "DIAGG" 387158 NIL DIAGG (NIL T) -9 NIL 387178) (-202 384285 384442 384694 "DIAGG-" 384699 NIL DIAGG- (NIL T T) -8 NIL NIL) (-201 379750 383244 383521 "DHMATRIX" 384054 NIL DHMATRIX (NIL T) -8 NIL NIL) (-200 375362 376271 377281 "DFSFUN" 378760 T DFSFUN (NIL) -7 NIL NIL) (-199 370148 374076 374441 "DFLOAT" 375017 T DFLOAT (NIL) -8 NIL NIL) (-198 368381 368662 369057 "DFINTTLS" 369856 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-197 365414 366416 366814 "DERHAM" 368048 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-196 363263 365189 365278 "DEQUEUE" 365358 NIL DEQUEUE (NIL T) -8 NIL NIL) (-195 362481 362614 362809 "DEGRED" 363125 NIL DEGRED (NIL T T) -7 NIL NIL) (-194 358897 359638 360486 "DEFINTRF" 361713 NIL DEFINTRF (NIL T) -7 NIL NIL) (-193 356436 356903 357499 "DEFINTEF" 358418 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-192 350267 355877 356043 "DECIMAL" 356290 T DECIMAL (NIL) -8 NIL NIL) (-191 347779 348237 348743 "DDFACT" 349811 NIL DDFACT (NIL T T) -7 NIL NIL) (-190 347375 347418 347569 "DBLRESP" 347730 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-189 345085 345419 345788 "DBASE" 347133 NIL DBASE (NIL T) -8 NIL NIL) (-188 344220 345044 345072 "D03FAFA" 345077 T D03FAFA (NIL) -8 NIL NIL) (-187 343356 344179 344207 "D03EEFA" 344212 T D03EEFA (NIL) -8 NIL NIL) (-186 341306 341772 342261 "D03AGNT" 342887 T D03AGNT (NIL) -7 NIL NIL) (-185 340624 341265 341293 "D02EJFA" 341298 T D02EJFA (NIL) -8 NIL NIL) (-184 339942 340583 340611 "D02CJFA" 340616 T D02CJFA (NIL) -8 NIL NIL) (-183 339260 339901 339929 "D02BHFA" 339934 T D02BHFA (NIL) -8 NIL NIL) (-182 338578 339219 339247 "D02BBFA" 339252 T D02BBFA (NIL) -8 NIL NIL) (-181 331776 333364 334970 "D02AGNT" 336992 T D02AGNT (NIL) -7 NIL NIL) (-180 329557 330076 330619 "D01WGTS" 331253 T D01WGTS (NIL) -7 NIL NIL) (-179 328664 329516 329544 "D01TRNS" 329549 T D01TRNS (NIL) -8 NIL NIL) (-178 327771 328623 328651 "D01GBFA" 328656 T D01GBFA (NIL) -8 NIL NIL) (-177 326878 327730 327758 "D01FCFA" 327763 T D01FCFA (NIL) -8 NIL NIL) (-176 325985 326837 326865 "D01ASFA" 326870 T D01ASFA (NIL) -8 NIL NIL) (-175 325092 325944 325972 "D01AQFA" 325977 T D01AQFA (NIL) -8 NIL NIL) (-174 324199 325051 325079 "D01APFA" 325084 T D01APFA (NIL) -8 NIL NIL) (-173 323306 324158 324186 "D01ANFA" 324191 T D01ANFA (NIL) -8 NIL NIL) (-172 322413 323265 323293 "D01AMFA" 323298 T D01AMFA (NIL) -8 NIL NIL) (-171 321520 322372 322400 "D01ALFA" 322405 T D01ALFA (NIL) -8 NIL NIL) (-170 320627 321479 321507 "D01AKFA" 321512 T D01AKFA (NIL) -8 NIL NIL) (-169 319734 320586 320614 "D01AJFA" 320619 T D01AJFA (NIL) -8 NIL NIL) (-168 313066 314608 316160 "D01AGNT" 318202 T D01AGNT (NIL) -7 NIL NIL) (-167 312403 312531 312683 "CYCLOTOM" 312934 T CYCLOTOM (NIL) -7 NIL NIL) (-166 309138 309851 310578 "CYCLES" 311696 T CYCLES (NIL) -7 NIL NIL) (-165 308450 308584 308755 "CVMP" 308999 NIL CVMP (NIL T) -7 NIL NIL) (-164 306232 306489 306864 "CTRIGMNP" 308178 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-163 305606 305705 305858 "CSTTOOLS" 306129 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-162 301405 302062 302820 "CRFP" 304918 NIL CRFP (NIL T T) -7 NIL NIL) (-161 300452 300637 300865 "CRAPACK" 301209 NIL CRAPACK (NIL T) -7 NIL NIL) (-160 299836 299937 300141 "CPMATCH" 300328 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-159 299561 299589 299695 "CPIMA" 299802 NIL CPIMA (NIL T T T) -7 NIL NIL) (-158 295925 296597 297315 "COORDSYS" 298896 NIL COORDSYS (NIL T) -7 NIL NIL) (-157 291786 293928 294420 "CONTFRAC" 295465 NIL CONTFRAC (NIL T) -8 NIL NIL) (-156 290939 291503 291532 "COMRING" 291537 T COMRING (NIL) -9 NIL 291588) (-155 290020 290297 290481 "COMPPROP" 290775 T COMPPROP (NIL) -8 NIL NIL) (-154 289681 289716 289844 "COMPLPAT" 289979 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-153 279662 289490 289599 "COMPLEX" 289604 NIL COMPLEX (NIL T) -8 NIL NIL) (-152 279298 279355 279462 "COMPLEX2" 279599 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-151 279016 279051 279149 "COMPFACT" 279257 NIL COMPFACT (NIL T T) -7 NIL NIL) (-150 263350 273644 273685 "COMPCAT" 274687 NIL COMPCAT (NIL T) -9 NIL 276080) (-149 252865 255789 259416 "COMPCAT-" 259772 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-148 252596 252624 252726 "COMMUPC" 252831 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-147 252391 252424 252483 "COMMONOP" 252557 T COMMONOP (NIL) -7 NIL NIL) (-146 251974 252142 252229 "COMM" 252324 T COMM (NIL) -8 NIL NIL) (-145 251228 251420 251449 "COMBOPC" 251785 T COMBOPC (NIL) -9 NIL 251958) (-144 250124 250334 250576 "COMBINAT" 251018 NIL COMBINAT (NIL T) -7 NIL NIL) (-143 246330 246901 247539 "COMBF" 249548 NIL COMBF (NIL T T) -7 NIL NIL) (-142 245116 245446 245681 "COLOR" 246115 T COLOR (NIL) -8 NIL NIL) (-141 244756 244803 244928 "CMPLXRT" 245063 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-140 240314 241328 242394 "CLIP" 243710 T CLIP (NIL) -7 NIL NIL) (-139 238652 239422 239660 "CLIF" 240142 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-138 234874 236798 236840 "CLAGG" 237769 NIL CLAGG (NIL T) -9 NIL 238305) (-137 233296 233753 234336 "CLAGG-" 234341 NIL CLAGG- (NIL T T) -8 NIL NIL) (-136 232840 232925 233065 "CINTSLPE" 233205 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-135 230341 230812 231360 "CHVAR" 232368 NIL CHVAR (NIL T T T) -7 NIL NIL) (-134 229563 230127 230156 "CHARZ" 230161 T CHARZ (NIL) -9 NIL 230175) (-133 229317 229357 229435 "CHARPOL" 229517 NIL CHARPOL (NIL T) -7 NIL NIL) (-132 228423 229020 229049 "CHARNZ" 229096 T CHARNZ (NIL) -9 NIL 229151) (-131 226446 227113 227448 "CHAR" 228108 T CHAR (NIL) -8 NIL NIL) (-130 226171 226232 226261 "CFCAT" 226372 T CFCAT (NIL) -9 NIL NIL) (-129 225416 225527 225709 "CDEN" 226055 NIL CDEN (NIL T T T) -7 NIL NIL) (-128 221408 224569 224849 "CCLASS" 225156 T CCLASS (NIL) -8 NIL NIL) (-127 216461 217437 218190 "CARTEN" 220711 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-126 215569 215717 215938 "CARTEN2" 216308 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-125 213866 214721 214977 "CARD" 215333 T CARD (NIL) -8 NIL NIL) (-124 213238 213566 213595 "CACHSET" 213727 T CACHSET (NIL) -9 NIL 213804) (-123 212734 213030 213059 "CABMON" 213109 T CABMON (NIL) -9 NIL 213165) (-122 210291 212426 212533 "BTREE" 212660 NIL BTREE (NIL T) -8 NIL NIL) (-121 207789 209939 210061 "BTOURN" 210201 NIL BTOURN (NIL T) -8 NIL NIL) (-120 205207 207260 207302 "BTCAT" 207370 NIL BTCAT (NIL T) -9 NIL 207447) (-119 204874 204954 205103 "BTCAT-" 205108 NIL BTCAT- (NIL T T) -8 NIL NIL) (-118 200094 203965 203994 "BTAGG" 204250 T BTAGG (NIL) -9 NIL 204429) (-117 199517 199661 199891 "BTAGG-" 199896 NIL BTAGG- (NIL T) -8 NIL NIL) (-116 196561 198795 199010 "BSTREE" 199334 NIL BSTREE (NIL T) -8 NIL NIL) (-115 195699 195825 196009 "BRILL" 196417 NIL BRILL (NIL T) -7 NIL NIL) (-114 192400 194427 194469 "BRAGG" 195118 NIL BRAGG (NIL T) -9 NIL 195375) (-113 190929 191335 191890 "BRAGG-" 191895 NIL BRAGG- (NIL T T) -8 NIL NIL) (-112 184137 190275 190459 "BPADICRT" 190777 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-111 182441 184074 184119 "BPADIC" 184124 NIL BPADIC (NIL NIL) -8 NIL NIL) (-110 182141 182171 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\ No newline at end of file
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+NIL 
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+NIL 
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+NIL 
+NIL 
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"XPBWPOLY" 3103521 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1174 3096162 3098475 3098518 "XF" 3099139 NIL XF (NIL T) -9 NIL 3099538) (-1173 3095783 3095871 3096040 "XF-" 3096045 NIL XF- (NIL T T) -8 NIL NIL) (-1172 3091162 3092461 3092516 "XFALG" 3094664 NIL XFALG (NIL T T) -9 NIL 3095451) (-1171 3090299 3090403 3090607 "XEXPPKG" 3091054 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1170 3088397 3090150 3090245 "XDPOLY" 3090250 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1169 3087275 3087885 3087928 "XALG" 3087990 NIL XALG (NIL T) -9 NIL 3088109) (-1168 3080751 3085259 3085752 "WUTSET" 3086867 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1167 3078563 3079370 3079721 "WP" 3080533 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1166 3077449 3077647 3077942 "WFFINTBS" 3078360 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1165 3075353 3075780 3076242 "WEIER" 3077021 NIL WEIER (NIL T) -7 NIL NIL) (-1164 3074501 3074925 3074968 "VSPACE" 3075104 NIL VSPACE (NIL T) -9 NIL 3075178) (-1163 3074339 3074366 3074457 "VSPACE-" 3074462 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1162 3074085 3074128 3074199 "VOID" 3074290 T VOID (NIL) -8 NIL NIL) (-1161 3072221 3072580 3072986 "VIEW" 3073701 T VIEW (NIL) -7 NIL NIL) (-1160 3068646 3069284 3070021 "VIEWDEF" 3071506 T VIEWDEF (NIL) -7 NIL NIL) (-1159 3057985 3060194 3062367 "VIEW3D" 3066495 T VIEW3D (NIL) -8 NIL NIL) (-1158 3050267 3051896 3053475 "VIEW2D" 3056428 T VIEW2D (NIL) -8 NIL NIL) (-1157 3045676 3050037 3050129 "VECTOR" 3050210 NIL VECTOR (NIL T) -8 NIL NIL) (-1156 3044253 3044512 3044830 "VECTOR2" 3045406 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1155 3037792 3042044 3042088 "VECTCAT" 3043076 NIL VECTCAT (NIL T) -9 NIL 3043660) (-1154 3036806 3037060 3037450 "VECTCAT-" 3037455 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1153 3036287 3036457 3036577 "VARIABLE" 3036721 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1152 3036219 3036224 3036255 "UTYPE" 3036260 T UTYPE (NIL) -9 NIL NIL) (-1151 3035054 3035208 3035469 "UTSODETL" 3036045 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1150 3032494 3032954 3033478 "UTSODE" 3034595 NIL UTSODE (NIL T T) -7 NIL NIL) (-1149 3024341 3030134 3030622 "UTS" 3032063 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1148 3015689 3021051 3021094 "UTSCAT" 3022195 NIL UTSCAT (NIL T) -9 NIL 3022952) (-1147 3013045 3013760 3014748 "UTSCAT-" 3014753 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1146 3012676 3012719 3012850 "UTS2" 3012996 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1145 3006951 3009516 3009560 "URAGG" 3011630 NIL URAGG (NIL T) -9 NIL 3012352) (-1144 3003890 3004753 3005876 "URAGG-" 3005881 NIL URAGG- (NIL T T) -8 NIL NIL) (-1143 2999576 3002507 3002978 "UPXSSING" 3003554 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1142 2991470 2998697 2998977 "UPXS" 2999353 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1141 2984502 2991375 2991446 "UPXSCONS" 2991451 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1140 2974794 2981621 2981683 "UPXSCCA" 2982332 NIL UPXSCCA (NIL T T) -9 NIL 2982573) (-1139 2974433 2974518 2974691 "UPXSCCA-" 2974696 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) 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NIL) (-1126 2921158 2921270 2921455 "UPCDEN" 2921807 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1125 2920681 2920750 2920897 "UP2" 2921083 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1124 2919200 2919887 2920163 "UNISEG" 2920440 NIL UNISEG (NIL T) -8 NIL NIL) (-1123 2918415 2918542 2918747 "UNISEG2" 2919043 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1122 2917475 2917655 2917881 "UNIFACT" 2918231 NIL UNIFACT (NIL T) -7 NIL NIL) (-1121 2901374 2916656 2916906 "ULS" 2917282 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1120 2889342 2901279 2901350 "ULSCONS" 2901355 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1119 2872095 2884105 2884167 "ULSCCAT" 2884879 NIL ULSCCAT (NIL T T) -9 NIL 2885175) (-1118 2871146 2871391 2871778 "ULSCCAT-" 2871783 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1117 2861139 2867653 2867696 "ULSCAT" 2868552 NIL ULSCAT (NIL T) -9 NIL 2869282) (-1116 2860573 2860652 2860829 "ULS2" 2861054 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1115 2858970 2859937 2859968 "UFD" 2860180 T UFD (NIL) -9 NIL 2860294) (-1114 2858764 2858810 2858905 "UFD-" 2858910 NIL UFD- (NIL T) -8 NIL NIL) (-1113 2857846 2858029 2858245 "UDVO" 2858570 T UDVO (NIL) -7 NIL NIL) (-1112 2855662 2856071 2856542 "UDPO" 2857410 NIL UDPO (NIL T) -7 NIL NIL) (-1111 2855594 2855599 2855630 "TYPE" 2855635 T TYPE (NIL) -9 NIL NIL) (-1110 2854565 2854767 2855007 "TWOFACT" 2855388 NIL TWOFACT (NIL T) -7 NIL NIL) (-1109 2853503 2853840 2854103 "TUPLE" 2854337 NIL TUPLE (NIL T) -8 NIL NIL) (-1108 2851194 2851713 2852252 "TUBETOOL" 2852986 T TUBETOOL (NIL) -7 NIL NIL) (-1107 2850043 2850248 2850489 "TUBE" 2850987 NIL TUBE (NIL T) -8 NIL NIL) (-1106 2844767 2849021 2849303 "TS" 2849795 NIL TS (NIL T) -8 NIL NIL) (-1105 2833470 2837562 2837659 "TSETCAT" 2842893 NIL TSETCAT (NIL T T T T) -9 NIL 2844424) (-1104 2828205 2829803 2831693 "TSETCAT-" 2831698 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1103 2822468 2823314 2824256 "TRMANIP" 2827341 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1102 2821909 2821972 2822135 "TRIMAT" 2822400 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1101 2819715 2819952 2820315 "TRIGMNIP" 2821658 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1100 2819234 2819347 2819378 "TRIGCAT" 2819591 T TRIGCAT (NIL) -9 NIL NIL) (-1099 2818903 2818982 2819123 "TRIGCAT-" 2819128 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1098 2815802 2817763 2818043 "TREE" 2818658 NIL TREE (NIL T) -8 NIL NIL) (-1097 2815075 2815603 2815634 "TRANFUN" 2815669 T TRANFUN (NIL) -9 NIL 2815735) (-1096 2814354 2814545 2814825 "TRANFUN-" 2814830 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1095 2814158 2814190 2814251 "TOPSP" 2814315 T TOPSP (NIL) -7 NIL NIL) (-1094 2813510 2813625 2813778 "TOOLSIGN" 2814039 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1093 2812171 2812687 2812926 "TEXTFILE" 2813293 T TEXTFILE (NIL) -8 NIL NIL) (-1092 2810036 2810550 2810988 "TEX" 2811755 T TEX (NIL) -8 NIL NIL) (-1091 2809817 2809848 2809920 "TEX1" 2809999 NIL TEX1 (NIL T) -7 NIL NIL) (-1090 2809465 2809528 2809618 "TEMUTL" 2809749 T TEMUTL (NIL) -7 NIL NIL) (-1089 2807619 2807899 2808224 "TBCMPPK" 2809188 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1088 2799507 2805779 2805836 "TBAGG" 2806236 NIL TBAGG (NIL T T) -9 NIL 2806447) (-1087 2794577 2796065 2797819 "TBAGG-" 2797824 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1086 2793961 2794068 2794213 "TANEXP" 2794466 NIL TANEXP (NIL T) -7 NIL NIL) (-1085 2787462 2793818 2793911 "TABLE" 2793916 NIL TABLE (NIL T T) -8 NIL NIL) (-1084 2786875 2786973 2787111 "TABLEAU" 2787359 NIL TABLEAU (NIL T) -8 NIL NIL) (-1083 2781483 2782703 2783951 "TABLBUMP" 2785661 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1082 2777946 2778641 2779424 "SYSSOLP" 2780734 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1081 2774456 2775035 2775752 "SYNTAX" 2777251 T SYNTAX (NIL) -8 NIL NIL) (-1080 2771590 2772198 2772836 "SYMTAB" 2773840 T SYMTAB (NIL) -8 NIL NIL) (-1079 2766839 2767741 2768724 "SYMS" 2770629 T SYMS (NIL) -8 NIL NIL) (-1078 2764072 2766299 2766528 "SYMPOLY" 2766644 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1077 2763592 2763667 2763789 "SYMFUNC" 2763984 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1076 2759570 2760829 2761651 "SYMBOL" 2762792 T SYMBOL (NIL) -8 NIL NIL) (-1075 2753109 2754798 2756518 "SWITCH" 2757872 T SWITCH (NIL) -8 NIL NIL) (-1074 2746342 2751936 2752238 "SUTS" 2752864 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1073 2738235 2745463 2745743 "SUPXS" 2746119 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1072 2729767 2737856 2737981 "SUP" 2738144 NIL SUP (NIL T) -8 NIL NIL) (-1071 2728926 2729053 2729270 "SUPFRACF" 2729635 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1070 2728551 2728610 2728721 "SUP2" 2728861 NIL SUP2 (NIL T T) -7 NIL NIL) (-1069 2726977 2727249 2727609 "SUMRF" 2728252 NIL SUMRF (NIL T) -7 NIL NIL) (-1068 2726298 2726363 2726560 "SUMFS" 2726899 NIL SUMFS (NIL T T) -7 NIL NIL) (-1067 2710237 2725479 2725729 "SULS" 2726105 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1066 2709559 2709762 2709902 "SUCH" 2710145 NIL SUCH (NIL T T) -8 NIL NIL) (-1065 2703486 2704498 2705456 "SUBSPACE" 2708647 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1064 2702916 2703006 2703170 "SUBRESP" 2703374 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1063 2696285 2697581 2698892 "STTF" 2701652 NIL STTF (NIL T) -7 NIL NIL) (-1062 2690458 2691578 2692725 "STTFNC" 2695185 NIL STTFNC (NIL T) -7 NIL NIL) (-1061 2681809 2683676 2685469 "STTAYLOR" 2688699 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1060 2675053 2681673 2681756 "STRTBL" 2681761 NIL STRTBL (NIL T) -8 NIL NIL) (-1059 2670444 2675008 2675039 "STRING" 2675044 T STRING (NIL) -8 NIL NIL) (-1058 2665332 2669817 2669848 "STRICAT" 2669907 T STRICAT (NIL) -9 NIL 2669969) (-1057 2658048 2662855 2663475 "STREAM" 2664747 NIL STREAM (NIL T) -8 NIL NIL) (-1056 2657558 2657635 2657779 "STREAM3" 2657965 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1055 2656540 2656723 2656958 "STREAM2" 2657371 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1054 2656228 2656280 2656373 "STREAM1" 2656482 NIL STREAM1 (NIL T) -7 NIL NIL) (-1053 2655244 2655425 2655656 "STINPROD" 2656044 NIL STINPROD (NIL T) -7 NIL NIL) (-1052 2654822 2655006 2655037 "STEP" 2655117 T STEP (NIL) -9 NIL 2655195) (-1051 2648365 2654721 2654798 "STBL" 2654803 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1050 2643540 2647587 2647631 "STAGG" 2647784 NIL STAGG (NIL T) -9 NIL 2647873) (-1049 2641242 2641844 2642716 "STAGG-" 2642721 NIL STAGG- (NIL T T) -8 NIL NIL) (-1048 2639437 2641012 2641104 "STACK" 2641185 NIL STACK (NIL T) -8 NIL NIL) (-1047 2632168 2637584 2638039 "SREGSET" 2639067 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1046 2624608 2625976 2627488 "SRDCMPK" 2630774 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1045 2617575 2622048 2622079 "SRAGG" 2623382 T SRAGG (NIL) -9 NIL 2623990) (-1044 2616592 2616847 2617226 "SRAGG-" 2617231 NIL SRAGG- (NIL T) -8 NIL NIL) (-1043 2611041 2615511 2615938 "SQMATRIX" 2616211 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1042 2604793 2607761 2608487 "SPLTREE" 2610387 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1041 2600783 2601449 2602095 "SPLNODE" 2604219 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1040 2599829 2600062 2600093 "SPFCAT" 2600537 T SPFCAT (NIL) -9 NIL NIL) (-1039 2598566 2598776 2599040 "SPECOUT" 2599587 T SPECOUT (NIL) -7 NIL NIL) (-1038 2598327 2598367 2598436 "SPADPRSR" 2598519 T SPADPRSR (NIL) -7 NIL NIL) (-1037 2590349 2592096 2592139 "SPACEC" 2596462 NIL SPACEC (NIL T) -9 NIL 2598278) (-1036 2588521 2590282 2590330 "SPACE3" 2590335 NIL SPACE3 (NIL T) -8 NIL NIL) (-1035 2587273 2587444 2587735 "SORTPAK" 2588326 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1034 2585329 2585632 2586050 "SOLVETRA" 2586937 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1033 2584340 2584562 2584836 "SOLVESER" 2585102 NIL SOLVESER (NIL T) -7 NIL NIL) (-1032 2579560 2580441 2581443 "SOLVERAD" 2583392 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1031 2575375 2575984 2576713 "SOLVEFOR" 2578927 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1030 2569674 2574726 2574823 "SNTSCAT" 2574828 NIL SNTSCAT (NIL T T T T) -9 NIL 2574898) (-1029 2563779 2568005 2568395 "SMTS" 2569364 NIL SMTS (NIL T T T) -8 NIL NIL) (-1028 2558190 2563668 2563744 "SMP" 2563749 NIL SMP (NIL T T) -8 NIL NIL) (-1027 2556349 2556650 2557048 "SMITH" 2557887 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1026 2549313 2553509 2553612 "SMATCAT" 2554952 NIL SMATCAT (NIL NIL T T T) -9 NIL 2555501) (-1025 2546254 2547077 2548254 "SMATCAT-" 2548259 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1024 2543967 2545490 2545534 "SKAGG" 2545795 NIL SKAGG (NIL T) -9 NIL 2545930) (-1023 2540025 2543071 2543349 "SINT" 2543711 T SINT (NIL) -8 NIL NIL) (-1022 2539797 2539835 2539901 "SIMPAN" 2539981 T SIMPAN (NIL) -7 NIL NIL) (-1021 2538635 2538856 2539131 "SIGNRF" 2539556 NIL SIGNRF (NIL T) -7 NIL NIL) (-1020 2537444 2537595 2537885 "SIGNEF" 2538464 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1019 2535134 2535588 2536094 "SHP" 2536985 NIL SHP (NIL T NIL) -7 NIL NIL) (-1018 2528987 2535035 2535111 "SHDP" 2535116 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1017 2528476 2528668 2528699 "SGROUP" 2528851 T SGROUP (NIL) -9 NIL 2528938) (-1016 2528246 2528298 2528402 "SGROUP-" 2528407 NIL SGROUP- (NIL T) -8 NIL NIL) (-1015 2525082 2525779 2526502 "SGCF" 2527545 T SGCF (NIL) -7 NIL NIL) (-1014 2519480 2524532 2524629 "SFRTCAT" 2524634 NIL SFRTCAT (NIL T T T T) -9 NIL 2524672) (-1013 2512940 2513955 2515089 "SFRGCD" 2518463 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1012 2506106 2507177 2508361 "SFQCMPK" 2511873 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1011 2505728 2505817 2505927 "SFORT" 2506047 NIL SFORT (NIL T T) -8 NIL NIL) (-1010 2504873 2505568 2505689 "SEXOF" 2505694 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1009 2504007 2504754 2504822 "SEX" 2504827 T SEX (NIL) -8 NIL NIL) (-1008 2498783 2499472 2499568 "SEXCAT" 2503339 NIL SEXCAT (NIL T T T T T) -9 NIL 2503958) (-1007 2495963 2498717 2498765 "SET" 2498770 NIL SET (NIL T) -8 NIL NIL) (-1006 2494214 2494676 2494981 "SETMN" 2495704 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1005 2493821 2493947 2493978 "SETCAT" 2494095 T SETCAT (NIL) -9 NIL 2494179) (-1004 2493601 2493653 2493752 "SETCAT-" 2493757 NIL SETCAT- (NIL T) -8 NIL NIL) (-1003 2489988 2492062 2492106 "SETAGG" 2492976 NIL SETAGG (NIL T) -9 NIL 2493316) (-1002 2489446 2489562 2489799 "SETAGG-" 2489804 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1001 2488651 2488944 2489006 "SEGXCAT" 2489292 NIL SEGXCAT (NIL T T) -9 NIL 2489411) (-1000 2487709 2488319 2488500 "SEG" 2488505 NIL SEG (NIL T) -8 NIL NIL) (-999 2486626 2486839 2486881 "SEGCAT" 2487454 NIL SEGCAT (NIL T) -9 NIL 2487692) (-998 2485680 2486010 2486208 "SEGBIND" 2486461 NIL SEGBIND (NIL T) -8 NIL NIL) (-997 2485312 2485369 2485478 "SEGBIND2" 2485617 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-996 2484535 2484661 2484863 "SEG2" 2485156 NIL SEG2 (NIL T T) -7 NIL NIL) (-995 2483974 2484472 2484517 "SDVAR" 2484522 NIL SDVAR (NIL T) -8 NIL NIL) (-994 2476280 2483753 2483877 "SDPOL" 2483882 NIL SDPOL (NIL T) -8 NIL NIL) (-993 2474879 2475145 2475462 "SCPKG" 2475995 NIL SCPKG (NIL T) -7 NIL NIL) (-992 2474106 2474239 2474416 "SCACHE" 2474734 NIL SCACHE (NIL T) -7 NIL NIL) (-991 2473549 2473870 2473953 "SAOS" 2474043 T SAOS (NIL) -8 NIL NIL) (-990 2473117 2473152 2473323 "SAERFFC" 2473508 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-989 2467013 2473016 2473094 "SAE" 2473099 NIL SAE (NIL T T NIL) -8 NIL NIL) (-988 2466609 2466644 2466801 "SAEFACT" 2466972 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-987 2464935 2465249 2465648 "RURPK" 2466275 NIL RURPK (NIL T NIL) -7 NIL NIL) (-986 2463588 2463865 2464172 "RULESET" 2464771 NIL RULESET (NIL T T T) -8 NIL NIL) (-985 2460796 2461299 2461760 "RULE" 2463270 NIL RULE (NIL T T T) -8 NIL NIL) (-984 2460438 2460593 2460674 "RULECOLD" 2460748 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-983 2455330 2456124 2457040 "RSETGCD" 2459637 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-982 2444644 2449696 2449791 "RSETCAT" 2453856 NIL RSETCAT (NIL T T T T) -9 NIL 2454953) (-981 2442575 2443114 2443934 "RSETCAT-" 2443939 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-980 2435005 2436380 2437896 "RSDCMPK" 2441174 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-979 2433022 2433463 2433536 "RRCC" 2434612 NIL RRCC (NIL T T) -9 NIL 2434956) (-978 2432376 2432550 2432826 "RRCC-" 2432831 NIL RRCC- (NIL T T T) -8 NIL NIL) (-977 2406742 2416367 2416432 "RPOLCAT" 2426934 NIL RPOLCAT (NIL T T T) -9 NIL 2430092) (-976 2398246 2400584 2403702 "RPOLCAT-" 2403707 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-975 2389312 2396476 2396956 "ROUTINE" 2397786 T ROUTINE (NIL) -8 NIL NIL) (-974 2386017 2388868 2389015 "ROMAN" 2389185 T ROMAN (NIL) -8 NIL NIL) (-973 2384303 2384888 2385145 "ROIRC" 2385823 NIL ROIRC (NIL T T) -8 NIL NIL) (-972 2380707 2383011 2383040 "RNS" 2383336 T RNS (NIL) -9 NIL 2383606) (-971 2379221 2379604 2380135 "RNS-" 2380208 NIL RNS- (NIL T) -8 NIL NIL) (-970 2378646 2379054 2379083 "RNG" 2379088 T RNG (NIL) -9 NIL 2379109) (-969 2378043 2378405 2378446 "RMODULE" 2378506 NIL RMODULE (NIL T) -9 NIL 2378548) (-968 2376895 2376989 2377319 "RMCAT2" 2377944 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-967 2373609 2376078 2376399 "RMATRIX" 2376630 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-966 2366605 2368839 2368952 "RMATCAT" 2372261 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2373243) (-965 2365984 2366131 2366434 "RMATCAT-" 2366439 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-964 2365554 2365629 2365755 "RINTERP" 2365903 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-963 2364604 2365168 2365197 "RING" 2365307 T RING (NIL) -9 NIL 2365401) (-962 2364399 2364443 2364537 "RING-" 2364542 NIL RING- (NIL T) -8 NIL NIL) (-961 2363247 2363484 2363740 "RIDIST" 2364163 T RIDIST (NIL) -7 NIL NIL) (-960 2354569 2362721 2362924 "RGCHAIN" 2363096 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-959 2351574 2352188 2352856 "RF" 2353933 NIL RF (NIL T) -7 NIL NIL) (-958 2351223 2351286 2351387 "RFFACTOR" 2351505 NIL RFFACTOR (NIL T) -7 NIL NIL) (-957 2350951 2350986 2351081 "RFFACT" 2351182 NIL RFFACT (NIL T) -7 NIL NIL) (-956 2349081 2349445 2349825 "RFDIST" 2350591 T RFDIST (NIL) -7 NIL NIL) (-955 2348539 2348631 2348791 "RETSOL" 2348983 NIL RETSOL (NIL T T) -7 NIL NIL) (-954 2348131 2348211 2348253 "RETRACT" 2348443 NIL RETRACT (NIL T) -9 NIL NIL) (-953 2347983 2348008 2348092 "RETRACT-" 2348097 NIL RETRACT- (NIL T T) -8 NIL NIL) (-952 2340841 2347640 2347765 "RESULT" 2347878 T RESULT (NIL) -8 NIL NIL) (-951 2339426 2340115 2340312 "RESRING" 2340744 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-950 2339066 2339115 2339211 "RESLATC" 2339363 NIL RESLATC (NIL T) -7 NIL NIL) (-949 2338775 2338809 2338914 "REPSQ" 2339025 NIL REPSQ (NIL T) -7 NIL NIL) (-948 2336206 2336786 2337386 "REP" 2338195 T REP (NIL) -7 NIL NIL) (-947 2335907 2335941 2336050 "REPDB" 2336165 NIL REPDB (NIL T) -7 NIL NIL) (-946 2329852 2331231 2332451 "REP2" 2334719 NIL REP2 (NIL T) -7 NIL NIL) (-945 2326258 2326939 2327744 "REP1" 2329079 NIL REP1 (NIL T) -7 NIL NIL) (-944 2319004 2324419 2324871 "REGSET" 2325889 NIL REGSET (NIL T T T T) -8 NIL NIL) (-943 2317825 2318160 2318408 "REF" 2318789 NIL REF (NIL T) -8 NIL NIL) (-942 2317206 2317309 2317474 "REDORDER" 2317709 NIL REDORDER (NIL T T) -7 NIL NIL) (-941 2313175 2316440 2316661 "RECLOS" 2317037 NIL RECLOS (NIL T) -8 NIL NIL) (-940 2312232 2312413 2312626 "REALSOLV" 2312982 T REALSOLV (NIL) -7 NIL NIL) (-939 2312079 2312120 2312149 "REAL" 2312154 T REAL (NIL) -9 NIL 2312189) (-938 2308570 2309372 2310254 "REAL0Q" 2311244 NIL REAL0Q (NIL T) -7 NIL NIL) (-937 2304181 2305169 2306228 "REAL0" 2307551 NIL REAL0 (NIL T) -7 NIL NIL) (-936 2303589 2303661 2303866 "RDIV" 2304103 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-935 2302662 2302836 2303047 "RDIST" 2303411 NIL RDIST (NIL T) -7 NIL NIL) (-934 2301266 2301553 2301922 "RDETRS" 2302370 NIL RDETRS (NIL T T) -7 NIL NIL) (-933 2299087 2299541 2300076 "RDETR" 2300808 NIL RDETR (NIL T T) -7 NIL NIL) (-932 2297703 2297981 2298382 "RDEEFS" 2298803 NIL RDEEFS (NIL T T) -7 NIL NIL) (-931 2296203 2296509 2296938 "RDEEF" 2297391 NIL RDEEF (NIL T T) -7 NIL NIL) (-930 2290487 2293419 2293448 "RCFIELD" 2294725 T RCFIELD (NIL) -9 NIL 2295455) (-929 2288556 2289060 2289753 "RCFIELD-" 2289826 NIL RCFIELD- (NIL T) -8 NIL NIL) (-928 2284887 2286672 2286714 "RCAGG" 2287785 NIL RCAGG (NIL T) -9 NIL 2288250) (-927 2284518 2284612 2284772 "RCAGG-" 2284777 NIL RCAGG- (NIL T T) -8 NIL NIL) (-926 2283863 2283974 2284136 "RATRET" 2284402 NIL RATRET (NIL T) -7 NIL NIL) (-925 2283420 2283487 2283606 "RATFACT" 2283791 NIL RATFACT (NIL T) -7 NIL NIL) (-924 2282735 2282855 2283005 "RANDSRC" 2283290 T RANDSRC (NIL) -7 NIL NIL) (-923 2282472 2282516 2282587 "RADUTIL" 2282684 T RADUTIL (NIL) -7 NIL NIL) (-922 2275479 2281215 2281532 "RADIX" 2282187 NIL RADIX (NIL NIL) -8 NIL NIL) (-921 2267049 2275323 2275451 "RADFF" 2275456 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-920 2266700 2266775 2266804 "RADCAT" 2266961 T RADCAT (NIL) -9 NIL NIL) (-919 2266485 2266533 2266630 "RADCAT-" 2266635 NIL RADCAT- (NIL T) -8 NIL NIL) (-918 2264636 2266260 2266349 "QUEUE" 2266429 NIL QUEUE (NIL T) -8 NIL NIL) (-917 2261133 2264573 2264618 "QUAT" 2264623 NIL QUAT (NIL T) -8 NIL NIL) (-916 2260771 2260814 2260941 "QUATCT2" 2261084 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-915 2254564 2257944 2257985 "QUATCAT" 2258764 NIL QUATCAT (NIL T) -9 NIL 2259529) (-914 2250708 2251745 2253132 "QUATCAT-" 2253226 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-913 2248228 2249792 2249834 "QUAGG" 2250209 NIL QUAGG (NIL T) -9 NIL 2250384) (-912 2247153 2247626 2247798 "QFORM" 2248100 NIL QFORM (NIL NIL T) -8 NIL NIL) (-911 2238449 2243707 2243748 "QFCAT" 2244406 NIL QFCAT (NIL T) -9 NIL 2245399) (-910 2234021 2235222 2236813 "QFCAT-" 2236907 NIL QFCAT- (NIL T T) -8 NIL NIL) (-909 2233659 2233702 2233829 "QFCAT2" 2233972 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-908 2233119 2233229 2233359 "QEQUAT" 2233549 T QEQUAT (NIL) -8 NIL NIL) (-907 2226305 2227376 2228558 "QCMPACK" 2232052 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-906 2223881 2224302 2224730 "QALGSET" 2225960 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-905 2223126 2223300 2223532 "QALGSET2" 2223701 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-904 2221817 2222040 2222357 "PWFFINTB" 2222899 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-903 2220005 2220173 2220526 "PUSHVAR" 2221631 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-902 2215922 2216976 2217018 "PTRANFN" 2218902 NIL PTRANFN (NIL T) -9 NIL NIL) (-901 2214334 2214625 2214946 "PTPACK" 2215633 NIL PTPACK (NIL T) -7 NIL NIL) (-900 2213970 2214027 2214134 "PTFUNC2" 2214271 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-899 2208446 2212787 2212828 "PTCAT" 2213196 NIL PTCAT (NIL T) -9 NIL 2213358) (-898 2208104 2208139 2208263 "PSQFR" 2208405 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-897 2206699 2206997 2207331 "PSEUDLIN" 2207802 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-896 2193507 2195871 2198194 "PSETPK" 2204459 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-895 2186593 2189307 2189402 "PSETCAT" 2192383 NIL PSETCAT (NIL T T T T) -9 NIL 2193197) (-894 2184431 2185065 2185884 "PSETCAT-" 2185889 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-893 2183779 2183944 2183973 "PSCURVE" 2184241 T PSCURVE (NIL) -9 NIL 2184408) (-892 2180230 2181756 2181821 "PSCAT" 2182657 NIL PSCAT (NIL T T T) -9 NIL 2182897) (-891 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POLTOPOL (NIL NIL T) -7 NIL NIL) (-866 2105961 2110375 2110420 "POINT" 2110425 NIL POINT (NIL T) -8 NIL NIL) (-865 2104148 2104505 2104880 "PNTHEORY" 2105606 T PNTHEORY (NIL) -7 NIL NIL) (-864 2102576 2102873 2103282 "PMTOOLS" 2103846 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-863 2102169 2102247 2102364 "PMSYM" 2102492 NIL PMSYM (NIL T) -7 NIL NIL) (-862 2101679 2101748 2101922 "PMQFCAT" 2102094 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-861 2101034 2101144 2101300 "PMPRED" 2101556 NIL PMPRED (NIL T) -7 NIL NIL) (-860 2100430 2100516 2100677 "PMPREDFS" 2100935 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-859 2099076 2099284 2099668 "PMPLCAT" 2100192 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-858 2098608 2098687 2098839 "PMLSAGG" 2098991 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-857 2098085 2098161 2098341 "PMKERNEL" 2098526 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-856 2097702 2097777 2097890 "PMINS" 2098004 NIL PMINS (NIL T) -7 NIL NIL) (-855 2097132 2097201 2097416 "PMFS" 2097627 NIL PMFS (NIL T T T) -7 NIL NIL) (-854 2096363 2096481 2096685 "PMDOWN" 2097009 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-853 2095526 2095685 2095867 "PMASS" 2096201 T PMASS (NIL) -7 NIL NIL) (-852 2094800 2094911 2095074 "PMASSFS" 2095412 NIL PMASSFS (NIL T T) -7 NIL NIL) (-851 2094455 2094523 2094617 "PLOTTOOL" 2094726 T PLOTTOOL (NIL) -7 NIL NIL) (-850 2089077 2090266 2091414 "PLOT" 2093327 T PLOT (NIL) -8 NIL NIL) (-849 2084891 2085925 2086846 "PLOT3D" 2088176 T PLOT3D (NIL) -8 NIL NIL) (-848 2083803 2083980 2084215 "PLOT1" 2084695 NIL PLOT1 (NIL T) -7 NIL NIL) (-847 2059198 2063869 2068720 "PLEQN" 2079069 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-846 2058516 2058638 2058818 "PINTERP" 2059063 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-845 2058209 2058256 2058359 "PINTERPA" 2058463 NIL PINTERPA (NIL T T) -7 NIL NIL) (-844 2057436 2058003 2058096 "PI" 2058136 T PI (NIL) -8 NIL NIL) (-843 2055827 2056812 2056841 "PID" 2057023 T PID (NIL) -9 NIL 2057157) (-842 2055552 2055589 2055677 "PICOERCE" 2055784 NIL PICOERCE (NIL T) -7 NIL NIL) (-841 2054873 2055011 2055187 "PGROEB" 2055408 NIL PGROEB (NIL T) -7 NIL NIL) (-840 2050460 2051274 2052179 "PGE" 2053988 T PGE (NIL) -7 NIL NIL) (-839 2048584 2048830 2049196 "PGCD" 2050177 NIL PGCD (NIL T T T T) -7 NIL NIL) (-838 2047922 2048025 2048186 "PFRPAC" 2048468 NIL PFRPAC (NIL T) -7 NIL NIL) (-837 2044537 2046470 2046823 "PFR" 2047601 NIL PFR (NIL T) -8 NIL NIL) (-836 2042926 2043170 2043495 "PFOTOOLS" 2044284 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-835 2041459 2041698 2042049 "PFOQ" 2042683 NIL PFOQ (NIL T T T) -7 NIL NIL) (-834 2039936 2040148 2040510 "PFO" 2041243 NIL PFO (NIL T T T T T) -7 NIL NIL) (-833 2036459 2039825 2039894 "PF" 2039899 NIL PF (NIL NIL) -8 NIL NIL) (-832 2033887 2035168 2035197 "PFECAT" 2035782 T PFECAT (NIL) -9 NIL 2036166) (-831 2033332 2033486 2033700 "PFECAT-" 2033705 NIL PFECAT- (NIL T) -8 NIL NIL) (-830 2031936 2032187 2032488 "PFBRU" 2033081 NIL PFBRU (NIL T T) -7 NIL NIL) (-829 2029803 2030154 2030586 "PFBR" 2031587 NIL PFBR (NIL T T T 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"PBWLB" 2003980 NIL PBWLB (NIL T) -8 NIL NIL) (-815 1994966 1996534 1997870 "PATTERN" 2001142 NIL PATTERN (NIL T) -8 NIL NIL) (-814 1994598 1994655 1994764 "PATTERN2" 1994903 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-813 1992355 1992743 1993200 "PATTERN1" 1994187 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-812 1989750 1990304 1990785 "PATRES" 1991920 NIL PATRES (NIL T T) -8 NIL NIL) (-811 1989314 1989381 1989513 "PATRES2" 1989677 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-810 1987211 1987611 1988016 "PATMATCH" 1988983 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-809 1986747 1986930 1986972 "PATMAB" 1987079 NIL PATMAB (NIL T) -9 NIL 1987162) (-808 1985292 1985601 1985859 "PATLRES" 1986552 NIL PATLRES (NIL T T T) -8 NIL NIL) (-807 1984837 1984960 1985002 "PATAB" 1985007 NIL PATAB (NIL T) -9 NIL 1985179) (-806 1982318 1982850 1983423 "PARTPERM" 1984284 T PARTPERM (NIL) -7 NIL NIL) (-805 1981939 1982002 1982104 "PARSURF" 1982249 NIL PARSURF (NIL T) -8 NIL NIL) (-804 1981571 1981628 1981737 "PARSU2" 1981876 NIL PARSU2 (NIL T T) -7 NIL NIL) (-803 1981335 1981375 1981442 "PARSER" 1981524 T PARSER (NIL) -7 NIL NIL) (-802 1980956 1981019 1981121 "PARSCURV" 1981266 NIL PARSCURV (NIL T) -8 NIL NIL) (-801 1980588 1980645 1980754 "PARSC2" 1980893 NIL PARSC2 (NIL T T) -7 NIL NIL) (-800 1980227 1980285 1980382 "PARPCURV" 1980524 NIL PARPCURV (NIL T) -8 NIL NIL) (-799 1979859 1979916 1980025 "PARPC2" 1980164 NIL PARPC2 (NIL T T) -7 NIL NIL) (-798 1979379 1979465 1979584 "PAN2EXPR" 1979760 T PAN2EXPR (NIL) -7 NIL NIL) (-797 1978185 1978500 1978728 "PALETTE" 1979171 T PALETTE (NIL) -8 NIL NIL) (-796 1972035 1977444 1977638 "PADICRC" 1978040 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-795 1965243 1971381 1971565 "PADICRAT" 1971883 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-794 1963547 1965180 1965225 "PADIC" 1965230 NIL PADIC (NIL NIL) -8 NIL NIL) (-793 1960751 1962325 1962366 "PADICCT" 1962947 NIL PADICCT (NIL NIL) -9 NIL 1963229) (-792 1959708 1959908 1960176 "PADEPAC" 1960538 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-791 1958920 1959053 1959259 "PADE" 1959570 NIL PADE (NIL T T T) -7 NIL NIL) (-790 1956931 1957763 1958078 "OWP" 1958688 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-789 1956040 1956536 1956708 "OVAR" 1956799 NIL OVAR (NIL NIL) -8 NIL NIL) (-788 1955304 1955425 1955586 "OUT" 1955899 T OUT (NIL) -7 NIL NIL) (-787 1944350 1946529 1948699 "OUTFORM" 1953154 T OUTFORM (NIL) -8 NIL NIL) (-786 1943758 1944079 1944168 "OSI" 1944281 T OSI (NIL) -8 NIL NIL) (-785 1942503 1942730 1943015 "ORTHPOL" 1943505 NIL ORTHPOL (NIL T) -7 NIL NIL) (-784 1939874 1942164 1942302 "OREUP" 1942446 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-783 1937270 1939567 1939693 "ORESUP" 1939816 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-782 1934805 1935305 1935865 "OREPCTO" 1936759 NIL OREPCTO (NIL T T) -7 NIL NIL) (-781 1928714 1930920 1930961 "OREPCAT" 1933282 NIL OREPCAT (NIL T) -9 NIL 1934385) (-780 1925862 1926644 1927701 "OREPCAT-" 1927706 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-779 1925039 1925311 1925340 "ORDSET" 1925649 T ORDSET (NIL) -9 NIL 1925813) (-778 1924558 1924680 1924873 "ORDSET-" 1924878 NIL ORDSET- (NIL T) -8 NIL NIL) (-777 1923171 1923972 1924001 "ORDRING" 1924203 T ORDRING (NIL) -9 NIL 1924327) (-776 1922816 1922910 1923054 "ORDRING-" 1923059 NIL ORDRING- (NIL T) -8 NIL NIL) (-775 1922191 1922672 1922701 "ORDMON" 1922706 T ORDMON (NIL) -9 NIL 1922727) (-774 1921353 1921500 1921695 "ORDFUNS" 1922040 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-773 1920864 1921223 1921252 "ORDFIN" 1921257 T ORDFIN (NIL) -9 NIL 1921278) (-772 1917376 1919450 1919859 "ORDCOMP" 1920488 NIL ORDCOMP (NIL T) -8 NIL NIL) (-771 1916642 1916769 1916955 "ORDCOMP2" 1917236 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-770 1913150 1914032 1914869 "OPTPROB" 1915825 T OPTPROB (NIL) -8 NIL NIL) (-769 1909992 1910621 1911315 "OPTPACK" 1912476 T OPTPACK (NIL) -7 NIL NIL) (-768 1907717 1908453 1908482 "OPTCAT" 1909297 T OPTCAT (NIL) -9 NIL 1909943) (-767 1907485 1907524 1907590 "OPQUERY" 1907671 T OPQUERY (NIL) -7 NIL NIL) (-766 1904621 1905812 1906312 "OP" 1907017 NIL OP (NIL T) -8 NIL NIL) (-765 1901386 1903418 1903787 "ONECOMP" 1904285 NIL ONECOMP (NIL T) -8 NIL NIL) (-764 1900691 1900806 1900980 "ONECOMP2" 1901258 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-763 1900110 1900216 1900346 "OMSERVER" 1900581 T OMSERVER (NIL) -7 NIL NIL) (-762 1896998 1899550 1899591 "OMSAGG" 1899652 NIL OMSAGG (NIL T) -9 NIL 1899716) (-761 1895621 1895884 1896166 "OMPKG" 1896736 T OMPKG (NIL) -7 NIL NIL) (-760 1895050 1895153 1895182 "OM" 1895481 T OM (NIL) -9 NIL NIL) (-759 1893589 1894602 1894770 "OMLO" 1894931 NIL OMLO (NIL T T) -8 NIL NIL) (-758 1892519 1892666 1892892 "OMEXPR" 1893415 NIL OMEXPR (NIL T) -7 NIL NIL) (-757 1891837 1892065 1892201 "OMERR" 1892403 T OMERR (NIL) -8 NIL NIL) (-756 1891015 1891258 1891418 "OMERRK" 1891697 T OMERRK (NIL) -8 NIL NIL) (-755 1890493 1890692 1890800 "OMENC" 1890927 T OMENC (NIL) -8 NIL NIL) (-754 1884388 1885573 1886744 "OMDEV" 1889342 T OMDEV (NIL) -8 NIL NIL) (-753 1883457 1883628 1883822 "OMCONN" 1884214 T OMCONN (NIL) -8 NIL NIL) (-752 1882072 1883058 1883087 "OINTDOM" 1883092 T OINTDOM (NIL) -9 NIL 1883113) (-751 1877834 1879064 1879779 "OFMONOID" 1881389 NIL OFMONOID (NIL T) -8 NIL NIL) (-750 1877272 1877771 1877816 "ODVAR" 1877821 NIL ODVAR (NIL T) -8 NIL NIL) (-749 1874397 1876769 1876954 "ODR" 1877147 NIL ODR (NIL T T NIL) -8 NIL NIL) (-748 1866703 1874176 1874300 "ODPOL" 1874305 NIL ODPOL (NIL T) -8 NIL NIL) (-747 1860526 1866575 1866680 "ODP" 1866685 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-746 1859292 1859507 1859782 "ODETOOLS" 1860300 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-745 1856261 1856917 1857633 "ODESYS" 1858625 NIL ODESYS (NIL T T) -7 NIL NIL) (-744 1851165 1852073 1853096 "ODERTRIC" 1855336 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-743 1850591 1850673 1850867 "ODERED" 1851077 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-742 1847493 1848041 1848716 "ODERAT" 1850014 NIL ODERAT (NIL T T) -7 NIL NIL) (-741 1844461 1844925 1845521 "ODEPRRIC" 1847022 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-740 1842332 1842899 1843408 "ODEPROB" 1843972 T ODEPROB (NIL) -8 NIL NIL) (-739 1838864 1839347 1839993 "ODEPRIM" 1841811 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-738 1838117 1838219 1838477 "ODEPAL" 1838756 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-737 1834319 1835100 1835954 "ODEPACK" 1837283 T ODEPACK (NIL) -7 NIL NIL) (-736 1833356 1833463 1833691 "ODEINT" 1834208 NIL ODEINT (NIL T T) -7 NIL NIL) (-735 1827457 1828882 1830329 "ODEIFTBL" 1831929 T ODEIFTBL (NIL) -8 NIL NIL) (-734 1822801 1823587 1824545 "ODEEF" 1826616 NIL ODEEF (NIL T T) -7 NIL NIL) (-733 1822138 1822227 1822456 "ODECONST" 1822706 NIL ODECONST (NIL T T T) -7 NIL NIL) (-732 1820295 1820928 1820957 "ODECAT" 1821560 T ODECAT (NIL) -9 NIL 1822089) (-731 1817167 1820007 1820126 "OCT" 1820208 NIL OCT (NIL T) -8 NIL NIL) (-730 1816805 1816848 1816975 "OCTCT2" 1817118 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-729 1811638 1814076 1814117 "OC" 1815213 NIL OC (NIL T) -9 NIL 1816070) (-728 1808865 1809613 1810603 "OC-" 1810697 NIL OC- (NIL T T) -8 NIL NIL) (-727 1808243 1808685 1808714 "OCAMON" 1808719 T OCAMON (NIL) -9 NIL 1808740) (-726 1807696 1808103 1808132 "OASGP" 1808137 T OASGP (NIL) -9 NIL 1808157) (-725 1806983 1807446 1807475 "OAMONS" 1807515 T OAMONS (NIL) -9 NIL 1807558) (-724 1806423 1806830 1806859 "OAMON" 1806864 T OAMON (NIL) -9 NIL 1806884) (-723 1805727 1806219 1806248 "OAGROUP" 1806253 T OAGROUP (NIL) -9 NIL 1806273) (-722 1805417 1805467 1805555 "NUMTUBE" 1805671 NIL NUMTUBE (NIL T) -7 NIL NIL) (-721 1798990 1800508 1802044 "NUMQUAD" 1803901 T NUMQUAD (NIL) -7 NIL NIL) (-720 1794746 1795734 1796759 "NUMODE" 1797985 T NUMODE (NIL) -7 NIL NIL) (-719 1792149 1792995 1793024 "NUMINT" 1793941 T NUMINT (NIL) -9 NIL 1794697) (-718 1791097 1791294 1791512 "NUMFMT" 1791951 T NUMFMT (NIL) -7 NIL NIL) (-717 1777479 1780413 1782943 "NUMERIC" 1788606 NIL NUMERIC (NIL T) -7 NIL NIL) (-716 1771879 1776931 1777026 "NTSCAT" 1777031 NIL NTSCAT (NIL T T T T) -9 NIL 1777069) (-715 1771073 1771238 1771431 "NTPOLFN" 1771718 NIL NTPOLFN (NIL T) -7 NIL NIL) (-714 1758929 1767915 1768725 "NSUP" 1770295 NIL NSUP (NIL T) -8 NIL NIL) (-713 1758565 1758622 1758729 "NSUP2" 1758866 NIL NSUP2 (NIL T T) -7 NIL NIL) (-712 1748527 1758344 1758474 "NSMP" 1758479 NIL NSMP (NIL T T) -8 NIL NIL) (-711 1746959 1747260 1747617 "NREP" 1748215 NIL NREP (NIL T) -7 NIL NIL) (-710 1745550 1745802 1746160 "NPCOEF" 1746702 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-709 1744616 1744731 1744947 "NORMRETR" 1745431 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-708 1742669 1742959 1743366 "NORMPK" 1744324 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-707 1742354 1742382 1742506 "NORMMA" 1742635 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-706 1742181 1742311 1742340 "NONE" 1742345 T NONE (NIL) -8 NIL NIL) (-705 1741970 1741999 1742068 "NONE1" 1742145 NIL NONE1 (NIL T) -7 NIL NIL) (-704 1741455 1741517 1741702 "NODE1" 1741902 NIL NODE1 (NIL T T) -7 NIL NIL) (-703 1739748 1740618 1740873 "NNI" 1741220 T NNI (NIL) -8 NIL NIL) (-702 1738168 1738481 1738845 "NLINSOL" 1739416 NIL NLINSOL (NIL T) -7 NIL NIL) (-701 1734336 1735303 1736225 "NIPROB" 1737266 T NIPROB (NIL) -8 NIL NIL) (-700 1733093 1733327 1733629 "NFINTBAS" 1734098 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-699 1731801 1732032 1732313 "NCODIV" 1732861 NIL NCODIV (NIL T T) -7 NIL NIL) (-698 1731563 1731600 1731675 "NCNTFRAC" 1731758 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-697 1729743 1730107 1730527 "NCEP" 1731188 NIL NCEP (NIL T) -7 NIL NIL) (-696 1728654 1729393 1729422 "NASRING" 1729532 T NASRING (NIL) -9 NIL 1729606) (-695 1728449 1728493 1728587 "NASRING-" 1728592 NIL NASRING- (NIL T) -8 NIL NIL) (-694 1727602 1728101 1728130 "NARNG" 1728247 T NARNG (NIL) -9 NIL 1728338) (-693 1727294 1727361 1727495 "NARNG-" 1727500 NIL NARNG- (NIL T) -8 NIL NIL) (-692 1726173 1726380 1726615 "NAGSP" 1727079 T NAGSP (NIL) -7 NIL NIL) (-691 1717597 1719243 1720878 "NAGS" 1724558 T NAGS (NIL) -7 NIL NIL) (-690 1716161 1716465 1716792 "NAGF07" 1717290 T NAGF07 (NIL) -7 NIL NIL) (-689 1710743 1712023 1713319 "NAGF04" 1714885 T NAGF04 (NIL) -7 NIL NIL) (-688 1703775 1705373 1706990 "NAGF02" 1709146 T NAGF02 (NIL) -7 NIL NIL) (-687 1699039 1700129 1701236 "NAGF01" 1702688 T NAGF01 (NIL) -7 NIL NIL) (-686 1692699 1694257 1695834 "NAGE04" 1697482 T NAGE04 (NIL) -7 NIL NIL) (-685 1683940 1686043 1688155 "NAGE02" 1690607 T NAGE02 (NIL) -7 NIL NIL) (-684 1679933 1680870 1681824 "NAGE01" 1683006 T NAGE01 (NIL) -7 NIL NIL) (-683 1677740 1678271 1678826 "NAGD03" 1679398 T NAGD03 (NIL) -7 NIL NIL) (-682 1669526 1671445 1673390 "NAGD02" 1675815 T NAGD02 (NIL) -7 NIL NIL) (-681 1663385 1664798 1666226 "NAGD01" 1668118 T NAGD01 (NIL) -7 NIL NIL) (-680 1659642 1660452 1661277 "NAGC06" 1662580 T NAGC06 (NIL) -7 NIL NIL) (-679 1658119 1658448 1658801 "NAGC05" 1659309 T NAGC05 (NIL) -7 NIL NIL) (-678 1657503 1657620 1657762 "NAGC02" 1657997 T NAGC02 (NIL) -7 NIL NIL) (-677 1656564 1657121 1657162 "NAALG" 1657241 NIL NAALG (NIL T) -9 NIL 1657302) (-676 1656399 1656428 1656518 "NAALG-" 1656523 NIL NAALG- (NIL T T) -8 NIL NIL) (-675 1650349 1651457 1652644 "MULTSQFR" 1655295 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-674 1649668 1649743 1649927 "MULTFACT" 1650261 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-673 1642861 1646772 1646825 "MTSCAT" 1647885 NIL MTSCAT (NIL T T) -9 NIL 1648399) (-672 1642573 1642627 1642719 "MTHING" 1642801 NIL MTHING (NIL T) -7 NIL NIL) (-671 1642365 1642398 1642458 "MSYSCMD" 1642533 T MSYSCMD (NIL) -7 NIL NIL) (-670 1638477 1641120 1641440 "MSET" 1642078 NIL MSET (NIL T) -8 NIL NIL) (-669 1635572 1638038 1638080 "MSETAGG" 1638085 NIL MSETAGG (NIL T) -9 NIL 1638119) (-668 1631428 1632970 1633711 "MRING" 1634875 NIL MRING (NIL T T) -8 NIL NIL) (-667 1630998 1631065 1631194 "MRF2" 1631355 NIL MRF2 (NIL T T T) -7 NIL NIL) (-666 1630616 1630651 1630795 "MRATFAC" 1630957 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-665 1628228 1628523 1628954 "MPRFF" 1630321 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-664 1622248 1628083 1628179 "MPOLY" 1628184 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-663 1621738 1621773 1621981 "MPCPF" 1622207 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-662 1621254 1621297 1621480 "MPC3" 1621689 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-661 1620455 1620536 1620755 "MPC2" 1621169 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-660 1618756 1619093 1619483 "MONOTOOL" 1620115 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-659 1617880 1618215 1618244 "MONOID" 1618521 T MONOID (NIL) -9 NIL 1618693) (-658 1617258 1617421 1617664 "MONOID-" 1617669 NIL MONOID- (NIL T) -8 NIL NIL) (-657 1608238 1614224 1614284 "MONOGEN" 1614958 NIL MONOGEN (NIL T T) -9 NIL 1615414) (-656 1605456 1606191 1607191 "MONOGEN-" 1607310 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-655 1604315 1604735 1604764 "MONADWU" 1605156 T MONADWU (NIL) -9 NIL 1605394) (-654 1603687 1603846 1604094 "MONADWU-" 1604099 NIL MONADWU- (NIL T) -8 NIL NIL) (-653 1603072 1603290 1603319 "MONAD" 1603526 T MONAD (NIL) -9 NIL 1603638) (-652 1602757 1602835 1602967 "MONAD-" 1602972 NIL MONAD- (NIL T) -8 NIL NIL) (-651 1601008 1601670 1601949 "MOEBIUS" 1602510 NIL MOEBIUS (NIL T) -8 NIL NIL) (-650 1600401 1600779 1600820 "MODULE" 1600825 NIL MODULE (NIL T) -9 NIL 1600851) (-649 1599969 1600065 1600255 "MODULE-" 1600260 NIL MODULE- (NIL T T) -8 NIL NIL) (-648 1597640 1598335 1598661 "MODRING" 1599794 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-647 1594596 1595761 1596278 "MODOP" 1597172 NIL MODOP (NIL T T) -8 NIL NIL) (-646 1592783 1593235 1593576 "MODMONOM" 1594395 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-645 1582501 1590987 1591409 "MODMON" 1592411 NIL MODMON (NIL T T) -8 NIL NIL) (-644 1579627 1581345 1581621 "MODFIELD" 1582376 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-643 1579153 1579196 1579375 "MMAP" 1579578 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-642 1577389 1578166 1578207 "MLO" 1578624 NIL MLO (NIL T) -9 NIL 1578865) (-641 1574756 1575271 1575873 "MLIFT" 1576870 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-640 1574147 1574231 1574385 "MKUCFUNC" 1574667 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-639 1573746 1573816 1573939 "MKRECORD" 1574070 NIL MKRECORD (NIL T T) -7 NIL NIL) (-638 1572794 1572955 1573183 "MKFUNC" 1573557 NIL MKFUNC (NIL T) -7 NIL NIL) (-637 1572182 1572286 1572442 "MKFLCFN" 1572677 NIL MKFLCFN (NIL T) -7 NIL NIL) (-636 1571608 1571975 1572064 "MKCHSET" 1572126 NIL MKCHSET (NIL T) -8 NIL NIL) (-635 1570885 1570987 1571172 "MKBCFUNC" 1571501 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-634 1567569 1570439 1570575 "MINT" 1570769 T MINT (NIL) -8 NIL NIL) (-633 1566381 1566624 1566901 "MHROWRED" 1567324 NIL MHROWRED (NIL T) -7 NIL NIL) (-632 1561652 1564826 1565250 "MFLOAT" 1565977 T MFLOAT (NIL) -8 NIL NIL) (-631 1561009 1561085 1561256 "MFINFACT" 1561564 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-630 1557324 1558172 1559056 "MESH" 1560145 T MESH (NIL) -7 NIL NIL) (-629 1555714 1556026 1556379 "MDDFACT" 1557011 NIL MDDFACT (NIL T) -7 NIL NIL) (-628 1552556 1554873 1554915 "MDAGG" 1555170 NIL MDAGG (NIL T) -9 NIL 1555313) (-627 1542254 1551849 1552056 "MCMPLX" 1552369 T MCMPLX (NIL) -8 NIL NIL) (-626 1541395 1541541 1541741 "MCDEN" 1542103 NIL MCDEN (NIL T T) -7 NIL NIL) (-625 1539285 1539555 1539935 "MCALCFN" 1541125 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-624 1536907 1537430 1537991 "MATSTOR" 1538756 NIL MATSTOR (NIL T) -7 NIL NIL) (-623 1532915 1536282 1536529 "MATRIX" 1536692 NIL MATRIX (NIL T) -8 NIL NIL) (-622 1528685 1529388 1530124 "MATLIN" 1532272 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-621 1518882 1522020 1522097 "MATCAT" 1526935 NIL MATCAT (NIL T T T) -9 NIL 1528352) (-620 1515247 1516260 1517615 "MATCAT-" 1517620 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-619 1513849 1514002 1514333 "MATCAT2" 1515082 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-618 1511961 1512285 1512669 "MAPPKG3" 1513524 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-617 1510942 1511115 1511337 "MAPPKG2" 1511785 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-616 1509441 1509725 1510052 "MAPPKG1" 1510648 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-615 1509052 1509110 1509233 "MAPHACK3" 1509377 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-614 1508644 1508705 1508819 "MAPHACK2" 1508984 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-613 1508082 1508185 1508327 "MAPHACK1" 1508535 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-612 1506190 1506784 1507087 "MAGMA" 1507811 NIL MAGMA (NIL T) -8 NIL NIL) (-611 1502664 1504434 1504894 "M3D" 1505763 NIL M3D (NIL T) -8 NIL NIL) (-610 1496819 1501034 1501076 "LZSTAGG" 1501858 NIL LZSTAGG (NIL T) -9 NIL 1502153) (-609 1492792 1493950 1495407 "LZSTAGG-" 1495412 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-608 1489908 1490685 1491171 "LWORD" 1492338 NIL LWORD (NIL T) -8 NIL NIL) (-607 1483068 1489679 1489813 "LSQM" 1489818 NIL LSQM (NIL NIL T) -8 NIL NIL) (-606 1482292 1482431 1482659 "LSPP" 1482923 NIL LSPP (NIL T T T T) -7 NIL NIL) (-605 1480104 1480405 1480861 "LSMP" 1481981 NIL LSMP (NIL T T T T) -7 NIL NIL) (-604 1476883 1477557 1478287 "LSMP1" 1479406 NIL LSMP1 (NIL T) -7 NIL NIL) (-603 1470809 1476051 1476093 "LSAGG" 1476155 NIL LSAGG (NIL T) -9 NIL 1476233) (-602 1467504 1468428 1469641 "LSAGG-" 1469646 NIL LSAGG- (NIL T T) -8 NIL NIL) (-601 1465130 1466648 1466897 "LPOLY" 1467299 NIL LPOLY (NIL T T) -8 NIL NIL) (-600 1464712 1464797 1464920 "LPEFRAC" 1465039 NIL LPEFRAC (NIL T) -7 NIL NIL) (-599 1463059 1463806 1464059 "LO" 1464544 NIL LO (NIL T T T) -8 NIL NIL) (-598 1462712 1462824 1462853 "LOGIC" 1462964 T LOGIC (NIL) -9 NIL 1463044) (-597 1462574 1462597 1462668 "LOGIC-" 1462673 NIL LOGIC- (NIL T) -8 NIL NIL) (-596 1461767 1461907 1462100 "LODOOPS" 1462430 NIL LODOOPS (NIL T T) -7 NIL NIL) (-595 1459185 1461684 1461749 "LODO" 1461754 NIL LODO (NIL T NIL) -8 NIL NIL) (-594 1457731 1457966 1458317 "LODOF" 1458932 NIL LODOF (NIL T T) -7 NIL NIL) (-593 1454150 1456586 1456627 "LODOCAT" 1457059 NIL LODOCAT (NIL T) -9 NIL 1457270) (-592 1453884 1453942 1454068 "LODOCAT-" 1454073 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-591 1451198 1453725 1453843 "LODO2" 1453848 NIL LODO2 (NIL T T) -8 NIL NIL) (-590 1448627 1451135 1451180 "LODO1" 1451185 NIL LODO1 (NIL T) -8 NIL NIL) (-589 1447490 1447655 1447966 "LODEEF" 1448450 NIL LODEEF (NIL T T T) -7 NIL NIL) (-588 1442776 1445620 1445662 "LNAGG" 1446609 NIL LNAGG (NIL T) -9 NIL 1447053) (-587 1441923 1442137 1442479 "LNAGG-" 1442484 NIL LNAGG- (NIL T T) -8 NIL NIL) (-586 1438088 1438850 1439488 "LMOPS" 1441339 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-585 1437485 1437847 1437888 "LMODULE" 1437948 NIL LMODULE (NIL T) -9 NIL 1437990) (-584 1434731 1437130 1437253 "LMDICT" 1437395 NIL LMDICT (NIL T) -8 NIL NIL) (-583 1427958 1433677 1433975 "LIST" 1434466 NIL LIST (NIL T) -8 NIL NIL) (-582 1427483 1427557 1427696 "LIST3" 1427878 NIL LIST3 (NIL T T T) -7 NIL NIL) (-581 1426490 1426668 1426896 "LIST2" 1427301 NIL LIST2 (NIL T T) -7 NIL NIL) (-580 1424624 1424936 1425335 "LIST2MAP" 1426137 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-579 1423336 1424016 1424057 "LINEXP" 1424310 NIL LINEXP (NIL T) -9 NIL 1424458) (-578 1421983 1422243 1422540 "LINDEP" 1423088 NIL LINDEP (NIL T T) -7 NIL NIL) (-577 1418750 1419469 1420246 "LIMITRF" 1421238 NIL LIMITRF (NIL T) -7 NIL NIL) (-576 1417030 1417325 1417740 "LIMITPS" 1418445 NIL LIMITPS (NIL T T) -7 NIL NIL) (-575 1411485 1416541 1416769 "LIE" 1416851 NIL LIE (NIL T T) -8 NIL NIL) (-574 1410535 1410978 1411019 "LIECAT" 1411159 NIL LIECAT (NIL T) -9 NIL 1411310) (-573 1410376 1410403 1410491 "LIECAT-" 1410496 NIL LIECAT- (NIL T T) -8 NIL NIL) (-572 1402988 1409825 1409990 "LIB" 1410231 T LIB (NIL) -8 NIL NIL) (-571 1398625 1399506 1400441 "LGROBP" 1402105 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-570 1396495 1396768 1397129 "LF" 1398347 NIL LF (NIL T T) -7 NIL NIL) (-569 1395335 1396026 1396055 "LFCAT" 1396262 T LFCAT (NIL) -9 NIL 1396401) (-568 1392247 1392873 1393559 "LEXTRIPK" 1394701 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-567 1388953 1389817 1390320 "LEXP" 1391827 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-566 1387351 1387664 1388065 "LEADCDET" 1388635 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-565 1386547 1386621 1386848 "LAZM3PK" 1387272 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-564 1381463 1384626 1385163 "LAUPOL" 1386060 NIL LAUPOL (NIL T T) -8 NIL NIL) (-563 1381030 1381074 1381241 "LAPLACE" 1381413 NIL LAPLACE (NIL T T) -7 NIL NIL) (-562 1378958 1380131 1380382 "LA" 1380863 NIL LA (NIL T T T) -8 NIL NIL) (-561 1378020 1378614 1378655 "LALG" 1378716 NIL LALG (NIL T) -9 NIL 1378774) (-560 1377735 1377794 1377929 "LALG-" 1377934 NIL LALG- (NIL T T) -8 NIL NIL) (-559 1376645 1376832 1377129 "KOVACIC" 1377535 NIL KOVACIC (NIL T T) -7 NIL NIL) (-558 1376479 1376503 1376545 "KONVERT" 1376607 NIL KONVERT (NIL T) -9 NIL NIL) (-557 1376313 1376337 1376379 "KOERCE" 1376441 NIL KOERCE (NIL T) -9 NIL NIL) (-556 1374047 1374807 1375200 "KERNEL" 1375952 NIL KERNEL (NIL T) -8 NIL NIL) (-555 1373549 1373630 1373760 "KERNEL2" 1373961 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-554 1367400 1372088 1372143 "KDAGG" 1372520 NIL KDAGG (NIL T T) -9 NIL 1372726) (-553 1366929 1367053 1367258 "KDAGG-" 1367263 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-552 1360104 1366590 1366745 "KAFILE" 1366807 NIL KAFILE (NIL T) -8 NIL NIL) (-551 1354559 1359615 1359843 "JORDAN" 1359925 NIL JORDAN (NIL T T) -8 NIL NIL) (-550 1350858 1352764 1352819 "IXAGG" 1353748 NIL IXAGG (NIL T T) -9 NIL 1354207) (-549 1349777 1350083 1350502 "IXAGG-" 1350507 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-548 1345362 1349699 1349758 "IVECTOR" 1349763 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-547 1344128 1344365 1344631 "ITUPLE" 1345129 NIL ITUPLE (NIL T) -8 NIL NIL) (-546 1342564 1342741 1343047 "ITRIGMNP" 1343950 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-545 1341309 1341513 1341796 "ITFUN3" 1342340 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-544 1340941 1340998 1341107 "ITFUN2" 1341246 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-543 1338743 1339814 1340111 "ITAYLOR" 1340676 NIL ITAYLOR (NIL T) -8 NIL NIL) (-542 1327734 1332929 1334088 "ISUPS" 1337616 NIL ISUPS (NIL T) -8 NIL NIL) (-541 1326838 1326978 1327214 "ISUMP" 1327581 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-540 1322102 1326639 1326718 "ISTRING" 1326791 NIL ISTRING (NIL NIL) -8 NIL NIL) (-539 1321315 1321396 1321611 "IRURPK" 1322016 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-538 1320251 1320452 1320692 "IRSN" 1321095 T IRSN (NIL) -7 NIL NIL) (-537 1318286 1318641 1319076 "IRRF2F" 1319889 NIL IRRF2F (NIL T) -7 NIL NIL) (-536 1318033 1318071 1318147 "IRREDFFX" 1318242 NIL IRREDFFX (NIL T) -7 NIL NIL) (-535 1316648 1316907 1317206 "IROOT" 1317766 NIL IROOT (NIL T) -7 NIL NIL) (-534 1313286 1314337 1315027 "IR" 1315990 NIL IR (NIL T) -8 NIL NIL) (-533 1310899 1311394 1311960 "IR2" 1312764 NIL IR2 (NIL T T) -7 NIL NIL) (-532 1309975 1310088 1310308 "IR2F" 1310782 NIL IR2F (NIL T T) -7 NIL NIL) (-531 1309766 1309800 1309860 "IPRNTPK" 1309935 T IPRNTPK (NIL) -7 NIL NIL) (-530 1306320 1309655 1309724 "IPF" 1309729 NIL IPF (NIL NIL) -8 NIL NIL) (-529 1304637 1306245 1306302 "IPADIC" 1306307 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-528 1304136 1304194 1304383 "INVLAPLA" 1304573 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-527 1293785 1296138 1298524 "INTTR" 1301800 NIL INTTR (NIL T T) -7 NIL NIL) (-526 1290133 1290874 1291737 "INTTOOLS" 1292971 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-525 1289719 1289810 1289927 "INTSLPE" 1290036 T INTSLPE (NIL) -7 NIL NIL) (-524 1287669 1289642 1289701 "INTRVL" 1289706 NIL INTRVL (NIL T) -8 NIL NIL) (-523 1285276 1285788 1286362 "INTRF" 1287154 NIL INTRF (NIL T) -7 NIL NIL) (-522 1284691 1284788 1284929 "INTRET" 1285174 NIL INTRET (NIL T) -7 NIL NIL) (-521 1282693 1283082 1283551 "INTRAT" 1284299 NIL INTRAT (NIL T T) -7 NIL NIL) (-520 1279926 1280509 1281134 "INTPM" 1282178 NIL INTPM (NIL T T) -7 NIL NIL) (-519 1276635 1277234 1277978 "INTPAF" 1279312 NIL INTPAF (NIL T T T) -7 NIL NIL) (-518 1271886 1272830 1273863 "INTPACK" 1275622 T INTPACK (NIL) -7 NIL NIL) (-517 1268740 1271615 1271742 "INT" 1271779 T INT (NIL) -8 NIL NIL) (-516 1267992 1268144 1268352 "INTHERTR" 1268582 NIL INTHERTR (NIL T T) -7 NIL NIL) (-515 1267431 1267511 1267699 "INTHERAL" 1267906 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-514 1265277 1265720 1266177 "INTHEORY" 1266994 T INTHEORY (NIL) -7 NIL NIL) (-513 1256600 1258220 1259998 "INTG0" 1263629 NIL INTG0 (NIL T T T) -7 NIL NIL) (-512 1237173 1241963 1246773 "INTFTBL" 1251810 T INTFTBL (NIL) -8 NIL NIL) (-511 1236422 1236560 1236733 "INTFACT" 1237032 NIL INTFACT (NIL T) -7 NIL NIL) (-510 1233813 1234259 1234822 "INTEF" 1235976 NIL INTEF (NIL T T) -7 NIL NIL) (-509 1232274 1233023 1233052 "INTDOM" 1233353 T INTDOM (NIL) -9 NIL 1233560) (-508 1231643 1231817 1232059 "INTDOM-" 1232064 NIL INTDOM- (NIL T) -8 NIL NIL) (-507 1228135 1230067 1230122 "INTCAT" 1230921 NIL INTCAT (NIL T) -9 NIL 1231240) (-506 1227608 1227710 1227838 "INTBIT" 1228027 T INTBIT (NIL) -7 NIL NIL) (-505 1226283 1226437 1226750 "INTALG" 1227453 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-504 1225740 1225830 1226000 "INTAF" 1226187 NIL INTAF (NIL T T) -7 NIL NIL) (-503 1219194 1225550 1225690 "INTABL" 1225695 NIL INTABL (NIL T T T) -8 NIL NIL) (-502 1214144 1216873 1216902 "INS" 1217870 T INS (NIL) -9 NIL 1218551) (-501 1211384 1212155 1213129 "INS-" 1213202 NIL INS- (NIL T) -8 NIL NIL) (-500 1210163 1210390 1210687 "INPSIGN" 1211137 NIL INPSIGN (NIL T T) -7 NIL NIL) (-499 1209281 1209398 1209595 "INPRODPF" 1210043 NIL INPRODPF (NIL T T) -7 NIL NIL) (-498 1208175 1208292 1208529 "INPRODFF" 1209161 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-497 1207175 1207327 1207587 "INNMFACT" 1208011 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-496 1206372 1206469 1206657 "INMODGCD" 1207074 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-495 1204881 1205125 1205449 "INFSP" 1206117 NIL INFSP (NIL T T T) -7 NIL NIL) (-494 1204065 1204182 1204365 "INFPROD0" 1204761 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-493 1201075 1202234 1202725 "INFORM" 1203582 T INFORM (NIL) -8 NIL NIL) (-492 1200685 1200745 1200843 "INFORM1" 1201010 NIL INFORM1 (NIL T) -7 NIL NIL) (-491 1200208 1200297 1200411 "INFINITY" 1200591 T INFINITY (NIL) -7 NIL NIL) (-490 1198826 1199074 1199395 "INEP" 1199956 NIL INEP (NIL T T T) -7 NIL NIL) (-489 1198102 1198723 1198788 "INDE" 1198793 NIL INDE (NIL T) -8 NIL NIL) (-488 1197666 1197734 1197851 "INCRMAPS" 1198029 NIL INCRMAPS (NIL T) -7 NIL NIL) (-487 1192977 1193902 1194846 "INBFF" 1196754 NIL INBFF (NIL T) -7 NIL NIL) (-486 1189472 1192822 1192925 "IMATRIX" 1192930 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-485 1188184 1188307 1188622 "IMATQF" 1189328 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-484 1186404 1186631 1186968 "IMATLIN" 1187940 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-483 1181030 1186328 1186386 "ILIST" 1186391 NIL ILIST (NIL T NIL) -8 NIL NIL) (-482 1178983 1180890 1181003 "IIARRAY2" 1181008 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-481 1174351 1178894 1178958 "IFF" 1178963 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-480 1169394 1173643 1173831 "IFARRAY" 1174208 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-479 1168601 1169298 1169371 "IFAMON" 1169376 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-478 1168184 1168249 1168304 "IEVALAB" 1168511 NIL IEVALAB (NIL T T) -9 NIL NIL) (-477 1167859 1167927 1168087 "IEVALAB-" 1168092 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-476 1167517 1167773 1167836 "IDPO" 1167841 NIL IDPO (NIL T T) -8 NIL NIL) (-475 1166794 1167406 1167481 "IDPOAMS" 1167486 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-474 1166128 1166683 1166758 "IDPOAM" 1166763 NIL IDPOAM (NIL T T) -8 NIL NIL) (-473 1165213 1165463 1165517 "IDPC" 1165930 NIL IDPC (NIL T T) -9 NIL 1166079) (-472 1164709 1165105 1165178 "IDPAM" 1165183 NIL IDPAM (NIL T T) -8 NIL NIL) (-471 1164112 1164601 1164674 "IDPAG" 1164679 NIL IDPAG (NIL T T) -8 NIL NIL) (-470 1160367 1161215 1162110 "IDECOMP" 1163269 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-469 1153241 1154290 1155337 "IDEAL" 1159403 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-468 1152405 1152517 1152716 "ICDEN" 1153125 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-467 1151504 1151885 1152032 "ICARD" 1152278 T ICARD (NIL) -8 NIL NIL) (-466 1149576 1149889 1150292 "IBPTOOLS" 1151181 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-465 1145190 1149196 1149309 "IBITS" 1149495 NIL IBITS (NIL NIL) -8 NIL NIL) (-464 1141913 1142489 1143184 "IBATOOL" 1144607 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-463 1139693 1140154 1140687 "IBACHIN" 1141448 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-462 1137570 1139539 1139642 "IARRAY2" 1139647 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-461 1133723 1137496 1137553 "IARRAY1" 1137558 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-460 1127662 1132141 1132619 "IAN" 1133265 T IAN (NIL) -8 NIL NIL) (-459 1127173 1127230 1127403 "IALGFACT" 1127599 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-458 1126700 1126813 1126842 "HYPCAT" 1127049 T HYPCAT (NIL) -9 NIL NIL) (-457 1126238 1126355 1126541 "HYPCAT-" 1126546 NIL HYPCAT- (NIL T) -8 NIL NIL) (-456 1122917 1124248 1124290 "HOAGG" 1125271 NIL HOAGG (NIL T) -9 NIL 1125950) (-455 1121511 1121910 1122436 "HOAGG-" 1122441 NIL HOAGG- (NIL T T) -8 NIL NIL) (-454 1115342 1120952 1121118 "HEXADEC" 1121365 T HEXADEC (NIL) -8 NIL NIL) (-453 1114090 1114312 1114575 "HEUGCD" 1115119 NIL HEUGCD (NIL T) -7 NIL NIL) (-452 1113193 1113927 1114057 "HELLFDIV" 1114062 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-451 1111421 1112970 1113058 "HEAP" 1113137 NIL HEAP (NIL T) -8 NIL NIL) (-450 1105288 1111336 1111398 "HDP" 1111403 NIL HDP (NIL NIL T) -8 NIL NIL) (-449 1099000 1104925 1105076 "HDMP" 1105189 NIL HDMP (NIL NIL T) -8 NIL NIL) (-448 1098325 1098464 1098628 "HB" 1098856 T HB (NIL) -7 NIL NIL) (-447 1091822 1098171 1098275 "HASHTBL" 1098280 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-446 1089575 1091450 1091629 "HACKPI" 1091663 T HACKPI (NIL) -8 NIL NIL) (-445 1085271 1089429 1089541 "GTSET" 1089546 NIL GTSET (NIL T T T T) -8 NIL NIL) (-444 1078797 1085149 1085247 "GSTBL" 1085252 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-443 1071033 1077833 1078097 "GSERIES" 1078588 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-442 1070055 1070508 1070537 "GROUP" 1070798 T GROUP (NIL) -9 NIL 1070957) (-441 1069171 1069394 1069738 "GROUP-" 1069743 NIL GROUP- (NIL T) -8 NIL NIL) (-440 1067540 1067859 1068246 "GROEBSOL" 1068848 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-439 1066480 1066742 1066794 "GRMOD" 1067323 NIL GRMOD (NIL T T) -9 NIL 1067491) (-438 1066248 1066284 1066412 "GRMOD-" 1066417 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-437 1061576 1062602 1063602 "GRIMAGE" 1065268 T GRIMAGE (NIL) -8 NIL NIL) (-436 1060043 1060303 1060627 "GRDEF" 1061272 T GRDEF (NIL) -7 NIL NIL) (-435 1059487 1059603 1059744 "GRAY" 1059922 T GRAY (NIL) -7 NIL NIL) (-434 1058720 1059100 1059152 "GRALG" 1059305 NIL GRALG (NIL T T) -9 NIL 1059397) (-433 1058381 1058454 1058617 "GRALG-" 1058622 NIL GRALG- (NIL T T T) -8 NIL NIL) (-432 1055189 1057970 1058146 "GPOLSET" 1058288 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-431 1054545 1054602 1054859 "GOSPER" 1055126 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-430 1050304 1050983 1051509 "GMODPOL" 1054244 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-429 1049309 1049493 1049731 "GHENSEL" 1050116 NIL GHENSEL (NIL T T) -7 NIL NIL) (-428 1043375 1044218 1045244 "GENUPS" 1048393 NIL GENUPS (NIL T T) -7 NIL NIL) (-427 1043072 1043123 1043212 "GENUFACT" 1043318 NIL GENUFACT (NIL T) -7 NIL NIL) (-426 1042484 1042561 1042726 "GENPGCD" 1042990 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-425 1041958 1041993 1042206 "GENMFACT" 1042443 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-424 1040526 1040781 1041088 "GENEEZ" 1041701 NIL GENEEZ (NIL T T) -7 NIL NIL) (-423 1034400 1040139 1040300 "GDMP" 1040449 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-422 1023782 1028171 1029277 "GCNAALG" 1033383 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-421 1022203 1023075 1023104 "GCDDOM" 1023359 T GCDDOM (NIL) -9 NIL 1023516) (-420 1021673 1021800 1022015 "GCDDOM-" 1022020 NIL GCDDOM- (NIL T) -8 NIL NIL) (-419 1020345 1020530 1020834 "GB" 1021452 NIL GB (NIL T T T T) -7 NIL NIL) (-418 1008965 1011291 1013683 "GBINTERN" 1018036 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-417 1006802 1007094 1007515 "GBF" 1008640 NIL GBF (NIL T T T T) -7 NIL NIL) (-416 1005583 1005748 1006015 "GBEUCLID" 1006618 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-415 1004932 1005057 1005206 "GAUSSFAC" 1005454 T GAUSSFAC (NIL) -7 NIL NIL) (-414 1003309 1003611 1003924 "GALUTIL" 1004651 NIL GALUTIL (NIL T) -7 NIL NIL) (-413 1001626 1001900 1002223 "GALPOLYU" 1003036 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-412 999015 999305 999710 "GALFACTU" 1001323 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-411 990821 992320 993928 "GALFACT" 997447 NIL GALFACT (NIL T) -7 NIL NIL) (-410 988208 988866 988895 "FVFUN" 990051 T FVFUN (NIL) -9 NIL 990771) (-409 987473 987655 987684 "FVC" 987975 T FVC (NIL) -9 NIL 988158) (-408 987115 987270 987351 "FUNCTION" 987425 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-407 984785 985336 985825 "FT" 986646 T FT (NIL) -8 NIL NIL) (-406 983603 984086 984289 "FTEM" 984602 T FTEM (NIL) -8 NIL NIL) (-405 981868 982156 982558 "FSUPFACT" 983295 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-404 980265 980554 980886 "FST" 981556 T FST (NIL) -8 NIL NIL) (-403 979440 979546 979740 "FSRED" 980147 NIL FSRED (NIL T T) -7 NIL NIL) (-402 978119 978374 978728 "FSPRMELT" 979155 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-401 975204 975642 976141 "FSPECF" 977682 NIL FSPECF (NIL T T) -7 NIL NIL) (-400 957577 966134 966175 "FS" 970013 NIL FS (NIL T) -9 NIL 972295) (-399 946227 949217 953273 "FS-" 953570 NIL FS- (NIL T T) -8 NIL NIL) (-398 945743 945797 945973 "FSINT" 946168 NIL FSINT (NIL T T) -7 NIL NIL) (-397 944024 944736 945039 "FSERIES" 945522 NIL FSERIES (NIL T T) -8 NIL NIL) (-396 943042 943158 943388 "FSCINT" 943904 NIL FSCINT (NIL T T) -7 NIL NIL) (-395 939276 941986 942028 "FSAGG" 942398 NIL FSAGG (NIL T) -9 NIL 942657) (-394 937038 937639 938435 "FSAGG-" 938530 NIL FSAGG- (NIL T T) -8 NIL NIL) (-393 936080 936223 936450 "FSAGG2" 936891 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-392 933739 934018 934571 "FS2UPS" 935798 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-391 933325 933368 933521 "FS2" 933690 NIL FS2 (NIL T T T T) -7 NIL NIL) (-390 932185 932356 932664 "FS2EXPXP" 933150 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-389 931611 931726 931878 "FRUTIL" 932065 NIL FRUTIL (NIL T) -7 NIL NIL) (-388 923032 927110 928466 "FR" 930287 NIL FR (NIL T) -8 NIL NIL) (-387 918108 920751 920792 "FRNAALG" 922188 NIL FRNAALG (NIL T) -9 NIL 922795) (-386 913787 914857 916132 "FRNAALG-" 916882 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-385 913425 913468 913595 "FRNAAF2" 913738 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-384 911790 912282 912576 "FRMOD" 913238 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-383 909513 910181 910497 "FRIDEAL" 911581 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-382 908712 908799 909086 "FRIDEAL2" 909420 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-381 907969 908377 908419 "FRETRCT" 908424 NIL FRETRCT (NIL T) -9 NIL 908595) (-380 907081 907312 907663 "FRETRCT-" 907668 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-379 904290 905510 905570 "FRAMALG" 906452 NIL FRAMALG (NIL T T) -9 NIL 906744) (-378 902423 902879 903509 "FRAMALG-" 903732 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-377 896325 901898 902174 "FRAC" 902179 NIL FRAC (NIL T) -8 NIL NIL) (-376 895961 896018 896125 "FRAC2" 896262 NIL FRAC2 (NIL T T) -7 NIL NIL) (-375 895597 895654 895761 "FR2" 895898 NIL FR2 (NIL T T) -7 NIL NIL) (-374 890270 893183 893212 "FPS" 894331 T FPS (NIL) -9 NIL 894887) (-373 889719 889828 889992 "FPS-" 890138 NIL FPS- (NIL T) -8 NIL NIL) (-372 887167 888864 888893 "FPC" 889118 T FPC (NIL) -9 NIL 889260) (-371 886960 887000 887097 "FPC-" 887102 NIL FPC- (NIL T) -8 NIL NIL) (-370 885838 886448 886490 "FPATMAB" 886495 NIL FPATMAB (NIL T) -9 NIL 886647) (-369 883538 884014 884440 "FPARFRAC" 885475 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-368 878933 879430 880112 "FORTRAN" 882970 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-367 876649 877149 877688 "FORT" 878414 T FORT (NIL) -7 NIL NIL) (-366 874324 874886 874915 "FORTFN" 875975 T FORTFN (NIL) -9 NIL 876599) (-365 874087 874137 874166 "FORTCAT" 874225 T FORTCAT (NIL) -9 NIL 874287) (-364 872147 872630 873029 "FORMULA" 873708 T FORMULA (NIL) -8 NIL NIL) (-363 871935 871965 872034 "FORMULA1" 872111 NIL FORMULA1 (NIL T) -7 NIL NIL) (-362 871458 871510 871683 "FORDER" 871877 NIL FORDER (NIL T T T T) -7 NIL NIL) (-361 870554 870718 870911 "FOP" 871285 T FOP (NIL) -7 NIL NIL) (-360 869162 869834 870008 "FNLA" 870436 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-359 867830 868219 868248 "FNCAT" 868820 T FNCAT (NIL) -9 NIL 869113) (-358 867396 867789 867817 "FNAME" 867822 T FNAME (NIL) -8 NIL NIL) (-357 866055 867028 867057 "FMTC" 867062 T FMTC (NIL) -9 NIL 867097) (-356 862373 863580 864208 "FMONOID" 865460 NIL FMONOID (NIL T) -8 NIL NIL) (-355 861593 862116 862264 "FM" 862269 NIL FM (NIL T T) -8 NIL NIL) (-354 859016 859662 859691 "FMFUN" 860835 T FMFUN (NIL) -9 NIL 861543) (-353 858284 858465 858494 "FMC" 858784 T FMC (NIL) -9 NIL 858966) (-352 855513 856347 856401 "FMCAT" 857583 NIL FMCAT (NIL T T) -9 NIL 858077) (-351 854408 855281 855380 "FM1" 855458 NIL FM1 (NIL T T) -8 NIL NIL) (-350 852182 852598 853092 "FLOATRP" 853959 NIL FLOATRP (NIL T) -7 NIL NIL) (-349 845668 849838 850468 "FLOAT" 851572 T FLOAT (NIL) -8 NIL NIL) (-348 843106 843606 844184 "FLOATCP" 845135 NIL FLOATCP (NIL T) -7 NIL NIL) (-347 841894 842742 842783 "FLINEXP" 842788 NIL FLINEXP (NIL T) -9 NIL 842881) (-346 841049 841284 841611 "FLINEXP-" 841616 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-345 840125 840269 840493 "FLASORT" 840901 NIL FLASORT (NIL T T) -7 NIL NIL) (-344 837343 838185 838238 "FLALG" 839465 NIL FLALG (NIL T T) -9 NIL 839932) (-343 831127 834829 834871 "FLAGG" 836133 NIL FLAGG (NIL T) -9 NIL 836785) (-342 829853 830192 830682 "FLAGG-" 830687 NIL FLAGG- (NIL T T) -8 NIL NIL) (-341 828895 829038 829265 "FLAGG2" 829706 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-340 825867 826885 826945 "FINRALG" 828073 NIL FINRALG (NIL T T) -9 NIL 828581) (-339 825027 825256 825595 "FINRALG-" 825600 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-338 824433 824646 824675 "FINITE" 824871 T FINITE (NIL) -9 NIL 824978) (-337 816892 819053 819094 "FINAALG" 822761 NIL FINAALG (NIL T) -9 NIL 824214) (-336 812233 813274 814418 "FINAALG-" 815797 NIL FINAALG- (NIL T T) -8 NIL NIL) (-335 811628 811988 812091 "FILE" 812163 NIL FILE (NIL T) -8 NIL NIL) (-334 810312 810624 810679 "FILECAT" 811363 NIL FILECAT (NIL T T) -9 NIL 811579) (-333 808174 809730 809759 "FIELD" 809799 T FIELD (NIL) -9 NIL 809879) (-332 806794 807179 807690 "FIELD-" 807695 NIL FIELD- (NIL T) -8 NIL NIL) (-331 804609 805431 805777 "FGROUP" 806481 NIL FGROUP (NIL T) -8 NIL NIL) (-330 803699 803863 804083 "FGLMICPK" 804441 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-329 799501 803624 803681 "FFX" 803686 NIL FFX (NIL T NIL) -8 NIL NIL) (-328 799102 799163 799298 "FFSLPE" 799434 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-327 795097 795874 796670 "FFPOLY" 798338 NIL FFPOLY (NIL T) -7 NIL NIL) (-326 794601 794637 794846 "FFPOLY2" 795055 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-325 790423 794520 794583 "FFP" 794588 NIL FFP (NIL T NIL) -8 NIL NIL) (-324 785791 790334 790398 "FF" 790403 NIL FF (NIL NIL NIL) -8 NIL NIL) (-323 780887 785134 785324 "FFNBX" 785645 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-322 775797 780022 780280 "FFNBP" 780741 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-321 770400 775081 775292 "FFNB" 775630 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-320 769232 769430 769745 "FFINTBAS" 770197 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-319 765455 767695 767724 "FFIELDC" 768344 T FFIELDC (NIL) -9 NIL 768720) (-318 764118 764488 764985 "FFIELDC-" 764990 NIL FFIELDC- (NIL T) -8 NIL NIL) (-317 763688 763733 763857 "FFHOM" 764060 NIL FFHOM (NIL T T T) -7 NIL NIL) (-316 761386 761870 762387 "FFF" 763203 NIL FFF (NIL T) -7 NIL NIL) (-315 756974 761128 761229 "FFCGX" 761329 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-314 752576 756706 756813 "FFCGP" 756917 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-313 747729 752303 752411 "FFCG" 752512 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-312 729674 738797 738884 "FFCAT" 744049 NIL FFCAT (NIL T T T) -9 NIL 745536) (-311 724872 725919 727233 "FFCAT-" 728463 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-310 724283 724326 724561 "FFCAT2" 724823 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-309 713483 717273 718490 "FEXPR" 723138 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-308 712482 712917 712959 "FEVALAB" 713043 NIL FEVALAB (NIL T) -9 NIL 713304) (-307 711641 711851 712189 "FEVALAB-" 712194 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-306 710234 711024 711227 "FDIV" 711540 NIL FDIV (NIL T T T T) -8 NIL NIL) (-305 707300 708015 708131 "FDIVCAT" 709699 NIL FDIVCAT (NIL T T T T) -9 NIL 710136) (-304 707062 707089 707259 "FDIVCAT-" 707264 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-303 706282 706369 706646 "FDIV2" 706969 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-302 704975 705232 705519 "FCPAK1" 706015 T FCPAK1 (NIL) -7 NIL NIL) (-301 704103 704475 704616 "FCOMP" 704866 NIL FCOMP (NIL T) -8 NIL NIL) (-300 687743 691155 694715 "FC" 700563 T FC (NIL) -8 NIL NIL) (-299 680338 684384 684425 "FAXF" 686227 NIL FAXF (NIL T) -9 NIL 686918) (-298 677617 678272 679097 "FAXF-" 679562 NIL FAXF- (NIL T T) -8 NIL NIL) (-297 672717 676993 677169 "FARRAY" 677474 NIL FARRAY (NIL T) -8 NIL NIL) (-296 668107 670178 670231 "FAMR" 671243 NIL FAMR (NIL T T) -9 NIL 671703) (-295 666998 667300 667734 "FAMR-" 667739 NIL FAMR- (NIL T T T) -8 NIL NIL) (-294 666194 666920 666973 "FAMONOID" 666978 NIL FAMONOID (NIL T) -8 NIL NIL) (-293 664026 664710 664764 "FAMONC" 665705 NIL FAMONC (NIL T T) -9 NIL 666090) (-292 662718 663780 663917 "FAGROUP" 663922 NIL FAGROUP (NIL T) -8 NIL NIL) (-291 660521 660840 661242 "FACUTIL" 662399 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-290 659620 659805 660027 "FACTFUNC" 660331 NIL FACTFUNC (NIL T) -7 NIL NIL) (-289 651943 658871 659083 "EXPUPXS" 659476 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-288 649426 649966 650552 "EXPRTUBE" 651377 T EXPRTUBE (NIL) -7 NIL NIL) (-287 645620 646212 646949 "EXPRODE" 648765 NIL EXPRODE (NIL T T) -7 NIL NIL) (-286 630782 644279 644705 "EXPR" 645226 NIL EXPR (NIL T) -8 NIL NIL) (-285 625210 625797 626609 "EXPR2UPS" 630080 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-284 624846 624903 625010 "EXPR2" 625147 NIL EXPR2 (NIL T T) -7 NIL NIL) (-283 616200 623983 624278 "EXPEXPAN" 624684 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-282 616027 616157 616186 "EXIT" 616191 T EXIT (NIL) -8 NIL NIL) (-281 615654 615716 615829 "EVALCYC" 615959 NIL EVALCYC (NIL T) -7 NIL NIL) (-280 615194 615312 615354 "EVALAB" 615524 NIL EVALAB (NIL T) -9 NIL 615628) (-279 614675 614797 615018 "EVALAB-" 615023 NIL EVALAB- (NIL T T) -8 NIL NIL) (-278 612137 613449 613478 "EUCDOM" 614033 T EUCDOM (NIL) -9 NIL 614383) (-277 610542 610984 611574 "EUCDOM-" 611579 NIL EUCDOM- (NIL T) -8 NIL NIL) (-276 598120 600868 603608 "ESTOOLS" 607822 T ESTOOLS (NIL) -7 NIL NIL) (-275 597756 597813 597920 "ESTOOLS2" 598057 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-274 597507 597549 597629 "ESTOOLS1" 597708 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-273 591444 593168 593197 "ES" 595961 T ES (NIL) -9 NIL 597367) (-272 586392 587678 589495 "ES-" 589659 NIL ES- (NIL T) -8 NIL NIL) (-271 582767 583527 584307 "ESCONT" 585632 T ESCONT (NIL) -7 NIL NIL) (-270 582512 582544 582626 "ESCONT1" 582729 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-269 582187 582237 582337 "ES2" 582456 NIL ES2 (NIL T T) -7 NIL NIL) (-268 581817 581875 581984 "ES1" 582123 NIL ES1 (NIL T T) -7 NIL NIL) (-267 581033 581162 581338 "ERROR" 581661 T ERROR (NIL) -7 NIL NIL) (-266 574536 580892 580983 "EQTBL" 580988 NIL EQTBL (NIL T T) -8 NIL NIL) (-265 566973 569854 571301 "EQ" 573122 NIL -3221 (NIL T) -8 NIL NIL) (-264 566605 566662 566771 "EQ2" 566910 NIL EQ2 (NIL T T) -7 NIL NIL) (-263 561897 562943 564036 "EP" 565544 NIL EP (NIL T) -7 NIL NIL) (-262 561056 561620 561649 "ENTIRER" 561654 T ENTIRER (NIL) -9 NIL 561699) (-261 557512 559011 559381 "EMR" 560855 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-260 556655 556840 556895 "ELTAGG" 557275 NIL ELTAGG (NIL T T) -9 NIL 557486) (-259 556374 556436 556577 "ELTAGG-" 556582 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-258 556162 556191 556246 "ELTAB" 556330 NIL ELTAB (NIL T T) -9 NIL NIL) (-257 555288 555434 555633 "ELFUTS" 556013 NIL ELFUTS (NIL T T) -7 NIL NIL) (-256 555029 555085 555114 "ELEMFUN" 555219 T ELEMFUN (NIL) -9 NIL NIL) (-255 554899 554920 554988 "ELEMFUN-" 554993 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-254 549790 552999 553041 "ELAGG" 553981 NIL ELAGG (NIL T) -9 NIL 554444) (-253 548075 548509 549172 "ELAGG-" 549177 NIL ELAGG- (NIL T T) -8 NIL NIL) (-252 540943 542742 543569 "EFUPXS" 547351 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-251 534393 536194 537004 "EFULS" 540219 NIL EFULS (NIL T T T) -8 NIL NIL) (-250 531824 532182 532660 "EFSTRUC" 534025 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-249 520896 522461 524021 "EF" 530339 NIL EF (NIL T T) -7 NIL NIL) (-248 519997 520381 520530 "EAB" 520767 T EAB (NIL) -8 NIL NIL) (-247 519210 519956 519984 "E04UCFA" 519989 T E04UCFA (NIL) -8 NIL NIL) (-246 518423 519169 519197 "E04NAFA" 519202 T E04NAFA (NIL) -8 NIL NIL) (-245 517636 518382 518410 "E04MBFA" 518415 T E04MBFA (NIL) -8 NIL NIL) (-244 516849 517595 517623 "E04JAFA" 517628 T E04JAFA (NIL) -8 NIL NIL) (-243 516064 516808 516836 "E04GCFA" 516841 T E04GCFA (NIL) -8 NIL NIL) (-242 515279 516023 516051 "E04FDFA" 516056 T E04FDFA (NIL) -8 NIL NIL) (-241 514492 515238 515266 "E04DGFA" 515271 T E04DGFA (NIL) -8 NIL NIL) (-240 508677 510022 511384 "E04AGNT" 513150 T E04AGNT (NIL) -7 NIL NIL) (-239 507403 507883 507924 "DVARCAT" 508399 NIL DVARCAT (NIL T) -9 NIL 508597) (-238 506607 506819 507133 "DVARCAT-" 507138 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-237 499469 506409 506536 "DSMP" 506541 NIL DSMP (NIL T T T) -8 NIL NIL) (-236 494279 495414 496482 "DROPT" 498421 T DROPT (NIL) -8 NIL NIL) (-235 493944 494003 494101 "DROPT1" 494214 NIL DROPT1 (NIL T) -7 NIL NIL) (-234 489059 490185 491322 "DROPT0" 492827 T DROPT0 (NIL) -7 NIL NIL) (-233 487404 487729 488115 "DRAWPT" 488693 T DRAWPT (NIL) -7 NIL NIL) (-232 482079 482978 484033 "DRAW" 486402 NIL DRAW (NIL T) -7 NIL NIL) (-231 481720 481771 481887 "DRAWHACK" 482022 NIL DRAWHACK (NIL T) -7 NIL NIL) (-230 480451 480720 481011 "DRAWCX" 481449 T DRAWCX (NIL) -7 NIL NIL) (-229 479969 480037 480187 "DRAWCURV" 480377 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-228 470441 472399 474514 "DRAWCFUN" 477874 T DRAWCFUN (NIL) -7 NIL NIL) (-227 467254 469136 469178 "DQAGG" 469807 NIL DQAGG (NIL T) -9 NIL 470080) (-226 455760 462498 462581 "DPOLCAT" 464419 NIL DPOLCAT (NIL T T T T) -9 NIL 464963) (-225 450600 451946 453903 "DPOLCAT-" 453908 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-224 444684 450462 450559 "DPMO" 450564 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-223 438671 444465 444631 "DPMM" 444636 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-222 438304 438380 438478 "DOMAIN" 438593 T DOMAIN (NIL) -8 NIL NIL) (-221 432016 437941 438092 "DMP" 438205 NIL DMP (NIL NIL T) -8 NIL NIL) (-220 431616 431672 431816 "DLP" 431954 NIL DLP (NIL T) -7 NIL NIL) (-219 425260 430717 430944 "DLIST" 431421 NIL DLIST (NIL T) -8 NIL NIL) (-218 422106 424115 424157 "DLAGG" 424707 NIL DLAGG (NIL T) -9 NIL 424936) (-217 420815 421507 421536 "DIVRING" 421686 T DIVRING (NIL) -9 NIL 421794) (-216 419803 420056 420449 "DIVRING-" 420454 NIL DIVRING- (NIL T) -8 NIL NIL) (-215 417905 418262 418668 "DISPLAY" 419417 T DISPLAY (NIL) -7 NIL NIL) (-214 411794 417819 417882 "DIRPROD" 417887 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-213 410642 410845 411110 "DIRPROD2" 411587 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-212 400272 406277 406331 "DIRPCAT" 406739 NIL DIRPCAT (NIL NIL T) -9 NIL 407566) (-211 397598 398240 399121 "DIRPCAT-" 399458 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-210 396885 397045 397231 "DIOSP" 397432 T DIOSP (NIL) -7 NIL NIL) (-209 393587 395797 395839 "DIOPS" 396273 NIL DIOPS (NIL T) -9 NIL 396502) (-208 393136 393250 393441 "DIOPS-" 393446 NIL DIOPS- (NIL T T) -8 NIL NIL) (-207 392007 392645 392674 "DIFRING" 392861 T DIFRING (NIL) -9 NIL 392970) (-206 391653 391730 391882 "DIFRING-" 391887 NIL DIFRING- (NIL T) -8 NIL NIL) (-205 389442 390724 390765 "DIFEXT" 391124 NIL DIFEXT (NIL T) -9 NIL 391417) (-204 387728 388156 388821 "DIFEXT-" 388826 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-203 385050 387260 387302 "DIAGG" 387307 NIL DIAGG (NIL T) -9 NIL 387327) (-202 384434 384591 384843 "DIAGG-" 384848 NIL DIAGG- (NIL T T) -8 NIL NIL) (-201 379899 383393 383670 "DHMATRIX" 384203 NIL DHMATRIX (NIL T) -8 NIL NIL) (-200 375511 376420 377430 "DFSFUN" 378909 T DFSFUN (NIL) -7 NIL NIL) (-199 370297 374225 374590 "DFLOAT" 375166 T DFLOAT (NIL) -8 NIL NIL) (-198 368530 368811 369206 "DFINTTLS" 370005 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-197 365563 366565 366963 "DERHAM" 368197 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-196 363412 365338 365427 "DEQUEUE" 365507 NIL DEQUEUE (NIL T) -8 NIL NIL) (-195 362630 362763 362958 "DEGRED" 363274 NIL DEGRED (NIL T T) -7 NIL NIL) (-194 359046 359787 360635 "DEFINTRF" 361862 NIL DEFINTRF (NIL T) -7 NIL NIL) (-193 356585 357052 357648 "DEFINTEF" 358567 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-192 350416 356026 356192 "DECIMAL" 356439 T DECIMAL (NIL) -8 NIL NIL) (-191 347928 348386 348892 "DDFACT" 349960 NIL DDFACT (NIL T T) -7 NIL NIL) (-190 347524 347567 347718 "DBLRESP" 347879 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-189 345234 345568 345937 "DBASE" 347282 NIL DBASE (NIL T) -8 NIL NIL) (-188 344369 345193 345221 "D03FAFA" 345226 T D03FAFA (NIL) -8 NIL NIL) (-187 343505 344328 344356 "D03EEFA" 344361 T D03EEFA (NIL) -8 NIL NIL) (-186 341455 341921 342410 "D03AGNT" 343036 T D03AGNT (NIL) -7 NIL NIL) (-185 340773 341414 341442 "D02EJFA" 341447 T D02EJFA (NIL) -8 NIL NIL) (-184 340091 340732 340760 "D02CJFA" 340765 T D02CJFA (NIL) -8 NIL NIL) (-183 339409 340050 340078 "D02BHFA" 340083 T D02BHFA (NIL) -8 NIL NIL) (-182 338727 339368 339396 "D02BBFA" 339401 T D02BBFA (NIL) -8 NIL NIL) (-181 331925 333513 335119 "D02AGNT" 337141 T D02AGNT (NIL) -7 NIL NIL) (-180 329694 330216 330762 "D01WGTS" 331399 T D01WGTS (NIL) -7 NIL NIL) (-179 328797 329653 329681 "D01TRNS" 329686 T D01TRNS (NIL) -8 NIL NIL) (-178 327900 328756 328784 "D01GBFA" 328789 T D01GBFA (NIL) -8 NIL NIL) (-177 327003 327859 327887 "D01FCFA" 327892 T D01FCFA (NIL) -8 NIL NIL) (-176 326106 326962 326990 "D01ASFA" 326995 T D01ASFA (NIL) -8 NIL NIL) (-175 325209 326065 326093 "D01AQFA" 326098 T D01AQFA (NIL) -8 NIL NIL) (-174 324312 325168 325196 "D01APFA" 325201 T D01APFA (NIL) -8 NIL NIL) (-173 323415 324271 324299 "D01ANFA" 324304 T D01ANFA (NIL) -8 NIL NIL) (-172 322518 323374 323402 "D01AMFA" 323407 T D01AMFA (NIL) -8 NIL NIL) (-171 321621 322477 322505 "D01ALFA" 322510 T D01ALFA (NIL) -8 NIL NIL) (-170 320724 321580 321608 "D01AKFA" 321613 T D01AKFA (NIL) -8 NIL NIL) (-169 319827 320683 320711 "D01AJFA" 320716 T D01AJFA (NIL) -8 NIL NIL) (-168 313131 314680 316239 "D01AGNT" 318288 T D01AGNT (NIL) -7 NIL NIL) (-167 312468 312596 312748 "CYCLOTOM" 312999 T CYCLOTOM (NIL) -7 NIL NIL) (-166 309203 309916 310643 "CYCLES" 311761 T CYCLES (NIL) -7 NIL NIL) (-165 308515 308649 308820 "CVMP" 309064 NIL CVMP (NIL T) -7 NIL NIL) (-164 306297 306554 306929 "CTRIGMNP" 308243 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-163 305671 305770 305923 "CSTTOOLS" 306194 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-162 301470 302127 302885 "CRFP" 304983 NIL CRFP (NIL T T) -7 NIL NIL) (-161 300517 300702 300930 "CRAPACK" 301274 NIL CRAPACK (NIL T) -7 NIL NIL) (-160 299901 300002 300206 "CPMATCH" 300393 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-159 299626 299654 299760 "CPIMA" 299867 NIL CPIMA (NIL T T T) -7 NIL NIL) (-158 295990 296662 297380 "COORDSYS" 298961 NIL COORDSYS (NIL T) -7 NIL NIL) (-157 291851 293993 294485 "CONTFRAC" 295530 NIL CONTFRAC (NIL T) -8 NIL NIL) (-156 291004 291568 291597 "COMRING" 291602 T COMRING (NIL) -9 NIL 291653) (-155 290085 290362 290546 "COMPPROP" 290840 T COMPPROP (NIL) -8 NIL NIL) (-154 289746 289781 289909 "COMPLPAT" 290044 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-153 279727 289555 289664 "COMPLEX" 289669 NIL COMPLEX (NIL T) -8 NIL NIL) (-152 279363 279420 279527 "COMPLEX2" 279664 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-151 279081 279116 279214 "COMPFACT" 279322 NIL COMPFACT (NIL T T) -7 NIL NIL) (-150 263415 273709 273750 "COMPCAT" 274752 NIL COMPCAT (NIL T) -9 NIL 276145) (-149 252930 255854 259481 "COMPCAT-" 259837 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-148 252661 252689 252791 "COMMUPC" 252896 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-147 252456 252489 252548 "COMMONOP" 252622 T COMMONOP (NIL) -7 NIL NIL) (-146 252039 252207 252294 "COMM" 252389 T COMM (NIL) -8 NIL NIL) (-145 251293 251485 251514 "COMBOPC" 251850 T COMBOPC (NIL) -9 NIL 252023) (-144 250189 250399 250641 "COMBINAT" 251083 NIL COMBINAT (NIL T) -7 NIL NIL) (-143 246395 246966 247604 "COMBF" 249613 NIL COMBF (NIL T T) -7 NIL NIL) (-142 245181 245511 245746 "COLOR" 246180 T COLOR (NIL) -8 NIL NIL) (-141 244821 244868 244993 "CMPLXRT" 245128 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-140 240323 241351 242431 "CLIP" 243761 T CLIP (NIL) -7 NIL NIL) (-139 238661 239431 239669 "CLIF" 240151 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-138 234883 236807 236849 "CLAGG" 237778 NIL CLAGG (NIL T) -9 NIL 238314) (-137 233305 233762 234345 "CLAGG-" 234350 NIL CLAGG- (NIL T T) -8 NIL NIL) (-136 232849 232934 233074 "CINTSLPE" 233214 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-135 230350 230821 231369 "CHVAR" 232377 NIL CHVAR (NIL T T T) -7 NIL NIL) (-134 229572 230136 230165 "CHARZ" 230170 T CHARZ (NIL) -9 NIL 230184) (-133 229326 229366 229444 "CHARPOL" 229526 NIL CHARPOL (NIL T) -7 NIL NIL) (-132 228432 229029 229058 "CHARNZ" 229105 T CHARNZ (NIL) -9 NIL 229160) (-131 226455 227122 227457 "CHAR" 228117 T CHAR (NIL) -8 NIL NIL) (-130 226180 226241 226270 "CFCAT" 226381 T CFCAT (NIL) -9 NIL NIL) (-129 225425 225536 225718 "CDEN" 226064 NIL CDEN (NIL T T T) -7 NIL NIL) (-128 221417 224578 224858 "CCLASS" 225165 T CCLASS (NIL) -8 NIL NIL) (-127 216470 217446 218199 "CARTEN" 220720 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-126 215578 215726 215947 "CARTEN2" 216317 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-125 213875 214730 214986 "CARD" 215342 T CARD (NIL) -8 NIL NIL) (-124 213247 213575 213604 "CACHSET" 213736 T CACHSET (NIL) -9 NIL 213813) (-123 212743 213039 213068 "CABMON" 213118 T CABMON (NIL) -9 NIL 213174) (-122 210300 212435 212542 "BTREE" 212669 NIL BTREE (NIL T) -8 NIL NIL) (-121 207798 209948 210070 "BTOURN" 210210 NIL BTOURN (NIL T) -8 NIL NIL) (-120 205216 207269 207311 "BTCAT" 207379 NIL BTCAT (NIL T) -9 NIL 207456) (-119 204883 204963 205112 "BTCAT-" 205117 NIL BTCAT- (NIL T T) -8 NIL NIL) (-118 200103 203974 204003 "BTAGG" 204259 T BTAGG (NIL) -9 NIL 204438) (-117 199526 199670 199900 "BTAGG-" 199905 NIL BTAGG- (NIL T) -8 NIL NIL) (-116 196570 198804 199019 "BSTREE" 199343 NIL BSTREE (NIL T) -8 NIL NIL) (-115 195708 195834 196018 "BRILL" 196426 NIL BRILL (NIL T) -7 NIL NIL) (-114 192409 194436 194478 "BRAGG" 195127 NIL BRAGG (NIL T) -9 NIL 195384) (-113 190938 191344 191899 "BRAGG-" 191904 NIL BRAGG- (NIL T T) -8 NIL NIL) (-112 184146 190284 190468 "BPADICRT" 190786 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-111 182450 184083 184128 "BPADIC" 184133 NIL BPADIC (NIL NIL) -8 NIL NIL) (-110 182150 182180 182293 "BOUNDZRO" 182414 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-109 177665 178756 179623 "BOP" 181303 T BOP (NIL) -8 NIL NIL) (-108 175286 175730 176250 "BOP1" 177178 NIL BOP1 (NIL T) -7 NIL NIL) (-107 173639 174329 174623 "BOOLEAN" 175012 T BOOLEAN (NIL) -8 NIL NIL) (-106 173005 173383 173436 "BMODULE" 173441 NIL BMODULE (NIL T T) -9 NIL 173505) (-105 168815 172803 172876 "BITS" 172952 T BITS (NIL) -8 NIL NIL) (-104 167912 168347 168499 "BINFILE" 168683 T BINFILE (NIL) -8 NIL NIL) (-103 161747 167356 167521 "BINARY" 167767 T BINARY (NIL) -8 NIL NIL) (-102 159574 161002 161044 "BGAGG" 161304 NIL BGAGG (NIL T) -9 NIL 161441) (-101 159405 159437 159528 "BGAGG-" 159533 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158503 158789 158994 "BFUNCT" 159220 T BFUNCT (NIL) -8 NIL NIL) (-99 157204 157382 157667 "BEZOUT" 158327 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 153729 156064 156392 "BBTREE" 156907 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153466 153519 153546 "BASTYPE" 153663 T BASTYPE (NIL) -9 NIL NIL) (-96 153321 153350 153420 "BASTYPE-" 153425 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 152759 152835 152985 "BALFACT" 153232 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151581 152178 152363 "AUTOMOR" 152604 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151306 151311 151338 "ATTREG" 151343 T ATTREG (NIL) -9 NIL NIL) (-92 149585 150003 150355 "ATTRBUT" 150972 T ATTRBUT (NIL) -8 NIL NIL) (-91 149120 149233 149260 "ATRIG" 149461 T ATRIG (NIL) -9 NIL NIL) (-90 148929 148970 149057 "ATRIG-" 149062 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147126 148705 148793 "ASTACK" 148872 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145631 145928 146293 "ASSOCEQ" 146808 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144663 145290 145414 "ASP9" 145538 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144427 144611 144650 "ASP8" 144655 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143297 144032 144174 "ASP80" 144316 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142196 142932 143064 "ASP7" 143196 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141152 141873 141991 "ASP78" 142109 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140123 140832 140949 "ASP77" 141066 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139038 139761 139892 "ASP74" 140023 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 137939 138673 138805 "ASP73" 138937 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 136894 137616 137734 "ASP6" 137852 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 135843 136571 136689 "ASP55" 136807 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 134793 135517 135636 "ASP50" 135755 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 133881 134494 134604 "ASP4" 134714 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 132969 133582 133692 "ASP49" 133802 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 131754 132508 132676 "ASP42" 132858 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130532 131287 131457 "ASP41" 131641 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129484 130209 130327 "ASP35" 130445 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129249 129432 129471 "ASP34" 129476 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 128986 129053 129129 "ASP33" 129204 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 127882 128621 128753 "ASP31" 128885 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127647 127830 127869 "ASP30" 127874 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127382 127451 127527 "ASP29" 127602 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127147 127330 127369 "ASP28" 127374 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 126912 127095 127134 "ASP27" 127139 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 125996 126610 126721 "ASP24" 126832 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 124913 125637 125767 "ASP20" 125897 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124001 124614 124724 "ASP1" 124834 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 122945 123675 123794 "ASP19" 123913 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122682 122749 122825 "ASP12" 122900 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121535 122281 122425 "ASP10" 122569 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119434 121379 121470 "ARRAY2" 121475 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115250 119082 119196 "ARRAY1" 119351 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114282 114455 114676 "ARRAY12" 115073 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108641 110512 110588 "ARR2CAT" 113218 NIL ARR2CAT (NIL T T T) -9 NIL 113976) (-54 106075 106819 107773 "ARR2CAT-" 107778 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 104835 104985 105288 "APPRULE" 105913 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104488 104536 104654 "APPLYORE" 104781 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103462 103753 103948 "ANY" 104311 T ANY (NIL) -8 NIL NIL) (-50 102740 102863 103020 "ANY1" 103336 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100272 101190 101515 "ANTISYM" 102465 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100099 100231 100258 "ANON" 100263 T ANON (NIL) -8 NIL NIL) (-47 94176 98644 99095 "AN" 99666 T AN (NIL) -8 NIL NIL) (-46 90529 91927 91978 "AMR" 92717 NIL AMR (NIL T T) -9 NIL 93316) (-45 89642 89863 90225 "AMR-" 90230 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74192 89559 89620 "ALIST" 89625 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71029 73786 73955 "ALGSC" 74110 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67585 68139 68746 "ALGPKG" 70469 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66862 66963 67147 "ALGMFACT" 67471 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62612 63292 63946 "ALGMANIP" 66386 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53931 62238 62388 "ALGFF" 62545 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53127 53258 53437 "ALGFACT" 53789 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52117 52727 52766 "ALGEBRA" 52826 NIL ALGEBRA (NIL T) -9 NIL 52884) (-36 51835 51894 52026 "ALGEBRA-" 52031 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34095 49838 49891 "ALAGG" 50027 NIL ALAGG (NIL T T) -9 NIL 50188) (-34 33630 33743 33770 "AHYP" 33971 T AHYP (NIL) -9 NIL NIL) (-33 32560 32808 32835 "AGG" 33334 T AGG (NIL) -9 NIL 33613) (-32 31994 32156 32370 "AGG-" 32375 NIL AGG- (NIL T) -8 NIL NIL) (-31 29681 30099 30516 "AF" 31637 NIL AF (NIL T T) -7 NIL NIL) (-30 28950 29208 29364 "ACPLOT" 29543 T ACPLOT (NIL) -8 NIL NIL) (-29 18416 26362 26414 "ACFS" 27125 NIL ACFS (NIL T) -9 NIL 27364) (-28 16430 16920 17695 "ACFS-" 17700 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12697 14653 14680 "ACF" 15559 T ACF (NIL) -9 NIL 15971) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL) (-25 10999 11168 11195 "ABELSG" 11287 T ABELSG (NIL) -9 NIL 11352) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10235 10496 10523 "ABELMON" 10693 T ABELMON (NIL) -9 NIL 10805) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9233 9579 9606 "ABELGRP" 9731 T ABELGRP (NIL) -9 NIL 9813) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8075 "A1AGG" 8080 NIL A1AGG (NIL T) -9 NIL 8120) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL)) 
\ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index 132dc5eb..14519fd0 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,1286 +1,1389 @@
 
-(721460 . 3409262766)        
+(721991 . 3409435992)        
+(((*1 *2 *3 *3 *4 *3 *4 *4 *4 *5 *5 *5 *5 *4 *4 *6 *7)
+  (-12 (-5 *4 (-517)) (-5 *5 (-623 (-199)))
+   (-5 *6 (-3 (|:| |fn| (-358)) (|:| |fp| (-82 FCNF))))
+   (-5 *7 (-3 (|:| |fn| (-358)) (|:| |fp| (-83 FCNG)))) (-5 *3 (-199))
+   (-5 *2 (-952)) (-5 *1 (-682))))) 
+(((*1 *2 *1 *3)
+  (-12 (-5 *3 (-866 (-199))) (-5 *2 (-1162)) (-5 *1 (-437))))) 
+(((*1 *1 *2)
+  (-12 (-5 *2 (-844)) (-4 *1 (-212 *3 *4)) (-4 *4 (-963))
+   (-4 *4 (-1111))))
+ ((*1 *1 *2)
+  (-12 (-14 *3 (-583 (-1076))) (-4 *4 (-156))
+   (-4 *5 (-212 (-3535 *3) (-703)))
+   (-14 *6
+    (-1 (-107) (-2 (|:| -2812 *2) (|:| -2121 *5))
+     (-2 (|:| -2812 *2) (|:| -2121 *5))))
+   (-5 *1 (-430 *3 *4 *2 *5 *6 *7)) (-4 *2 (-779))
+   (-4 *7 (-872 *4 *5 (-789 *3)))))
+ ((*1 *2 *2) (-12 (-5 *2 (-866 (-199))) (-5 *1 (-1108))))) 
 (((*1 *2 *3 *4)
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-(((*1 *2 *2 *3 *3)
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-(((*1 *1 *2 *2 *2 *2) (-12 (-5 *1 (-651 *2)) (-4 *2 (-333))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1058)) (-5 *2 (-1161)) (-5 *1 (-787))))) 
+  (-12 (-5 *3 (-1 *5 *4)) (-4 *4 (-1005)) (-4 *5 (-1005))
+   (-5 *2 (-1 *5)) (-5 *1 (-617 *4 *5))))) 
+(((*1 *2)
+  (-12 (-4 *1 (-312 *3 *4 *5)) (-4 *3 (-1115)) (-4 *4 (-1133 *3))
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+(((*1 *2 *1 *3 *3)
+  (-12 (-5 *3 (-703)) (-5 *2 (-1162)) (-5 *1 (-1158))))
+ ((*1 *2 *1 *3 *3)
+  (-12 (-5 *3 (-703)) (-5 *2 (-1162)) (-5 *1 (-1159))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-583 *2)) (-4 *2 (-400 *4)) (-5 *1 (-143 *4 *2))
-   (-4 *4 (-13 (-779) (-509)))))) 
-(((*1 *2 *3 *2) (-12 (-5 *3 (-703)) (-5 *1 (-785 *2)) (-4 *2 (-156))))
- ((*1 *2 *3 *3 *2)
-  (-12 (-5 *3 (-703)) (-5 *1 (-785 *2)) (-4 *2 (-156))))) 
-(((*1 *2) (-12 (-5 *2 (-583 (-1058))) (-5 *1 (-761))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-866 *2)) (-5 *1 (-900 *2)) (-4 *2 (-962))))) 
+  (-12 (-4 *4 (-725))
+   (-4 *5 (-13 (-779) (-10 -8 (-15 -3359 ((-1076) $))))) (-4 *6 (-509))
+   (-5 *2 (-2 (|:| -2948 (-875 *6)) (|:| -2890 (-875 *6))))
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+(((*1 *2 *1) (-12 (-5 *2 (-754)) (-5 *1 (-753))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-509)) (-5 *2 (-583 *3)) (-5 *1 (-42 *4 *3))
-   (-4 *3 (-387 *4))))) 
+  (-12 (-5 *3 (-583 (-449 *4 *5))) (-14 *4 (-583 (-1076)))
+   (-4 *5 (-421)) (-5 *2 (-583 (-221 *4 *5))) (-5 *1 (-571 *4 *5))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-107)) (-5 *1 (-1076))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-1057 (-1057 *4))) (-5 *2 (-1057 *4)) (-5 *1 (-1061 *4))
+   (-4 *4 (-37 (-377 (-517)))) (-4 *4 (-963))))) 
+(((*1 *2 *3)
+  (|partial| -12 (-5 *3 (-556 *4)) (-4 *4 (-779)) (-4 *2 (-779))
+      (-5 *1 (-555 *2 *4))))) 
+(((*1 *2 *3)
+  (-12 (-5 *2 (-107)) (-5 *1 (-115 *3)) (-4 *3 (-1133 (-517)))))) 
+(((*1 *1 *1 *2)
+  (-12 (-4 *1 (-895 *3 *4 *2 *5)) (-4 *3 (-963)) (-4 *4 (-725))
+   (-4 *2 (-779)) (-4 *5 (-977 *3 *4 *2))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-107)) (-5 *1 (-404))))) 
+(((*1 *2 *2 *2)
+  (-12 (-4 *3 (-1111)) (-5 *1 (-163 *3 *2)) (-4 *2 (-610 *3))))) 
+(((*1 *1 *1 *1 *2 *3)
+  (-12 (-5 *2 (-866 *5)) (-5 *3 (-703)) (-4 *5 (-963))
+   (-5 *1 (-1065 *4 *5)) (-14 *4 (-844))))) 
+(((*1 *1 *1 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1111)) (-4 *2 (-779))))
+ ((*1 *1 *2 *1 *1)
+  (-12 (-5 *2 (-1 (-107) *3 *3)) (-4 *1 (-254 *3)) (-4 *3 (-1111))))
+ ((*1 *1 *1 *1) (-12 (-4 *1 (-888 *2)) (-4 *2 (-779))))) 
+(((*1 *2 *3 *3 *3 *3)
+  (-12 (-4 *4 (-421)) (-4 *3 (-725)) (-4 *5 (-779)) (-5 *2 (-107))
+   (-5 *1 (-418 *4 *3 *5 *6)) (-4 *6 (-872 *4 *3 *5))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-1156 *4)) (-4 *4 (-579 (-517)))
-      (-5 *2 (-1156 (-517))) (-5 *1 (-1181 *4))))) 
+  (-12 (-5 *3 (-583 *4)) (-4 *4 (-963)) (-5 *2 (-1157 *4))
+   (-5 *1 (-1077 *4))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *4 (-844)) (-5 *2 (-1157 *3)) (-5 *1 (-1077 *3))
+   (-4 *3 (-963))))) 
 (((*1 *2 *3 *4 *5)
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-(((*1 *2 *1)
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-(((*1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *3 (-1110)) (-4 *1 (-102 *3))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-517)) (-5 *2 (-1161)) (-5 *1 (-754))))) 
-(((*1 *2 *3 *3 *3 *3 *4 *3 *5 *5 *5 *3)
-  (-12 (-5 *3 (-517)) (-5 *5 (-623 (-199))) (-5 *4 (-199))
-   (-5 *2 (-951)) (-5 *1 (-683))))) 
+  (-12 (-5 *3 (-1 (-107) *6 *6)) (-4 *6 (-779)) (-5 *4 (-583 *6))
+   (-5 *2 (-2 (|:| |fs| (-107)) (|:| |sd| *4) (|:| |td| (-583 *4))))
+   (-5 *1 (-1083 *6)) (-5 *5 (-583 *4))))) 
+(((*1 *2) (-12 (-5 *2 (-107)) (-5 *1 (-850))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-610 *3)) (-4 *3 (-1111)) (-5 *2 (-107))))) 
+(((*1 *2 *2 *3 *4)
+  (-12 (-5 *3 (-583 (-556 *6))) (-5 *4 (-1076)) (-5 *2 (-556 *6))
+   (-4 *6 (-400 *5)) (-4 *5 (-779)) (-5 *1 (-526 *5 *6))))) 
+(((*1 *2 *3)
+  (-12 (-5 *2 (-1078 (-377 (-517)))) (-5 *1 (-166)) (-5 *3 (-517))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-1 *5 *5)) (-4 *5 (-1148 *4))
+   (-4 *4 (-37 (-377 (-517)))) (-5 *2 (-1 (-1057 *4) (-1057 *4)))
+   (-5 *1 (-1150 *4 *5))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-583 (-517))) (-5 *2 (-827 (-517))) (-5 *1 (-840))))
+ ((*1 *2) (-12 (-5 *2 (-827 (-517))) (-5 *1 (-840))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-377 (-517))) (-5 *1 (-289 *3 *4 *5))
-   (-4 *3 (-13 (-333) (-779))) (-14 *4 (-1075)) (-14 *5 *3)))) 
-(((*1 *1 *1 *1 *1) (-5 *1 (-787)))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-583 (-787))) (-5 *1 (-787))))) 
-(((*1 *2 *3 *4 *3)
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-   (-5 *1 (-680))))) 
-(((*1 *2 *3 *3 *4 *5)
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-   (-5 *2 (-583 (-583 *7))) (-5 *1 (-495 *6 *7 *5)) (-4 *7 (-333))
-   (-4 *5 (-13 (-333) (-777)))))) 
+  (-12 (-4 *1 (-1008 *3 *4 *5 *6 *7)) (-4 *3 (-1005)) (-4 *4 (-1005))
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+(((*1 *2 *2 *2)
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+(((*1 *2 *3 *2)
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 (((*1 *2 *2)
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-(((*1 *2 *2) (-12 (-5 *2 (-286 (-199))) (-5 *1 (-186))))) 
+  (-12 (-5 *2 (-583 *6)) (-4 *6 (-872 *3 *4 *5)) (-4 *3 (-421))
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 (((*1 *2 *3)
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   (-12 (-5 *4 (-703)) (-5 *2 (-388 *3)) (-5 *1 (-411 *3))
-   (-4 *3 (-1132 (-517)))))
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   (-12 (-5 *4 (-583 (-703))) (-5 *2 (-388 *3)) (-5 *1 (-411 *3))
-   (-4 *3 (-1132 (-517)))))
+   (-4 *3 (-1133 (-517)))))
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   (-12 (-5 *4 (-583 (-703))) (-5 *5 (-703)) (-5 *2 (-388 *3))
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  ((*1 *2 *3 *4 *4)
   (-12 (-5 *4 (-703)) (-5 *2 (-388 *3)) (-5 *1 (-411 *3))
-   (-4 *3 (-1132 (-517)))))
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  ((*1 *2 *3)
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@@ -1288,63 +1391,63 @@
   (-12
    (-4 *4
     (-13 (-779)
-     (-10 -8 (-15 -3357 ((-1075) $))
-      (-15 -3750 ((-3 $ "failed") (-1075))))))
+     (-10 -8 (-15 -3359 ((-1076) $))
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    (-4 *5 (-725)) (-4 *7 (-509)) (-5 *2 (-388 *3))
    (-5 *1 (-425 *4 *5 *6 *7 *3)) (-4 *6 (-509))
    (-4 *3 (-872 *7 *5 *4))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-278)) (-5 *2 (-388 (-1071 *4))) (-5 *1 (-427 *4))
-   (-5 *3 (-1071 *4))))
+  (-12 (-4 *4 (-278)) (-5 *2 (-388 (-1072 *4))) (-5 *1 (-427 *4))
+   (-5 *3 (-1072 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 (-388 *6) *6)) (-4 *6 (-1132 *5)) (-4 *5 (-333))
+  (-12 (-5 *4 (-1 (-388 *6) *6)) (-4 *6 (-1133 *5)) (-4 *5 (-333))
    (-4 *7 (-13 (-333) (-134) (-657 *5 *6))) (-5 *2 (-388 *3))
-   (-5 *1 (-459 *5 *6 *7 *3)) (-4 *3 (-1132 *7))))
+   (-5 *1 (-459 *5 *6 *7 *3)) (-4 *3 (-1133 *7))))
  ((*1 *2 *3 *4)
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+  (-12 (-5 *4 (-1 (-388 (-1072 *7)) (-1072 *7)))
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    (-5 *2 (-388 *3)) (-5 *1 (-497 *5 *6 *7 *3))
    (-4 *3 (-872 *7 *6 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 (-388 (-1071 *7)) (-1071 *7)))
+  (-12 (-5 *4 (-1 (-388 (-1072 *7)) (-1072 *7)))
    (-4 *7 (-13 (-278) (-134))) (-4 *5 (-779)) (-4 *6 (-725))
-   (-4 *8 (-872 *7 *6 *5)) (-5 *2 (-388 (-1071 *8)))
-   (-5 *1 (-497 *5 *6 *7 *8)) (-5 *3 (-1071 *8))))
+   (-4 *8 (-872 *7 *6 *5)) (-5 *2 (-388 (-1072 *8)))
+   (-5 *1 (-497 *5 *6 *7 *8)) (-5 *3 (-1072 *8))))
  ((*1 *2 *3) (-12 (-5 *2 (-388 *3)) (-5 *1 (-511 *3)) (-4 *3 (-502))))
  ((*1 *2 *3 *4)
   (-12 (-5 *4 (-1 (-583 *5) *6))
-   (-4 *5 (-13 (-333) (-134) (-953 (-517)) (-953 (-377 (-517)))))
-   (-4 *6 (-1132 *5)) (-5 *2 (-583 (-590 (-377 *6))))
+   (-4 *5 (-13 (-333) (-134) (-954 (-517)) (-954 (-377 (-517)))))
+   (-4 *6 (-1133 *5)) (-5 *2 (-583 (-590 (-377 *6))))
    (-5 *1 (-594 *5 *6)) (-5 *3 (-590 (-377 *6)))))
  ((*1 *2 *3)
   (-12 (-4 *4 (-27))
-   (-4 *4 (-13 (-333) (-134) (-953 (-517)) (-953 (-377 (-517)))))
-   (-4 *5 (-1132 *4)) (-5 *2 (-583 (-590 (-377 *5))))
+   (-4 *4 (-13 (-333) (-134) (-954 (-517)) (-954 (-377 (-517)))))
+   (-4 *5 (-1133 *4)) (-5 *2 (-583 (-590 (-377 *5))))
    (-5 *1 (-594 *4 *5)) (-5 *3 (-590 (-377 *5)))))
  ((*1 *2 *3)
   (-12 (-5 *3 (-751 *4)) (-4 *4 (-779)) (-5 *2 (-583 (-608 *4)))
    (-5 *1 (-608 *4))))
  ((*1 *2 *3 *4)
   (-12 (-5 *4 (-517)) (-5 *2 (-583 *3)) (-5 *1 (-629 *3))
-   (-4 *3 (-1132 *4))))
+   (-4 *3 (-1133 *4))))
  ((*1 *2 *3)
   (-12 (-4 *4 (-779)) (-4 *5 (-725)) (-4 *6 (-319)) (-5 *2 (-388 *3))
    (-5 *1 (-631 *4 *5 *6 *3)) (-4 *3 (-872 *6 *5 *4))))
  ((*1 *2 *3)
   (-12 (-4 *4 (-779)) (-4 *5 (-725)) (-4 *6 (-319))
-   (-4 *7 (-872 *6 *5 *4)) (-5 *2 (-388 (-1071 *7)))
-   (-5 *1 (-631 *4 *5 *6 *7)) (-5 *3 (-1071 *7))))
+   (-4 *7 (-872 *6 *5 *4)) (-5 *2 (-388 (-1072 *7)))
+   (-5 *1 (-631 *4 *5 *6 *7)) (-5 *3 (-1072 *7))))
  ((*1 *2 *3)
   (-12 (-4 *4 (-725))
    (-4 *5
     (-13 (-779)
-     (-10 -8 (-15 -3357 ((-1075) $))
-      (-15 -3750 ((-3 $ "failed") (-1075))))))
+     (-10 -8 (-15 -3359 ((-1076) $))
+      (-15 -3752 ((-3 $ "failed") (-1076))))))
    (-4 *6 (-278)) (-5 *2 (-388 *3)) (-5 *1 (-663 *4 *5 *6 *3))
    (-4 *3 (-872 (-875 *6) *4 *5))))
  ((*1 *2 *3)
   (-12 (-4 *4 (-725))
-   (-4 *5 (-13 (-779) (-10 -8 (-15 -3357 ((-1075) $))))) (-4 *6 (-509))
+   (-4 *5 (-13 (-779) (-10 -8 (-15 -3359 ((-1076) $))))) (-4 *6 (-509))
    (-5 *2 (-388 *3)) (-5 *1 (-665 *4 *5 *6 *3))
    (-4 *3 (-872 (-377 (-875 *6)) *4 *5))))
  ((*1 *2 *3)
@@ -1357,117 +1460,88 @@
    (-4 *3 (-872 *6 *5 *4))))
  ((*1 *2 *3)
   (-12 (-4 *4 (-779)) (-4 *5 (-725)) (-4 *6 (-13 (-278) (-134)))
-   (-4 *7 (-872 *6 *5 *4)) (-5 *2 (-388 (-1071 *7)))
-   (-5 *1 (-674 *4 *5 *6 *7)) (-5 *3 (-1071 *7))))
+   (-4 *7 (-872 *6 *5 *4)) (-5 *2 (-388 (-1072 *7)))
+   (-5 *1 (-674 *4 *5 *6 *7)) (-5 *3 (-1072 *7))))
  ((*1 *2 *3)
-  (-12 (-5 *2 (-388 *3)) (-5 *1 (-924 *3))
-   (-4 *3 (-1132 (-377 (-517))))))
+  (-12 (-5 *2 (-388 *3)) (-5 *1 (-925 *3))
+   (-4 *3 (-1133 (-377 (-517))))))
  ((*1 *2 *3)
-  (-12 (-5 *2 (-388 *3)) (-5 *1 (-956 *3))
-   (-4 *3 (-1132 (-377 (-875 (-517)))))))
+  (-12 (-5 *2 (-388 *3)) (-5 *1 (-957 *3))
+   (-4 *3 (-1133 (-377 (-875 (-517)))))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-1132 (-377 (-517))))
+  (-12 (-4 *4 (-1133 (-377 (-517))))
    (-4 *5 (-13 (-333) (-134) (-657 (-377 (-517)) *4)))
-   (-5 *2 (-388 *3)) (-5 *1 (-987 *4 *5 *3)) (-4 *3 (-1132 *5))))
+   (-5 *2 (-388 *3)) (-5 *1 (-988 *4 *5 *3)) (-4 *3 (-1133 *5))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-1132 (-377 (-875 (-517)))))
+  (-12 (-4 *4 (-1133 (-377 (-875 (-517)))))
    (-4 *5 (-13 (-333) (-134) (-657 (-377 (-875 (-517))) *4)))
-   (-5 *2 (-388 *3)) (-5 *1 (-989 *4 *5 *3)) (-4 *3 (-1132 *5))))
+   (-5 *2 (-388 *3)) (-5 *1 (-990 *4 *5 *3)) (-4 *3 (-1133 *5))))
  ((*1 *2 *3)
   (-12 (-4 *4 (-725)) (-4 *5 (-779)) (-4 *6 (-421))
-   (-4 *7 (-872 *6 *4 *5)) (-5 *2 (-388 (-1071 (-377 *7))))
-   (-5 *1 (-1070 *4 *5 *6 *7)) (-5 *3 (-1071 (-377 *7)))))
- ((*1 *2 *1) (-12 (-5 *2 (-388 *1)) (-4 *1 (-1114))))
+   (-4 *7 (-872 *6 *4 *5)) (-5 *2 (-388 (-1072 (-377 *7))))
+   (-5 *1 (-1071 *4 *5 *6 *7)) (-5 *3 (-1072 (-377 *7)))))
+ ((*1 *2 *1) (-12 (-5 *2 (-388 *1)) (-4 *1 (-1115))))
  ((*1 *2 *3)
-  (-12 (-5 *2 (-388 *3)) (-5 *1 (-1121 *3)) (-4 *3 (-1132 (-517)))))) 
-(((*1 *2 *3 *4 *5)
-  (-12 (-5 *4 (-1075)) (-5 *5 (-999 (-199))) (-5 *2 (-850))
-   (-5 *1 (-848 *3)) (-4 *3 (-558 (-493)))))
- ((*1 *2 *3 *3 *4 *5)
-  (-12 (-5 *4 (-1075)) (-5 *5 (-999 (-199))) (-5 *2 (-850))
-   (-5 *1 (-848 *3)) (-4 *3 (-558 (-493)))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-999 (-199))) (-5 *1 (-849))))
- ((*1 *1 *2 *2 *2 *2 *3 *3 *3 *3)
-  (-12 (-5 *2 (-1 (-199) (-199))) (-5 *3 (-999 (-199))) (-5 *1 (-849))))
- ((*1 *1 *2 *2 *2 *2 *3)
-  (-12 (-5 *2 (-1 (-199) (-199))) (-5 *3 (-999 (-199))) (-5 *1 (-849))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-999 (-199))) (-5 *1 (-850))))
- ((*1 *1 *2 *2 *3 *3 *3)
-  (-12 (-5 *2 (-1 (-199) (-199))) (-5 *3 (-999 (-199))) (-5 *1 (-850))))
- ((*1 *1 *2 *2 *3)
-  (-12 (-5 *2 (-1 (-199) (-199))) (-5 *3 (-999 (-199))) (-5 *1 (-850))))
- ((*1 *1 *2 *3 *3)
-  (-12 (-5 *2 (-583 (-1 (-199) (-199)))) (-5 *3 (-999 (-199)))
-   (-5 *1 (-850))))
- ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-583 (-1 (-199) (-199)))) (-5 *3 (-999 (-199)))
-   (-5 *1 (-850))))
- ((*1 *1 *2 *3 *3)
-  (-12 (-5 *2 (-1 (-199) (-199))) (-5 *3 (-999 (-199))) (-5 *1 (-850))))
- ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1 (-199) (-199))) (-5 *3 (-999 (-199))) (-5 *1 (-850))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-703)) (-5 *2 (-349)) (-5 *1 (-955))))) 
-(((*1 *1 *1 *2)
-  (-12 (-5 *2 (-583 (-51))) (-5 *1 (-815 *3)) (-4 *3 (-1004))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-616 *3)) (-4 *3 (-1004))))) 
+  (-12 (-5 *2 (-388 *3)) (-5 *1 (-1122 *3)) (-4 *3 (-1133 (-517)))))) 
+(((*1 *2)
+  (-12 (-5 *2 (-377 (-875 *3))) (-5 *1 (-422 *3 *4 *5 *6))
+   (-4 *3 (-509)) (-4 *3 (-156)) (-14 *4 (-844))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1157 (-623 *3)))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *3 (-199)) (-5 *4 (-517)) (-5 *2 (-952)) (-5 *1 (-691))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1156 *1)) (-4 *1 (-340 *4 *5)) (-4 *4 (-156))
-   (-4 *5 (-1132 *4)) (-5 *2 (-623 *4))))
- ((*1 *2)
-  (-12 (-4 *4 (-156)) (-4 *5 (-1132 *4)) (-5 *2 (-623 *4))
-   (-5 *1 (-378 *3 *4 *5)) (-4 *3 (-379 *4 *5))))
- ((*1 *2)
-  (-12 (-4 *1 (-379 *3 *4)) (-4 *3 (-156)) (-4 *4 (-1132 *3))
-   (-5 *2 (-623 *3))))) 
-(((*1 *2 *1)
-  (-12 (-5 *2 (-1006 *3)) (-5 *1 (-828 *3)) (-4 *3 (-338))
-   (-4 *3 (-1004))))) 
-(((*1 *2 *2 *3)
-  (-12 (-5 *2 (-623 *3)) (-4 *3 (-278)) (-5 *1 (-633 *3))))) 
-(((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-509) (-134))) (-5 *1 (-494 *3 *2))
-   (-4 *2 (-1147 *3))))
- ((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-333) (-338) (-558 (-517)))) (-4 *4 (-1132 *3))
-   (-4 *5 (-657 *3 *4)) (-5 *1 (-498 *3 *4 *5 *2)) (-4 *2 (-1147 *5))))
- ((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-333) (-338) (-558 (-517)))) (-5 *1 (-499 *3 *2))
-   (-4 *2 (-1147 *3))))
- ((*1 *2 *2)
-  (-12 (-5 *2 (-1056 *3)) (-4 *3 (-13 (-509) (-134)))
-   (-5 *1 (-1052 *3))))) 
-(((*1 *2 *3 *2)
-  (-12 (-5 *2 (-844)) (-5 *3 (-583 (-236))) (-5 *1 (-234))))
- ((*1 *1 *2) (-12 (-5 *2 (-844)) (-5 *1 (-236))))) 
-(((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-585 *3)) (-4 *3 (-962))
-   (-5 *1 (-647 *3 *4))))
- ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-962)) (-5 *1 (-766 *3))))) 
+  (-12 (-5 *3 (-844)) (-5 *2 (-1072 *4)) (-5 *1 (-327 *4))
+   (-4 *4 (-319))))) 
+(((*1 *2 *3 *4 *5)
+  (-12 (-5 *3 (-703)) (-4 *6 (-333)) (-5 *4 (-1106 *6))
+   (-5 *2 (-1 (-1057 *4) (-1057 *4))) (-5 *1 (-1165 *6))
+   (-5 *5 (-1057 *4))))) 
+(((*1 *2 *3 *3 *3 *3)
+  (-12 (-5 *3 (-517)) (-5 *2 (-107)) (-5 *1 (-448))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-107)) (-5 *1 (-756))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-875 *4)) (-4 *4 (-962)) (-4 *4 (-558 *2))
-      (-5 *2 (-349)) (-5 *1 (-717 *4))))
- ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-875 *5)) (-5 *4 (-844)) (-4 *5 (-962))
-      (-4 *5 (-558 *2)) (-5 *2 (-349)) (-5 *1 (-717 *5))))
+  (-12 (-5 *3 (-590 (-377 *2))) (-4 *2 (-1133 *4)) (-5 *1 (-742 *4 *2))
+   (-4 *4 (-13 (-333) (-134) (-954 (-517)) (-954 (-377 (-517)))))))
  ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-377 (-875 *4))) (-4 *4 (-509))
-      (-4 *4 (-558 *2)) (-5 *2 (-349)) (-5 *1 (-717 *4))))
- ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-377 (-875 *5))) (-5 *4 (-844)) (-4 *5 (-509))
-      (-4 *5 (-558 *2)) (-5 *2 (-349)) (-5 *1 (-717 *5))))
- ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-286 *4)) (-4 *4 (-509)) (-4 *4 (-779))
-      (-4 *4 (-558 *2)) (-5 *2 (-349)) (-5 *1 (-717 *4))))
- ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-286 *5)) (-5 *4 (-844)) (-4 *5 (-509))
-      (-4 *5 (-779)) (-4 *5 (-558 *2)) (-5 *2 (-349))
-      (-5 *1 (-717 *5))))) 
+  (-12 (-5 *3 (-591 *2 (-377 *2))) (-4 *2 (-1133 *4))
+   (-5 *1 (-742 *4 *2))
+   (-4 *4 (-13 (-333) (-134) (-954 (-517)) (-954 (-377 (-517)))))))) 
+(((*1 *1 *1 *2 *2 *1)
+  (-12 (-5 *2 (-517)) (-4 *1 (-621 *3 *4 *5)) (-4 *3 (-963))
+   (-4 *4 (-343 *3)) (-4 *5 (-343 *3))))) 
+(((*1 *2 *3 *4 *3 *5)
+  (-12 (-5 *3 (-1059)) (-5 *4 (-153 (-199))) (-5 *5 (-517))
+   (-5 *2 (-952)) (-5 *1 (-691))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-221 *4 *5)) (-14 *4 (-583 (-1076))) (-4 *5 (-963))
+   (-5 *2 (-875 *5)) (-5 *1 (-867 *4 *5))))) 
 (((*1 *2 *2 *3)
-  (-12 (-4 *3 (-962)) (-5 *1 (-413 *3 *2)) (-4 *2 (-1132 *3))))) 
+  (|partial| -12 (-5 *3 (-703)) (-4 *4 (-13 (-509) (-134)))
+      (-5 *1 (-1127 *4 *2)) (-4 *2 (-1133 *4))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-249 *3 *2))
-   (-4 *2 (-13 (-400 *3) (-919)))))) 
+  (|partial| -12 (-4 *3 (-333)) (-4 *4 (-343 *3)) (-4 *5 (-343 *3))
+      (-5 *1 (-484 *3 *4 *5 *2)) (-4 *2 (-621 *3 *4 *5))))
+ ((*1 *2 *3)
+  (|partial| -12 (-4 *4 (-509)) (-4 *5 (-343 *4)) (-4 *6 (-343 *4))
+      (-4 *7 (-911 *4)) (-4 *2 (-621 *7 *8 *9))
+      (-5 *1 (-485 *4 *5 *6 *3 *7 *8 *9 *2)) (-4 *3 (-621 *4 *5 *6))
+      (-4 *8 (-343 *7)) (-4 *9 (-343 *7))))
+ ((*1 *1 *1)
+  (|partial| -12 (-4 *1 (-621 *2 *3 *4)) (-4 *2 (-963))
+      (-4 *3 (-343 *2)) (-4 *4 (-343 *2)) (-4 *2 (-333))))
+ ((*1 *2 *2)
+  (|partial| -12 (-4 *3 (-333)) (-4 *3 (-156)) (-4 *4 (-343 *3))
+      (-4 *5 (-343 *3)) (-5 *1 (-622 *3 *4 *5 *2))
+      (-4 *2 (-621 *3 *4 *5))))
+ ((*1 *1 *1)
+  (|partial| -12 (-5 *1 (-623 *2)) (-4 *2 (-333)) (-4 *2 (-963))))
+ ((*1 *1 *1)
+  (|partial| -12 (-4 *1 (-1026 *2 *3 *4 *5)) (-4 *3 (-963))
+      (-4 *4 (-212 *2 *3)) (-4 *5 (-212 *2 *3)) (-4 *3 (-333))))
+ ((*1 *2 *2) (-12 (-5 *2 (-583 *3)) (-4 *3 (-779)) (-5 *1 (-1083 *3))))) 
+(((*1 *2 *3 *1)
+  (-12 (-5 *3 (-1041 *4 *5)) (-4 *4 (-13 (-1005) (-33)))
+   (-4 *5 (-13 (-1005) (-33))) (-5 *2 (-107)) (-5 *1 (-1042 *4 *5))))) 
 (((*1 *1 *2 *1) (-12 (-4 *1 (-21)) (-5 *2 (-517))))
  ((*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-703))))
  ((*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-844))))
@@ -1477,32 +1551,32 @@
  ((*1 *1 *2 *1) (-12 (-5 *2 (-199)) (-5 *1 (-142))))
  ((*1 *1 *2 *1) (-12 (-5 *2 (-844)) (-5 *1 (-142))))
  ((*1 *2 *1 *2)
-  (-12 (-5 *2 (-866 *3)) (-4 *3 (-13 (-333) (-1096)))
+  (-12 (-5 *2 (-866 *3)) (-4 *3 (-13 (-333) (-1097)))
    (-5 *1 (-201 *3))))
  ((*1 *1 *2 *1)
-  (-12 (-4 *1 (-212 *3 *2)) (-4 *2 (-1110)) (-4 *2 (-659))))
+  (-12 (-4 *1 (-212 *3 *2)) (-4 *2 (-1111)) (-4 *2 (-659))))
  ((*1 *1 *1 *2)
-  (-12 (-4 *1 (-212 *3 *2)) (-4 *2 (-1110)) (-4 *2 (-659))))
+  (-12 (-4 *1 (-212 *3 *2)) (-4 *2 (-1111)) (-4 *2 (-659))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *1 (-265 *2)) (-4 *2 (-1016)) (-4 *2 (-1110))))
+  (-12 (-5 *1 (-265 *2)) (-4 *2 (-1017)) (-4 *2 (-1111))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *1 (-265 *2)) (-4 *2 (-1016)) (-4 *2 (-1110))))
+  (-12 (-5 *1 (-265 *2)) (-4 *2 (-1017)) (-4 *2 (-1111))))
  ((*1 *1 *2 *3)
-  (-12 (-4 *1 (-293 *3 *2)) (-4 *3 (-1004)) (-4 *2 (-123))))
- ((*1 *1 *1 *2) (-12 (-5 *1 (-331 *2)) (-4 *2 (-1004))))
- ((*1 *1 *2 *1) (-12 (-5 *1 (-331 *2)) (-4 *2 (-1004))))
+  (-12 (-4 *1 (-293 *3 *2)) (-4 *3 (-1005)) (-4 *2 (-123))))
+ ((*1 *1 *1 *2) (-12 (-5 *1 (-331 *2)) (-4 *2 (-1005))))
+ ((*1 *1 *2 *1) (-12 (-5 *1 (-331 *2)) (-4 *2 (-1005))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *1 (-351 *3 *2)) (-4 *3 (-962)) (-4 *2 (-779))))
+  (-12 (-5 *1 (-351 *3 *2)) (-4 *3 (-963)) (-4 *2 (-779))))
  ((*1 *1 *2 *3)
-  (-12 (-4 *1 (-352 *2 *3)) (-4 *2 (-962)) (-4 *3 (-1004))))
- ((*1 *1 *1 *2) (-12 (-5 *1 (-356 *2)) (-4 *2 (-1004))))
- ((*1 *1 *2 *1) (-12 (-5 *1 (-356 *2)) (-4 *2 (-1004))))
+  (-12 (-4 *1 (-352 *2 *3)) (-4 *2 (-963)) (-4 *3 (-1005))))
+ ((*1 *1 *1 *2) (-12 (-5 *1 (-356 *2)) (-4 *2 (-1005))))
+ ((*1 *1 *2 *1) (-12 (-5 *1 (-356 *2)) (-4 *2 (-1005))))
  ((*1 *1 *2 *1)
-  (-12 (-14 *3 (-583 (-1075))) (-4 *4 (-156))
-   (-4 *6 (-212 (-3533 *3) (-703)))
+  (-12 (-14 *3 (-583 (-1076))) (-4 *4 (-156))
+   (-4 *6 (-212 (-3535 *3) (-703)))
    (-14 *7
-    (-1 (-107) (-2 (|:| -2810 *5) (|:| -2356 *6))
-     (-2 (|:| -2810 *5) (|:| -2356 *6))))
+    (-1 (-107) (-2 (|:| -2812 *5) (|:| -2121 *6))
+     (-2 (|:| -2812 *5) (|:| -2121 *6))))
    (-5 *1 (-430 *3 *4 *5 *6 *7 *2)) (-4 *5 (-779))
    (-4 *2 (-872 *4 *6 (-789 *3)))))
  ((*1 *1 *1 *2)
@@ -1513,252 +1587,347 @@
   (-12 (-4 *2 (-333)) (-4 *3 (-725)) (-4 *4 (-779))
    (-5 *1 (-469 *2 *3 *4 *5)) (-4 *5 (-872 *2 *3 *4))))
  ((*1 *2 *2 *2)
-  (-12 (-5 *2 (-1156 *3)) (-4 *3 (-319)) (-5 *1 (-487 *3))))
+  (-12 (-5 *2 (-1157 *3)) (-4 *3 (-319)) (-5 *1 (-487 *3))))
  ((*1 *1 *1 *1) (-5 *1 (-493)))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-517)) (-5 *1 (-543 *3)) (-4 *3 (-962))))
- ((*1 *1 *1 *2) (-12 (-5 *1 (-543 *2)) (-4 *2 (-962))))
- ((*1 *1 *2 *1) (-12 (-5 *1 (-543 *2)) (-4 *2 (-962))))
- ((*1 *1 *2 *1) (-12 (-4 *1 (-585 *2)) (-4 *2 (-969))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-517)) (-5 *1 (-543 *3)) (-4 *3 (-963))))
+ ((*1 *1 *1 *2) (-12 (-5 *1 (-543 *2)) (-4 *2 (-963))))
+ ((*1 *1 *2 *1) (-12 (-5 *1 (-543 *2)) (-4 *2 (-963))))
+ ((*1 *1 *2 *1) (-12 (-4 *1 (-585 *2)) (-4 *2 (-970))))
  ((*1 *1 *1 *1) (-12 (-5 *1 (-612 *2)) (-4 *2 (-779))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-1 *6 *5)) (-4 *5 (-1004))
-   (-4 *6 (-1004)) (-4 *7 (-1004)) (-5 *2 (-1 *7 *5))
+  (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-1 *6 *5)) (-4 *5 (-1005))
+   (-4 *6 (-1005)) (-4 *7 (-1005)) (-5 *2 (-1 *7 *5))
    (-5 *1 (-618 *5 *6 *7))))
  ((*1 *2 *2 *1)
-  (-12 (-4 *1 (-621 *3 *2 *4)) (-4 *3 (-962)) (-4 *2 (-343 *3))
+  (-12 (-4 *1 (-621 *3 *2 *4)) (-4 *3 (-963)) (-4 *2 (-343 *3))
    (-4 *4 (-343 *3))))
  ((*1 *2 *1 *2)
-  (-12 (-4 *1 (-621 *3 *4 *2)) (-4 *3 (-962)) (-4 *4 (-343 *3))
+  (-12 (-4 *1 (-621 *3 *4 *2)) (-4 *3 (-963)) (-4 *4 (-343 *3))
    (-4 *2 (-343 *3))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-517)) (-4 *1 (-621 *3 *4 *5)) (-4 *3 (-962))
+  (-12 (-5 *2 (-517)) (-4 *1 (-621 *3 *4 *5)) (-4 *3 (-963))
    (-4 *4 (-343 *3)) (-4 *5 (-343 *3))))
  ((*1 *1 *1 *2)
-  (-12 (-4 *1 (-621 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-343 *2))
+  (-12 (-4 *1 (-621 *2 *3 *4)) (-4 *2 (-963)) (-4 *3 (-343 *2))
    (-4 *4 (-343 *2))))
  ((*1 *1 *2 *1)
-  (-12 (-4 *1 (-621 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-343 *2))
+  (-12 (-4 *1 (-621 *2 *3 *4)) (-4 *2 (-963)) (-4 *3 (-343 *2))
    (-4 *4 (-343 *2))))
  ((*1 *1 *1 *1)
-  (-12 (-4 *1 (-621 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-343 *2))
+  (-12 (-4 *1 (-621 *2 *3 *4)) (-4 *2 (-963)) (-4 *3 (-343 *2))
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 (((*1 *2 *1)
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@@ -2136,631 +2222,586 @@
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-                  (|:| |lowerSingular|
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-                  (|:| |upperSingular|
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-                  (|:| |bothSingular|
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-                  (|:| |notEvaluated|
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-                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
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-  (-12 (-4 *4 (-962)) (-4 *3 (-779)) (-4 *5 (-239 *3)) (-4 *6 (-725))
-   (-5 *2 (-1 *1 (-703))) (-4 *1 (-226 *4 *3 *5 *6))))
- ((*1 *1 *2 *3) (-12 (-5 *3 (-703)) (-4 *1 (-239 *2)) (-4 *2 (-779))))) 
-(((*1 *2 *3 *1)
-  (-12 (-5 *3 (-828 *4)) (-4 *4 (-1004)) (-5 *2 (-583 (-703)))
-   (-5 *1 (-827 *4))))) 
-(((*1 *1 *2 *3) (-12 (-5 *2 (-1008)) (-5 *3 (-706)) (-5 *1 (-51))))) 
-(((*1 *2 *2)
-  (-12 (-5 *2 (-583 *7)) (-4 *7 (-981 *3 *4 *5 *6)) (-4 *3 (-421))
-   (-4 *4 (-725)) (-4 *5 (-779)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *1 (-906 *3 *4 *5 *6 *7))))
+(((*1 *2 *3 *4 *5 *6 *7 *6)
+  (|partial| -12
+      (-5 *5
+       (-2 (|:| |contp| *3)
+        (|:| -1510 (-583 (-2 (|:| |irr| *10) (|:| -1992 (-517)))))))
+      (-5 *6 (-583 *3)) (-5 *7 (-583 *8)) (-4 *8 (-779)) (-4 *3 (-278))
+      (-4 *10 (-872 *3 *9 *8)) (-4 *9 (-725))
+      (-5 *2
+       (-2 (|:| |polfac| (-583 *10)) (|:| |correct| *3)
+        (|:| |corrfact| (-583 (-1072 *3)))))
+      (-5 *1 (-566 *8 *9 *3 *10)) (-5 *4 (-583 (-1072 *3)))))) 
+(((*1 *2 *2 *3 *3)
+  (|partial| -12 (-5 *3 (-1076))
+      (-4 *4 (-13 (-278) (-779) (-134) (-954 (-517)) (-579 (-517))))
+      (-5 *1 (-528 *4 *2))
+      (-4 *2 (-13 (-1097) (-881) (-1040) (-29 *4)))))) 
+(((*1 *2 *2 *3)
+  (-12 (-5 *3 (-1 (-107) *4 *4)) (-4 *4 (-1111)) (-5 *1 (-1035 *4 *2))
+   (-4 *2 (-13 (-550 (-517) *4) (-10 -7 (-6 -4192) (-6 -4193))))))
  ((*1 *2 *2)
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-   (-5 *1 (-1011 *3 *4 *5 *6 *7))))) 
-(((*1 *2 *1 *1)
-  (-12 (-4 *3 (-509)) (-4 *3 (-962))
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-   (-4 *3 (-781 *5))))) 
-(((*1 *2 *1)
-  (-12 (-4 *1 (-507 *3)) (-4 *3 (-13 (-374) (-1096))) (-5 *2 (-107))))
- ((*1 *2 *1) (-12 (-4 *1 (-777)) (-5 *2 (-107))))
- ((*1 *2 *3 *1)
-  (-12 (-4 *1 (-978 *4 *3)) (-4 *4 (-13 (-777) (-333)))
-   (-4 *3 (-1132 *4)) (-5 *2 (-107))))) 
+  (-12 (-4 *3 (-779)) (-4 *3 (-1111)) (-5 *1 (-1035 *3 *2))
+   (-4 *2 (-13 (-550 (-517) *3) (-10 -7 (-6 -4192) (-6 -4193))))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *4 (-703)) (-5 *2 (-107)) (-5 *1 (-535 *3)) (-4 *3 (-502))))) 
+(((*1 *2 *2)
+  (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-249 *3 *2))
+   (-4 *2 (-13 (-400 *3) (-920)))))) 
+(((*1 *2 *3 *2)
+  (-12 (-5 *2 (-797)) (-5 *3 (-583 (-236))) (-5 *1 (-234))))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-1009)) (-5 *3 (-706)) (-5 *1 (-51))))) 
+(((*1 *2 *2 *2 *2 *3)
+  (-12 (-4 *3 (-509)) (-5 *1 (-889 *3 *2)) (-4 *2 (-1133 *3))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1162)) (-5 *1 (-754))))) 
+(((*1 *1 *1)
+  (-12 (-4 *2 (-333)) (-4 *3 (-725)) (-4 *4 (-779))
+   (-5 *1 (-469 *2 *3 *4 *5)) (-4 *5 (-872 *2 *3 *4))))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *3 (-377 *5)) (-4 *4 (-1114)) (-4 *5 (-1132 *4))
-   (-5 *1 (-135 *4 *5 *2)) (-4 *2 (-1132 *3))))
+  (-12 (-5 *3 (-377 *5)) (-4 *4 (-1115)) (-4 *5 (-1133 *4))
+   (-5 *1 (-135 *4 *5 *2)) (-4 *2 (-1133 *3))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1077 (-377 (-517)))) (-5 *2 (-377 (-517)))
+  (-12 (-5 *3 (-1078 (-377 (-517)))) (-5 *2 (-377 (-517)))
    (-5 *1 (-166))))
  ((*1 *2 *2 *3 *4)
-  (-12 (-5 *2 (-623 (-286 (-199)))) (-5 *3 (-583 (-1075)))
-   (-5 *4 (-1156 (-286 (-199)))) (-5 *1 (-181))))
+  (-12 (-5 *2 (-623 (-286 (-199)))) (-5 *3 (-583 (-1076)))
+   (-5 *4 (-1157 (-286 (-199)))) (-5 *1 (-181))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-583 (-265 *3))) (-4 *3 (-280 *3)) (-4 *3 (-1004))
-   (-4 *3 (-1110)) (-5 *1 (-265 *3))))
+  (-12 (-5 *2 (-583 (-265 *3))) (-4 *3 (-280 *3)) (-4 *3 (-1005))
+   (-4 *3 (-1111)) (-5 *1 (-265 *3))))
  ((*1 *1 *1 *1)
-  (-12 (-4 *2 (-280 *2)) (-4 *2 (-1004)) (-4 *2 (-1110))
+  (-12 (-4 *2 (-280 *2)) (-4 *2 (-1005)) (-4 *2 (-1111))
    (-5 *1 (-265 *2))))
  ((*1 *1 *1 *2 *3)
   (-12 (-5 *2 (-109)) (-5 *3 (-1 *1 *1)) (-4 *1 (-273))))
@@ -3321,20 +3300,20 @@
  ((*1 *1 *1 *2 *3)
   (-12 (-5 *2 (-583 (-109))) (-5 *3 (-583 (-1 *1 *1))) (-4 *1 (-273))))
  ((*1 *1 *1 *2 *3)
-  (-12 (-5 *2 (-1075)) (-5 *3 (-1 *1 *1)) (-4 *1 (-273))))
+  (-12 (-5 *2 (-1076)) (-5 *3 (-1 *1 *1)) (-4 *1 (-273))))
  ((*1 *1 *1 *2 *3)
-  (-12 (-5 *2 (-1075)) (-5 *3 (-1 *1 (-583 *1))) (-4 *1 (-273))))
+  (-12 (-5 *2 (-1076)) (-5 *3 (-1 *1 (-583 *1))) (-4 *1 (-273))))
  ((*1 *1 *1 *2 *3)
-  (-12 (-5 *2 (-583 (-1075))) (-5 *3 (-583 (-1 *1 (-583 *1))))
+  (-12 (-5 *2 (-583 (-1076))) (-5 *3 (-583 (-1 *1 (-583 *1))))
    (-4 *1 (-273))))
  ((*1 *1 *1 *2 *3)
-  (-12 (-5 *2 (-583 (-1075))) (-5 *3 (-583 (-1 *1 *1))) (-4 *1 (-273))))
+  (-12 (-5 *2 (-583 (-1076))) (-5 *3 (-583 (-1 *1 *1))) (-4 *1 (-273))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-583 (-265 *3))) (-4 *1 (-280 *3)) (-4 *3 (-1004))))
+  (-12 (-5 *2 (-583 (-265 *3))) (-4 *1 (-280 *3)) (-4 *3 (-1005))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-265 *3)) (-4 *1 (-280 *3)) (-4 *3 (-1004))))
+  (-12 (-5 *2 (-265 *3)) (-4 *1 (-280 *3)) (-4 *3 (-1005))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *2 (-517))) (-5 *4 (-1077 (-377 (-517))))
+  (-12 (-5 *3 (-1 *2 (-517))) (-5 *4 (-1078 (-377 (-517))))
    (-5 *1 (-281 *2)) (-4 *2 (-37 (-377 (-517))))))
  ((*1 *1 *1 *2 *3)
   (-12 (-5 *2 (-583 *4)) (-5 *3 (-583 *1)) (-4 *1 (-344 *4 *5))
@@ -3342,350 +3321,306 @@
  ((*1 *1 *1 *2 *1)
   (-12 (-4 *1 (-344 *2 *3)) (-4 *2 (-779)) (-4 *3 (-156))))
  ((*1 *1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-1075)) (-5 *3 (-703)) (-5 *4 (-1 *1 *1))
-   (-4 *1 (-400 *5)) (-4 *5 (-779)) (-4 *5 (-962))))
+  (-12 (-5 *2 (-1076)) (-5 *3 (-703)) (-5 *4 (-1 *1 *1))
+   (-4 *1 (-400 *5)) (-4 *5 (-779)) (-4 *5 (-963))))
  ((*1 *1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-1075)) (-5 *3 (-703)) (-5 *4 (-1 *1 (-583 *1)))
-   (-4 *1 (-400 *5)) (-4 *5 (-779)) (-4 *5 (-962))))
+  (-12 (-5 *2 (-1076)) (-5 *3 (-703)) (-5 *4 (-1 *1 (-583 *1)))
+   (-4 *1 (-400 *5)) (-4 *5 (-779)) (-4 *5 (-963))))
  ((*1 *1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-583 (-1075))) (-5 *3 (-583 (-703)))
+  (-12 (-5 *2 (-583 (-1076))) (-5 *3 (-583 (-703)))
    (-5 *4 (-583 (-1 *1 (-583 *1)))) (-4 *1 (-400 *5)) (-4 *5 (-779))
-   (-4 *5 (-962))))
+   (-4 *5 (-963))))
  ((*1 *1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-583 (-1075))) (-5 *3 (-583 (-703)))
+  (-12 (-5 *2 (-583 (-1076))) (-5 *3 (-583 (-703)))
    (-5 *4 (-583 (-1 *1 *1))) (-4 *1 (-400 *5)) (-4 *5 (-779))
-   (-4 *5 (-962))))
+   (-4 *5 (-963))))
  ((*1 *1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-583 (-109))) (-5 *3 (-583 *1)) (-5 *4 (-1075))
+  (-12 (-5 *2 (-583 (-109))) (-5 *3 (-583 *1)) (-5 *4 (-1076))
    (-4 *1 (-400 *5)) (-4 *5 (-779)) (-4 *5 (-558 (-493)))))
  ((*1 *1 *1 *2 *1 *3)
-  (-12 (-5 *2 (-109)) (-5 *3 (-1075)) (-4 *1 (-400 *4)) (-4 *4 (-779))
+  (-12 (-5 *2 (-109)) (-5 *3 (-1076)) (-4 *1 (-400 *4)) (-4 *4 (-779))
    (-4 *4 (-558 (-493)))))
  ((*1 *1 *1)
   (-12 (-4 *1 (-400 *2)) (-4 *2 (-779)) (-4 *2 (-558 (-493)))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-583 (-1075))) (-4 *1 (-400 *3)) (-4 *3 (-779))
+  (-12 (-5 *2 (-583 (-1076))) (-4 *1 (-400 *3)) (-4 *3 (-779))
    (-4 *3 (-558 (-493)))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1075)) (-4 *1 (-400 *3)) (-4 *3 (-779))
+  (-12 (-5 *2 (-1076)) (-4 *1 (-400 *3)) (-4 *3 (-779))
    (-4 *3 (-558 (-493)))))
  ((*1 *1 *1 *2 *3)
-  (-12 (-4 *1 (-478 *2 *3)) (-4 *2 (-1004)) (-4 *3 (-1110))))
+  (-12 (-4 *1 (-478 *2 *3)) (-4 *2 (-1005)) (-4 *3 (-1111))))
  ((*1 *1 *1 *2 *3)
   (-12 (-5 *2 (-583 *4)) (-5 *3 (-583 *5)) (-4 *1 (-478 *4 *5))
-   (-4 *4 (-1004)) (-4 *5 (-1110))))
+   (-4 *4 (-1005)) (-4 *5 (-1111))))
  ((*1 *2 *1 *2)
   (-12 (-5 *2 (-765 *3)) (-4 *3 (-333)) (-5 *1 (-651 *3))))
  ((*1 *2 *1 *2) (-12 (-5 *1 (-651 *2)) (-4 *2 (-333))))
- ((*1 *2 *1 *2) (-12 (-4 *1 (-826 *2)) (-4 *2 (-1004))))
+ ((*1 *2 *1 *2) (-12 (-4 *1 (-826 *2)) (-4 *2 (-1005))))
  ((*1 *2 *2 *3 *2)
-  (-12 (-5 *2 (-377 (-875 *4))) (-5 *3 (-1075)) (-4 *4 (-509))
-   (-5 *1 (-958 *4))))
+  (-12 (-5 *2 (-377 (-875 *4))) (-5 *3 (-1076)) (-4 *4 (-509))
+   (-5 *1 (-959 *4))))
  ((*1 *2 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-1075))) (-5 *4 (-583 (-377 (-875 *5))))
-   (-5 *2 (-377 (-875 *5))) (-4 *5 (-509)) (-5 *1 (-958 *5))))
+  (-12 (-5 *3 (-583 (-1076))) (-5 *4 (-583 (-377 (-875 *5))))
+   (-5 *2 (-377 (-875 *5))) (-4 *5 (-509)) (-5 *1 (-959 *5))))
  ((*1 *2 *2 *3)
   (-12 (-5 *3 (-265 (-377 (-875 *4)))) (-5 *2 (-377 (-875 *4)))
-   (-4 *4 (-509)) (-5 *1 (-958 *4))))
+   (-4 *4 (-509)) (-5 *1 (-959 *4))))
  ((*1 *2 *2 *3)
   (-12 (-5 *3 (-583 (-265 (-377 (-875 *4))))) (-5 *2 (-377 (-875 *4)))
-   (-4 *4 (-509)) (-5 *1 (-958 *4))))
+   (-4 *4 (-509)) (-5 *1 (-959 *4))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1056 *3)) (-4 *3 (-962)) (-5 *1 (-1060 *3))))
+  (-12 (-5 *2 (-1057 *3)) (-4 *3 (-963)) (-5 *1 (-1061 *3))))
  ((*1 *2 *1 *3)
-  (-12 (-4 *1 (-1134 *3 *4)) (-4 *3 (-962)) (-4 *4 (-724))
-   (|has| *3 (-15 ** (*3 *3 *4))) (-5 *2 (-1056 *3))))) 
-(((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-13 (-333) (-134) (-953 (-517))))
-      (-4 *5 (-1132 *4))
-      (-5 *2 (-2 (|:| -1306 (-377 *5)) (|:| |coeff| (-377 *5))))
-      (-5 *1 (-521 *4 *5)) (-5 *3 (-377 *5))))) 
-(((*1 *1) (-5 *1 (-407)))) 
-(((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-143 *3 *2))
-   (-4 *2 (-400 *3))))
- ((*1 *2 *2 *3)
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-   (-4 *2 (-400 *4))))
- ((*1 *1 *1 *2) (-12 (-4 *1 (-145)) (-5 *2 (-1075))))
- ((*1 *1 *1) (-4 *1 (-145)))) 
-(((*1 *2 *3 *3)
-  (-12 (-4 *3 (-1114)) (-4 *5 (-1132 *3)) (-4 *6 (-1132 (-377 *5)))
-   (-5 *2 (-107)) (-5 *1 (-311 *4 *3 *5 *6)) (-4 *4 (-312 *3 *5 *6))))
- ((*1 *2 *3 *3)
-  (-12 (-4 *1 (-312 *3 *4 *5)) (-4 *3 (-1114)) (-4 *4 (-1132 *3))
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-(((*1 *2 *3 *4 *5 *5)
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-   (-4 *6 (-962)) (-5 *2 (-583 (-583 (-623 *6)))) (-5 *1 (-945 *6))
-   (-5 *3 (-583 (-623 *6)))))
+  (-12 (-4 *1 (-1135 *3 *4)) (-4 *3 (-963)) (-4 *4 (-724))
+   (|has| *3 (-15 ** (*3 *3 *4))) (-5 *2 (-1057 *3))))) 
+(((*1 *2 *3)
+  (-12 (-4 *1 (-312 *4 *3 *5)) (-4 *4 (-1115)) (-4 *3 (-1133 *4))
+   (-4 *5 (-1133 (-377 *3))) (-5 *2 (-107))))
  ((*1 *2 *3)
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-   (-5 *2 (-583 (-583 (-623 *4)))) (-5 *1 (-945 *4))
-   (-5 *3 (-583 (-623 *4)))))
- ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-107)) (-4 *5 (-333)) (-4 *5 (-338)) (-4 *5 (-962))
-   (-5 *2 (-583 (-583 (-623 *5)))) (-5 *1 (-945 *5))
-   (-5 *3 (-583 (-623 *5)))))
+  (-12 (-4 *1 (-312 *3 *4 *5)) (-4 *3 (-1115)) (-4 *4 (-1133 *3))
+   (-4 *5 (-1133 (-377 *4))) (-5 *2 (-107))))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-1072 *1)) (-5 *3 (-1076)) (-4 *1 (-27))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1072 *1)) (-4 *1 (-27))))
+ ((*1 *1 *2) (-12 (-5 *2 (-875 *1)) (-4 *1 (-27))))
+ ((*1 *1 *1 *2)
+  (-12 (-5 *2 (-1076)) (-4 *1 (-29 *3)) (-4 *3 (-13 (-779) (-509)))))
+ ((*1 *1 *1) (-12 (-4 *1 (-29 *2)) (-4 *2 (-13 (-779) (-509)))))
  ((*1 *2 *3 *4)
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-   (-5 *3 (-583 (-623 *5)))))) 
-(((*1 *2 *3)
-  (-12 (-5 *2 (-1071 (-517))) (-5 *1 (-865)) (-5 *3 (-517))))) 
+  (-12 (-5 *3 (-1072 *2)) (-5 *4 (-1076)) (-4 *2 (-400 *5))
+   (-5 *1 (-31 *5 *2)) (-4 *5 (-13 (-779) (-509)))))
+ ((*1 *1 *2 *3)
+  (|partial| -12 (-5 *2 (-1072 *1)) (-5 *3 (-844)) (-4 *1 (-930))))
+ ((*1 *1 *2 *3 *4)
+  (|partial| -12 (-5 *2 (-1072 *1)) (-5 *3 (-844)) (-5 *4 (-787))
+      (-4 *1 (-930))))
+ ((*1 *1 *2 *3)
+  (|partial| -12 (-5 *3 (-844)) (-4 *4 (-13 (-777) (-333)))
+      (-4 *1 (-979 *4 *2)) (-4 *2 (-1133 *4))))) 
+(((*1 *2 *3 *4 *3)
+  (-12 (-5 *3 (-517)) (-5 *4 (-623 (-199))) (-5 *2 (-952))
+   (-5 *1 (-680))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-621 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-343 *3))
-   (-4 *5 (-343 *3)) (-5 *2 (-107))))
- ((*1 *2 *1)
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-   (-4 *6 (-212 *4 *5)) (-4 *7 (-212 *3 *5)) (-5 *2 (-107))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-517)) (-4 *4 (-421)) (-4 *5 (-725)) (-4 *6 (-779))
-   (-5 *2 (-1161)) (-5 *1 (-418 *4 *5 *6 *7)) (-4 *7 (-872 *4 *5 *6))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-199)) (-5 *1 (-200))))
- ((*1 *2 *2) (-12 (-5 *2 (-153 (-199))) (-5 *1 (-200))))
- ((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-401 *3 *2))
-   (-4 *2 (-400 *3))))
- ((*1 *1 *1) (-4 *1 (-1039)))) 
+  (-12 (-4 *1 (-1026 *3 *4 *2 *5)) (-4 *4 (-963)) (-4 *5 (-212 *3 *4))
+   (-4 *2 (-212 *3 *4))))) 
+(((*1 *2 *3 *4 *5 *4 *5 *5 *6 *4 *4 *4 *4 *4 *5 *4 *5 *5 *7 *4)
+  (-12 (-5 *3 (-1059)) (-5 *5 (-623 (-199))) (-5 *6 (-199))
+   (-5 *7 (-623 (-517))) (-5 *4 (-517)) (-5 *2 (-952)) (-5 *1 (-685))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-286 (-199))) (-5 *2 (-199)) (-5 *1 (-276))))) 
+(((*1 *2 *3 *4 *3 *4 *3)
+  (-12 (-5 *3 (-517)) (-5 *4 (-623 (-199))) (-5 *2 (-952))
+   (-5 *1 (-689))))) 
+(((*1 *2 *3 *3 *3 *4)
+  (-12 (-5 *3 (-199)) (-5 *4 (-517)) (-5 *2 (-952)) (-5 *1 (-691))))) 
+(((*1 *2)
+  (-12 (-5 *2 (-1157 (-1006 *3 *4))) (-5 *1 (-1006 *3 *4))
+   (-14 *3 (-844)) (-14 *4 (-844))))) 
 (((*1 *2 *2 *2)
-  (|partial| -12 (-4 *3 (-333)) (-5 *1 (-819 *2 *3))
-      (-4 *2 (-1132 *3))))) 
+  (-12 (-5 *2 (-583 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-421))
+   (-4 *3 (-509)) (-4 *4 (-725)) (-4 *5 (-779))
+   (-5 *1 (-896 *3 *4 *5 *6))))) 
 (((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1075)) (-5 *3 (-583 *1)) (-4 *1 (-400 *4))
+  (-12 (-5 *2 (-1076)) (-5 *3 (-583 *1)) (-4 *1 (-400 *4))
    (-4 *4 (-779))))
  ((*1 *1 *2 *1 *1 *1 *1)
-  (-12 (-5 *2 (-1075)) (-4 *1 (-400 *3)) (-4 *3 (-779))))
+  (-12 (-5 *2 (-1076)) (-4 *1 (-400 *3)) (-4 *3 (-779))))
  ((*1 *1 *2 *1 *1 *1)
-  (-12 (-5 *2 (-1075)) (-4 *1 (-400 *3)) (-4 *3 (-779))))
+  (-12 (-5 *2 (-1076)) (-4 *1 (-400 *3)) (-4 *3 (-779))))
  ((*1 *1 *2 *1 *1)
-  (-12 (-5 *2 (-1075)) (-4 *1 (-400 *3)) (-4 *3 (-779))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1075)) (-4 *1 (-400 *3)) (-4 *3 (-779))))) 
-(((*1 *1 *1 *1 *2)
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-   (-4 *4 (-724)) (-4 *3 (-156))))) 
-(((*1 *1 *1) (-4 *1 (-971)))
- ((*1 *1 *1 *2 *2)
-  (-12 (-4 *1 (-1134 *3 *2)) (-4 *3 (-962)) (-4 *2 (-724))))
- ((*1 *1 *1 *2)
-  (-12 (-4 *1 (-1134 *3 *2)) (-4 *3 (-962)) (-4 *2 (-724))))) 
-(((*1 *2) (-12 (-5 *2 (-107)) (-5 *1 (-436))))
- ((*1 *2 *2) (-12 (-5 *2 (-107)) (-5 *1 (-436))))) 
+  (-12 (-5 *2 (-1076)) (-4 *1 (-400 *3)) (-4 *3 (-779))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1076)) (-4 *1 (-400 *3)) (-4 *3 (-779))))) 
+(((*1 *2 *1 *3) (-12 (-4 *1 (-124)) (-5 *3 (-703)) (-5 *2 (-1162))))) 
+(((*1 *2 *2)
+  (-12 (-5 *2 (-107)) (-5 *1 (-411 *3)) (-4 *3 (-1133 (-517)))))) 
+(((*1 *1 *1 *2) (-12 (-5 *2 (-517)) (-5 *1 (-837 *3)) (-4 *3 (-278))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-509)) (-4 *5 (-725)) (-4 *6 (-779))
-   (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-583 (-2 (|:| -1723 *1) (|:| -3674 (-583 *7)))))
-   (-5 *3 (-583 *7)) (-4 *1 (-1104 *4 *5 *6 *7))))) 
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+   (-5 *8 (-3 (|:| |fn| (-358)) (|:| |fp| (-84 FCN))))
+   (-5 *9 (-3 (|:| |fn| (-358)) (|:| |fp| (-69 PEDERV))))
+   (-5 *10 (-3 (|:| |fn| (-358)) (|:| |fp| (-86 OUTPUT))))
+   (-5 *3 (-199)) (-5 *2 (-952)) (-5 *1 (-682))))) 
+(((*1 *2 *3 *1)
+  (-12 (-4 *4 (-333)) (-4 *5 (-725)) (-4 *6 (-779)) (-5 *2 (-107))
+   (-5 *1 (-469 *4 *5 *6 *3)) (-4 *3 (-872 *4 *5 *6))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-319)) (-5 *2 (-107))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1071 *4)) (-4 *4 (-319)) (-5 *2 (-107))
+  (-12 (-5 *3 (-1072 *4)) (-4 *4 (-319)) (-5 *2 (-107))
    (-5 *1 (-327 *4))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-583 (-1058))) (-5 *1 (-364))))
- ((*1 *2 *1) (-12 (-5 *2 (-583 (-1058))) (-5 *1 (-1091))))) 
+(((*1 *1)
+  (-12 (-4 *1 (-374)) (-2479 (|has| *1 (-6 -4183)))
+   (-2479 (|has| *1 (-6 -4175)))))
+ ((*1 *2 *1) (-12 (-4 *1 (-395 *2)) (-4 *2 (-1005)) (-4 *2 (-779))))
+ ((*1 *2 *1) (-12 (-4 *1 (-762 *2)) (-4 *2 (-779))))
+ ((*1 *1 *1 *1) (-4 *1 (-779))) ((*1 *1) (-5 *1 (-1023)))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *3 (-583 (-1 (-107) *8))) (-4 *8 (-977 *5 *6 *7))
+   (-4 *5 (-509)) (-4 *6 (-725)) (-4 *7 (-779))
+   (-5 *2 (-2 (|:| |goodPols| (-583 *8)) (|:| |badPols| (-583 *8))))
+   (-5 *1 (-896 *5 *6 *7 *8)) (-5 *4 (-583 *8))))) 
+(((*1 *2 *3 *4 *4 *5 *3)
+  (-12 (-5 *3 (-517)) (-5 *4 (-623 (-199))) (-5 *5 (-199))
+   (-5 *2 (-952)) (-5 *1 (-685))))) 
+(((*1 *2 *3 *3)
+  (-12 (-4 *4 (-509)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -2157 *4)))
+   (-5 *1 (-889 *4 *3)) (-4 *3 (-1133 *4))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *5 (-999 *3)) (-4 *3 (-872 *7 *6 *4)) (-4 *6 (-725))
+  (-12 (-5 *5 (-1000 *3)) (-4 *3 (-872 *7 *6 *4)) (-4 *6 (-725))
    (-4 *4 (-779)) (-4 *7 (-509))
    (-5 *2 (-2 (|:| |num| *3) (|:| |den| (-517))))
    (-5 *1 (-541 *6 *4 *7 *3))))
@@ -3696,410 +3631,412 @@
  ((*1 *1 *1 *1 *1) (-5 *1 (-787))) ((*1 *1 *1 *1) (-5 *1 (-787)))
  ((*1 *1 *1) (-5 *1 (-787)))
  ((*1 *2 *2 *3)
-  (-12 (-5 *3 (-1075))
-   (-4 *4 (-13 (-509) (-779) (-953 (-517)) (-579 (-517))))
-   (-5 *1 (-1067 *4 *2)) (-4 *2 (-13 (-400 *4) (-145) (-27) (-1096)))))
+  (-12 (-5 *3 (-1076))
+   (-4 *4 (-13 (-509) (-779) (-954 (-517)) (-579 (-517))))
+   (-5 *1 (-1068 *4 *2)) (-4 *2 (-13 (-400 *4) (-145) (-27) (-1097)))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *3 (-997 *2)) (-4 *2 (-13 (-400 *4) (-145) (-27) (-1096)))
-   (-4 *4 (-13 (-509) (-779) (-953 (-517)) (-579 (-517))))
-   (-5 *1 (-1067 *4 *2))))
+  (-12 (-5 *3 (-998 *2)) (-4 *2 (-13 (-400 *4) (-145) (-27) (-1097)))
+   (-4 *4 (-13 (-509) (-779) (-954 (-517)) (-579 (-517))))
+   (-5 *1 (-1068 *4 *2))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1075)) (-4 *5 (-13 (-509) (-779) (-953 (-517))))
-   (-5 *2 (-377 (-875 *5))) (-5 *1 (-1068 *5)) (-5 *3 (-875 *5))))
+  (-12 (-5 *4 (-1076)) (-4 *5 (-13 (-509) (-779) (-954 (-517))))
+   (-5 *2 (-377 (-875 *5))) (-5 *1 (-1069 *5)) (-5 *3 (-875 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1075)) (-4 *5 (-13 (-509) (-779) (-953 (-517))))
-   (-5 *2 (-3 (-377 (-875 *5)) (-286 *5))) (-5 *1 (-1068 *5))
+  (-12 (-5 *4 (-1076)) (-4 *5 (-13 (-509) (-779) (-954 (-517))))
+   (-5 *2 (-3 (-377 (-875 *5)) (-286 *5))) (-5 *1 (-1069 *5))
    (-5 *3 (-377 (-875 *5)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-997 (-875 *5))) (-5 *3 (-875 *5))
-   (-4 *5 (-13 (-509) (-779) (-953 (-517)))) (-5 *2 (-377 *3))
-   (-5 *1 (-1068 *5))))
+  (-12 (-5 *4 (-998 (-875 *5))) (-5 *3 (-875 *5))
+   (-4 *5 (-13 (-509) (-779) (-954 (-517)))) (-5 *2 (-377 *3))
+   (-5 *1 (-1069 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-997 (-377 (-875 *5)))) (-5 *3 (-377 (-875 *5)))
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-   (-5 *1 (-1068 *5))))) 
-(((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-779) (-421))) (-5 *1 (-1102 *3 *2))
-   (-4 *2 (-13 (-400 *3) (-1096)))))) 
-(((*1 *2 *2) (-12 (-5 *1 (-144 *2)) (-4 *2 (-502))))
- ((*1 *1 *2) (-12 (-5 *2 (-583 (-517))) (-5 *1 (-889))))) 
-(((*1 *2) (-12 (-5 *2 (-797)) (-5 *1 (-1159))))
- ((*1 *2 *2) (-12 (-5 *2 (-797)) (-5 *1 (-1159))))) 
+  (-12 (-5 *4 (-998 (-377 (-875 *5)))) (-5 *3 (-377 (-875 *5)))
+   (-4 *5 (-13 (-509) (-779) (-954 (-517)))) (-5 *2 (-3 *3 (-286 *5)))
+   (-5 *1 (-1069 *5))))) 
+(((*1 *2)
+  (-12 (-4 *4 (-156)) (-5 *2 (-107)) (-5 *1 (-336 *3 *4))
+   (-4 *3 (-337 *4))))
+ ((*1 *2) (-12 (-4 *1 (-337 *3)) (-4 *3 (-156)) (-5 *2 (-107))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-583 (-1059))) (-5 *1 (-364))))
+ ((*1 *2 *1) (-12 (-5 *2 (-583 (-1059))) (-5 *1 (-1092))))) 
+(((*1 *2 *1 *3 *3)
+  (-12 (-5 *3 (-844)) (-5 *2 (-1162)) (-5 *1 (-1158))))
+ ((*1 *2 *1 *3 *3)
+  (-12 (-5 *3 (-844)) (-5 *2 (-1162)) (-5 *1 (-1159))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-583 (-51))) (-5 *1 (-815 *3)) (-4 *3 (-1004))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-583 *4)) (-4 *4 (-333)) (-5 *2 (-623 *4))
-   (-5 *1 (-746 *4 *5)) (-4 *5 (-593 *4))))
- ((*1 *2 *3 *4)
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-   (-5 *2 (-623 *5)) (-5 *1 (-746 *5 *6)) (-4 *6 (-593 *5))))) 
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+(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5)
+  (-12 (-5 *3 (-1 (-349) (-349))) (-5 *4 (-349))
+   (-5 *2
+    (-2 (|:| -3121 *4) (|:| -3110 *4) (|:| |totalpts| (-517))
+     (|:| |success| (-107))))
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 (((*1 *2 *2)
   (-12 (-4 *3 (-779)) (-5 *1 (-852 *3 *2)) (-4 *2 (-400 *3))))
  ((*1 *2 *3)
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-(((*1 *2 *3 *2)
-  (-12 (-5 *2 (-1056 *4)) (-5 *3 (-1 *4 (-517))) (-4 *4 (-962))
-   (-5 *1 (-1060 *4))))) 
+  (-12 (-5 *3 (-1076)) (-5 *2 (-286 (-517))) (-5 *1 (-853))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-623 (-377 (-875 *4)))) (-4 *4 (-421))
+   (-5 *2 (-583 (-3 (-377 (-875 *4)) (-1066 (-1076) (-875 *4)))))
+   (-5 *1 (-263 *4))))) 
+(((*1 *2 *2)
+  (-12 (-4 *3 (-13 (-779) (-421))) (-5 *1 (-1103 *3 *2))
+   (-4 *2 (-13 (-400 *3) (-1097)))))) 
+(((*1 *2 *1 *1)
+  (-12 (-5 *2 (-2 (|:| -2370 (-714 *3)) (|:| |coef2| (-714 *3))))
+   (-5 *1 (-714 *3)) (-4 *3 (-509)) (-4 *3 (-963))))
+ ((*1 *2 *1 *1)
+  (-12 (-4 *3 (-509)) (-4 *3 (-963)) (-4 *4 (-725)) (-4 *5 (-779))
+   (-5 *2 (-2 (|:| -2370 *1) (|:| |coef2| *1)))
+   (-4 *1 (-977 *3 *4 *5))))) 
 (((*1 *2)
-  (-12 (-4 *1 (-312 *3 *4 *5)) (-4 *3 (-1114)) (-4 *4 (-1132 *3))
-   (-4 *5 (-1132 (-377 *4))) (-5 *2 (-107))))) 
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-(((*1 *2 *1)
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-   (-4 *5 (-343 *3)) (-5 *2 (-517))))
- ((*1 *2 *1)
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-(((*1 *1 *2 *3)
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-(((*1 *1 *2) (-12 (-5 *2 (-517)) (-5 *1 (-973))))
- ((*1 *1 *2) (-12 (-5 *2 (-1075)) (-5 *1 (-973))))) 
+  (-12 (-4 *4 (-1115)) (-4 *5 (-1133 *4)) (-4 *6 (-1133 (-377 *5)))
+   (-5 *2 (-107)) (-5 *1 (-311 *3 *4 *5 *6)) (-4 *3 (-312 *4 *5 *6))))
+ ((*1 *2)
+  (-12 (-4 *1 (-312 *3 *4 *5)) (-4 *3 (-1115)) (-4 *4 (-1133 *3))
+   (-4 *5 (-1133 (-377 *4))) (-5 *2 (-107))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-875 (-517))) (-5 *2 (-583 *1)) (-4 *1 (-930))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-875 (-377 (-517)))) (-5 *2 (-583 *1)) (-4 *1 (-930))))
+ ((*1 *2 *3) (-12 (-5 *3 (-875 *1)) (-4 *1 (-930)) (-5 *2 (-583 *1))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1072 (-517))) (-5 *2 (-583 *1)) (-4 *1 (-930))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1072 (-377 (-517)))) (-5 *2 (-583 *1)) (-4 *1 (-930))))
+ ((*1 *2 *3) (-12 (-5 *3 (-1072 *1)) (-4 *1 (-930)) (-5 *2 (-583 *1))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-13 (-777) (-333))) (-4 *3 (-1133 *4)) (-5 *2 (-583 *1))
+   (-4 *1 (-979 *4 *3))))) 
+(((*1 *2 *3)
+  (-12 (-5 *2 (-388 (-1072 *1))) (-5 *1 (-286 *4)) (-5 *3 (-1072 *1))
+   (-4 *4 (-421)) (-4 *4 (-509)) (-4 *4 (-779))))
+ ((*1 *2 *3)
+  (-12 (-4 *1 (-832)) (-5 *2 (-388 (-1072 *1))) (-5 *3 (-1072 *1))))) 
+(((*1 *2 *2) (-12 (-5 *1 (-144 *2)) (-4 *2 (-502))))
+ ((*1 *1 *2) (-12 (-5 *2 (-583 (-517))) (-5 *1 (-890))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-583 *1)) (-4 *1 (-273))))
  ((*1 *1 *1) (-4 *1 (-273))) ((*1 *1 *1) (-5 *1 (-787)))) 
-(((*1 *2 *3 *4 *5 *6 *5)
-  (-12 (-5 *4 (-153 (-199))) (-5 *5 (-517)) (-5 *6 (-1058))
-   (-5 *3 (-199)) (-5 *2 (-951)) (-5 *1 (-691))))) 
+(((*1 *1 *1 *2)
+  (|partial| -12 (-4 *1 (-1105 *3 *4 *5 *2)) (-4 *3 (-509))
+      (-4 *4 (-725)) (-4 *5 (-779)) (-4 *2 (-977 *3 *4 *5))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-1 (-866 *3) (-866 *3))) (-5 *1 (-158 *3))
-   (-4 *3 (-13 (-333) (-1096) (-919)))))) 
-(((*1 *2 *3 *3)
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-   (-5 *3 (-583 (-517)))))
- ((*1 *2 *3)
-  (-12 (-5 *2 (-1056 (-583 (-517)))) (-5 *1 (-806))
-   (-5 *3 (-583 (-517)))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-844)) (|has| *1 (-6 -4181)) (-4 *1 (-374))))
+  (-12 (-4 *4 (-509)) (-5 *2 (-703)) (-5 *1 (-42 *4 *3))
+   (-4 *3 (-387 *4))))) 
+(((*1 *2 *2 *3)
+  (-12 (-5 *3 (-556 *2)) (-4 *2 (-13 (-27) (-1097) (-400 *4)))
+   (-4 *4 (-13 (-509) (-779) (-954 (-517)) (-579 (-517))))
+   (-5 *1 (-250 *4 *2))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-844)) (|has| *1 (-6 -4183)) (-4 *1 (-374))))
  ((*1 *2) (-12 (-4 *1 (-374)) (-5 *2 (-844))))
  ((*1 *2 *2) (-12 (-5 *2 (-844)) (-5 *1 (-632))))
  ((*1 *2) (-12 (-5 *2 (-844)) (-5 *1 (-632))))) 
 (((*1 *2 *3)
-  (-12
-   (-5 *3
-    (-2
-     (|:| |endPointContinuity|
-          (-3 (|:| |continuous| "Continuous at the end points")
-           (|:| |lowerSingular|
-                "There is a singularity at the lower end point")
-           (|:| |upperSingular|
-                "There is a singularity at the upper end point")
-           (|:| |bothSingular|
-                "There are singularities at both end points")
-           (|:| |notEvaluated|
-                "End point continuity not yet evaluated")))
-     (|:| |singularitiesStream|
-          (-3 (|:| |str| (-1056 (-199)))
-           (|:| |notEvaluated|
-                "Internal singularities not yet evaluated")))
-     (|:| -2192
-          (-3 (|:| |finite| "The range is finite")
-           (|:| |lowerInfinite| "The bottom of range is infinite")
-           (|:| |upperInfinite| "The top of range is infinite")
-           (|:| |bothInfinite|
-                "Both top and bottom points are infinite")
-           (|:| |notEvaluated| "Range not yet evaluated")))))
-   (-5 *2 (-951)) (-5 *1 (-276))))) 
-(((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-875 *5))) (-5 *4 (-583 (-1075))) (-4 *5 (-509))
-   (-5 *2 (-583 (-583 (-265 (-377 (-875 *5)))))) (-5 *1 (-702 *5))))
+  (-12 (-5 *3 (-1157 *1)) (-4 *1 (-337 *4)) (-4 *4 (-156))
+   (-5 *2 (-583 (-875 *4)))))
+ ((*1 *2)
+  (-12 (-4 *4 (-156)) (-5 *2 (-583 (-875 *4))) (-5 *1 (-386 *3 *4))
+   (-4 *3 (-387 *4))))
+ ((*1 *2)
+  (-12 (-4 *1 (-387 *3)) (-4 *3 (-156)) (-5 *2 (-583 (-875 *3)))))
+ ((*1 *2)
+  (-12 (-5 *2 (-583 (-875 *3))) (-5 *1 (-422 *3 *4 *5 *6))
+   (-4 *3 (-509)) (-4 *3 (-156)) (-14 *4 (-844))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1157 (-623 *3)))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-875 *4))) (-4 *4 (-509))
-   (-5 *2 (-583 (-583 (-265 (-377 (-875 *4)))))) (-5 *1 (-702 *4))))
- ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-623 *7))
-   (-5 *5
-    (-1 (-2 (|:| |particular| (-3 *6 "failed")) (|:| -2062 (-583 *6)))
-     *7 *6))
-   (-4 *6 (-333)) (-4 *7 (-593 *6))
-   (-5 *2
-    (-2 (|:| |particular| (-3 (-1156 *6) "failed"))
-     (|:| -2062 (-583 (-1156 *6)))))
-   (-5 *1 (-745 *6 *7)) (-5 *4 (-1156 *6))))) 
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+   (-14 *5 (-844)) (-14 *6 (-583 (-1076))) (-14 *7 (-1157 (-623 *4)))))) 
+(((*1 *2) (-12 (-5 *2 (-797)) (-5 *1 (-1160))))
+ ((*1 *2 *2) (-12 (-5 *2 (-797)) (-5 *1 (-1160))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1075))
-   (-4 *4 (-13 (-421) (-779) (-953 (-517)) (-579 (-517))))
+  (-12 (-5 *3 (-1076))
+   (-4 *4 (-13 (-421) (-779) (-954 (-517)) (-579 (-517))))
    (-5 *2 (-51)) (-5 *1 (-285 *4 *5))
-   (-4 *5 (-13 (-27) (-1096) (-400 *4)))))
+   (-4 *5 (-13 (-27) (-1097) (-400 *4)))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-421) (-779) (-953 (-517)) (-579 (-517))))
+  (-12 (-4 *4 (-13 (-421) (-779) (-954 (-517)) (-579 (-517))))
    (-5 *2 (-51)) (-5 *1 (-285 *4 *3))
-   (-4 *3 (-13 (-27) (-1096) (-400 *4)))))
+   (-4 *3 (-13 (-27) (-1097) (-400 *4)))))
  ((*1 *2 *3 *4)
   (-12 (-5 *4 (-377 (-517)))
-   (-4 *5 (-13 (-421) (-779) (-953 (-517)) (-579 (-517))))
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    (-5 *2 (-51)) (-5 *1 (-285 *5 *3))
-   (-4 *3 (-13 (-27) (-1096) (-400 *5)))))
+   (-4 *3 (-13 (-27) (-1097) (-400 *5)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-265 *3)) (-4 *3 (-13 (-27) (-1096) (-400 *5)))
-   (-4 *5 (-13 (-421) (-779) (-953 (-517)) (-579 (-517))))
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    (-5 *2 (-51)) (-5 *1 (-285 *5 *3))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *4 (-265 *3)) (-5 *5 (-377 (-517)))
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    (-5 *2 (-51)) (-5 *1 (-285 *6 *3))))
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   (-12 (-5 *3 (-1 *6 (-517))) (-5 *4 (-265 *6))
-   (-4 *6 (-13 (-27) (-1096) (-400 *5)))
-   (-4 *5 (-13 (-509) (-779) (-953 (-517)) (-579 (-517))))
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    (-5 *2 (-51)) (-5 *1 (-428 *5 *6))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *4 (-1075)) (-5 *5 (-265 *3))
-   (-4 *3 (-13 (-27) (-1096) (-400 *6)))
-   (-4 *6 (-13 (-509) (-779) (-953 (-517)) (-579 (-517))))
+  (-12 (-5 *4 (-1076)) (-5 *5 (-265 *3))
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    (-5 *2 (-51)) (-5 *1 (-428 *6 *3))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *7 (-517))) (-5 *4 (-265 *7)) (-5 *5 (-1123 (-517)))
-   (-4 *7 (-13 (-27) (-1096) (-400 *6)))
-   (-4 *6 (-13 (-509) (-779) (-953 (-517)) (-579 (-517))))
+  (-12 (-5 *3 (-1 *7 (-517))) (-5 *4 (-265 *7)) (-5 *5 (-1124 (-517)))
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    (-5 *2 (-51)) (-5 *1 (-428 *6 *7))))
  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *4 (-1075)) (-5 *5 (-265 *3)) (-5 *6 (-1123 (-517)))
-   (-4 *3 (-13 (-27) (-1096) (-400 *7)))
-   (-4 *7 (-13 (-509) (-779) (-953 (-517)) (-579 (-517))))
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    (-5 *2 (-51)) (-5 *1 (-428 *7 *3))))
  ((*1 *2 *3 *4 *5 *6)
   (-12 (-5 *3 (-1 *8 (-377 (-517)))) (-5 *4 (-265 *8))
-   (-5 *5 (-1123 (-377 (-517)))) (-5 *6 (-377 (-517)))
-   (-4 *8 (-13 (-27) (-1096) (-400 *7)))
-   (-4 *7 (-13 (-509) (-779) (-953 (-517)) (-579 (-517))))
+   (-5 *5 (-1124 (-377 (-517)))) (-5 *6 (-377 (-517)))
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    (-5 *2 (-51)) (-5 *1 (-428 *7 *8))))
  ((*1 *2 *3 *4 *5 *6 *7)
-  (-12 (-5 *4 (-1075)) (-5 *5 (-265 *3)) (-5 *6 (-1123 (-377 (-517))))
-   (-5 *7 (-377 (-517))) (-4 *3 (-13 (-27) (-1096) (-400 *8)))
-   (-4 *8 (-13 (-509) (-779) (-953 (-517)) (-579 (-517))))
+  (-12 (-5 *4 (-1076)) (-5 *5 (-265 *3)) (-5 *6 (-1124 (-377 (-517))))
+   (-5 *7 (-377 (-517))) (-4 *3 (-13 (-27) (-1097) (-400 *8)))
+   (-4 *8 (-13 (-509) (-779) (-954 (-517)) (-579 (-517))))
    (-5 *2 (-51)) (-5 *1 (-428 *8 *3))))
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-             (-583 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
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+(((*1 *2 *2) (-12 (-5 *2 (-107)) (-5 *1 (-952))))) 
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+  (|partial| -12 (-5 *2 (-583 (-815 *3))) (-5 *1 (-815 *3))
+      (-4 *3 (-1005))))) 
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 (((*1 *1 *1)
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+     (|:| |polj| *4)))
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  ((*1 *1 *2)
   (-12 (-5 *2 (-377 (-875 (-349)))) (-5 *1 (-309 *3 *4 *5))
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  ((*1 *1 *2)
   (-12 (-5 *2 (-286 (-349))) (-5 *1 (-309 *3 *4 *5))
-   (-4 *5 (-953 (-349))) (-14 *3 (-583 (-1075)))
-   (-14 *4 (-583 (-1075))) (-4 *5 (-357))))
+   (-4 *5 (-954 (-349))) (-14 *3 (-583 (-1076)))
+   (-14 *4 (-583 (-1076))) (-4 *5 (-357))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-875 (-517))) (-5 *1 (-309 *3 *4 *5))
-   (-4 *5 (-953 (-517))) (-14 *3 (-583 (-1075)))
-   (-14 *4 (-583 (-1075))) (-4 *5 (-357))))
+   (-4 *5 (-954 (-517))) (-14 *3 (-583 (-1076)))
+   (-14 *4 (-583 (-1076))) (-4 *5 (-357))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-377 (-875 (-517)))) (-5 *1 (-309 *3 *4 *5))
-   (-4 *5 (-953 (-517))) (-14 *3 (-583 (-1075)))
-   (-14 *4 (-583 (-1075))) (-4 *5 (-357))))
+   (-4 *5 (-954 (-517))) (-14 *3 (-583 (-1076)))
+   (-14 *4 (-583 (-1076))) (-4 *5 (-357))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-286 (-517))) (-5 *1 (-309 *3 *4 *5))
-   (-4 *5 (-953 (-517))) (-14 *3 (-583 (-1075)))
-   (-14 *4 (-583 (-1075))) (-4 *5 (-357))))
+   (-4 *5 (-954 (-517))) (-14 *3 (-583 (-1076)))
+   (-14 *4 (-583 (-1076))) (-4 *5 (-357))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1075)) (-5 *1 (-309 *3 *4 *5)) (-14 *3 (-583 *2))
+  (-12 (-5 *2 (-1076)) (-5 *1 (-309 *3 *4 *5)) (-14 *3 (-583 *2))
    (-14 *4 (-583 *2)) (-4 *5 (-357))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-286 *5)) (-4 *5 (-357)) (-5 *1 (-309 *3 *4 *5))
-   (-14 *3 (-583 (-1075))) (-14 *4 (-583 (-1075)))))
+   (-14 *3 (-583 (-1076))) (-14 *4 (-583 (-1076)))))
  ((*1 *1 *2) (-12 (-5 *2 (-623 (-377 (-875 (-517))))) (-4 *1 (-354))))
  ((*1 *1 *2) (-12 (-5 *2 (-623 (-377 (-875 (-349))))) (-4 *1 (-354))))
  ((*1 *1 *2) (-12 (-5 *2 (-623 (-875 (-517)))) (-4 *1 (-354))))
@@ -4112,30 +4049,30 @@
  ((*1 *1 *2) (-12 (-5 *2 (-875 (-349))) (-4 *1 (-366))))
  ((*1 *1 *2) (-12 (-5 *2 (-286 (-517))) (-4 *1 (-366))))
  ((*1 *1 *2) (-12 (-5 *2 (-286 (-349))) (-4 *1 (-366))))
- ((*1 *1 *2) (-12 (-5 *2 (-1156 (-377 (-875 (-517))))) (-4 *1 (-410))))
- ((*1 *1 *2) (-12 (-5 *2 (-1156 (-377 (-875 (-349))))) (-4 *1 (-410))))
- ((*1 *1 *2) (-12 (-5 *2 (-1156 (-875 (-517)))) (-4 *1 (-410))))
- ((*1 *1 *2) (-12 (-5 *2 (-1156 (-875 (-349)))) (-4 *1 (-410))))
- ((*1 *1 *2) (-12 (-5 *2 (-1156 (-286 (-517)))) (-4 *1 (-410))))
- ((*1 *1 *2) (-12 (-5 *2 (-1156 (-286 (-349)))) (-4 *1 (-410))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1157 (-377 (-875 (-517))))) (-4 *1 (-410))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1157 (-377 (-875 (-349))))) (-4 *1 (-410))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1157 (-875 (-517)))) (-4 *1 (-410))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1157 (-875 (-349)))) (-4 *1 (-410))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1157 (-286 (-517)))) (-4 *1 (-410))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1157 (-286 (-349)))) (-4 *1 (-410))))
  ((*1 *2 *1)
   (-12
    (-5 *2
     (-3
      (|:| |nia|
-          (-2 (|:| |var| (-1075)) (|:| |fn| (-286 (-199)))
-           (|:| -2192 (-999 (-772 (-199)))) (|:| |abserr| (-199))
+          (-2 (|:| |var| (-1076)) (|:| |fn| (-286 (-199)))
+           (|:| -2758 (-1000 (-772 (-199)))) (|:| |abserr| (-199))
            (|:| |relerr| (-199))))
      (|:| |mdnia|
           (-2 (|:| |fn| (-286 (-199)))
-           (|:| -2192 (-583 (-999 (-772 (-199)))))
+           (|:| -2758 (-583 (-1000 (-772 (-199)))))
            (|:| |abserr| (-199)) (|:| |relerr| (-199))))))
    (-5 *1 (-701))))
  ((*1 *2 *1)
   (-12
    (-5 *2
     (-2 (|:| |xinit| (-199)) (|:| |xend| (-199))
-     (|:| |fn| (-1156 (-286 (-199)))) (|:| |yinit| (-583 (-199)))
+     (|:| |fn| (-1157 (-286 (-199)))) (|:| |yinit| (-583 (-199)))
      (|:| |intvals| (-583 (-199))) (|:| |g| (-286 (-199)))
      (|:| |abserr| (-199)) (|:| |relerr| (-199))))
    (-5 *1 (-740))))
@@ -4144,13 +4081,13 @@
    (-5 *2
     (-3
      (|:| |noa|
-          (-2 (|:| |fn| (-286 (-199))) (|:| -2585 (-583 (-199)))
+          (-2 (|:| |fn| (-286 (-199))) (|:| -2587 (-583 (-199)))
            (|:| |lb| (-583 (-772 (-199))))
            (|:| |cf| (-583 (-286 (-199))))
            (|:| |ub| (-583 (-772 (-199))))))
      (|:| |lsa|
           (-2 (|:| |lfn| (-583 (-286 (-199))))
-           (|:| -2585 (-583 (-199)))))))
+           (|:| -2587 (-583 (-199)))))))
    (-5 *1 (-770))))
  ((*1 *2 *1)
   (-12
@@ -4161,83 +4098,90 @@
            (-2 (|:| |start| (-199)) (|:| |finish| (-199))
             (|:| |grid| (-703)) (|:| |boundaryType| (-517))
             (|:| |dStart| (-623 (-199))) (|:| |dFinish| (-623 (-199))))))
-     (|:| |f| (-583 (-583 (-286 (-199))))) (|:| |st| (-1058))
+     (|:| |f| (-583 (-583 (-286 (-199))))) (|:| |st| (-1059))
      (|:| |tol| (-199))))
    (-5 *1 (-821))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-583 *6)) (-4 *6 (-976 *3 *4 *5)) (-4 *3 (-962))
-   (-4 *4 (-725)) (-4 *5 (-779)) (-4 *1 (-894 *3 *4 *5 *6))))
- ((*1 *2 *1) (-12 (-4 *1 (-953 *2)) (-4 *2 (-1110))))
+  (-12 (-5 *2 (-583 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-963))
+   (-4 *4 (-725)) (-4 *5 (-779)) (-4 *1 (-895 *3 *4 *5 *6))))
+ ((*1 *2 *1) (-12 (-4 *1 (-954 *2)) (-4 *2 (-1111))))
  ((*1 *1 *2)
-  (-3745
+  (-3747
    (-12 (-5 *2 (-875 *3))
-    (-12 (-2477 (-4 *3 (-37 (-377 (-517)))))
-     (-2477 (-4 *3 (-37 (-517)))) (-4 *5 (-558 (-1075))))
-    (-4 *3 (-962)) (-4 *1 (-976 *3 *4 *5)) (-4 *4 (-725))
+    (-12 (-2479 (-4 *3 (-37 (-377 (-517)))))
+     (-2479 (-4 *3 (-37 (-517)))) (-4 *5 (-558 (-1076))))
+    (-4 *3 (-963)) (-4 *1 (-977 *3 *4 *5)) (-4 *4 (-725))
     (-4 *5 (-779)))
    (-12 (-5 *2 (-875 *3))
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-     (-4 *3 (-37 (-517))) (-4 *5 (-558 (-1075))))
-    (-4 *3 (-962)) (-4 *1 (-976 *3 *4 *5)) (-4 *4 (-725))
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+    (-4 *3 (-963)) (-4 *1 (-977 *3 *4 *5)) (-4 *4 (-725))
     (-4 *5 (-779)))))
  ((*1 *1 *2)
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+   (-4 *4 (-725)) (-4 *5 (-779)) (-4 *6 (-963))
+   (-5 *1 (-291 *4 *5 *6 *7))))) 
 (((*1 *2 *2)
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-(((*1 *2 *3 *4)
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-   (-4 *6 (-1132 *4))))) 
-(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1058)) (-5 *3 (-706)) (-5 *1 (-109))))) 
+  (-12
+   (-5 *2
+    (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4)
+     (|:| |xpnt| (-517))))
+   (-4 *4 (-13 (-1133 *3) (-509) (-10 -8 (-15 -2370 ($ $ $)))))
+   (-4 *3 (-509)) (-5 *1 (-1136 *3 *4))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-517)) (-5 *1 (-974))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1076)) (-5 *1 (-974))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *5 *5)) (-4 *1 (-312 *4 *5 *6)) (-4 *4 (-1114))
-   (-4 *5 (-1132 *4)) (-4 *6 (-1132 (-377 *5)))
-   (-5 *2 (-2 (|:| |num| (-623 *5)) (|:| |den| *5)))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-1077 (-377 (-517)))) (-5 *1 (-166))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-107)) (-5 *1 (-756))))) 
+  (-12 (-4 *4 (-278)) (-4 *5 (-343 *4)) (-4 *6 (-343 *4))
+   (-5 *2
+    (-2 (|:| |Smith| *3) (|:| |leftEqMat| *3) (|:| |rightEqMat| *3)))
+   (-5 *1 (-1027 *4 *5 *6 *3)) (-4 *3 (-621 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-583 *2)) (-4 *2 (-400 *4)) (-5 *1 (-143 *4 *2))
-   (-4 *4 (-13 (-779) (-509)))))) 
-(((*1 *1 *2)
-  (-12 (-5 *2 (-583 (-583 *3))) (-4 *3 (-1004)) (-4 *1 (-826 *3))))) 
+  (-12 (-5 *3 (-875 *5)) (-4 *5 (-963)) (-5 *2 (-449 *4 *5))
+   (-5 *1 (-867 *4 *5)) (-14 *4 (-583 (-1076)))))) 
+(((*1 *2 *2)
+  (-12 (-4 *3 (-13 (-779) (-421))) (-5 *1 (-1103 *3 *2))
+   (-4 *2 (-13 (-400 *3) (-1097)))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *4 (-583 *3)) (-4 *3 (-1014 *5 *6 *7 *8))
+   (-4 *5 (-13 (-278) (-134))) (-4 *6 (-725)) (-4 *7 (-779))
+   (-4 *8 (-977 *5 *6 *7)) (-5 *2 (-107))
+   (-5 *1 (-539 *5 *6 *7 *8 *3))))) 
+(((*1 *2 *3 *4 *3)
+  (-12 (-5 *3 (-517)) (-5 *4 (-623 (-199))) (-5 *2 (-952))
+   (-5 *1 (-680))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
@@ -4250,66 +4194,43 @@
      (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save")
      (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")))
    (-5 *1 (-300))))) 
-(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5)
-  (-12 (-5 *3 (-199)) (-5 *4 (-517))
-   (-5 *5 (-3 (|:| |fn| (-358)) (|:| |fp| (-62 -1724)))) (-5 *2 (-951))
-   (-5 *1 (-681))))) 
-(((*1 *2 *3 *4)
-  (-12 (-5 *3 (-199)) (-5 *4 (-517)) (-5 *2 (-951)) (-5 *1 (-691))))) 
-(((*1 *2 *1 *3)
-  (-12 (-5 *3 (-517)) (-4 *1 (-293 *4 *2)) (-4 *4 (-1004))
-   (-4 *2 (-123))))) 
-(((*1 *2 *1)
-  (-12 (-4 *3 (-962)) (-4 *4 (-1004)) (-5 *2 (-583 *1))
-   (-4 *1 (-352 *3 *4))))
- ((*1 *2 *1)
-  (-12 (-5 *2 (-583 (-668 *3 *4))) (-5 *1 (-668 *3 *4)) (-4 *3 (-962))
-   (-4 *4 (-659))))
- ((*1 *2 *1)
-  (-12 (-4 *3 (-962)) (-4 *4 (-725)) (-4 *5 (-779)) (-5 *2 (-583 *1))
-   (-4 *1 (-872 *3 *4 *5))))) 
-(((*1 *1 *2)
-  (-12 (-5 *2 (-1 (-866 (-199)) (-866 (-199)))) (-5 *1 (-236))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1156 *1)) (-4 *1 (-299 *4)) (-4 *4 (-333))
-   (-5 *2 (-623 *4))))
- ((*1 *2 *1) (-12 (-4 *1 (-299 *3)) (-4 *3 (-333)) (-5 *2 (-1156 *3))))
- ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-1156 *1)) (-4 *1 (-337 *4)) (-4 *4 (-156))
-   (-5 *2 (-623 *4))))
- ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-1156 *1)) (-4 *1 (-337 *4)) (-4 *4 (-156))
-   (-5 *2 (-1156 *4))))
- ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-1156 *1)) (-4 *1 (-340 *4 *5)) (-4 *4 (-156))
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- ((*1 *2 *1 *3)
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-   (-4 *5 (-1132 *4)) (-5 *2 (-1156 *4))))
- ((*1 *2 *3)
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+           (|:| |upperSingular|
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+           (|:| |bothSingular|
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+           (|:| |notEvaluated|
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+           (|:| |notEvaluated|
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+           (|:| |upperInfinite| "The top of range is infinite")
+           (|:| |bothInfinite|
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+           (|:| |notEvaluated| "Range not yet evaluated")))))
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-  (-12 (-5 *4 (-623 (-199))) (-5 *5 (-623 (-517))) (-5 *3 (-517))
-   (-5 *2 (-951)) (-5 *1 (-687))))) 
-(((*1 *2 *2 *2 *2 *2 *3)
-  (-12 (-5 *2 (-623 *4)) (-5 *3 (-703)) (-4 *4 (-962))
-   (-5 *1 (-624 *4))))) 
-(((*1 *1 *2 *3) (-12 (-5 *3 (-517)) (-5 *1 (-388 *2)) (-4 *2 (-509))))) 
-(((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-556 *3)) (-4 *3 (-13 (-400 *5) (-27) (-1096)))
-   (-4 *5 (-13 (-421) (-953 (-517)) (-779) (-134) (-579 (-517))))
-   (-5 *2 (-534 *3)) (-5 *1 (-519 *5 *3 *6)) (-4 *6 (-1004))))) 
+  (-12 (-4 *4 (-13 (-278) (-134))) (-4 *5 (-13 (-779) (-558 (-1076))))
+   (-4 *6 (-725)) (-4 *7 (-872 *4 *6 *5))
+   (-5 *2
+    (-2 (|:| |sysok| (-107)) (|:| |z0| (-583 *7)) (|:| |n0| (-583 *7))))
+   (-5 *1 (-847 *4 *5 *6 *7)) (-5 *3 (-583 *7))))) 
+(((*1 *2 *3 *3 *2)
+  (-12 (-5 *2 (-1057 *4)) (-5 *3 (-517)) (-4 *4 (-963))
+   (-5 *1 (-1061 *4))))
+ ((*1 *1 *2 *2 *1)
+  (-12 (-5 *2 (-517)) (-5 *1 (-1149 *3 *4 *5)) (-4 *3 (-963))
+   (-14 *4 (-1076)) (-14 *5 *3)))) 
+(((*1 *2 *3 *4 *5 *3)
+  (-12 (-5 *4 (-1 *7 *7))
+   (-5 *5
+    (-1 (-2 (|:| |ans| *6) (|:| -3300 *6) (|:| |sol?| (-107))) (-517)
+     *6))
+   (-4 *6 (-333)) (-4 *7 (-1133 *6))
+   (-5 *2
+    (-3 (-2 (|:| |answer| (-377 *7)) (|:| |a0| *6))
+     (-2 (|:| -2212 (-377 *7)) (|:| |coeff| (-377 *7))) "failed"))
+   (-5 *1 (-527 *6 *7)) (-5 *3 (-377 *7))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-1110)) (-5 *2 (-703)) (-5 *1 (-163 *4 *3))
-   (-4 *3 (-610 *4))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1058)) (-5 *2 (-1161)) (-5 *1 (-406))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-377 (-517))) (-5 *1 (-103))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-583 (-493))) (-5 *1 (-493))))) 
-(((*1 *2 *2)
-  (-12 (-5 *2 (-1156 *1)) (-4 *1 (-312 *3 *4 *5)) (-4 *3 (-1114))
-   (-4 *4 (-1132 *3)) (-4 *5 (-1132 (-377 *4)))))) 
+  (-12 (-5 *3 (-583 (-517))) (-5 *2 (-517)) (-5 *1 (-453 *4))
+   (-4 *4 (-1133 *2))))) 
+(((*1 *2 *3 *4)
+  (|partial| -12 (-5 *3 (-1157 *4)) (-4 *4 (-579 (-517)))
+      (-5 *2 (-1157 (-377 (-517)))) (-5 *1 (-1182 *4))))) 
 (((*1 *2 *2)
   (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-249 *3 *2))
-   (-4 *2 (-13 (-400 *3) (-919)))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-517)) (-5 *1 (-787))))) 
+   (-4 *2 (-13 (-400 *3) (-920)))))) 
+(((*1 *2 *3)
+  (-12
+   (-5 *3
+    (-3
+     (|:| |noa|
+          (-2 (|:| |fn| (-286 (-199))) (|:| -2587 (-583 (-199)))
+           (|:| |lb| (-583 (-772 (-199))))
+           (|:| |cf| (-583 (-286 (-199))))
+           (|:| |ub| (-583 (-772 (-199))))))
+     (|:| |lsa|
+          (-2 (|:| |lfn| (-583 (-286 (-199))))
+           (|:| -2587 (-583 (-199)))))))
+   (-5 *2 (-583 (-1059))) (-5 *1 (-240))))) 
+(((*1 *2) (-12 (-5 *2 (-349)) (-5 *1 (-956))))) 
 (((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-46 *3 *4)) (-4 *3 (-962))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-46 *3 *4)) (-4 *3 (-963))
    (-4 *4 (-724))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-962)) (-5 *1 (-49 *3 *4))
-   (-14 *4 (-583 (-1075)))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-963)) (-5 *1 (-49 *3 *4))
+   (-14 *4 (-583 (-1076)))))
  ((*1 *1 *2 *1 *1 *3)
-  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-55 *3 *4 *5)) (-4 *3 (-1110))
+  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-55 *3 *4 *5)) (-4 *3 (-1111))
    (-4 *4 (-343 *3)) (-4 *5 (-343 *3))))
  ((*1 *1 *2 *1 *1)
-  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-55 *3 *4 *5)) (-4 *3 (-1110))
+  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-55 *3 *4 *5)) (-4 *3 (-1111))
    (-4 *4 (-343 *3)) (-4 *5 (-343 *3))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-55 *3 *4 *5)) (-4 *3 (-1110))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-55 *3 *4 *5)) (-4 *3 (-1111))
    (-4 *4 (-343 *3)) (-4 *5 (-343 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-57 *5)) (-4 *5 (-1110))
-   (-4 *6 (-1110)) (-5 *2 (-57 *6)) (-5 *1 (-56 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-57 *5)) (-4 *5 (-1111))
+   (-4 *6 (-1111)) (-5 *2 (-57 *6)) (-5 *1 (-56 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *8 *7)) (-5 *4 (-127 *5 *6 *7)) (-14 *5 (-517))
    (-14 *6 (-703)) (-4 *7 (-156)) (-4 *8 (-156))
@@ -4691,51 +4687,51 @@
   (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-153 *5)) (-4 *5 (-156))
    (-4 *6 (-156)) (-5 *2 (-153 *6)) (-5 *1 (-152 *5 *6))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 (-286 *3) (-286 *3))) (-4 *3 (-13 (-962) (-779)))
-   (-5 *1 (-197 *3 *4)) (-14 *4 (-583 (-1075)))))
+  (-12 (-5 *2 (-1 (-286 *3) (-286 *3))) (-4 *3 (-13 (-963) (-779)))
+   (-5 *1 (-197 *3 *4)) (-14 *4 (-583 (-1076)))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-214 *5 *6)) (-14 *5 (-703))
-   (-4 *6 (-1110)) (-4 *7 (-1110)) (-5 *2 (-214 *5 *7))
+   (-4 *6 (-1111)) (-4 *7 (-1111)) (-5 *2 (-214 *5 *7))
    (-5 *1 (-213 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-265 *5)) (-4 *5 (-1110))
-   (-4 *6 (-1110)) (-5 *2 (-265 *6)) (-5 *1 (-264 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-265 *5)) (-4 *5 (-1111))
+   (-4 *6 (-1111)) (-5 *2 (-265 *6)) (-5 *1 (-264 *5 *6))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1110)) (-5 *1 (-265 *3))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1111)) (-5 *1 (-265 *3))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1058)) (-5 *5 (-556 *6))
-   (-4 *6 (-273)) (-4 *2 (-1110)) (-5 *1 (-268 *6 *2))))
+  (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1059)) (-5 *5 (-556 *6))
+   (-4 *6 (-273)) (-4 *2 (-1111)) (-5 *1 (-268 *6 *2))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *2 *5)) (-5 *4 (-556 *5)) (-4 *5 (-273))
    (-4 *2 (-273)) (-5 *1 (-269 *5 *2))))
  ((*1 *1 *2 *3)
   (-12 (-5 *2 (-1 *1 *1)) (-5 *3 (-556 *1)) (-4 *1 (-273))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-623 *5)) (-4 *5 (-962))
-   (-4 *6 (-962)) (-5 *2 (-623 *6)) (-5 *1 (-275 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-623 *5)) (-4 *5 (-963))
+   (-4 *6 (-963)) (-5 *2 (-623 *6)) (-5 *1 (-275 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-286 *5)) (-4 *5 (-779))
    (-4 *6 (-779)) (-5 *2 (-286 *6)) (-5 *1 (-284 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-306 *5 *6 *7 *8)) (-4 *5 (-333))
-   (-4 *6 (-1132 *5)) (-4 *7 (-1132 (-377 *6))) (-4 *8 (-312 *5 *6 *7))
-   (-4 *9 (-333)) (-4 *10 (-1132 *9)) (-4 *11 (-1132 (-377 *10)))
+   (-4 *6 (-1133 *5)) (-4 *7 (-1133 (-377 *6))) (-4 *8 (-312 *5 *6 *7))
+   (-4 *9 (-333)) (-4 *10 (-1133 *9)) (-4 *11 (-1133 (-377 *10)))
    (-5 *2 (-306 *9 *10 *11 *12))
    (-5 *1 (-303 *5 *6 *7 *8 *9 *10 *11 *12))
    (-4 *12 (-312 *9 *10 *11))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-308 *3)) (-4 *3 (-1004))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-308 *3)) (-4 *3 (-1005))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1114)) (-4 *8 (-1114))
-   (-4 *6 (-1132 *5)) (-4 *7 (-1132 (-377 *6))) (-4 *9 (-1132 *8))
+  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1115)) (-4 *8 (-1115))
+   (-4 *6 (-1133 *5)) (-4 *7 (-1133 (-377 *6))) (-4 *9 (-1133 *8))
    (-4 *2 (-312 *8 *9 *10)) (-5 *1 (-310 *5 *6 *7 *4 *8 *9 *10 *2))
-   (-4 *4 (-312 *5 *6 *7)) (-4 *10 (-1132 (-377 *9)))))
+   (-4 *4 (-312 *5 *6 *7)) (-4 *10 (-1133 (-377 *9)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1110)) (-4 *6 (-1110))
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1111)) (-4 *6 (-1111))
    (-4 *2 (-343 *6)) (-5 *1 (-341 *5 *4 *6 *2)) (-4 *4 (-343 *5))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-352 *3 *4)) (-4 *3 (-962))
-   (-4 *4 (-1004))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-352 *3 *4)) (-4 *3 (-963))
+   (-4 *4 (-1005))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-388 *5)) (-4 *5 (-509))
    (-4 *6 (-509)) (-5 *2 (-388 *6)) (-5 *1 (-375 *5 *6))))
@@ -4744,37 +4740,37 @@
    (-4 *6 (-509)) (-5 *2 (-377 *6)) (-5 *1 (-376 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-383 *5 *6 *7 *8)) (-4 *5 (-278))
-   (-4 *6 (-910 *5)) (-4 *7 (-1132 *6))
-   (-4 *8 (-13 (-379 *6 *7) (-953 *6))) (-4 *9 (-278))
-   (-4 *10 (-910 *9)) (-4 *11 (-1132 *10))
+   (-4 *6 (-911 *5)) (-4 *7 (-1133 *6))
+   (-4 *8 (-13 (-379 *6 *7) (-954 *6))) (-4 *9 (-278))
+   (-4 *10 (-911 *9)) (-4 *11 (-1133 *10))
    (-5 *2 (-383 *9 *10 *11 *12))
    (-5 *1 (-382 *5 *6 *7 *8 *9 *10 *11 *12))
-   (-4 *12 (-13 (-379 *10 *11) (-953 *10)))))
+   (-4 *12 (-13 (-379 *10 *11) (-954 *10)))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-156)) (-4 *6 (-156))
    (-4 *2 (-387 *6)) (-5 *1 (-385 *4 *5 *2 *6)) (-4 *4 (-387 *5))))
  ((*1 *1 *2 *1)
   (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-509)) (-5 *1 (-388 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-13 (-962) (-779)))
-   (-4 *6 (-13 (-962) (-779))) (-4 *2 (-400 *6))
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-13 (-963) (-779)))
+   (-4 *6 (-13 (-963) (-779))) (-4 *2 (-400 *6))
    (-5 *1 (-391 *5 *4 *6 *2)) (-4 *4 (-400 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1004)) (-4 *6 (-1004))
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1005)) (-4 *6 (-1005))
    (-4 *2 (-395 *6)) (-5 *1 (-393 *5 *4 *6 *2)) (-4 *4 (-395 *5))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-456 *3)) (-4 *3 (-1110))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-456 *3)) (-4 *3 (-1111))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-473 *3 *4)) (-4 *3 (-1004))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-473 *3 *4)) (-4 *3 (-1005))
    (-4 *4 (-779))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-534 *5)) (-4 *5 (-333))
    (-4 *6 (-333)) (-5 *2 (-534 *6)) (-5 *1 (-533 *5 *6))))
  ((*1 *2 *3 *4)
   (|partial| -12 (-5 *3 (-1 *6 *5))
-      (-5 *4 (-3 (-2 (|:| -1306 *5) (|:| |coeff| *5)) "failed"))
+      (-5 *4 (-3 (-2 (|:| -2212 *5) (|:| |coeff| *5)) "failed"))
       (-4 *5 (-333)) (-4 *6 (-333))
-      (-5 *2 (-2 (|:| -1306 *6) (|:| |coeff| *6)))
+      (-5 *2 (-2 (|:| -2212 *6) (|:| |coeff| *6)))
       (-5 *1 (-533 *5 *6))))
  ((*1 *2 *3 *4)
   (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed"))
@@ -4794,561 +4790,632 @@
              (-583 (-2 (|:| |coeff| *6) (|:| |logand| *6))))))
       (-5 *1 (-533 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-547 *5)) (-4 *5 (-1110))
-   (-4 *6 (-1110)) (-5 *2 (-547 *6)) (-5 *1 (-544 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-547 *5)) (-4 *5 (-1111))
+   (-4 *6 (-1111)) (-5 *2 (-547 *6)) (-5 *1 (-544 *5 *6))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-547 *6)) (-5 *5 (-547 *7))
-   (-4 *6 (-1110)) (-4 *7 (-1110)) (-4 *8 (-1110)) (-5 *2 (-547 *8))
+   (-4 *6 (-1111)) (-4 *7 (-1111)) (-4 *8 (-1111)) (-5 *2 (-547 *8))
    (-5 *1 (-545 *6 *7 *8))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-1056 *6)) (-5 *5 (-547 *7))
-   (-4 *6 (-1110)) (-4 *7 (-1110)) (-4 *8 (-1110)) (-5 *2 (-1056 *8))
+  (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-1057 *6)) (-5 *5 (-547 *7))
+   (-4 *6 (-1111)) (-4 *7 (-1111)) (-4 *8 (-1111)) (-5 *2 (-1057 *8))
    (-5 *1 (-545 *6 *7 *8))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-547 *6)) (-5 *5 (-1056 *7))
-   (-4 *6 (-1110)) (-4 *7 (-1110)) (-4 *8 (-1110)) (-5 *2 (-1056 *8))
+  (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-547 *6)) (-5 *5 (-1057 *7))
+   (-4 *6 (-1111)) (-4 *7 (-1111)) (-4 *8 (-1111)) (-5 *2 (-1057 *8))
    (-5 *1 (-545 *6 *7 *8))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1110)) (-5 *1 (-547 *3))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1111)) (-5 *1 (-547 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-583 *5)) (-4 *5 (-1110))
-   (-4 *6 (-1110)) (-5 *2 (-583 *6)) (-5 *1 (-581 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-583 *5)) (-4 *5 (-1111))
+   (-4 *6 (-1111)) (-5 *2 (-583 *6)) (-5 *1 (-581 *5 *6))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-583 *6)) (-5 *5 (-583 *7))
-   (-4 *6 (-1110)) (-4 *7 (-1110)) (-4 *8 (-1110)) (-5 *2 (-583 *8))
+   (-4 *6 (-1111)) (-4 *7 (-1111)) (-4 *8 (-1111)) (-5 *2 (-583 *8))
    (-5 *1 (-582 *6 *7 *8))))
  ((*1 *1 *2 *1 *1)
-  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-588 *3)) (-4 *3 (-1110))))
+  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-588 *3)) (-4 *3 (-1111))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-962)) (-4 *8 (-962))
+  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-963)) (-4 *8 (-963))
    (-4 *6 (-343 *5)) (-4 *7 (-343 *5)) (-4 *2 (-621 *8 *9 *10))
    (-5 *1 (-619 *5 *6 *7 *4 *8 *9 *10 *2)) (-4 *4 (-621 *5 *6 *7))
    (-4 *9 (-343 *8)) (-4 *10 (-343 *8))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1 (-3 *8 "failed") *5)) (-4 *5 (-962))
-      (-4 *8 (-962)) (-4 *6 (-343 *5)) (-4 *7 (-343 *5))
+  (|partial| -12 (-5 *3 (-1 (-3 *8 "failed") *5)) (-4 *5 (-963))
+      (-4 *8 (-963)) (-4 *6 (-343 *5)) (-4 *7 (-343 *5))
       (-4 *2 (-621 *8 *9 *10)) (-5 *1 (-619 *5 *6 *7 *4 *8 *9 *10 *2))
       (-4 *4 (-621 *5 *6 *7)) (-4 *9 (-343 *8)) (-4 *10 (-343 *8))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-509)) (-4 *7 (-509))
-   (-4 *6 (-1132 *5)) (-4 *2 (-1132 (-377 *8)))
-   (-5 *1 (-643 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1132 (-377 *6)))
-   (-4 *8 (-1132 *7))))
+   (-4 *6 (-1133 *5)) (-4 *2 (-1133 (-377 *8)))
+   (-5 *1 (-643 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1133 (-377 *6)))
+   (-4 *8 (-1133 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *9 *8)) (-4 *8 (-962)) (-4 *9 (-962)) (-4 *5 (-779))
+  (-12 (-5 *3 (-1 *9 *8)) (-4 *8 (-963)) (-4 *9 (-963)) (-4 *5 (-779))
    (-4 *6 (-725)) (-4 *2 (-872 *9 *7 *5))
    (-5 *1 (-661 *5 *6 *7 *8 *9 *4 *2)) (-4 *7 (-725))
    (-4 *4 (-872 *8 *6 *5))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-779)) (-4 *6 (-779)) (-4 *7 (-725))
-   (-4 *9 (-962)) (-4 *2 (-872 *9 *8 *6))
+   (-4 *9 (-963)) (-4 *2 (-872 *9 *8 *6))
    (-5 *1 (-662 *5 *6 *7 *8 *9 *4 *2)) (-4 *8 (-725))
    (-4 *4 (-872 *9 *7 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-668 *5 *7)) (-4 *5 (-962))
-   (-4 *6 (-962)) (-4 *7 (-659)) (-5 *2 (-668 *6 *7))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-668 *5 *7)) (-4 *5 (-963))
+   (-4 *6 (-963)) (-4 *7 (-659)) (-5 *2 (-668 *6 *7))
    (-5 *1 (-667 *5 *6 *7))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-962)) (-5 *1 (-668 *3 *4))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-963)) (-5 *1 (-668 *3 *4))
    (-4 *4 (-659))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-714 *5)) (-4 *5 (-962))
-   (-4 *6 (-962)) (-5 *2 (-714 *6)) (-5 *1 (-713 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-714 *5)) (-4 *5 (-963))
+   (-4 *6 (-963)) (-5 *2 (-714 *6)) (-5 *1 (-713 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-156)) (-4 *6 (-156))
    (-4 *2 (-729 *6)) (-5 *1 (-730 *4 *5 *2 *6)) (-4 *4 (-729 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-765 *5)) (-4 *5 (-1004))
-   (-4 *6 (-1004)) (-5 *2 (-765 *6)) (-5 *1 (-764 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-765 *5)) (-4 *5 (-1005))
+   (-4 *6 (-1005)) (-5 *2 (-765 *6)) (-5 *1 (-764 *5 *6))))
  ((*1 *2 *3 *4 *2)
   (-12 (-5 *2 (-765 *6)) (-5 *3 (-1 *6 *5)) (-5 *4 (-765 *5))
-   (-4 *5 (-1004)) (-4 *6 (-1004)) (-5 *1 (-764 *5 *6))))
+   (-4 *5 (-1005)) (-4 *6 (-1005)) (-5 *1 (-764 *5 *6))))
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+ ((*1 *2) (-12 (-4 *1 (-387 *2)) (-4 *2 (-156))))) 
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+  (-12 (-5 *3 (-583 *1)) (-4 *1 (-977 *4 *5 *6)) (-4 *4 (-963))
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+ ((*1 *2 *3 *1 *4)
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+ ((*1 *1 *2 *1) (-12 (-5 *1 (-121 *2)) (-4 *2 (-779))))
+ ((*1 *1 *1 *1 *2)
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+ ((*1 *1 *2 *1 *3)
+  (-12 (-5 *3 (-517)) (-4 *1 (-254 *2)) (-4 *2 (-1111))))
+ ((*1 *1 *2)
   (-12
-   (-5 *3
-    (-583 (-2 (|:| -3286 (-377 (-517))) (|:| -3298 (-377 (-517))))))
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-   (-4 *4 (-1132 *2))))) 
-(((*1 *1 *1 *2) (-12 (-5 *2 (-517)) (-5 *1 (-297 *3)) (-4 *3 (-1110))))
+   (-5 *2
+    (-2
+     (|:| -2585
+          (-2 (|:| |var| (-1076)) (|:| |fn| (-286 (-199)))
+           (|:| -2758 (-1000 (-772 (-199)))) (|:| |abserr| (-199))
+           (|:| |relerr| (-199))))
+     (|:| -1859
+          (-2
+           (|:| |endPointContinuity|
+                (-3 (|:| |continuous| "Continuous at the end points")
+                 (|:| |lowerSingular|
+                      "There is a singularity at the lower end point")
+                 (|:| |upperSingular|
+                      "There is a singularity at the upper end point")
+                 (|:| |bothSingular|
+                      "There are singularities at both end points")
+                 (|:| |notEvaluated|
+                      "End point continuity not yet evaluated")))
+           (|:| |singularitiesStream|
+                (-3 (|:| |str| (-1057 (-199)))
+                 (|:| |notEvaluated|
+                      "Internal singularities not yet evaluated")))
+           (|:| -2758
+                (-3 (|:| |finite| "The range is finite")
+                 (|:| |lowerInfinite|
+                      "The bottom of range is infinite")
+                 (|:| |upperInfinite| "The top of range is infinite")
+                 (|:| |bothInfinite|
+                      "Both top and bottom points are infinite")
+                 (|:| |notEvaluated| "Range not yet evaluated")))))))
+   (-5 *1 (-512))))
+ ((*1 *1 *2 *1 *3)
+  (-12 (-5 *3 (-703)) (-4 *1 (-628 *2)) (-4 *2 (-1005))))
+ ((*1 *1 *2)
+  (-12
+   (-5 *2
+    (-2
+     (|:| -2585
+          (-2 (|:| |xinit| (-199)) (|:| |xend| (-199))
+           (|:| |fn| (-1157 (-286 (-199)))) (|:| |yinit| (-583 (-199)))
+           (|:| |intvals| (-583 (-199))) (|:| |g| (-286 (-199)))
+           (|:| |abserr| (-199)) (|:| |relerr| (-199))))
+     (|:| -1859
+          (-2 (|:| |stiffness| (-349)) (|:| |stability| (-349))
+           (|:| |expense| (-349)) (|:| |accuracy| (-349))
+           (|:| |intermediateResults| (-349))))))
+   (-5 *1 (-735))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *2 (-1162)) (-5 *1 (-1089 *3 *4)) (-4 *3 (-1005))
+   (-4 *4 (-1005))))) 
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+  (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-585 *3)) (-4 *3 (-963))
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-  (-12 (-5 *5 (-517)) (-4 *6 (-725)) (-4 *7 (-779)) (-4 *8 (-278))
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-  (|partial| -12 (-4 *1 (-337 *2)) (-4 *2 (-156)) (-4 *2 (-509))))
- ((*1 *1 *1) (|partial| -4 *1 (-655)))) 
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-963)) (-5 *1 (-766 *3))))) 
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+  (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-249 *3 *2))
+   (-4 *2 (-13 (-400 *3) (-920)))))) 
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+ ((*1 *2 *2 *2)
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+ ((*1 *2 *2)
+  (-12 (-5 *2 (-583 (-623 *3))) (-4 *3 (-963)) (-5 *1 (-945 *3))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-779) (-509))) (-5 *2 (-107)) (-5 *1 (-249 *4 *3))
-   (-4 *3 (-13 (-400 *4) (-919)))))) 
+  (-12 (-4 *4 (-509)) (-5 *2 (-583 *3)) (-5 *1 (-42 *4 *3))
+   (-4 *3 (-387 *4))))) 
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+  (-12 (-5 *2 (-583 (-1041 *4 *5))) (-5 *3 (-1 (-107) *5 *5))
+   (-4 *4 (-13 (-1005) (-33))) (-4 *5 (-13 (-1005) (-33)))
+   (-5 *1 (-1042 *4 *5))))
+ ((*1 *1 *1 *1 *2)
+  (-12 (-5 *2 (-583 (-1041 *3 *4))) (-4 *3 (-13 (-1005) (-33)))
+   (-4 *4 (-13 (-1005) (-33))) (-5 *1 (-1042 *3 *4))))) 
+(((*1 *2 *2)
+  (-12 (-4 *3 (-13 (-509) (-134))) (-5 *1 (-494 *3 *2))
+   (-4 *2 (-1148 *3))))
+ ((*1 *2 *2)
+  (-12 (-4 *3 (-13 (-333) (-338) (-558 (-517)))) (-4 *4 (-1133 *3))
+   (-4 *5 (-657 *3 *4)) (-5 *1 (-498 *3 *4 *5 *2)) (-4 *2 (-1148 *5))))
+ ((*1 *2 *2)
+  (-12 (-4 *3 (-13 (-333) (-338) (-558 (-517)))) (-5 *1 (-499 *3 *2))
+   (-4 *2 (-1148 *3))))
+ ((*1 *2 *2)
+  (-12 (-5 *2 (-1057 *3)) (-4 *3 (-13 (-509) (-134)))
+   (-5 *1 (-1053 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-872 *4 *6 *5))
-   (-4 *4 (-13 (-278) (-134))) (-4 *5 (-13 (-779) (-558 (-1075))))
-   (-4 *6 (-725)) (-5 *2 (-107)) (-5 *1 (-847 *4 *5 *6 *7))))
+  (|partial| -12 (-5 *3 (-875 *4)) (-4 *4 (-963)) (-4 *4 (-558 *2))
+      (-5 *2 (-349)) (-5 *1 (-717 *4))))
+ ((*1 *2 *3 *4)
+  (|partial| -12 (-5 *3 (-875 *5)) (-5 *4 (-844)) (-4 *5 (-963))
+      (-4 *5 (-558 *2)) (-5 *2 (-349)) (-5 *1 (-717 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-875 *4))) (-4 *4 (-13 (-278) (-134)))
-   (-4 *5 (-13 (-779) (-558 (-1075)))) (-4 *6 (-725)) (-5 *2 (-107))
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-  (-12 (-5 *2 (-107)) (-5 *1 (-1088 *3 *4)) (-4 *3 (-1004))
-   (-4 *4 (-1004))))) 
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-  (-12 (-5 *2 (-517)) (-4 *1 (-55 *4 *5 *3)) (-4 *4 (-1110))
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-  (-12 (-5 *3 (-1058)) (-4 *4 (-13 (-278) (-134)))
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-   (-5 *2
-    (-583
-     (-2 (|:| |eqzro| (-583 *7)) (|:| |neqzro| (-583 *7))
-      (|:| |wcond| (-583 (-875 *4)))
-      (|:| |bsoln|
-           (-2 (|:| |partsol| (-1156 (-377 (-875 *4))))
-            (|:| -2062 (-583 (-1156 (-377 (-875 *4))))))))))
-   (-5 *1 (-847 *4 *5 *6 *7)) (-4 *7 (-872 *4 *6 *5))))) 
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-  (-12 (-5 *3 (-1075)) (-5 *4 (-875 (-517))) (-5 *2 (-300))
-   (-5 *1 (-302))))
- ((*1 *2 *3 *4 *4)
-  (-12 (-5 *3 (-1075)) (-5 *4 (-997 (-875 (-517)))) (-5 *2 (-300))
-   (-5 *1 (-302))))
- ((*1 *1 *2 *2 *2)
-  (-12 (-5 *2 (-703)) (-5 *1 (-611 *3)) (-4 *3 (-962)) (-4 *3 (-1004))))) 
-(((*1 *1 *1 *2 *1) (-12 (-4 *1 (-1044)) (-5 *2 (-1123 (-517)))))) 
-(((*1 *2 *3 *3)
-  (-12 (-4 *4 (-13 (-421) (-134))) (-5 *2 (-388 *3))
-   (-5 *1 (-95 *4 *3)) (-4 *3 (-1132 *4))))
+  (|partial| -12 (-5 *3 (-377 (-875 *4))) (-4 *4 (-509))
+      (-4 *4 (-558 *2)) (-5 *2 (-349)) (-5 *1 (-717 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-583 *3)) (-4 *3 (-1132 *5)) (-4 *5 (-13 (-421) (-134)))
-   (-5 *2 (-388 *3)) (-5 *1 (-95 *5 *3))))) 
-(((*1 *1 *2 *3)
-  (-12 (-5 *2 (-756)) (-5 *3 (-583 (-1075))) (-5 *1 (-757))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1161)) (-5 *1 (-754))))) 
+  (|partial| -12 (-5 *3 (-377 (-875 *5))) (-5 *4 (-844)) (-4 *5 (-509))
+      (-4 *5 (-558 *2)) (-5 *2 (-349)) (-5 *1 (-717 *5))))
+ ((*1 *2 *3)
+  (|partial| -12 (-5 *3 (-286 *4)) (-4 *4 (-509)) (-4 *4 (-779))
+      (-4 *4 (-558 *2)) (-5 *2 (-349)) (-5 *1 (-717 *4))))
+ ((*1 *2 *3 *4)
+  (|partial| -12 (-5 *3 (-286 *5)) (-5 *4 (-844)) (-4 *5 (-509))
+      (-4 *5 (-779)) (-4 *5 (-558 *2)) (-5 *2 (-349))
+      (-5 *1 (-717 *5))))) 
+(((*1 *1 *1 *2 *1) (-12 (-4 *1 (-1045)) (-5 *2 (-1124 (-517)))))) 
+(((*1 *1 *1 *1 *2)
+  (-12 (-4 *1 (-977 *3 *4 *2)) (-4 *3 (-963)) (-4 *4 (-725))
+   (-4 *2 (-779))))
+ ((*1 *1 *1 *1)
+  (-12 (-4 *1 (-977 *2 *3 *4)) (-4 *2 (-963)) (-4 *3 (-725))
+   (-4 *4 (-779))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-51)) (-5 *1 (-50 *2)) (-4 *2 (-1110))))
+  (|partial| -12 (-5 *3 (-1157 *4)) (-4 *4 (-579 (-517)))
+      (-5 *2 (-1157 (-517))) (-5 *1 (-1182 *4))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-150 *2)) (-4 *2 (-156)) (-4 *2 (-1097))))
+ ((*1 *2 *1) (-12 (-5 *1 (-301 *2)) (-4 *2 (-779))))
+ ((*1 *2 *1) (-12 (-5 *2 (-583 *3)) (-5 *1 (-556 *3)) (-4 *3 (-779))))) 
+(((*1 *2 *3)
+  (|partial| -12 (-5 *3 (-51)) (-5 *1 (-50 *2)) (-4 *2 (-1111))))
  ((*1 *1 *2)
   (|partial| -12 (-5 *2 (-875 (-349))) (-5 *1 (-309 *3 *4 *5))
-      (-4 *5 (-953 (-349))) (-14 *3 (-583 (-1075)))
-      (-14 *4 (-583 (-1075))) (-4 *5 (-357))))
+      (-4 *5 (-954 (-349))) (-14 *3 (-583 (-1076)))
+      (-14 *4 (-583 (-1076))) (-4 *5 (-357))))
  ((*1 *1 *2)
   (|partial| -12 (-5 *2 (-377 (-875 (-349)))) (-5 *1 (-309 *3 *4 *5))
-      (-4 *5 (-953 (-349))) (-14 *3 (-583 (-1075)))
-      (-14 *4 (-583 (-1075))) (-4 *5 (-357))))
+      (-4 *5 (-954 (-349))) (-14 *3 (-583 (-1076)))
+      (-14 *4 (-583 (-1076))) (-4 *5 (-357))))
  ((*1 *1 *2)
   (|partial| -12 (-5 *2 (-286 (-349))) (-5 *1 (-309 *3 *4 *5))
-      (-4 *5 (-953 (-349))) (-14 *3 (-583 (-1075)))
-      (-14 *4 (-583 (-1075))) (-4 *5 (-357))))
+      (-4 *5 (-954 (-349))) (-14 *3 (-583 (-1076)))
+      (-14 *4 (-583 (-1076))) (-4 *5 (-357))))
  ((*1 *1 *2)
   (|partial| -12 (-5 *2 (-875 (-517))) (-5 *1 (-309 *3 *4 *5))
-      (-4 *5 (-953 (-517))) (-14 *3 (-583 (-1075)))
-      (-14 *4 (-583 (-1075))) (-4 *5 (-357))))
+      (-4 *5 (-954 (-517))) (-14 *3 (-583 (-1076)))
+      (-14 *4 (-583 (-1076))) (-4 *5 (-357))))
  ((*1 *1 *2)
   (|partial| -12 (-5 *2 (-377 (-875 (-517)))) (-5 *1 (-309 *3 *4 *5))
-      (-4 *5 (-953 (-517))) (-14 *3 (-583 (-1075)))
-      (-14 *4 (-583 (-1075))) (-4 *5 (-357))))
+      (-4 *5 (-954 (-517))) (-14 *3 (-583 (-1076)))
+      (-14 *4 (-583 (-1076))) (-4 *5 (-357))))
  ((*1 *1 *2)
   (|partial| -12 (-5 *2 (-286 (-517))) (-5 *1 (-309 *3 *4 *5))
-      (-4 *5 (-953 (-517))) (-14 *3 (-583 (-1075)))
-      (-14 *4 (-583 (-1075))) (-4 *5 (-357))))
+      (-4 *5 (-954 (-517))) (-14 *3 (-583 (-1076)))
+      (-14 *4 (-583 (-1076))) (-4 *5 (-357))))
  ((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-1075)) (-5 *1 (-309 *3 *4 *5))
+  (|partial| -12 (-5 *2 (-1076)) (-5 *1 (-309 *3 *4 *5))
       (-14 *3 (-583 *2)) (-14 *4 (-583 *2)) (-4 *5 (-357))))
  ((*1 *1 *2)
   (|partial| -12 (-5 *2 (-286 *5)) (-4 *5 (-357))
-      (-5 *1 (-309 *3 *4 *5)) (-14 *3 (-583 (-1075)))
-      (-14 *4 (-583 (-1075)))))
+      (-5 *1 (-309 *3 *4 *5)) (-14 *3 (-583 (-1076)))
+      (-14 *4 (-583 (-1076)))))
  ((*1 *1 *2)
   (|partial| -12 (-5 *2 (-623 (-377 (-875 (-517))))) (-4 *1 (-354))))
  ((*1 *1 *2)
@@ -5370,191 +5437,171 @@
  ((*1 *1 *2) (|partial| -12 (-5 *2 (-286 (-517))) (-4 *1 (-366))))
  ((*1 *1 *2) (|partial| -12 (-5 *2 (-286 (-349))) (-4 *1 (-366))))
  ((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-1156 (-377 (-875 (-517))))) (-4 *1 (-410))))
+  (|partial| -12 (-5 *2 (-1157 (-377 (-875 (-517))))) (-4 *1 (-410))))
  ((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-1156 (-377 (-875 (-349))))) (-4 *1 (-410))))
+  (|partial| -12 (-5 *2 (-1157 (-377 (-875 (-349))))) (-4 *1 (-410))))
  ((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-1156 (-875 (-517)))) (-4 *1 (-410))))
+  (|partial| -12 (-5 *2 (-1157 (-875 (-517)))) (-4 *1 (-410))))
  ((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-1156 (-875 (-349)))) (-4 *1 (-410))))
+  (|partial| -12 (-5 *2 (-1157 (-875 (-349)))) (-4 *1 (-410))))
  ((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-1156 (-286 (-517)))) (-4 *1 (-410))))
+  (|partial| -12 (-5 *2 (-1157 (-286 (-517)))) (-4 *1 (-410))))
  ((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-1156 (-286 (-349)))) (-4 *1 (-410))))
+  (|partial| -12 (-5 *2 (-1157 (-286 (-349)))) (-4 *1 (-410))))
  ((*1 *2 *3)
-  (|partial| -12 (-4 *4 (-319)) (-4 *5 (-299 *4)) (-4 *6 (-1132 *5))
-      (-5 *2 (-1071 (-1071 *4))) (-5 *1 (-709 *4 *5 *6 *3 *7))
-      (-4 *3 (-1132 *6)) (-14 *7 (-844))))
+  (|partial| -12 (-4 *4 (-319)) (-4 *5 (-299 *4)) (-4 *6 (-1133 *5))
+      (-5 *2 (-1072 (-1072 *4))) (-5 *1 (-709 *4 *5 *6 *3 *7))
+      (-4 *3 (-1133 *6)) (-14 *7 (-844))))
  ((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-583 *6)) (-4 *6 (-976 *3 *4 *5))
-      (-4 *3 (-962)) (-4 *4 (-725)) (-4 *5 (-779))
-      (-4 *1 (-894 *3 *4 *5 *6))))
- ((*1 *2 *1) (|partial| -12 (-4 *1 (-953 *2)) (-4 *2 (-1110))))
+  (|partial| -12 (-5 *2 (-583 *6)) (-4 *6 (-977 *3 *4 *5))
+      (-4 *3 (-963)) (-4 *4 (-725)) (-4 *5 (-779))
+      (-4 *1 (-895 *3 *4 *5 *6))))
+ ((*1 *2 *1) (|partial| -12 (-4 *1 (-954 *2)) (-4 *2 (-1111))))
  ((*1 *1 *2)
-  (|partial| -3745
+  (|partial| -3747
       (-12 (-5 *2 (-875 *3))
-       (-12 (-2477 (-4 *3 (-37 (-377 (-517)))))
-        (-2477 (-4 *3 (-37 (-517)))) (-4 *5 (-558 (-1075))))
-       (-4 *3 (-962)) (-4 *1 (-976 *3 *4 *5)) (-4 *4 (-725))
+       (-12 (-2479 (-4 *3 (-37 (-377 (-517)))))
+        (-2479 (-4 *3 (-37 (-517)))) (-4 *5 (-558 (-1076))))
+       (-4 *3 (-963)) (-4 *1 (-977 *3 *4 *5)) (-4 *4 (-725))
        (-4 *5 (-779)))
       (-12 (-5 *2 (-875 *3))
-       (-12 (-2477 (-4 *3 (-502))) (-2477 (-4 *3 (-37 (-377 (-517)))))
-        (-4 *3 (-37 (-517))) (-4 *5 (-558 (-1075))))
-       (-4 *3 (-962)) (-4 *1 (-976 *3 *4 *5)) (-4 *4 (-725))
+       (-12 (-2479 (-4 *3 (-502))) (-2479 (-4 *3 (-37 (-377 (-517)))))
+        (-4 *3 (-37 (-517))) (-4 *5 (-558 (-1076))))
+       (-4 *3 (-963)) (-4 *1 (-977 *3 *4 *5)) (-4 *4 (-725))
        (-4 *5 (-779)))
       (-12 (-5 *2 (-875 *3))
-       (-12 (-2477 (-4 *3 (-910 (-517)))) (-4 *3 (-37 (-377 (-517))))
-        (-4 *5 (-558 (-1075))))
-       (-4 *3 (-962)) (-4 *1 (-976 *3 *4 *5)) (-4 *4 (-725))
+       (-12 (-2479 (-4 *3 (-911 (-517)))) (-4 *3 (-37 (-377 (-517))))
+        (-4 *5 (-558 (-1076))))
+       (-4 *3 (-963)) (-4 *1 (-977 *3 *4 *5)) (-4 *4 (-725))
        (-4 *5 (-779)))))
  ((*1 *1 *2)
-  (|partial| -3745
-      (-12 (-5 *2 (-875 (-517))) (-4 *1 (-976 *3 *4 *5))
-       (-12 (-2477 (-4 *3 (-37 (-377 (-517))))) (-4 *3 (-37 (-517)))
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-      (-12 (-5 *2 (-875 (-517))) (-4 *1 (-976 *3 *4 *5))
-       (-12 (-4 *3 (-37 (-377 (-517)))) (-4 *5 (-558 (-1075))))
-       (-4 *3 (-962)) (-4 *4 (-725)) (-4 *5 (-779)))))
+  (|partial| -3747
+      (-12 (-5 *2 (-875 (-517))) (-4 *1 (-977 *3 *4 *5))
+       (-12 (-2479 (-4 *3 (-37 (-377 (-517))))) (-4 *3 (-37 (-517)))
+        (-4 *5 (-558 (-1076))))
+       (-4 *3 (-963)) (-4 *4 (-725)) (-4 *5 (-779)))
+      (-12 (-5 *2 (-875 (-517))) (-4 *1 (-977 *3 *4 *5))
+       (-12 (-4 *3 (-37 (-377 (-517)))) (-4 *5 (-558 (-1076))))
+       (-4 *3 (-963)) (-4 *4 (-725)) (-4 *5 (-779)))))
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 (((*1 *1 *2)
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+(((*1 *2 *3 *4)
+  (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *8))
+      (-5 *4 (-623 (-1072 *8))) (-4 *5 (-963)) (-4 *8 (-963))
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 (((*1 *2 *2 *3)
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  ((*1 *1 *1 *1) (-5 *1 (-125)))
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@@ -5564,427 +5611,473 @@
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+   (-4 *5 (-1148 *4)) (-5 *1 (-251 *4 *5 *2)) (-4 *2 (-1119 *4 *5))))
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-   (-4 *6 (-901 *5))))
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+   (-4 *6 (-902 *5))))
  ((*1 *1 *1 *1) (-4 *1 (-256)))
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+            (|:| |endPointContinuity|
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+                  (|:| |lowerSingular|
+                       "There is a singularity at the lower end point")
+                  (|:| |upperSingular|
+                       "There is a singularity at the upper end point")
+                  (|:| |bothSingular|
+                       "There are singularities at both end points")
+                  (|:| |notEvaluated|
+                       "End point continuity not yet evaluated")))
+            (|:| |singularitiesStream|
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+                  (|:| |notEvaluated|
+                       "Internal singularities not yet evaluated")))
+            (|:| -2758
+                 (-3 (|:| |finite| "The range is finite")
+                  (|:| |lowerInfinite|
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+                  (|:| |upperInfinite| "The top of range is infinite")
+                  (|:| |bothInfinite|
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+                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
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+(((*1 *1 *2 *2 *2) (-12 (-5 *2 (-1059)) (-4 *1 (-359))))) 
 (((*1 *2 *1 *3 *3 *2)
-  (-12 (-5 *3 (-517)) (-4 *1 (-55 *2 *4 *5)) (-4 *2 (-1110))
+  (-12 (-5 *3 (-517)) (-4 *1 (-55 *2 *4 *5)) (-4 *2 (-1111))
    (-4 *4 (-343 *2)) (-4 *5 (-343 *2))))
  ((*1 *2 *1 *3 *3)
   (-12 (-5 *3 (-517)) (-4 *1 (-55 *2 *4 *5)) (-4 *4 (-343 *2))
-   (-4 *5 (-343 *2)) (-4 *2 (-1110))))
+   (-4 *5 (-343 *2)) (-4 *2 (-1111))))
  ((*1 *1 *1 *2)
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- ((*1 *1 *1 *2) (-12 (-5 *2 "left") (-4 *1 (-114 *3)) (-4 *3 (-1110))))
+  (-12 (-5 *2 "right") (-4 *1 (-114 *3)) (-4 *3 (-1111))))
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   (-12 (-5 *3 (-583 (-517))) (-4 *2 (-156)) (-5 *1 (-127 *4 *5 *2))
    (-14 *4 (-517)) (-14 *5 (-703))))
@@ -8407,29 +8426,29 @@
   (-12 (-4 *2 (-156)) (-5 *1 (-127 *3 *4 *2)) (-14 *3 (-517))
    (-14 *4 (-703))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-1075)) (-5 *2 (-219 (-1058))) (-5 *1 (-189 *4))
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    (-4 *4
     (-13 (-779)
-     (-10 -8 (-15 -2607 ((-1058) $ *3)) (-15 -1756 ((-1161) $))
-      (-15 -3177 ((-1161) $)))))))
+     (-10 -8 (-15 -2609 ((-1059) $ *3)) (-15 -1757 ((-1162) $))
+      (-15 -2691 ((-1162) $)))))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-907)) (-5 *1 (-189 *3))
+  (-12 (-5 *2 (-908)) (-5 *1 (-189 *3))
    (-4 *3
     (-13 (-779)
-     (-10 -8 (-15 -2607 ((-1058) $ (-1075))) (-15 -1756 ((-1161) $))
-      (-15 -3177 ((-1161) $)))))))
+     (-10 -8 (-15 -2609 ((-1059) $ (-1076))) (-15 -1757 ((-1162) $))
+      (-15 -2691 ((-1162) $)))))))
  ((*1 *2 *1 *3)
   (-12 (-5 *3 "count") (-5 *2 (-703)) (-5 *1 (-219 *4)) (-4 *4 (-779))))
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   (-12 (-5 *2 "unique") (-5 *1 (-219 *3)) (-4 *3 (-779))))
  ((*1 *2 *1 *3)
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  ((*1 *2 *1 *3 *2)
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   (-12 (-4 *3 (-156)) (-5 *1 (-261 *3 *2 *4 *5 *6 *7))
-   (-4 *2 (-1132 *3)) (-4 *4 (-23)) (-14 *5 (-1 *2 *2 *4))
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    (-14 *6 (-1 (-3 *4 "failed") *4 *4))
    (-14 *7 (-1 (-3 *2 "failed") *2 *2 *4))))
  ((*1 *1 *2 *3) (-12 (-5 *2 (-109)) (-5 *3 (-583 *1)) (-4 *1 (-273))))
@@ -8438,1365 +8457,1255 @@
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  ((*1 *1 *2 *1) (-12 (-4 *1 (-273)) (-5 *2 (-109))))
  ((*1 *2 *1 *2 *2)
-  (-12 (-4 *1 (-312 *2 *3 *4)) (-4 *2 (-1114)) (-4 *3 (-1132 *2))
-   (-4 *4 (-1132 (-377 *3)))))
+  (-12 (-4 *1 (-312 *2 *3 *4)) (-4 *2 (-1115)) (-4 *3 (-1133 *2))
+   (-4 *4 (-1133 (-377 *3)))))
  ((*1 *2 *1 *3) (-12 (-5 *3 (-517)) (-4 *1 (-387 *2)) (-4 *2 (-156))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1075)) (-5 *2 (-1058)) (-5 *1 (-467))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1075)) (-5 *2 (-51)) (-5 *1 (-572))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1076)) (-5 *2 (-1059)) (-5 *1 (-467))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1076)) (-5 *2 (-51)) (-5 *1 (-572))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1123 (-517))) (-4 *1 (-588 *3)) (-4 *3 (-1110))))
+  (-12 (-5 *2 (-1124 (-517))) (-4 *1 (-588 *3)) (-4 *3 (-1111))))
  ((*1 *2 *1 *3 *3 *3)
-  (-12 (-5 *3 (-703)) (-5 *1 (-611 *2)) (-4 *2 (-1004))))
+  (-12 (-5 *3 (-703)) (-5 *1 (-611 *2)) (-4 *2 (-1005))))
  ((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-583 (-517))) (-4 *1 (-621 *3 *4 *5)) (-4 *3 (-962))
+  (-12 (-5 *2 (-583 (-517))) (-4 *1 (-621 *3 *4 *5)) (-4 *3 (-963))
    (-4 *4 (-343 *3)) (-4 *5 (-343 *3))))
  ((*1 *1 *1 *2) (-12 (-5 *2 (-583 (-787))) (-5 *1 (-787))))
  ((*1 *1 *2 *3)
   (-12 (-5 *2 (-109)) (-5 *3 (-583 (-815 *4))) (-5 *1 (-815 *4))
-   (-4 *4 (-1004))))
- ((*1 *2 *1 *2) (-12 (-4 *1 (-826 *2)) (-4 *2 (-1004))))
+   (-4 *4 (-1005))))
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   (-12 (-5 *3 (-703)) (-5 *2 (-828 *4)) (-5 *1 (-827 *4))
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   (-12 (-5 *3 (-214 *4 *2)) (-14 *4 (-844)) (-4 *2 (-333))
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- ((*1 *2 *1) (-12 (-5 *1 (-942 *2)) (-4 *2 (-1110))))
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  ((*1 *2 *1 *3 *3 *2)
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  ((*1 *2 *3 *2)
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    (-4 *2 (-333))))
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    (-4 *3 (-509))))
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 (((*1 *2 *3 *3)
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 (((*1 *2 *1)
-  (-12 (-4 *1 (-1139 *3 *4)) (-4 *3 (-962)) (-4 *4 (-1116 *3))
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+  (-12 (-4 *3 (-963)) (-5 *2 (-1157 *3)) (-5 *1 (-645 *3 *4))
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+(((*1 *2 *3 *4 *5)
+  (-12 (-5 *4 (-1 *7 *7))
+   (-5 *5 (-1 (-3 (-2 (|:| -2212 *6) (|:| |coeff| *6)) "failed") *6))
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+(((*1 *1 *1 *1)
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+      (-14 *6 (-1 (-3 *4 "failed") *4 *4))
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+ ((*1 *1 *1 *1)
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+      (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3))
+      (-14 *5 (-1 (-3 *3 "failed") *3 *3))
+      (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))
+ ((*1 *1 *1 *1)
+  (|partial| -12 (-5 *1 (-648 *2 *3 *4 *5 *6)) (-4 *2 (-156))
+      (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3))
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+(((*1 *2 *3 *4 *2 *2 *5)
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 (((*1 *2 *3)
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-(((*1 *2 *3 *4 *3 *5 *5 *3 *5 *4)
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-(((*1 *2 *3 *1)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *1 *2)
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 (((*1 *1 *1 *2)
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-(((*1 *2 *3)
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- ((*1 *2 *3)
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+  (-12 (-5 *1 (-542 *2)) (-4 *2 (-37 (-377 (-517)))) (-4 *2 (-963))))) 
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-1056 (-199))) (-5 *2 (-583 (-1058))) (-5 *1 (-168))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1056 (-199))) (-5 *2 (-583 (-1058))) (-5 *1 (-271))))
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+ ((*1 *2 *3 *4)
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  ((*1 *2 *3)
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-(((*1 *2 *3 *4 *5 *6 *7 *7 *8)
-  (-12
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-   (-5 *4 (-623 *12)) (-5 *5 (-583 (-377 (-875 *9))))
-   (-5 *6 (-583 (-583 *12))) (-5 *7 (-703)) (-5 *8 (-517))
-   (-4 *9 (-13 (-278) (-134))) (-4 *12 (-872 *9 *11 *10))
-   (-4 *10 (-13 (-779) (-558 (-1075)))) (-4 *11 (-725))
-   (-5 *2
-    (-2 (|:| |eqzro| (-583 *12)) (|:| |neqzro| (-583 *12))
-     (|:| |wcond| (-583 (-875 *9)))
-     (|:| |bsoln|
-          (-2 (|:| |partsol| (-1156 (-377 (-875 *9))))
-           (|:| -2062 (-583 (-1156 (-377 (-875 *9)))))))))
-   (-5 *1 (-847 *9 *10 *11 *12))))) 
-(((*1 *2 *3)
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-   (-14 *6 (-844))))) 
-(((*1 *2 *3 *2)
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-(((*1 *2 *3 *4)
-  (-12 (-4 *5 (-725)) (-4 *6 (-779)) (-4 *7 (-509))
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-   (-5 *2
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-   (-5 *1 (-876 *5 *6 *7 *3 *8)) (-5 *4 (-703))
-   (-4 *8
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-     (-10 -8 (-15 -3824 (*3 $)) (-15 -2097 (*3 $)) (-15 -2269 ($ *3)))))))) 
-(((*1 *2 *2 *3)
-  (|partial| -12 (-5 *3 (-1 *6 *6)) (-4 *6 (-1132 *5))
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-      (-4 *7 (-1132 (-377 *6))) (-5 *1 (-505 *4 *5 *6 *7 *2))
-      (-4 *2 (-312 *5 *6 *7))))) 
+  (-12 (-5 *3 (-583 (-623 *4))) (-4 *4 (-333))
+   (-5 *2 (-1157 (-623 *4))) (-5 *1 (-993 *4))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1075)) (-5 *3 (-583 (-493))) (-5 *1 (-493))))) 
-(((*1 *1 *1 *1 *1) (-4 *1 (-694)))) 
-(((*1 *2 *3 *4)
-  (-12 (-5 *3 (-623 *8)) (-4 *8 (-872 *5 *7 *6))
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-   (-4 *7 (-725))
-   (-5 *2
-    (-583
-     (-2 (|:| |eqzro| (-583 *8)) (|:| |neqzro| (-583 *8))
-      (|:| |wcond| (-583 (-875 *5)))
-      (|:| |bsoln|
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-            (|:| -2062 (-583 (-1156 (-377 (-875 *5))))))))))
-   (-5 *1 (-847 *5 *6 *7 *8)) (-5 *4 (-583 *8))))
- ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-623 *8)) (-5 *4 (-583 (-1075))) (-4 *8 (-872 *5 *7 *6))
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-   (-4 *7 (-725))
-   (-5 *2
-    (-583
-     (-2 (|:| |eqzro| (-583 *8)) (|:| |neqzro| (-583 *8))
-      (|:| |wcond| (-583 (-875 *5)))
-      (|:| |bsoln|
-           (-2 (|:| |partsol| (-1156 (-377 (-875 *5))))
-            (|:| -2062 (-583 (-1156 (-377 (-875 *5))))))))))
-   (-5 *1 (-847 *5 *6 *7 *8))))
+  (-12 (-5 *2 (-1076)) (-5 *3 (-583 (-493))) (-5 *1 (-493))))) 
+(((*1 *2 *1)
+  (|partial| -12 (-4 *1 (-150 *3)) (-4 *3 (-156)) (-4 *3 (-502))
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+ ((*1 *2 *1)
+  (|partial| -12 (-5 *2 (-377 (-517))) (-5 *1 (-388 *3)) (-4 *3 (-502))
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+ ((*1 *2 *1) (|partial| -12 (-4 *1 (-502)) (-5 *2 (-377 (-517)))))
+ ((*1 *2 *1)
+  (|partial| -12 (-4 *1 (-729 *3)) (-4 *3 (-156)) (-4 *3 (-502))
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+ ((*1 *2 *1)
+  (|partial| -12 (-5 *2 (-377 (-517))) (-5 *1 (-765 *3)) (-4 *3 (-502))
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+ ((*1 *2 *1)
+  (|partial| -12 (-5 *2 (-377 (-517))) (-5 *1 (-772 *3)) (-4 *3 (-502))
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+ ((*1 *2 *1)
+  (|partial| -12 (-4 *1 (-915 *3)) (-4 *3 (-156)) (-4 *3 (-502))
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  ((*1 *2 *3)
-  (-12 (-5 *3 (-623 *7)) (-4 *7 (-872 *4 *6 *5))
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-   (-5 *2
-    (-583
-     (-2 (|:| |eqzro| (-583 *7)) (|:| |neqzro| (-583 *7))
-      (|:| |wcond| (-583 (-875 *4)))
-      (|:| |bsoln|
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-            (|:| -2062 (-583 (-1156 (-377 (-875 *4))))))))))
-   (-5 *1 (-847 *4 *5 *6 *7))))
- ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-623 *9)) (-5 *5 (-844)) (-4 *9 (-872 *6 *8 *7))
-   (-4 *6 (-13 (-278) (-134))) (-4 *7 (-13 (-779) (-558 (-1075))))
-   (-4 *8 (-725))
-   (-5 *2
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-      (|:| |wcond| (-583 (-875 *6)))
-      (|:| |bsoln|
-           (-2 (|:| |partsol| (-1156 (-377 (-875 *6))))
-            (|:| -2062 (-583 (-1156 (-377 (-875 *6))))))))))
-   (-5 *1 (-847 *6 *7 *8 *9)) (-5 *4 (-583 *9))))
- ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-623 *9)) (-5 *4 (-583 (-1075))) (-5 *5 (-844))
-   (-4 *9 (-872 *6 *8 *7)) (-4 *6 (-13 (-278) (-134)))
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-   (-5 *2
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-      (|:| |wcond| (-583 (-875 *6)))
-      (|:| |bsoln|
-           (-2 (|:| |partsol| (-1156 (-377 (-875 *6))))
-            (|:| -2062 (-583 (-1156 (-377 (-875 *6))))))))))
-   (-5 *1 (-847 *6 *7 *8 *9))))
- ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-623 *8)) (-5 *4 (-844)) (-4 *8 (-872 *5 *7 *6))
-   (-4 *5 (-13 (-278) (-134))) (-4 *6 (-13 (-779) (-558 (-1075))))
-   (-4 *7 (-725))
-   (-5 *2
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-   (-5 *1 (-84 *3)) (-14 *3 (-1075))))
+  (-12 (-5 *2 (-1157 (-309 (-2288 'X) (-2288 '-2011) (-632))))
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-  (-12 (-5 *2 (-623 (-309 (-2286 'XL 'XR 'ELAM) (-2286) (-632))))
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+  (-12 (-5 *2 (-623 (-309 (-2288 'XL 'XR 'ELAM) (-2288) (-632))))
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  ((*1 *1 *2)
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- ((*1 *2 *1) (-12 (-5 *2 (-921 2)) (-5 *1 (-103))))
+  (-12 (-5 *2 (-309 (-2288 'X) (-2288 '-2011) (-632))) (-5 *1 (-87 *3))
+   (-14 *3 (-1076))))
+ ((*1 *2 *1) (-12 (-5 *2 (-922 2)) (-5 *1 (-103))))
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   (-12 (-5 *2 (-583 (-127 *3 *4 *5))) (-5 *1 (-127 *3 *4 *5))
@@ -10546,45 +10554,45 @@
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    (-14 *3 (-517)) (-14 *4 (-703))))
  ((*1 *1 *2)
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+  (-12 (-5 *2 (-1043 *4 *5)) (-14 *4 (-703)) (-4 *5 (-156))
    (-5 *1 (-127 *3 *4 *5)) (-14 *3 (-517))))
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-   (-5 *2 (-1156 (-623 (-377 (-875 *4))))) (-5 *1 (-165 *4))))
+  (-12 (-5 *3 (-1157 (-623 *4))) (-4 *4 (-156))
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-      (-15 -3177 ((-1161) $)))))
+     (-10 -8 (-15 -2609 ((-1059) $ (-1076))) (-15 -1757 ((-1162) $))
+      (-15 -2691 ((-1162) $)))))
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+ ((*1 *2 *1) (-12 (-5 *2 (-922 10)) (-5 *1 (-192))))
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+  (-12 (-4 *2 (-1133 *3)) (-5 *1 (-261 *3 *2 *4 *5 *6 *7))
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    (-14 *6 (-1 (-3 *4 "failed") *4 *4))
    (-14 *7 (-1 (-3 *2 "failed") *2 *2 *4))))
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-   (-14 *5 (-1075)) (-14 *6 *4)
-   (-4 *3 (-13 (-779) (-953 (-517)) (-579 (-517)) (-421)))
+  (-12 (-5 *2 (-1142 *4 *5 *6)) (-4 *4 (-13 (-27) (-1097) (-400 *3)))
+   (-14 *5 (-1076)) (-14 *6 *4)
+   (-4 *3 (-13 (-779) (-954 (-517)) (-579 (-517)) (-421)))
    (-5 *1 (-283 *3 *4 *5 *6))))
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  ((*1 *2 *1)
   (-12 (-5 *2 (-286 *5)) (-5 *1 (-309 *3 *4 *5))
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+   (-14 *3 (-583 (-1076))) (-14 *4 (-583 (-1076))) (-4 *5 (-357))))
  ((*1 *2 *3)
   (-12 (-4 *4 (-319)) (-4 *2 (-299 *4)) (-5 *1 (-317 *3 *4 *2))
    (-4 *3 (-299 *4))))
@@ -10593,96 +10601,96 @@
    (-4 *3 (-299 *4))))
  ((*1 *2 *1)
   (-12 (-4 *1 (-344 *3 *4)) (-4 *3 (-779)) (-4 *4 (-156))
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  ((*1 *2 *1)
   (-12 (-4 *1 (-344 *3 *4)) (-4 *3 (-779)) (-4 *4 (-156))
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  ((*1 *1 *2)
   (-12
-   (-5 *2 (-2 (|:| |localSymbols| (-1079)) (|:| -2514 (-583 (-300)))))
+   (-5 *2 (-2 (|:| |localSymbols| (-1080)) (|:| -2516 (-583 (-300)))))
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  ((*1 *1 *2)
   (-12
-   (-5 *2 (-2 (|:| |localSymbols| (-1079)) (|:| -2514 (-583 (-300)))))
+   (-5 *2 (-2 (|:| |localSymbols| (-1080)) (|:| -2516 (-583 (-300)))))
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- ((*1 *2 *3) (-12 (-5 *2 (-364)) (-5 *1 (-363 *3)) (-4 *3 (-1004))))
+ ((*1 *2 *1) (-12 (-4 *1 (-359)) (-5 *2 (-1059))))
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  ((*1 *1 *2)
   (-12
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    (-4 *1 (-366))))
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   (-12 (-5 *2 (-265 (-286 (-153 (-349))))) (-5 *1 (-368 *3 *4 *5 *6))
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-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-14 *3 (-1076)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-286 (-153 (-349)))) (-5 *1 (-368 *3 *4 *5 *6))
-   (-14 *3 (-1075)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-14 *3 (-1076)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-286 (-349))) (-5 *1 (-368 *3 *4 *5 *6))
-   (-14 *3 (-1075)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-14 *3 (-1076)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-286 (-517))) (-5 *1 (-368 *3 *4 *5 *6))
-   (-14 *3 (-1075)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-14 *3 (-1076)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-265 (-286 (-627)))) (-5 *1 (-368 *3 *4 *5 *6))
-   (-14 *3 (-1075)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-14 *3 (-1076)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-265 (-286 (-632)))) (-5 *1 (-368 *3 *4 *5 *6))
-   (-14 *3 (-1075)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-14 *3 (-1076)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-265 (-286 (-634)))) (-5 *1 (-368 *3 *4 *5 *6))
-   (-14 *3 (-1075)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-14 *3 (-1076)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-286 (-627))) (-5 *1 (-368 *3 *4 *5 *6))
-   (-14 *3 (-1075)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-14 *3 (-1076)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-286 (-632))) (-5 *1 (-368 *3 *4 *5 *6))
-   (-14 *3 (-1075)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-14 *3 (-1076)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-286 (-634))) (-5 *1 (-368 *3 *4 *5 *6))
-   (-14 *3 (-1075)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-14 *3 (-1076)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12
-   (-5 *2 (-2 (|:| |localSymbols| (-1079)) (|:| -2514 (-583 (-300)))))
-   (-5 *1 (-368 *3 *4 *5 *6)) (-14 *3 (-1075))
-   (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-5 *2 (-2 (|:| |localSymbols| (-1080)) (|:| -2516 (-583 (-300)))))
+   (-5 *1 (-368 *3 *4 *5 *6)) (-14 *3 (-1076))
+   (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-583 (-300))) (-5 *1 (-368 *3 *4 *5 *6))
-   (-14 *3 (-1075)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+   (-14 *3 (-1076)) (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-300)) (-5 *1 (-368 *3 *4 *5 *6)) (-14 *3 (-1075))
-   (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2043 "void")))
-   (-14 *5 (-583 (-1075))) (-14 *6 (-1079))))
+  (-12 (-5 *2 (-300)) (-5 *1 (-368 *3 *4 *5 *6)) (-14 *3 (-1076))
+   (-14 *4 (-3 (|:| |fst| (-404)) (|:| -2044 "void")))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1080))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-301 *4)) (-4 *4 (-13 (-779) (-21)))
    (-5 *1 (-397 *3 *4)) (-4 *3 (-13 (-156) (-37 (-377 (-517)))))))
@@ -10699,55 +10707,55 @@
   (-12 (-5 *2 (-377 *3)) (-4 *3 (-509)) (-4 *3 (-779))
    (-4 *1 (-400 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1027 *3 (-556 *1))) (-4 *3 (-962)) (-4 *3 (-779))
+  (-12 (-5 *2 (-1028 *3 (-556 *1))) (-4 *3 (-963)) (-4 *3 (-779))
    (-4 *1 (-400 *3))))
- ((*1 *2 *1) (-12 (-5 *2 (-1008)) (-5 *1 (-404))))
- ((*1 *2 *1) (-12 (-5 *2 (-1075)) (-5 *1 (-404))))
- ((*1 *1 *2) (-12 (-5 *2 (-1075)) (-5 *1 (-404))))
- ((*1 *1 *2) (-12 (-5 *2 (-1058)) (-5 *1 (-404))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1009)) (-5 *1 (-404))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1076)) (-5 *1 (-404))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1076)) (-5 *1 (-404))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1059)) (-5 *1 (-404))))
  ((*1 *1 *2) (-12 (-5 *2 (-404)) (-5 *1 (-407))))
  ((*1 *2 *1) (-12 (-5 *2 (-787)) (-5 *1 (-407))))
  ((*1 *1 *2)
   (-12
-   (-5 *2 (-2 (|:| |localSymbols| (-1079)) (|:| -2514 (-583 (-300)))))
+   (-5 *2 (-2 (|:| |localSymbols| (-1080)) (|:| -2516 (-583 (-300)))))
    (-4 *1 (-409))))
  ((*1 *1 *2) (-12 (-5 *2 (-300)) (-4 *1 (-409))))
  ((*1 *1 *2) (-12 (-5 *2 (-583 (-300))) (-4 *1 (-409))))
- ((*1 *1 *2) (-12 (-5 *2 (-1156 (-632))) (-4 *1 (-409))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1157 (-632))) (-4 *1 (-409))))
  ((*1 *1 *2)
   (-12
-   (-5 *2 (-2 (|:| |localSymbols| (-1079)) (|:| -2514 (-583 (-300)))))
+   (-5 *2 (-2 (|:| |localSymbols| (-1080)) (|:| -2516 (-583 (-300)))))
    (-4 *1 (-410))))
  ((*1 *1 *2) (-12 (-5 *2 (-300)) (-4 *1 (-410))))
  ((*1 *1 *2) (-12 (-5 *2 (-583 (-300))) (-4 *1 (-410))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1156 (-377 (-875 *3)))) (-4 *3 (-156))
-   (-14 *6 (-1156 (-623 *3))) (-5 *1 (-422 *3 *4 *5 *6))
-   (-14 *4 (-844)) (-14 *5 (-583 (-1075)))))
+  (-12 (-5 *2 (-1157 (-377 (-875 *3)))) (-4 *3 (-156))
+   (-14 *6 (-1157 (-623 *3))) (-5 *1 (-422 *3 *4 *5 *6))
+   (-14 *4 (-844)) (-14 *5 (-583 (-1076)))))
  ((*1 *1 *2) (-12 (-5 *2 (-583 (-583 (-866 (-199))))) (-5 *1 (-437))))
  ((*1 *2 *1) (-12 (-5 *2 (-787)) (-5 *1 (-437))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1141 *3 *4 *5)) (-4 *3 (-962)) (-14 *4 (-1075))
+  (-12 (-5 *2 (-1142 *3 *4 *5)) (-4 *3 (-963)) (-14 *4 (-1076))
    (-14 *5 *3) (-5 *1 (-443 *3 *4 *5))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1152 *4)) (-14 *4 (-1075)) (-5 *1 (-443 *3 *4 *5))
-   (-4 *3 (-962)) (-14 *5 *3)))
- ((*1 *2 *1) (-12 (-5 *2 (-921 16)) (-5 *1 (-454))))
+  (-12 (-5 *2 (-1153 *4)) (-14 *4 (-1076)) (-5 *1 (-443 *3 *4 *5))
+   (-4 *3 (-963)) (-14 *5 *3)))
+ ((*1 *2 *1) (-12 (-5 *2 (-922 16)) (-5 *1 (-454))))
  ((*1 *2 *1) (-12 (-5 *2 (-377 (-517))) (-5 *1 (-454))))
- ((*1 *1 *2) (-12 (-5 *2 (-1027 (-517) (-556 (-460)))) (-5 *1 (-460))))
- ((*1 *1 *2) (-12 (-5 *2 (-1058)) (-5 *1 (-467))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1028 (-517) (-556 (-460)))) (-5 *1 (-460))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1059)) (-5 *1 (-467))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-583 *6)) (-4 *6 (-872 *3 *4 *5)) (-4 *3 (-333))
    (-4 *4 (-725)) (-4 *5 (-779)) (-5 *1 (-469 *3 *4 *5 *6))))
  ((*1 *1 *2)
   (-12 (-4 *3 (-156)) (-5 *1 (-551 *3 *2)) (-4 *2 (-677 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-557 *2)) (-4 *2 (-1110))))
- ((*1 *1 *2) (-12 (-4 *1 (-561 *2)) (-4 *2 (-962))))
+ ((*1 *2 *1) (-12 (-4 *1 (-557 *2)) (-4 *2 (-1111))))
+ ((*1 *1 *2) (-12 (-4 *1 (-561 *2)) (-4 *2 (-963))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-1174 *3 *4)) (-5 *1 (-567 *3 *4 *5)) (-4 *3 (-779))
+  (-12 (-5 *2 (-1175 *3 *4)) (-5 *1 (-567 *3 *4 *5)) (-4 *3 (-779))
    (-4 *4 (-13 (-156) (-650 (-377 (-517))))) (-14 *5 (-844))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-1169 *3 *4)) (-5 *1 (-567 *3 *4 *5)) (-4 *3 (-779))
+  (-12 (-5 *2 (-1170 *3 *4)) (-5 *1 (-567 *3 *4 *5)) (-4 *3 (-779))
    (-4 *4 (-13 (-156) (-650 (-377 (-517))))) (-14 *5 (-844))))
  ((*1 *1 *2)
   (-12 (-4 *3 (-156)) (-5 *1 (-575 *3 *2)) (-4 *2 (-677 *3))))
@@ -10755,14 +10763,14 @@
  ((*1 *2 *1) (-12 (-5 *2 (-751 *3)) (-5 *1 (-608 *3)) (-4 *3 (-779))))
  ((*1 *2 *1)
   (-12 (-5 *2 (-880 (-880 (-880 *3)))) (-5 *1 (-611 *3))
-   (-4 *3 (-1004))))
+   (-4 *3 (-1005))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-880 (-880 (-880 *3)))) (-4 *3 (-1004))
+  (-12 (-5 *2 (-880 (-880 (-880 *3)))) (-4 *3 (-1005))
    (-5 *1 (-611 *3))))
  ((*1 *2 *1) (-12 (-5 *2 (-751 *3)) (-5 *1 (-612 *3)) (-4 *3 (-779))))
- ((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-616 *3)) (-4 *3 (-1004))))
+ ((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-616 *3)) (-4 *3 (-1005))))
  ((*1 *1 *2)
-  (-12 (-4 *3 (-962)) (-4 *1 (-621 *3 *4 *2)) (-4 *4 (-343 *3))
+  (-12 (-4 *3 (-963)) (-4 *1 (-621 *3 *4 *2)) (-4 *4 (-343 *3))
    (-4 *2 (-343 *3))))
  ((*1 *2 *1) (-12 (-5 *2 (-153 (-349))) (-5 *1 (-627))))
  ((*1 *1 *2) (-12 (-5 *2 (-153 (-634))) (-5 *1 (-627))))
@@ -10773,26 +10781,26 @@
  ((*1 *2 *1) (-12 (-5 *2 (-349)) (-5 *1 (-632))))
  ((*1 *2 *3)
   (-12 (-5 *3 (-286 (-517))) (-5 *2 (-286 (-634))) (-5 *1 (-634))))
- ((*1 *1 *2) (-12 (-5 *1 (-636 *2)) (-4 *2 (-1004))))
+ ((*1 *1 *2) (-12 (-5 *1 (-636 *2)) (-4 *2 (-1005))))
  ((*1 *2 *1)
   (-12 (-4 *2 (-156)) (-5 *1 (-644 *2 *3 *4 *5 *6)) (-4 *3 (-23))
    (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
    (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))
  ((*1 *1 *2)
-  (-12 (-4 *3 (-962)) (-5 *1 (-645 *3 *2)) (-4 *2 (-1132 *3))))
+  (-12 (-4 *3 (-963)) (-5 *1 (-645 *3 *2)) (-4 *2 (-1133 *3))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-2 (|:| -2810 *3) (|:| -2356 *4)))
-   (-5 *1 (-646 *3 *4 *5)) (-4 *3 (-779)) (-4 *4 (-1004))
+  (-12 (-5 *2 (-2 (|:| -2812 *3) (|:| -2121 *4)))
+   (-5 *1 (-646 *3 *4 *5)) (-4 *3 (-779)) (-4 *4 (-1005))
    (-14 *5 (-1 (-107) *2 *2))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-2 (|:| -2810 *3) (|:| -2356 *4))) (-4 *3 (-779))
-   (-4 *4 (-1004)) (-5 *1 (-646 *3 *4 *5)) (-14 *5 (-1 (-107) *2 *2))))
+  (-12 (-5 *2 (-2 (|:| -2812 *3) (|:| -2121 *4))) (-4 *3 (-779))
+   (-4 *4 (-1005)) (-5 *1 (-646 *3 *4 *5)) (-14 *5 (-1 (-107) *2 *2))))
  ((*1 *2 *1)
   (-12 (-4 *2 (-156)) (-5 *1 (-648 *2 *3 *4 *5 *6)) (-4 *3 (-23))
    (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
    (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-583 (-2 (|:| -1580 *3) (|:| -2423 *4)))) (-4 *3 (-962))
+  (-12 (-5 *2 (-583 (-2 (|:| -1582 *3) (|:| -2425 *4)))) (-4 *3 (-963))
    (-4 *4 (-659)) (-5 *1 (-668 *3 *4))))
  ((*1 *1 *2) (-12 (-5 *2 (-517)) (-4 *1 (-696))))
  ((*1 *1 *2)
@@ -10800,82 +10808,82 @@
    (-5 *2
     (-3
      (|:| |nia|
-          (-2 (|:| |var| (-1075)) (|:| |fn| (-286 (-199)))
-           (|:| -2192 (-999 (-772 (-199)))) (|:| |abserr| (-199))
+          (-2 (|:| |var| (-1076)) (|:| |fn| (-286 (-199)))
+           (|:| -2758 (-1000 (-772 (-199)))) (|:| |abserr| (-199))
            (|:| |relerr| (-199))))
      (|:| |mdnia|
           (-2 (|:| |fn| (-286 (-199)))
-           (|:| -2192 (-583 (-999 (-772 (-199)))))
+           (|:| -2758 (-583 (-1000 (-772 (-199)))))
            (|:| |abserr| (-199)) (|:| |relerr| (-199))))))
    (-5 *1 (-701))))
  ((*1 *1 *2)
   (-12
    (-5 *2
     (-2 (|:| |fn| (-286 (-199)))
-     (|:| -2192 (-583 (-999 (-772 (-199))))) (|:| |abserr| (-199))
+     (|:| -2758 (-583 (-1000 (-772 (-199))))) (|:| |abserr| (-199))
      (|:| |relerr| (-199))))
    (-5 *1 (-701))))
  ((*1 *1 *2)
   (-12
    (-5 *2
-    (-2 (|:| |var| (-1075)) (|:| |fn| (-286 (-199)))
-     (|:| -2192 (-999 (-772 (-199)))) (|:| |abserr| (-199))
+    (-2 (|:| |var| (-1076)) (|:| |fn| (-286 (-199)))
+     (|:| -2758 (-1000 (-772 (-199)))) (|:| |abserr| (-199))
      (|:| |relerr| (-199))))
    (-5 *1 (-701))))
  ((*1 *2 *1) (-12 (-5 *2 (-787)) (-5 *1 (-701))))
- ((*1 *2 *3) (-12 (-5 *2 (-706)) (-5 *1 (-705 *3)) (-4 *3 (-1110))))
+ ((*1 *2 *3) (-12 (-5 *2 (-706)) (-5 *1 (-705 *3)) (-4 *3 (-1111))))
  ((*1 *1 *2)
   (-12
    (-5 *2
     (-2 (|:| |xinit| (-199)) (|:| |xend| (-199))
-     (|:| |fn| (-1156 (-286 (-199)))) (|:| |yinit| (-583 (-199)))
+     (|:| |fn| (-1157 (-286 (-199)))) (|:| |yinit| (-583 (-199)))
      (|:| |intvals| (-583 (-199))) (|:| |g| (-286 (-199)))
      (|:| |abserr| (-199)) (|:| |relerr| (-199))))
    (-5 *1 (-740))))
  ((*1 *2 *1) (-12 (-5 *2 (-787)) (-5 *1 (-740))))
  ((*1 *2 *1)
-  (-12 (-4 *2 (-823 *3)) (-5 *1 (-749 *3 *2 *4)) (-4 *3 (-1004))
+  (-12 (-4 *2 (-823 *3)) (-5 *1 (-749 *3 *2 *4)) (-4 *3 (-1005))
    (-14 *4 *3)))
  ((*1 *1 *2)
-  (-12 (-4 *3 (-1004)) (-14 *4 *3) (-5 *1 (-749 *3 *2 *4))
+  (-12 (-4 *3 (-1005)) (-14 *4 *3) (-5 *1 (-749 *3 *2 *4))
    (-4 *2 (-823 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1075)) (-5 *1 (-756))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1076)) (-5 *1 (-756))))
  ((*1 *1 *2)
   (-12
    (-5 *2
     (-3
      (|:| |noa|
-          (-2 (|:| |fn| (-286 (-199))) (|:| -2585 (-583 (-199)))
+          (-2 (|:| |fn| (-286 (-199))) (|:| -2587 (-583 (-199)))
            (|:| |lb| (-583 (-772 (-199))))
            (|:| |cf| (-583 (-286 (-199))))
            (|:| |ub| (-583 (-772 (-199))))))
      (|:| |lsa|
           (-2 (|:| |lfn| (-583 (-286 (-199))))
-           (|:| -2585 (-583 (-199)))))))
+           (|:| -2587 (-583 (-199)))))))
    (-5 *1 (-770))))
  ((*1 *1 *2)
   (-12
    (-5 *2
-    (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2585 (-583 (-199)))))
+    (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2587 (-583 (-199)))))
    (-5 *1 (-770))))
  ((*1 *1 *2)
   (-12
    (-5 *2
-    (-2 (|:| |fn| (-286 (-199))) (|:| -2585 (-583 (-199)))
+    (-2 (|:| |fn| (-286 (-199))) (|:| -2587 (-583 (-199)))
      (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199))))
      (|:| |ub| (-583 (-772 (-199))))))
    (-5 *1 (-770))))
  ((*1 *2 *1) (-12 (-5 *2 (-787)) (-5 *1 (-770))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1152 *3)) (-14 *3 (-1075)) (-5 *1 (-784 *3 *4 *5 *6))
-   (-4 *4 (-962)) (-14 *5 (-94 *4)) (-14 *6 (-1 *4 *4))))
+  (-12 (-5 *2 (-1153 *3)) (-14 *3 (-1076)) (-5 *1 (-784 *3 *4 *5 *6))
+   (-4 *4 (-963)) (-14 *5 (-94 *4)) (-14 *6 (-1 *4 *4))))
  ((*1 *1 *2) (-12 (-5 *2 (-517)) (-5 *1 (-786))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-875 *3)) (-4 *3 (-962)) (-5 *1 (-790 *3 *4 *5 *6))
-   (-14 *4 (-583 (-1075))) (-14 *5 (-583 (-703))) (-14 *6 (-703))))
+  (-12 (-5 *2 (-875 *3)) (-4 *3 (-963)) (-5 *1 (-790 *3 *4 *5 *6))
+   (-14 *4 (-583 (-1076))) (-14 *5 (-583 (-703))) (-14 *6 (-703))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-875 *3)) (-5 *1 (-790 *3 *4 *5 *6)) (-4 *3 (-962))
-   (-14 *4 (-583 (-1075))) (-14 *5 (-583 (-703))) (-14 *6 (-703))))
+  (-12 (-5 *2 (-875 *3)) (-5 *1 (-790 *3 *4 *5 *6)) (-4 *3 (-963))
+   (-14 *4 (-583 (-1076))) (-14 *5 (-583 (-703))) (-14 *6 (-703))))
  ((*1 *1 *2) (-12 (-5 *2 (-142)) (-5 *1 (-797))))
  ((*1 *2 *3)
   (-12 (-5 *3 (-875 (-47))) (-5 *2 (-286 (-517))) (-5 *1 (-798))))
@@ -10893,400 +10901,502 @@
            (-2 (|:| |start| (-199)) (|:| |finish| (-199))
             (|:| |grid| (-703)) (|:| |boundaryType| (-517))
             (|:| |dStart| (-623 (-199))) (|:| |dFinish| (-623 (-199))))))
-     (|:| |f| (-583 (-583 (-286 (-199))))) (|:| |st| (-1058))
+     (|:| |f| (-583 (-583 (-286 (-199))))) (|:| |st| (-1059))
      (|:| |tol| (-199))))
    (-5 *1 (-821))))
  ((*1 *2 *1) (-12 (-5 *2 (-787)) (-5 *1 (-821))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-1097 *3)) (-5 *1 (-824 *3)) (-4 *3 (-1004))))
+  (-12 (-5 *2 (-1098 *3)) (-5 *1 (-824 *3)) (-4 *3 (-1005))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-583 (-828 *3))) (-4 *3 (-1004)) (-5 *1 (-827 *3))))
+  (-12 (-5 *2 (-583 (-828 *3))) (-4 *3 (-1005)) (-5 *1 (-827 *3))))
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 (((*1 *2 *1 *3)
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@@ -11297,2102 +11407,1866 @@
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   (-12
-   (-5 *3
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+            (|:| |relerr| (-199))))
+      (|:| -1859
+           (-2
+            (|:| |endPointContinuity|
+                 (-3 (|:| |continuous| "Continuous at the end points")
+                  (|:| |lowerSingular|
+                       "There is a singularity at the lower end point")
+                  (|:| |upperSingular|
+                       "There is a singularity at the upper end point")
+                  (|:| |bothSingular|
+                       "There are singularities at both end points")
+                  (|:| |notEvaluated|
+                       "End point continuity not yet evaluated")))
+            (|:| |singularitiesStream|
+                 (-3 (|:| |str| (-1057 (-199)))
+                  (|:| |notEvaluated|
+                       "Internal singularities not yet evaluated")))
+            (|:| -2758
+                 (-3 (|:| |finite| "The range is finite")
+                  (|:| |lowerInfinite|
+                       "The bottom of range is infinite")
+                  (|:| |upperInfinite| "The top of range is infinite")
+                  (|:| |bothInfinite|
+                       "Both top and bottom points are infinite")
+                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
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 (((*1 *2 *3 *4)
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+  (-12 (-4 *3 (-509)) (-5 *2 (-583 *4)) (-5 *1 (-42 *3 *4))
+   (-4 *4 (-387 *3))))) 
+(((*1 *2 *3 *3 *3)
+  (|partial| -12 (-4 *4 (-13 (-333) (-134) (-954 (-517))))
+      (-4 *5 (-1133 *4)) (-5 *2 (-583 (-377 *5))) (-5 *1 (-934 *4 *5))
+      (-5 *3 (-377 *5))))) 
+(((*1 *1 *1 *2)
+  (-12 (-5 *2 (-583 (-517))) (-5 *1 (-221 *3 *4))
+   (-14 *3 (-583 (-1076))) (-4 *4 (-963))))
+ ((*1 *1 *1 *2)
+  (-12 (-5 *2 (-583 (-517))) (-14 *3 (-583 (-1076)))
+   (-5 *1 (-423 *3 *4 *5)) (-4 *4 (-963))
+   (-4 *5 (-212 (-3535 *3) (-703)))))
+ ((*1 *1 *1 *2)
+  (-12 (-5 *2 (-583 (-517))) (-5 *1 (-449 *3 *4))
+   (-14 *3 (-583 (-1076))) (-4 *4 (-963))))) 
+(((*1 *1 *1 *1) (-12 (-4 *1 (-781 *2)) (-4 *2 (-963)) (-4 *2 (-333))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-333) (-777)))
-   (-5 *2 (-2 (|:| |start| *3) (|:| -1878 (-388 *3))))
-   (-5 *1 (-162 *4 *3)) (-4 *3 (-1132 (-153 *4)))))) 
+  (-12 (-5 *3 (-517)) (|has| *1 (-6 -4183)) (-4 *1 (-374))
+   (-5 *2 (-844))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-333)) (-4 *4 (-509)) (-4 *5 (-1132 *4))
-   (-5 *2 (-2 (|:| -4156 (-564 *4 *5)) (|:| -2305 (-377 *5))))
-   (-5 *1 (-564 *4 *5)) (-5 *3 (-377 *5))))
- ((*1 *2 *1)
-  (-12 (-5 *2 (-583 (-1064 *3 *4))) (-5 *1 (-1064 *3 *4))
-   (-14 *3 (-844)) (-4 *4 (-962))))
- ((*1 *2 *1 *1)
-  (-12 (-4 *3 (-421)) (-4 *3 (-962))
-   (-5 *2 (-2 (|:| |primePart| *1) (|:| |commonPart| *1)))
-   (-4 *1 (-1132 *3))))) 
-(((*1 *1 *1 *2)
-  (-12 (-5 *2 (-583 (-703))) (-5 *1 (-1064 *3 *4)) (-14 *3 (-844))
-   (-4 *4 (-962))))) 
+  (-12 (-4 *4 (-13 (-333) (-954 (-377 *2)))) (-5 *2 (-517))
+   (-5 *1 (-110 *4 *3)) (-4 *3 (-1133 *4))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-358)) (-5 *2 (-1162)) (-5 *1 (-361))))
+ ((*1 *2 *3) (-12 (-5 *3 (-1059)) (-5 *2 (-1162)) (-5 *1 (-361))))) 
+(((*1 *2 *3 *2)
+  (-12 (-5 *3 (-109)) (-4 *4 (-963)) (-5 *1 (-647 *4 *2))
+   (-4 *2 (-585 *4))))
+ ((*1 *2 *3 *2) (-12 (-5 *3 (-109)) (-5 *1 (-766 *2)) (-4 *2 (-963))))) 
+(((*1 *2 *3 *4 *3 *4 *5 *3 *4 *3 *3 *3 *3)
+  (-12 (-5 *4 (-623 (-199))) (-5 *5 (-623 (-517))) (-5 *3 (-517))
+   (-5 *2 (-952)) (-5 *1 (-689))))) 
+(((*1 *2) (-12 (-5 *2 (-583 (-1059))) (-5 *1 (-1160))))) 
+(((*1 *2 *3 *3)
+  (-12 (-5 *3 (-1130 *5 *4)) (-4 *4 (-752)) (-14 *5 (-1076))
+   (-5 *2 (-583 *4)) (-5 *1 (-1019 *4 *5))))) 
+(((*1 *2) (-12 (-4 *1 (-337 *3)) (-4 *3 (-156)) (-5 *2 (-107))))) 
+(((*1 *2 *3 *3)
+  (-12 (-4 *4 (-421)) (-4 *5 (-725)) (-4 *6 (-779))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-107)) (-5 *1 (-907 *4 *5 *6 *7 *3))
+   (-4 *3 (-982 *4 *5 *6 *7))))
+ ((*1 *2 *3 *3)
+  (-12 (-4 *4 (-421)) (-4 *5 (-725)) (-4 *6 (-779))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-107))
+   (-5 *1 (-1012 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))) 
+(((*1 *1 *1) (-12 (-4 *1 (-400 *2)) (-4 *2 (-779)) (-4 *2 (-963))))
+ ((*1 *1 *1) (-12 (-4 *1 (-911 *2)) (-4 *2 (-509))))) 
+(((*1 *2 *3 *3)
+  (-12 (-5 *3 (-1130 *5 *4)) (-4 *4 (-421)) (-4 *4 (-752))
+   (-14 *5 (-1076)) (-5 *2 (-517)) (-5 *1 (-1019 *4 *5))))) 
+(((*1 *2 *1 *3) (-12 (-5 *3 (-1023)) (-5 *2 (-107)) (-5 *1 (-753))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1075)) (|:| |fn| (-286 (-199)))
-     (|:| -2192 (-999 (-772 (-199)))) (|:| |abserr| (-199))
+    (-2 (|:| |var| (-1076)) (|:| |fn| (-286 (-199)))
+     (|:| -2758 (-1000 (-772 (-199)))) (|:| |abserr| (-199))
      (|:| |relerr| (-199))))
    (-5 *2
     (-2
@@ -13407,10 +13281,10 @@
            (|:| |notEvaluated|
                 "End point continuity not yet evaluated")))
      (|:| |singularitiesStream|
-          (-3 (|:| |str| (-1056 (-199)))
+          (-3 (|:| |str| (-1057 (-199)))
            (|:| |notEvaluated|
                 "Internal singularities not yet evaluated")))
-     (|:| -2192
+     (|:| -2758
           (-3 (|:| |finite| "The range is finite")
            (|:| |lowerInfinite| "The bottom of range is infinite")
            (|:| |upperInfinite| "The top of range is infinite")
@@ -13418,745 +13292,668 @@
                 "Both top and bottom points are infinite")
            (|:| |notEvaluated| "Range not yet evaluated")))))
    (-5 *1 (-512))))) 
-(((*1 *2)
-  (-12 (-4 *1 (-312 *3 *4 *5)) (-4 *3 (-1114)) (-4 *4 (-1132 *3))
-   (-4 *5 (-1132 (-377 *4))) (-5 *2 (-107))))) 
-(((*1 *2 *2)
-  (-12 (-4 *3 (-962)) (-4 *4 (-1132 *3)) (-5 *1 (-148 *3 *4 *2))
-   (-4 *2 (-1132 *4))))
- ((*1 *1 *1) (-12 (-5 *1 (-265 *2)) (-4 *2 (-1110))))) 
-(((*1 *2)
-  (-12 (-4 *3 (-509)) (-5 *2 (-583 *4)) (-5 *1 (-42 *3 *4))
-   (-4 *4 (-387 *3))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *3 (-583 (-286 (-199)))) (-5 *4 (-703))
+   (-5 *2 (-623 (-199))) (-5 *1 (-240))))) 
 (((*1 *2 *1 *3 *3)
-  (-12 (-5 *3 (-844)) (-5 *2 (-703)) (-5 *1 (-1005 *4 *5)) (-14 *4 *3)
+  (-12 (-5 *3 (-844)) (-5 *2 (-703)) (-5 *1 (-1006 *4 *5)) (-14 *4 *3)
    (-14 *5 *3)))) 
-(((*1 *2 *3 *4 *5 *6 *7)
-  (-12 (-5 *3 (-1056 (-2 (|:| |k| (-517)) (|:| |c| *6))))
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-(((*1 *2 *2)
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-   (-4 *2 (-13 (-400 *3) (-919)))))) 
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-(((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *2 *2)) (-4 *5 (-333)) (-4 *6 (-1132 (-377 *2)))
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-(((*1 *1 *1 *2) (-12 (-5 *2 (-44 (-1058) (-706))) (-5 *1 (-109))))) 
-(((*1 *2 *3)
-  (-12 (-4 *4 (-509)) (-5 *2 (-1156 (-623 *4))) (-5 *1 (-88 *4 *5))
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-(((*1 *1 *2)
-  (-12 (-5 *2 (-1169 (-1075) *3)) (-4 *3 (-962)) (-5 *1 (-1176 *3))))
- ((*1 *1 *2)
-  (-12 (-5 *2 (-1169 *3 *4)) (-4 *3 (-779)) (-4 *4 (-962))
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-(((*1 *2 *1) (-12 (-5 *2 (-703)) (-5 *1 (-388 *3)) (-4 *3 (-509))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-2 (|:| -3866 *4) (|:| -2769 (-517)))))
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-(((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-509) (-134))) (-5 *1 (-494 *3 *2))
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-  (-12 (-4 *3 (-13 (-333) (-338) (-558 (-517)))) (-4 *4 (-1132 *3))
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- ((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-333) (-338) (-558 (-517)))) (-5 *1 (-499 *3 *2))
-   (-4 *2 (-1147 *3))))
- ((*1 *2 *2)
-  (-12 (-5 *2 (-1056 *3)) (-4 *3 (-13 (-509) (-134)))
-   (-5 *1 (-1052 *3))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-583 (-984 *4 *5 *2))) (-4 *4 (-1004))
-   (-4 *5 (-13 (-962) (-809 *4) (-779) (-558 (-815 *4))))
-   (-4 *2 (-13 (-400 *5) (-809 *4) (-558 (-815 *4))))
-   (-5 *1 (-53 *4 *5 *2))))
- ((*1 *2 *3 *2 *4)
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-   (-4 *6 (-13 (-962) (-809 *5) (-779) (-558 (-815 *5))))
-   (-4 *2 (-13 (-400 *6) (-809 *5) (-558 (-815 *5))))
-   (-5 *1 (-53 *5 *6 *2))))) 
+  (-12 (-5 *2 (-583 *1)) (-5 *3 (-583 *7)) (-4 *1 (-982 *4 *5 *6 *7))
+   (-4 *4 (-421)) (-4 *5 (-725)) (-4 *6 (-779))
+   (-4 *7 (-977 *4 *5 *6))))
+ ((*1 *2 *3 *1)
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-421))
+   (-4 *5 (-725)) (-4 *6 (-779)) (-5 *2 (-583 *1))
+   (-4 *1 (-982 *4 *5 *6 *7))))
+ ((*1 *2 *3 *2)
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+   (-4 *5 (-725)) (-4 *6 (-779)) (-4 *3 (-977 *4 *5 *6))))
+ ((*1 *2 *3 *1)
+  (-12 (-4 *4 (-421)) (-4 *5 (-725)) (-4 *6 (-779))
+   (-4 *3 (-977 *4 *5 *6)) (-5 *2 (-583 *1))
+   (-4 *1 (-982 *4 *5 *6 *3))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-509)) (-5 *2 (-703)) (-5 *1 (-42 *4 *3))
-   (-4 *3 (-387 *4))))) 
-(((*1 *1 *2)
-  (-12 (-5 *2 (-583 (-2 (|:| -2581 (-1075)) (|:| -1860 (-407)))))
-   (-5 *1 (-1079))))) 
-(((*1 *1 *1 *2)
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-   (-4 *4 (-156))))
- ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-703)) (-4 *1 (-1175 *3 *4)) (-4 *3 (-779))
-   (-4 *4 (-962))))) 
+  (-12 (-4 *4 (-13 (-333) (-134) (-954 (-377 (-517)))))
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+   (-5 *2 (-583 (-2 (|:| |deg| (-703)) (|:| -3781 *5))))
+   (-5 *1 (-741 *4 *5 *3 *6)) (-4 *3 (-593 *5))
+   (-4 *6 (-593 (-377 *5)))))) 
+(((*1 *2 *3 *3 *3 *3 *3 *4 *3 *4 *3 *5 *5 *3)
+  (-12 (-5 *3 (-517)) (-5 *4 (-107)) (-5 *5 (-623 (-153 (-199))))
+   (-5 *2 (-952)) (-5 *1 (-688))))) 
+(((*1 *2 *3 *4 *5 *5 *5 *5 *6 *4 *4 *4 *4 *4 *5 *4 *5 *5 *4)
+  (-12 (-5 *3 (-1059)) (-5 *4 (-517)) (-5 *5 (-623 (-199)))
+   (-5 *6 (-199)) (-5 *2 (-952)) (-5 *1 (-685))))) 
+(((*1 *2 *3 *4 *5)
+  (-12 (-5 *4 (-703)) (-5 *5 (-583 *3)) (-4 *3 (-278)) (-4 *6 (-779))
+   (-4 *7 (-725)) (-5 *2 (-107)) (-5 *1 (-566 *6 *7 *3 *8))
+   (-4 *8 (-872 *3 *7 *6))))) 
+(((*1 *2 *1 *3) (-12 (-4 *1 (-33)) (-5 *3 (-703)) (-5 *2 (-107))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-107)) (-5 *1 (-756))))) 
+(((*1 *1 *1) (-5 *1 (-199)))
+ ((*1 *1 *1)
+  (-12 (-5 *1 (-309 *2 *3 *4)) (-14 *2 (-583 (-1076)))
+   (-14 *3 (-583 (-1076))) (-4 *4 (-357))))
+ ((*1 *1 *1) (-5 *1 (-349))) ((*1 *1) (-5 *1 (-349)))) 
+(((*1 *2 *3 *3 *3 *4 *4 *3)
+  (-12 (-5 *3 (-517)) (-5 *4 (-623 (-199))) (-5 *2 (-952))
+   (-5 *1 (-688))))) 
+(((*1 *2 *1 *1)
+  (-12 (-5 *2 (-377 (-875 *3))) (-5 *1 (-422 *3 *4 *5 *6))
+   (-4 *3 (-509)) (-4 *3 (-156)) (-14 *4 (-844))
+   (-14 *5 (-583 (-1076))) (-14 *6 (-1157 (-623 *3)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-779) (-421))) (-5 *1 (-1102 *3 *2))
-   (-4 *2 (-13 (-400 *3) (-1096)))))) 
-(((*1 *2 *3 *2) (-12 (-5 *2 (-199)) (-5 *3 (-703)) (-5 *1 (-200))))
- ((*1 *2 *3 *2)
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- ((*1 *2 *2 *2)
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-   (-4 *2 (-400 *3))))
- ((*1 *1 *1 *1) (-4 *1 (-1039)))) 
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-(((*1 *2 *3 *4 *5 *6 *5 *3 *7)
-  (-12 (-5 *4 (-517))
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-    (-2 (|:| |try| (-349)) (|:| |did| (-349)) (|:| -3462 (-349))))
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-   (-5 *1 (-720))))
- ((*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3)
-  (-12 (-5 *4 (-517))
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-    (-2 (|:| |try| (-349)) (|:| |did| (-349)) (|:| -3462 (-349))))
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-   (-5 *3 (-1156 (-349))) (-5 *5 (-349)) (-5 *2 (-1161))
-   (-5 *1 (-720))))) 
-(((*1 *1) (-5 *1 (-128)))) 
-(((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-421))
-   (-4 *5 (-725)) (-4 *6 (-779)) (-5 *2 (-107))
-   (-5 *1 (-906 *4 *5 *6 *7 *8)) (-4 *8 (-981 *4 *5 *6 *7))))
- ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-976 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-725))
-   (-4 *5 (-779)) (-5 *2 (-107))))
- ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-421))
-   (-4 *5 (-725)) (-4 *6 (-779)) (-5 *2 (-107))
-   (-5 *1 (-1011 *4 *5 *6 *7 *8)) (-4 *8 (-981 *4 *5 *6 *7))))
- ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-1104 *3 *4 *5 *6)) (-4 *3 (-509)) (-4 *4 (-725))
-   (-4 *5 (-779)) (-4 *6 (-976 *3 *4 *5)) (-5 *2 (-107))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-507 *2)) (-4 *2 (-13 (-374) (-1096)))))
- ((*1 *1 *1 *1) (-4 *1 (-725)))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1058)) (-5 *2 (-844)) (-5 *1 (-718))))) 
-(((*1 *2 *3 *4)
-  (-12 (-5 *3 (-199)) (-5 *4 (-517)) (-5 *2 (-951)) (-5 *1 (-691))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-703)) (-5 *1 (-414 *3)) (-4 *3 (-962))))
- ((*1 *2) (-12 (-5 *2 (-703)) (-5 *1 (-414 *3)) (-4 *3 (-962))))) 
-(((*1 *1 *1 *1) (-5 *1 (-787)))) 
+  (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-249 *3 *2))
+   (-4 *2 (-13 (-400 *3) (-920)))))) 
+(((*1 *1 *2)
+  (-12 (-5 *2 (-583 (-2 (|:| -2585 (-1076)) (|:| -1859 (-407)))))
+   (-5 *1 (-1080))))) 
+(((*1 *2 *1 *1) (-12 (-4 *1 (-928 *3)) (-4 *3 (-1111)) (-5 *2 (-517))))) 
 (((*1 *2 *1)
-  (-12
-   (-5 *2
-    (-583
-     (-2
-      (|:| -2581
-           (-2 (|:| |var| (-1075)) (|:| |fn| (-286 (-199)))
-            (|:| -2192 (-999 (-772 (-199)))) (|:| |abserr| (-199))
-            (|:| |relerr| (-199))))
-      (|:| -1860
-           (-2
-            (|:| |endPointContinuity|
-                 (-3 (|:| |continuous| "Continuous at the end points")
-                  (|:| |lowerSingular|
-                       "There is a singularity at the lower end point")
-                  (|:| |upperSingular|
-                       "There is a singularity at the upper end point")
-                  (|:| |bothSingular|
-                       "There are singularities at both end points")
-                  (|:| |notEvaluated|
-                       "End point continuity not yet evaluated")))
-            (|:| |singularitiesStream|
-                 (-3 (|:| |str| (-1056 (-199)))
-                  (|:| |notEvaluated|
-                       "Internal singularities not yet evaluated")))
-            (|:| -2192
-                 (-3 (|:| |finite| "The range is finite")
-                  (|:| |lowerInfinite|
-                       "The bottom of range is infinite")
-                  (|:| |upperInfinite| "The top of range is infinite")
-                  (|:| |bothInfinite|
-                       "Both top and bottom points are infinite")
-                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
-   (-5 *1 (-512))))
+  (-12 (-4 *1 (-150 *3)) (-4 *3 (-156)) (-4 *3 (-502))
+   (-5 *2 (-377 (-517)))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-550 *3 *4)) (-4 *3 (-1004)) (-4 *4 (-1110))
-   (-5 *2 (-583 *4))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-349)) (-5 *2 (-1161)) (-5 *1 (-1158))))) 
-(((*1 *2 *1)
-  (-12 (-5 *2 (-583 (-517))) (-5 *1 (-921 *3)) (-14 *3 (-517))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1161)) (-5 *1 (-754))))) 
-(((*1 *2 *3 *4)
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-   (-4 *7 (-1132 (-377 *6)))
-   (-5 *2 (-2 (|:| |answer| *3) (|:| -3832 *3)))
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- ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1132 *5)) (-4 *5 (-333))
+  (-12 (-5 *2 (-377 (-517))) (-5 *1 (-388 *3)) (-4 *3 (-502))
+   (-4 *3 (-509))))
+ ((*1 *2 *1) (-12 (-4 *1 (-502)) (-5 *2 (-377 (-517)))))
+ ((*1 *2 *1)
+  (-12 (-4 *1 (-729 *3)) (-4 *3 (-156)) (-4 *3 (-502))
+   (-5 *2 (-377 (-517)))))
+ ((*1 *2 *1)
+  (-12 (-5 *2 (-377 (-517))) (-5 *1 (-765 *3)) (-4 *3 (-502))
+   (-4 *3 (-1005))))
+ ((*1 *2 *1)
+  (-12 (-5 *2 (-377 (-517))) (-5 *1 (-772 *3)) (-4 *3 (-502))
+   (-4 *3 (-1005))))
+ ((*1 *2 *1)
+  (-12 (-4 *1 (-915 *3)) (-4 *3 (-156)) (-4 *3 (-502))
+   (-5 *2 (-377 (-517)))))
+ ((*1 *2 *3)
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+(((*1 *1 *1) (-12 (-4 *1 (-150 *2)) (-4 *2 (-156))))
+ ((*1 *1 *1 *1) (-4 *1 (-442)))
+ ((*1 *1 *1) (-12 (-4 *1 (-729 *2)) (-4 *2 (-156))))
+ ((*1 *2 *2) (-12 (-5 *2 (-583 (-517))) (-5 *1 (-806))))
+ ((*1 *1 *1) (-5 *1 (-890)))
+ ((*1 *1 *1) (-12 (-4 *1 (-915 *2)) (-4 *2 (-156))))) 
+(((*1 *2 *2 *3)
+  (-12
    (-5 *2
-    (-2 (|:| |answer| (-377 *6)) (|:| -3832 (-377 *6))
-     (|:| |specpart| (-377 *6)) (|:| |polypart| *6)))
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-(((*1 *1 *1 *1) (-12 (-4 *1 (-1002 *2)) (-4 *2 (-1004))))) 
-(((*1 *2 *2 *1)
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-   (-4 *4 (-725)) (-4 *5 (-779)) (-4 *6 (-976 *3 *4 *5))
-   (-4 *3 (-509))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-844)) (-5 *2 (-827 (-517))) (-5 *1 (-840))))
+    (-2 (|:| |partsol| (-1157 (-377 (-875 *4))))
+     (|:| -1492 (-583 (-1157 (-377 (-875 *4)))))))
+   (-5 *3 (-583 *7)) (-4 *4 (-13 (-278) (-134)))
+   (-4 *7 (-872 *4 *6 *5)) (-4 *5 (-13 (-779) (-558 (-1076))))
+   (-4 *6 (-725)) (-5 *1 (-847 *4 *5 *6 *7))))) 
+(((*1 *2 *1 *2) (-12 (-5 *2 (-583 (-1059))) (-5 *1 (-364))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-1000 (-772 (-199)))) (-5 *2 (-199)) (-5 *1 (-168))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-517))) (-5 *2 (-827 (-517))) (-5 *1 (-840))))) 
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@@ -14172,232 +13969,263 @@
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    (-4 *2 (|SubsetCategory| (-659) *4))))
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       (-14 *5 (-703))))
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 (((*1 *2 *3)
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 (((*1 *1 *1) (-4 *1 (-34)))
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 (((*1 *1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1) (-4 *1 (-21)))
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  ((*1 *2 *3 *4 *2)
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  ((*1 *2 *3 *4 *2)
-  (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-962)) (-4 *2 (-962))
+  (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-963)) (-4 *2 (-963))
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    (-4 *4 (-621 *5 *6 *7)) (-4 *10 (-621 *2 *8 *9))))
@@ -15335,945 +15155,1024 @@
    (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
    (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))
  ((*1 *1 *2)
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   (-12 (-5 *1 (-648 *2 *3 *4 *5 *6)) (-4 *2 (-156)) (-4 *3 (-23))
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    (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))
  ((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-377 *4)) (-4 *4 (-1132 *3)) (-4 *3 (-333))
+  (|partial| -12 (-5 *2 (-377 *4)) (-4 *4 (-1133 *3)) (-4 *3 (-333))
       (-4 *3 (-156)) (-4 *1 (-657 *3 *4))))
  ((*1 *1 *2)
-  (-12 (-4 *3 (-156)) (-4 *1 (-657 *3 *2)) (-4 *2 (-1132 *3))))
+  (-12 (-4 *3 (-156)) (-4 *1 (-657 *3 *2)) (-4 *2 (-1133 *3))))
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   (-12 (-4 *3 (-333)) (-4 *4 (-725)) (-4 *5 (-779))
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    (-14 *6 (-583 *2))))
  ((*1 *2 *3 *4 *2)
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+   (-5 *1 (-968 *5 *6 *7 *8 *9 *4 *2 *10 *11 *12))
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-(((*1 *2 *3 *4 *5 *6)
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-   (-5 *2 (-2 (|:| |plist| (-583 *3)) (|:| |modulo| *5)))
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+  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-1157 *5)) (-4 *5 (-1111))
+   (-4 *2 (-1111)) (-5 *1 (-1156 *5 *2))))) 
+(((*1 *2 *3)
+  (-12 (-4 *4 (-1111)) (-5 *2 (-703)) (-5 *1 (-163 *4 *3))
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 (((*1 *2 *2)
   (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-249 *3 *2))
-   (-4 *2 (-13 (-400 *3) (-919)))))
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    (-5 *1 (-1062 *3))))
- ((*1 *1 *1) (-4 *1 (-1099)))) 
+ ((*1 *2 *2)
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+   (-4 *3 (-781 *5))))) 
 (((*1 *2 *3 *4)
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-     (|:| |fail| "failed") (|:| |pole| "potentialPole")))
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+ ((*1 *2 *3 *4)
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+      (-5 *2 (-2 (|:| |particular| *4) (|:| -1492 (-583 *4))))
+      (-5 *1 (-589 *6 *4 *3)) (-4 *3 (-593 *4))))
+ ((*1 *2 *3 *2 *4 *2 *5)
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-     (|:| |fail| "failed") (|:| |pole| "potentialPole")))
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+  (|partial| -12 (-5 *3 (-109)) (-5 *4 (-1076))
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- ((*1 *2 *3 *4 *5 *5 *6)
-  (-12 (-5 *3 (-286 (-349))) (-5 *4 (-583 (-999 (-772 (-349)))))
-   (-5 *5 (-349)) (-5 *6 (-974)) (-5 *2 (-951)) (-5 *1 (-518))))
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-      (-5 *5 (-1058)) (-5 *2 (-951)) (-5 *1 (-518))))
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+     (|:| |relerr| (-199))))
+   (-5 *2
+    (-3 (|:| |continuous| "Continuous at the end points")
+     (|:| |lowerSingular|
+          "There is a singularity at the lower end point")
+     (|:| |upperSingular|
+          "There is a singularity at the upper end point")
+     (|:| |bothSingular| "There are singularities at both end points")
+     (|:| |notEvaluated| "End point continuity not yet evaluated")))
+   (-5 *1 (-168))))) 
 (((*1 *2 *2)
   (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-249 *3 *2))
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+ ((*1 *1 *1 *1)
+  (-12 (-4 *2 (-156)) (-4 *2 (-963)) (-5 *1 (-647 *2 *3))
+   (-4 *3 (-585 *2))))
+ ((*1 *1 *1)
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 (((*1 *2 *3)
   (-12 (-5 *2 (-153 (-349))) (-5 *1 (-717 *3)) (-4 *3 (-558 (-349)))))
  ((*1 *2 *3 *4)
@@ -16292,10 +16191,10 @@
   (-12 (-5 *3 (-875 (-153 *5))) (-5 *4 (-844)) (-4 *5 (-156))
    (-4 *5 (-558 (-349))) (-5 *2 (-153 (-349))) (-5 *1 (-717 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-875 *4)) (-4 *4 (-962)) (-4 *4 (-558 (-349)))
+  (-12 (-5 *3 (-875 *4)) (-4 *4 (-963)) (-4 *4 (-558 (-349)))
    (-5 *2 (-153 (-349))) (-5 *1 (-717 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-875 *5)) (-5 *4 (-844)) (-4 *5 (-962))
+  (-12 (-5 *3 (-875 *5)) (-5 *4 (-844)) (-4 *5 (-963))
    (-4 *5 (-558 (-349))) (-5 *2 (-153 (-349))) (-5 *1 (-717 *5))))
  ((*1 *2 *3)
   (-12 (-5 *3 (-377 (-875 *4))) (-4 *4 (-509)) (-4 *4 (-558 (-349)))
@@ -16322,550 +16221,619 @@
   (-12 (-5 *3 (-286 (-153 *5))) (-5 *4 (-844)) (-4 *5 (-509))
    (-4 *5 (-779)) (-4 *5 (-558 (-349))) (-5 *2 (-153 (-349)))
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-   (-5 *2 (-951)) (-5 *1 (-682))))) 
+(((*1 *2 *3)
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+ ((*1 *2 *3 *1)
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 (((*1 *1 *2 *3) (-12 (-5 *2 (-109)) (-5 *3 (-583 *1)) (-4 *1 (-273))))
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 (((*1 *2 *3)
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 (((*1 *2 *2)
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 (((*1 *2 *3 *3)
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 (((*1 *2 *3)
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+  (-12 (-5 *2 (-583 *3)) (-5 *5 (-844)) (-4 *3 (-1133 *4))
+   (-4 *4 (-278)) (-5 *1 (-429 *4 *3))))) 
+(((*1 *2)
+  (-12 (-4 *1 (-312 *3 *4 *5)) (-4 *3 (-1115)) (-4 *4 (-1133 *3))
+   (-4 *5 (-1133 (-377 *4))) (-5 *2 (-107))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-583 (-517))) (-5 *2 (-703)) (-5 *1 (-538))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-583 (-583 (-703)))) (-5 *1 (-827 *3)) (-4 *3 (-1004))))) 
+  (-12 (-4 *1 (-977 *3 *4 *5)) (-4 *3 (-963)) (-4 *4 (-725))
+   (-4 *5 (-779)) (-5 *2 (-703))))) 
+(((*1 *2 *2) (|partial| -12 (-4 *1 (-902 *2)) (-4 *2 (-1097))))) 
+(((*1 *2 *3 *3 *4)
+  (-12 (-5 *4 (-703)) (-4 *5 (-509))
+   (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3)))
+   (-5 *1 (-889 *5 *3)) (-4 *3 (-1133 *5))))) 
 (((*1 *1 *1 *1 *2)
-  (-12 (-5 *2 (-1 *3 *3 *3 *3 *3)) (-4 *3 (-1004)) (-5 *1 (-98 *3))))
- ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-1 *2 *2 *2)) (-5 *1 (-98 *2)) (-4 *2 (-1004))))) 
-(((*1 *2 *1) (-12 (-5 *1 (-534 *2)) (-4 *2 (-333))))) 
+  (-12 (-5 *2 (-703)) (-4 *1 (-977 *3 *4 *5)) (-4 *3 (-963))
+   (-4 *4 (-725)) (-4 *5 (-779)) (-4 *3 (-509))))) 
+(((*1 *2 *2) (|partial| -12 (-4 *1 (-902 *2)) (-4 *2 (-1097))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1162)) (-5 *1 (-754))))) 
+(((*1 *2 *2)
+  (-12 (-5 *2 (-583 (-2 (|:| |val| (-583 *6)) (|:| -3834 *7))))
+   (-4 *6 (-977 *3 *4 *5)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-421))
+   (-4 *4 (-725)) (-4 *5 (-779)) (-5 *1 (-907 *3 *4 *5 *6 *7))))
+ ((*1 *2 *2)
+  (-12 (-5 *2 (-583 (-2 (|:| |val| (-583 *6)) (|:| -3834 *7))))
+   (-4 *6 (-977 *3 *4 *5)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-421))
+   (-4 *4 (-725)) (-4 *5 (-779)) (-5 *1 (-1012 *3 *4 *5 *6 *7))))) 
+(((*1 *2)
+  (-12 (-5 *2 (-107)) (-5 *1 (-1089 *3 *4)) (-4 *3 (-1005))
+   (-4 *4 (-1005))))) 
+(((*1 *2)
+  (-12 (-4 *4 (-333)) (-5 *2 (-703)) (-5 *1 (-298 *3 *4))
+   (-4 *3 (-299 *4))))
+ ((*1 *2) (-12 (-4 *1 (-1174 *3)) (-4 *3 (-333)) (-5 *2 (-703))))) 
+(((*1 *1) (-4 *1 (-319)))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-583 *5)) (-4 *5 (-400 *4))
+   (-4 *4 (-13 (-509) (-779) (-134)))
+   (-5 *2
+    (-2 (|:| |primelt| *5) (|:| |poly| (-583 (-1072 *5)))
+     (|:| |prim| (-1072 *5))))
+   (-5 *1 (-402 *4 *5))))
+ ((*1 *2 *3 *3)
+  (-12 (-4 *4 (-13 (-509) (-779) (-134)))
+   (-5 *2
+    (-2 (|:| |primelt| *3) (|:| |pol1| (-1072 *3))
+     (|:| |pol2| (-1072 *3)) (|:| |prim| (-1072 *3))))
+   (-5 *1 (-402 *4 *3)) (-4 *3 (-27)) (-4 *3 (-400 *4))))
+ ((*1 *2 *3 *4 *3 *4)
+  (-12 (-5 *3 (-875 *5)) (-5 *4 (-1076)) (-4 *5 (-13 (-333) (-134)))
+   (-5 *2
+    (-2 (|:| |coef1| (-517)) (|:| |coef2| (-517))
+     (|:| |prim| (-1072 *5))))
+   (-5 *1 (-882 *5))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-583 (-875 *5))) (-5 *4 (-583 (-1076)))
+   (-4 *5 (-13 (-333) (-134)))
+   (-5 *2
+    (-2 (|:| -1582 (-583 (-517))) (|:| |poly| (-583 (-1072 *5)))
+     (|:| |prim| (-1072 *5))))
+   (-5 *1 (-882 *5))))
+ ((*1 *2 *3 *4 *5)
+  (-12 (-5 *3 (-583 (-875 *6))) (-5 *4 (-583 (-1076))) (-5 *5 (-1076))
+   (-4 *6 (-13 (-333) (-134)))
+   (-5 *2
+    (-2 (|:| -1582 (-583 (-517))) (|:| |poly| (-583 (-1072 *6)))
+     (|:| |prim| (-1072 *6))))
+   (-5 *1 (-882 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-517)) (-4 *4 (-725)) (-4 *5 (-779)) (-4 *2 (-962))
-   (-5 *1 (-291 *4 *5 *2 *6)) (-4 *6 (-872 *2 *4 *5))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-877)) (-5 *2 (-583 (-583 (-866 (-199)))))))
- ((*1 *2 *1) (-12 (-4 *1 (-892)) (-5 *2 (-583 (-583 (-866 (-199)))))))) 
-(((*1 *2 *1 *1 *3 *4)
-  (-12 (-5 *3 (-1 (-107) *5 *5)) (-5 *4 (-1 (-107) *6 *6))
-   (-4 *5 (-13 (-1004) (-33))) (-4 *6 (-13 (-1004) (-33)))
-   (-5 *2 (-107)) (-5 *1 (-1040 *5 *6))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-107)) (-5 *1 (-125))))) 
+  (-12 (-4 *4 (-13 (-509) (-779) (-954 (-517)))) (-4 *5 (-400 *4))
+   (-5 *2 (-388 *3)) (-5 *1 (-405 *4 *5 *3)) (-4 *3 (-1133 *5))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-703)) (-5 *2 (-1129 *5 *4)) (-5 *1 (-1073 *4 *5 *6))
-   (-4 *4 (-962)) (-14 *5 (-1075)) (-14 *6 *4)))
- ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-703)) (-5 *2 (-1129 *5 *4)) (-5 *1 (-1148 *4 *5 *6))
-   (-4 *4 (-962)) (-14 *5 (-1075)) (-14 *6 *4)))) 
-(((*1 *2 *3 *4 *4 *2 *2 *2)
-  (-12 (-5 *2 (-517))
-   (-5 *3
-    (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-703)) (|:| |poli| *4)
-     (|:| |polj| *4)))
-   (-4 *6 (-725)) (-4 *4 (-872 *5 *6 *7)) (-4 *5 (-421)) (-4 *7 (-779))
-   (-5 *1 (-418 *5 *6 *7 *4))))) 
-(((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-779) (-421))) (-5 *1 (-1102 *3 *2))
-   (-4 *2 (-13 (-400 *3) (-1096)))))) 
-(((*1 *1 *1 *1) (-4 *1 (-130)))
+  (-12 (-5 *3 (-583 *6)) (-4 *1 (-872 *4 *5 *6)) (-4 *4 (-963))
+   (-4 *5 (-725)) (-4 *6 (-779)) (-5 *2 (-703))))
+ ((*1 *2 *1)
+  (-12 (-4 *1 (-872 *3 *4 *5)) (-4 *3 (-963)) (-4 *4 (-725))
+   (-4 *5 (-779)) (-5 *2 (-703))))) 
+(((*1 *2 *3 *2)
+  (-12 (-4 *2 (-13 (-333) (-777))) (-5 *1 (-162 *2 *3))
+   (-4 *3 (-1133 (-153 *2)))))
+ ((*1 *2 *3)
+  (-12 (-4 *2 (-13 (-333) (-777))) (-5 *1 (-162 *2 *3))
+   (-4 *3 (-1133 (-153 *2)))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *4 (-583 *3)) (-4 *3 (-872 *5 *6 *7)) (-4 *5 (-421))
+   (-4 *6 (-725)) (-4 *7 (-779))
+   (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5)))
+   (-5 *1 (-418 *5 *6 *7 *3))))) 
+(((*1 *2 *3)
+  (-12 (-5 *2 (-1 (-866 *3) (-866 *3))) (-5 *1 (-158 *3))
+   (-4 *3 (-13 (-333) (-1097) (-920)))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-199)) (-5 *1 (-200))))
+ ((*1 *2 *2 *2) (-12 (-5 *2 (-153 (-199))) (-5 *1 (-200))))
  ((*1 *2 *2 *2)
-  (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-143 *3 *2))
+  (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-401 *3 *2))
    (-4 *2 (-400 *3))))
- ((*1 *2 *2 *2) (-12 (-5 *1 (-144 *2)) (-4 *2 (-502))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1058)) (-5 *2 (-1161)) (-5 *1 (-1158))))) 
-(((*1 *2 *1)
-  (-12 (-4 *1 (-352 *3 *4)) (-4 *3 (-962)) (-4 *4 (-1004))
-   (-5 *2 (-2 (|:| |k| *4) (|:| |c| *3)))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-703)) (-5 *1 (-248))))) 
-(((*1 *2 *2 *3) (-12 (-5 *2 (-517)) (-5 *3 (-703)) (-5 *1 (-514))))) 
-(((*1 *1 *1 *1) (-12 (-4 *1 (-781 *2)) (-4 *2 (-962)) (-4 *2 (-333))))) 
-(((*1 *2 *1 *3)
-  (-12 (-5 *2 (-583 (-1058))) (-5 *1 (-974)) (-5 *3 (-1058))))) 
+ ((*1 *1 *1 *1) (-4 *1 (-1040)))) 
+(((*1 *2 *3 *3 *3 *3 *3 *3 *3 *3 *4 *5 *5 *5 *5 *5 *5 *6 *6 *6 *3 *3 *5
+      *7 *3 *8)
+  (-12 (-5 *5 (-623 (-199))) (-5 *6 (-107)) (-5 *7 (-623 (-517)))
+   (-5 *8 (-3 (|:| |fn| (-358)) (|:| |fp| (-63 QPHESS))))
+   (-5 *3 (-517)) (-5 *4 (-199)) (-5 *2 (-952)) (-5 *1 (-686))))) 
+(((*1 *1 *2)
+  (-12 (-5 *2 (-623 *5)) (-4 *5 (-963)) (-5 *1 (-967 *3 *4 *5))
+   (-14 *3 (-703)) (-14 *4 (-703))))) 
+(((*1 *2 *3)
+  (-12 (-5 *2 (-1 *3 *4)) (-5 *1 (-617 *4 *3)) (-4 *4 (-1005))
+   (-4 *3 (-1005))))) 
+(((*1 *2) (-12 (-5 *2 (-107)) (-5 *1 (-125))))) 
 (((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-517)) (-4 *1 (-621 *3 *4 *5)) (-4 *3 (-962))
-   (-4 *4 (-343 *3)) (-4 *5 (-343 *3))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1075)) (-5 *2 (-107)) (-5 *1 (-109))))
- ((*1 *2 *1 *3) (-12 (-4 *1 (-273)) (-5 *3 (-1075)) (-5 *2 (-107))))
- ((*1 *2 *1 *3) (-12 (-4 *1 (-273)) (-5 *3 (-109)) (-5 *2 (-107))))
- ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-1075)) (-5 *2 (-107)) (-5 *1 (-556 *4)) (-4 *4 (-779))))
- ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-109)) (-5 *2 (-107)) (-5 *1 (-556 *4)) (-4 *4 (-779))))
- ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-1004)) (-5 *2 (-107)) (-5 *1 (-810 *5 *3 *4))
-   (-4 *3 (-809 *5)) (-4 *4 (-558 (-815 *5)))))
- ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 *6)) (-4 *6 (-809 *5)) (-4 *5 (-1004))
-   (-5 *2 (-107)) (-5 *1 (-810 *5 *6 *4)) (-4 *4 (-558 (-815 *5)))))) 
-(((*1 *1 *1 *1)
-  (-12 (|has| *1 (-6 -4191)) (-4 *1 (-114 *2)) (-4 *2 (-1110))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-377 (-517))) (-5 *1 (-103))))
- ((*1 *2 *1) (-12 (-5 *2 (-377 (-517))) (-5 *1 (-192))))
- ((*1 *2 *1) (-12 (-5 *2 (-377 (-517))) (-5 *1 (-454))))
- ((*1 *1 *1) (-12 (-4 *1 (-910 *2)) (-4 *2 (-509)) (-4 *2 (-278))))
- ((*1 *2 *1)
-  (-12 (-5 *2 (-377 (-517))) (-5 *1 (-921 *3)) (-14 *3 (-517))))
- ((*1 *1 *1) (-4 *1 (-971)))) 
-(((*1 *1 *2 *1)
-  (-12 (-5 *1 (-586 *2 *3 *4)) (-4 *2 (-1004)) (-4 *3 (-23))
-   (-14 *4 *3)))) 
-(((*1 *2)
-  (-12 (-4 *4 (-156)) (-5 *2 (-107)) (-5 *1 (-336 *3 *4))
-   (-4 *3 (-337 *4))))
- ((*1 *2) (-12 (-4 *1 (-337 *3)) (-4 *3 (-156)) (-5 *2 (-107))))) 
-(((*1 *2 *3 *3)
-  (-12 (-4 *4 (-962)) (-4 *2 (-621 *4 *5 *6))
-   (-5 *1 (-99 *4 *3 *2 *5 *6)) (-4 *3 (-1132 *4)) (-4 *5 (-343 *4))
-   (-4 *6 (-343 *4))))) 
+  (-12 (-5 *2 (-517)) (-5 *1 (-127 *3 *4 *5)) (-14 *3 *2)
+   (-14 *4 (-703)) (-4 *5 (-156))))
+ ((*1 *1 *1)
+  (-12 (-5 *1 (-127 *2 *3 *4)) (-14 *2 (-517)) (-14 *3 (-703))
+   (-4 *4 (-156))))
+ ((*1 *1 *1)
+  (-12 (-4 *1 (-621 *2 *3 *4)) (-4 *2 (-963)) (-4 *3 (-343 *2))
+   (-4 *4 (-343 *2))))
+ ((*1 *1 *2)
+  (-12 (-4 *3 (-963)) (-4 *1 (-621 *3 *2 *4)) (-4 *2 (-343 *3))
+   (-4 *4 (-343 *3))))
+ ((*1 *1 *1)
+  (-12 (-5 *1 (-1043 *2 *3)) (-14 *2 (-703)) (-4 *3 (-963))))) 
+(((*1 *2 *1 *3)
+  (-12 (-5 *3 (-1157 *1)) (-4 *1 (-337 *4)) (-4 *4 (-156))
+   (-5 *2 (-623 *4))))
+ ((*1 *2 *1) (-12 (-4 *1 (-387 *3)) (-4 *3 (-156)) (-5 *2 (-623 *3))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1133 *5)) (-4 *5 (-333))
+   (-5 *2 (-2 (|:| -1387 (-388 *3)) (|:| |special| (-388 *3))))
+   (-5 *1 (-660 *5 *3))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-199)) (-5 *1 (-230))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-1037 *3)) (-4 *3 (-963)) (-5 *2 (-107))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-286 (-349))) (-5 *2 (-286 (-199))) (-5 *1 (-276))))) 
+(((*1 *2 *2) (|partial| -12 (-4 *1 (-902 *2)) (-4 *2 (-1097))))) 
+(((*1 *2 *3)
+  (-12 (-4 *4 (-509)) (-4 *5 (-725)) (-4 *6 (-779))
+   (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-2 (|:| |goodPols| (-583 *7)) (|:| |badPols| (-583 *7))))
+   (-5 *1 (-896 *4 *5 *6 *7)) (-5 *3 (-583 *7))))) 
 (((*1 *2 *3)
   (|partial| -12
       (-5 *3
-       (-2 (|:| |var| (-1075)) (|:| |fn| (-286 (-199)))
-        (|:| -2192 (-999 (-772 (-199)))) (|:| |abserr| (-199))
+       (-2 (|:| |var| (-1076)) (|:| |fn| (-286 (-199)))
+        (|:| -2758 (-1000 (-772 (-199)))) (|:| |abserr| (-199))
         (|:| |relerr| (-199))))
       (-5 *2
        (-2
@@ -16880,10 +16848,10 @@
               (|:| |notEvaluated|
                    "End point continuity not yet evaluated")))
         (|:| |singularitiesStream|
-             (-3 (|:| |str| (-1056 (-199)))
+             (-3 (|:| |str| (-1057 (-199)))
               (|:| |notEvaluated|
                    "Internal singularities not yet evaluated")))
-        (|:| -2192
+        (|:| -2758
              (-3 (|:| |finite| "The range is finite")
               (|:| |lowerInfinite| "The bottom of range is infinite")
               (|:| |upperInfinite| "The top of range is infinite")
@@ -16891,1146 +16859,1192 @@
                    "Both top and bottom points are infinite")
               (|:| |notEvaluated| "Range not yet evaluated")))))
       (-5 *1 (-512))))) 
-(((*1 *2 *3 *4)
-  (-12 (-5 *3 (-844)) (-5 *4 (-388 *6)) (-4 *6 (-1132 *5))
-   (-4 *5 (-962)) (-5 *2 (-583 *6)) (-5 *1 (-413 *5 *6))))) 
-(((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1132 *6))
-   (-4 *6 (-13 (-27) (-400 *5)))
-   (-4 *5 (-13 (-779) (-509) (-953 (-517)))) (-4 *8 (-1132 (-377 *7)))
-   (-5 *2 (-534 *3)) (-5 *1 (-505 *5 *6 *7 *8 *3))
-   (-4 *3 (-312 *6 *7 *8))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-844)) (-5 *2 (-437)) (-5 *1 (-1157))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-337 *3)) (-4 *3 (-156)) (-5 *2 (-1072 *3))))) 
+(((*1 *1 *1)
+  (-12 (-5 *1 (-542 *2)) (-4 *2 (-37 (-377 (-517)))) (-4 *2 (-963))))) 
+(((*1 *2) (-12 (-5 *2 (-1076)) (-5 *1 (-1079))))) 
+(((*1 *2 *2)
+  (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-401 *3 *2))
+   (-4 *2 (-400 *3))))) 
+(((*1 *2 *3 *4 *5 *5 *4 *6)
+  (-12 (-5 *4 (-517)) (-5 *6 (-1 (-1162) (-1157 *5) (-1157 *5) (-349)))
+   (-5 *3 (-1157 (-349))) (-5 *5 (-349)) (-5 *2 (-1162))
+   (-5 *1 (-720))))) 
+(((*1 *2 *2)
+  (-12 (-4 *3 (-13 (-779) (-421))) (-5 *1 (-1103 *3 *2))
+   (-4 *2 (-13 (-400 *3) (-1097)))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-377 *5)) (-4 *5 (-1133 *4)) (-4 *4 (-509))
+   (-4 *4 (-963)) (-4 *2 (-1148 *4)) (-5 *1 (-1151 *4 *5 *6 *2))
+   (-4 *6 (-593 *5))))) 
+(((*1 *2 *3 *2)
+  (-12 (-5 *3 (-377 (-517)))
+   (-4 *4 (-13 (-509) (-779) (-954 (-517)) (-579 (-517))))
+   (-5 *1 (-250 *4 *2)) (-4 *2 (-13 (-27) (-1097) (-400 *4)))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-517))) (-5 *1 (-961))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-844)) (-5 *2 (-1059)) (-5 *1 (-718))))) 
+(((*1 *1) (-5 *1 (-407)))) 
+(((*1 *2 *3)
+  (-12 (-5 *2 (-107)) (-5 *1 (-115 *3)) (-4 *3 (-1133 (-517)))))
+ ((*1 *2 *3 *2)
+  (-12 (-5 *2 (-107)) (-5 *1 (-115 *3)) (-4 *3 (-1133 (-517)))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-793 *3)) (-5 *2 (-517))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-509))
-   (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2272 *4)))
-   (-5 *1 (-888 *4 *3)) (-4 *3 (-1132 *4))))) 
-(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *4 *5)
-  (-12 (-5 *3 (-199)) (-5 *4 (-517))
-   (-5 *5 (-3 (|:| |fn| (-358)) (|:| |fp| (-62 G)))) (-5 *2 (-951))
-   (-5 *1 (-681))))) 
-(((*1 *2 *3 *3 *3 *4 *5 *4 *6)
-  (-12 (-5 *3 (-286 (-517))) (-5 *4 (-1 (-199) (-199)))
-   (-5 *5 (-999 (-199))) (-5 *6 (-517)) (-5 *2 (-1106 (-849)))
-   (-5 *1 (-288))))
- ((*1 *2 *3 *3 *3 *4 *5 *4 *6 *7)
-  (-12 (-5 *3 (-286 (-517))) (-5 *4 (-1 (-199) (-199)))
-   (-5 *5 (-999 (-199))) (-5 *6 (-517)) (-5 *7 (-1058))
-   (-5 *2 (-1106 (-849))) (-5 *1 (-288))))
- ((*1 *2 *3 *3 *3 *4 *5 *6 *7)
-  (-12 (-5 *3 (-286 (-517))) (-5 *4 (-1 (-199) (-199)))
-   (-5 *5 (-999 (-199))) (-5 *6 (-199)) (-5 *7 (-517))
-   (-5 *2 (-1106 (-849))) (-5 *1 (-288))))
- ((*1 *2 *3 *3 *3 *4 *5 *6 *7 *8)
-  (-12 (-5 *3 (-286 (-517))) (-5 *4 (-1 (-199) (-199)))
-   (-5 *5 (-999 (-199))) (-5 *6 (-199)) (-5 *7 (-517)) (-5 *8 (-1058))
-   (-5 *2 (-1106 (-849))) (-5 *1 (-288))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1075)) (-5 *2 (-1161)) (-5 *1 (-1078))))
- ((*1 *2) (-12 (-5 *2 (-1161)) (-5 *1 (-1078))))) 
-(((*1 *2 *2) (|partial| -12 (-4 *1 (-901 *2)) (-4 *2 (-1096))))) 
-(((*1 *1 *1) (-12 (-5 *1 (-388 *2)) (-4 *2 (-509))))) 
-(((*1 *2)
-  (-12 (-4 *3 (-509)) (-5 *2 (-583 *4)) (-5 *1 (-42 *3 *4))
-   (-4 *4 (-387 *3))))) 
-(((*1 *1 *2)
-  (-12 (-5 *2 (-583 *6)) (-4 *6 (-872 *3 *4 *5)) (-4 *3 (-333))
-   (-4 *4 (-725)) (-4 *5 (-779)) (-5 *1 (-469 *3 *4 *5 *6))))) 
-(((*1 *1 *1) (-12 (-5 *1 (-265 *2)) (-4 *2 (-21)) (-4 *2 (-1110))))) 
-(((*1 *2 *3 *3 *3 *4 *3 *3 *4 *4 *4 *5)
-  (-12 (-5 *3 (-199)) (-5 *4 (-517))
-   (-5 *5 (-3 (|:| |fn| (-358)) (|:| |fp| (-62 G)))) (-5 *2 (-951))
-   (-5 *1 (-681))))) 
-(((*1 *1 *1 *1)
-  (-12 (|has| *1 (-6 -4191)) (-4 *1 (-114 *2)) (-4 *2 (-1110))))) 
-(((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1058)) (-4 *4 (-421)) (-4 *5 (-725)) (-4 *6 (-779))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1161))
-   (-5 *1 (-906 *4 *5 *6 *7 *8)) (-4 *8 (-981 *4 *5 *6 *7))))
- ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1058)) (-4 *4 (-421)) (-4 *5 (-725)) (-4 *6 (-779))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1161))
-   (-5 *1 (-1011 *4 *5 *6 *7 *8)) (-4 *8 (-981 *4 *5 *6 *7))))) 
+  (-12
+   (-5 *3
+    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-703)) (|:| |poli| *7)
+     (|:| |polj| *7)))
+   (-4 *5 (-725)) (-4 *7 (-872 *4 *5 *6)) (-4 *4 (-421)) (-4 *6 (-779))
+   (-5 *2 (-107)) (-5 *1 (-418 *4 *5 *6 *7))))) 
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\ No newline at end of file
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+ (-4041 . 23185) (-4042 . 23074) (-4043 . 22958) (-4044 . 22905)
+ (-4045 . 22854) (-4046 . 22802) (-4047 . 22701) (-4048 . 22634)
+ (-4049 . 22579) (-4050 . 22506) (-4051 . 22279) (-4052 . 21907)
+ (-4053 . 21855) (-4054 . 21554) (-4055 . 21523) (-4056 . 21365)
+ (-4057 . 21152) (-4058 . 21067) (-4059 . 20975) (-4060 . 20879)
+ (-4061 . 20754) (-4062 . 20288) (-4063 . 20109) (-4064 . 19930)
+ (-4065 . 19830) (-4066 . 19777) (-4067 . 19743) (-4068 . 19687)
+ (-4069 . 19617) (-4070 . 19551) (-4071 . 19203) (-4072 . 19150)
+ (-4073 . 18791) (-4074 . 18763) (-4075 . 18570) (-4076 . 18443)
+ (-4077 . 18204) (-4078 . 17929) (-4079 . 17806) (-4080 . 17651)
+ (-4081 . 17481) (-4082 . 17363) (-4083 . 17189) (-4084 . 16909)
+ (-4085 . 16469) (-4086 . 16416) (-4087 . 16168) (-4088 . 16034)
+ (-4089 . 15846) (-4090 . 15543) (-4091 . 15439) (-4092 . 15387)
+ (-4093 . 15259) (-4094 . 15173) (-4095 . 15145) (-4096 . 14631)
+ (-4097 . 14077) (-4098 . 13885) (-4099 . 13029) (-4100 . 12848)
+ (-4101 . 12758) (-4102 . 12654) (-4103 . 12602) (-4104 . 12336)
+ (-4105 . 12253) (-4106 . 11955) (-4107 . 11831) (-4108 . 11660)
+ (-4109 . 11577) (-4110 . 10953) (-4111 . 10775) (-4112 . 10584)
+ (-4113 . 10528) (-4114 . 10305) (-4115 . 10184) (-4116 . 10129)
+ (-4117 . 8278) (-4118 . 7981) (-4119 . 7915) (-4120 . 7819)
+ (-4121 . 7747) (-4122 . 7610) (-4123 . 7231) (-4124 . 7175)
+ (-4125 . 6977) (-4126 . 6833) (-4127 . 6540) (-4128 . 6439)
+ (-4129 . 6370) (-4130 . 6186) (-4131 . 6087) (-4132 . 5741)
+ (-4133 . 5660) (-4134 . 5492) (-4135 . 5314) (-4136 . 5168)
+ (-4137 . 4929) (-4138 . 4834) (-4139 . 4653) (-4140 . 4512)
+ (-4141 . 4217) (-4142 . 4139) (-4143 . 4008) (-4144 . 3947)
+ (-4145 . 3794) (-4146 . 3657) (-4147 . 3504) (-4148 . 3420)
+ (-4149 . 3274) (-4150 . 3203) (-4151 . 3154) (-4152 . 2956)
+ (-4153 . 2762) (-4154 . 2615) (-4155 . 2397) (-4156 . 2275)
+ (-4157 . 2193) (-4158 . 2141) (-4159 . 2015) (-4160 . 1935)
+ (-4161 . 1826) (-4162 . 1691) (-4163 . 1638) (-4164 . 1495)
+ (-4165 . 1443) (-4166 . 1204) (-4167 . 1052) (-4168 . 928)
+ (-4169 . 810) (-4170 . 373) (-4171 . 293) (-4172 . 30)) 
\ No newline at end of file