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## [Axiom-developer] 20090220.01.tpd.patch (regression test )d op, )frame )

 From: daly Subject: [Axiom-developer] 20090220.01.tpd.patch (regression test )d op, )frame ) Date: Sat, 21 Feb 2009 23:55:48 -0600

Book Volume 5: Axiom Interpreter was updated with more code, more
documentation, and more structure. More boot code was rewritten in lisp.

The )frame code was rewritten and a regression test file was created
(src/input/frame.input)

Bug 7170 (X in comments) and bug 7171 (off-by-one printing) were fixed.

All )d op Example code was reviewed and a regression test file was
created (src/input/dop.input). About 5% of the functions now show
examples as part of the output of )d op function, such as:

)d op binaryTree

There are 2 exposed functions called binaryTree :
 (BinaryTree D1,D1,BinaryTree D1) -> BinaryTree D1 from
BinaryTree D1
if D1 has SETCAT
 D1 -> BinaryTree D1 from BinaryTree D1 if D1 has SETCAT

Examples of binaryTree from BinaryTree

t1:=binaryTree([1,2,3])
t2:=binaryTree([4,5,6])
binaryTree(t1,[7,8,9],t2)

t1:=binaryTree([1,2,3])

====================================================================
diff --git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet
index b842bb7..23f6c27 100644
--- a/books/bookvol10.4.pamphlet
+++ b/books/bookvol10.4.pamphlet
@@ -2982,7 +2982,7 @@ AnnaOrdinaryDifferentialEquationPackage(): with
++ numerically a system of ordinary differential equations i.e. equations
++ for the derivatives y'..y[n]' defined in terms of x,y..y[n],
++ together with a starting value for x and y..y[n] (called the initial
-    ++ conditions) and a final value of X.  A default value
+    ++ conditions) and a final value of x.  A default value
++ is used for the accuracy requirement.
++
++ It iterates over the \axiom{domains} of
@@ -94278,7 +94278,7 @@ TopLevelDrawFunctionsForPoints(): Exports ==
Implementation where
draw: (L SF, L SF, L SF) -> VIEW3
++ draw(lx,ly,lz) draws the surface constructed by projecting the values
++ in the \axiom{lz} list onto the rectangular grid formed by the
-      ++ \axiom{lx X ly}.
+      ++ \axiom{lx x ly}.
draw: (L SF, L SF, L SF, L DROP) -> VIEW3
++ draw(lx,ly,lz,l) draws the surface constructed by
++ projecting the values
diff --git a/books/bookvol5.pamphlet b/books/bookvol5.pamphlet
index 383055c..2becf4e 100644
--- a/books/bookvol5.pamphlet
+++ b/books/bookvol5.pamphlet
@@ -1395,7 +1395,7 @@ If there is only one then we clean it up and print it.
(setq line (subseq docstring (+ point 8)))
(do ((mark (search "spad{X}" line) (search "spad{X}" line)))
((null mark))
-    (princ (cleanupLine (subseq line (+ mark 8))))
+    (princ (cleanupLine (subseq line 0 mark)))
(|sayNewLine|)
(setq line (subseq line (+ mark 8))))
(princ (cleanupLine line))
@@ -4055,39 +4055,175 @@ prompt.
{\tt )history} \index{ugSysCmdhistory} and
{\tt )set} \index{ugSysCmdset}.

-\subsection{defun frameName}
+\section{Variables Used}
+The frame mechanism uses several dollar variables.
+\subsection{Primary variables}
+Primary variables are those which exist solely to make the frame
+mechanism work.
+
+The \$interpreterFrameName contains a symbol which is the name +of the current frame in use. + +The \$interpreterFrameRing contains a list of all of the existing
+frames. The first frame on the list is the current'' frame. When
+AXIOMsys is started directly there is only one frame named initial''.
+
+If the system is started under sman (using the axiom shell script,
+for example), there are two frames, initial'' and frame0''. In
+this case, frame0'' is the current frame. This can cause subtle
+problems because functions defined in the axiom initialization file
+(.axiom.input) will be defined in frame initial'' but the current
+frame will be frame0''. They will appear to be undefined. However,
+if the user does )frame next'' they can switch to the initial''
+frame and see the functions correctly defined.
+
+The \$frameMessages variable controls when frame messages will be +displayed. The variable is initially NIL. It can be set on (T) or off (NIL) +using the system command: \begin{verbatim} -frameName(frame) == CAR frame + )set message frame on | off \end{verbatim} +Setting frame messages on will output a line detailing the +current frame after every output is complete. + +\subsection{Used variables} + +The frame collects and uses a few top level variables. These are: +\$InteractiveFrame, \$IOindex, \$HiFiAccess, \$HistList, \$HistListLen,
+\$HistListAct, \$HistRecord, \$internalHistoryTable, and \$localExposureData.
+
+These variables can also be changed by the frame mechanism when the user
+requests changing to a different frame.
+
+\section{Data Structures}
+\subsection{Frames and the Interpreter Frame Ring}
+
+Axiom has the notion of frames''. A frame is a data structure which
+holds all the vital data from an Axiom session. There can be multiple
+frames and these live in a top-level variable called
+\$interpreterFrameRing. This variable holds a circular list of frames. +The parts of a frame and their initial, default values are: + +\begin{verbatim} +$interpreterFrameName      a string, named on creation
+  $InteractiveFrame (list (list nil)) +$IOindex                   an integer, 1
+  $HiFiAccess$HiFiAccess, see the variable description
+  $HistList$HistList, see the variable description
+  $HistListLen$HistListLen, see the variable description
+  $HistListAct$HistListAct, see the variable description
+  $HistRecord$HistRecord, see the variable description
+  $internalHistoryTable nil +$localExposureData         a copy of $localExposureData +\end{verbatim} + +\section{Accessor Functions} +These could be macros but we wish to export them to the API code +in the algebra so we keep them as functions. +\subsection{0th Frame Component -- frameName} +\subsection{defun frameName} <<defun frameName>>= -(defun |frameName| (frame) +(defun frameName (frame) (car frame)) @ +\subsection{1st Frame Component -- frameInteractive} +<<defun frameInteractive>>= +(defun frameInteractive (frame) + (nth 1 frame)) + +@ +\subsection{2nd Frame Component -- frameIOIndex} +<<defun frameIOIndex>>= +(defun frameIOIndex (frame) + (nth 2 frame)) + +@ +\subsection{3rd Frame Component -- frameHiFiAccess} +<<defun frameHiFiAccess>>= +(defun frameHiFiAccess (frame) + (nth 3 frame)) + +@ +\subsection{4th Frame Component -- frameHistList} +<<defun frameHistList>>= +(defun frameHistList (frame) + (nth 4 frame)) + +@ +\subsection{5th Frame Component -- frameHistListLen} +<<defun frameHistListLen>>= +(defun frameHistListLen (frame) + (nth 5 frame)) + +@ +\subsection{6th Frame Component -- frameHistListAct} +<<defun frameHistListAct>>= +(defun frameHistListAct (frame) + (nth 6 frame)) + +@ +\subsection{7th Frame Component -- frameHistRecord} +<<defun frameHistRecord>>= +(defun frameHistRecord (frame) + (nth 7 frame)) + +@ +\subsection{8th Frame Component -- frameHistoryTable} +<<defun frameHistoryTable>>= +(defun frameHistoryTable (frame) + (nth 8 frame)) + +@ +\subsection{9th Frame Component -- frameExposureData} +<<defun frameExposureData>>= +(defun frameExposureData (frame) + (nth 9 frame)) + +@ + \section{Variables Used} \section{Data Structures} \section{Functions} +\subsection{Initializing the Interpreter Frame Ring} + +Now that we know what a frame looks like we need a function to +initialize the list of frames. This function sets the initial frame +name to initial'' and creates a list of frames containing an empty +frame. This list is the interpreter frame ring and is not actually +circular but is managed as a circular list. + +As a final step we update the world from this frame. This has the +side-effect of resetting all the important global variables to their +initial values. + +<<defun initializeInterpreterFrameRing>>= +(defun |initializeInterpreterFrameRing| () + (setq |$interpreterFrameName| '|initial|)
+ (setq |$interpreterFrameRing| + (list (|emptyInterpreterFrame| |$interpreterFrameName|)))
+ (|updateFromCurrentInterpreterFrame|)
+ nil)
+
+@
+\subsection{Creating a List of all of the Frame Names}
\subsection{defun frameNames}
+This function simply walks across the frame in the frame ring and
+returns a list of the name of each frame.
\begin{verbatim}
frameNames() == [frameName f for f in $interpreterFrameRing] \end{verbatim} <<defun frameNames>>= (defun |frameNames| () - (prog () - (return - (seq - (prog (tmp0) - (spadlet tmp0 nil) - (return - (do ((tmp1 |$interpreterFrameRing| (cdr tmp1)) (f nil))
-          ((or (atom tmp1)
-               (progn (setq f (car tmp1)) nil))
-            (nreverse0 tmp0))
-       (seq
-        (exit
-         (setq tmp0 (cons (|frameName| f) tmp0)))))))))))
+ (mapcar #'frameName |$interpreterFrameRing|)) @ + +\subsection{Get Named Frame Environment (aka Interactive)} +If the frame is found we return the environment portion of the frame +otherwise we construct an empty environment and return it. +The initial values of an empty frame are created here. This function +returns a single frame that will be placed in the frame ring. \subsection{defun frameEnvironment} \begin{verbatim} frameEnvironment fname == @@ -4106,29 +4242,10 @@ frameEnvironment fname == \end{verbatim} <<defun frameEnvironment>>= (defun |frameEnvironment| (fname) - (prog - (tmp1 f e ifr) - (return - (seq - (cond - ((boot-equal fname (|frameName| (CAR |$interpreterFrameRing|)))
-       |$InteractiveFrame|) - (t - (spadlet ifr (cdr |$interpreterFrameRing|))
-       (spadlet e (list (list nil)))
-       (do ()
-           ((null ifr) nil)
-        (seq
-         (exit
-          (progn
-           (spadlet tmp1 ifr)
-           (spadlet f (car tmp1))
-           (spadlet ifr (cdr tmp1))
-           (cond
-            ((boot-equal fname (|frameName| f))
-              (spadlet e (cadr f))
-              (spadlet ifr nil))
-            (t nil)))))) e))))))
+ (let ((frame (|findFrameInRing| fname)))
+  (if frame
+   (frameInteractive frame)
+   (list (list nil)))))

@
\subsection{defun emptyInterpreterFrame}
@@ -4160,6 +4277,12 @@ emptyInterpreterFrame(name) ==
(copy-seq |$localExposureDataDefault|))) @ +\subsection{Collecting up the Environment into a Frame} + +We can collect up all the current environment information into +one frame element with this call. It creates a list of the current +values of the global variables and returns this as a frame element. + \subsection{defun createCurrentInterpreterFrame} \begin{verbatim} createCurrentInterpreterFrame() == @@ -4190,6 +4313,12 @@ createCurrentInterpreterFrame() == |$localExposureData|))

@
+\subsection{Updating from the Current Frame}
+
+The frames are kept on a circular list. The first element on that
+list is known as the current frame''. This will initialize all
+of the interesting interpreter data structures from that frame.
+
\subsection{defun updateFromCurrentInterpreterFrame}
\begin{verbatim}
updateFromCurrentInterpreterFrame() ==
@@ -4211,28 +4340,26 @@ updateFromCurrentInterpreterFrame() ==
\end{verbatim}
<<defun updateFromCurrentInterpreterFrame>>=
(defun |updateFromCurrentInterpreterFrame| ()
- (prog (tmp1)
-  (return
-   (progn
-    (spadlet tmp1 (CAR |$interpreterFrameRing|)) - (spadlet |$interpreterFrameName| (car tmp1))
-    (spadlet |$InteractiveFrame| (cadr tmp1)) - (spadlet |$IOindex| (caddr tmp1))
-    (spadlet |$HiFiAccess| (cadddr tmp1)) - (spadlet |$HistList| (car (cddddr tmp1)))
-    (spadlet |$HistListLen| (cadr (cddddr tmp1))) - (spadlet |$HistListAct| (caddr (cddddr tmp1)))
-    (spadlet |$HistRecord| (cadddr (cddddr tmp1))) - (spadlet |$internalHistoryTable| (car (cddddr (cddddr tmp1))))
-    (spadlet |$localExposureData| (cadr (cddddr (cddddr tmp1)))) - (when |$frameMessages|
-      (|sayMessage|
-       (cons
-        (makestring "   Current interpreter frame is called")
-        (|bright| |$interpreterFrameName|)))) - nil)))) + (let (tmp1) + (setq tmp1 (first |$interpreterFrameRing|))
+  (setq |$interpreterFrameName| (nth 0 tmp1)) + (setq |$InteractiveFrame|     (nth 1 tmp1))
+  (setq |$IOindex| (nth 2 tmp1)) + (setq |$HiFiAccess|           (nth 3 tmp1))
+  (setq |$HistList| (nth 4 tmp1)) + (setq |$HistListLen|          (nth 5 tmp1))
+  (setq |$HistListAct| (nth 6 tmp1)) + (setq |$HistRecord|           (nth 7 tmp1))
+  (setq |$internalHistoryTable| (nth 8 tmp1)) + (setq |$localExposureData|    (nth 9 tmp1))
+  (when |$frameMessages| + (|sayMessage| + (cons " Current interpreter frame is called" |$interpreterFrameName|)))))

@
+\subsection{Find a Frame in the Frame Ring by Name}
+Each frame contains its name as the 0th element.  We simply walk all
+the frames and if we find one we return it.
\subsection{defun findFrameInRing}
\begin{verbatim}
findFrameInRing(name) ==
@@ -4245,26 +4372,17 @@ findFrameInRing(name) ==
\end{verbatim}
<<defun findFrameInRing>>=
(defun |findFrameInRing| (name)
- (prog (val)
-  (return
-   (seq
-    (progn
-     (spadlet val nil)
-     (seq
-      (do ((tmp0 |$interpreterFrameRing| (cdr tmp0)) (frame nil)) - ((or (atom tmp0) - (progn (setq frame (car tmp0)) nil)) - nil) - (seq - (exit - (when (boot-equal (CAR frame) name) - (exit - (progn - (spadlet val frame) - (return frame))))))) - (exit val))))))) + (block () + (dolist (frame |$interpreterFrameRing|)
+   (when (boot-equal (frameName frame) name) (return frame)))))

@
+\subsection{Update the Current Interpreter Frame}
+
+This function collects the normal contents of the world into a
+frame object, places it first on the frame list, and then sets
+the current values of the world from the frame object.
+
\subsection{defun updateCurrentInterpreterFrame}
\begin{verbatim}
updateCurrentInterpreterFrame() ==
@@ -4274,10 +4392,9 @@ updateCurrentInterpreterFrame() ==
\end{verbatim}
<<defun updateCurrentInterpreterFrame>>=
(defun |updateCurrentInterpreterFrame| ()
- (progn
(rplaca |$interpreterFrameRing| (|createCurrentInterpreterFrame|)) (|updateFromCurrentInterpreterFrame|) - nil)) + nil) @ \subsection{defun initializeInterpreterFrameRing} @@ -4290,14 +4407,23 @@ initializeInterpreterFrameRing() == \end{verbatim} <<defun initializeInterpreterFrameRing>>= (defun |initializeInterpreterFrameRing| () - (progn (spadlet |$interpreterFrameName| '|initial|)
(spadlet |$interpreterFrameRing| (cons (|emptyInterpreterFrame| |$interpreterFrameName|) nil))
-  (|updateFromCurrentInterpreterFrame|) nil))
+  (|updateFromCurrentInterpreterFrame|)
+  nil)

@
\subsection{defun nextInterpreterFrame}
+
+This function updates the current frame to make sure all of the
+current information is recorded. If there are more frame elements
+in the list then this will destructively move the current frame
+to the end of the list, that is, assume the frame list reads (1 2 3)
+this function will destructively change it to (2 3 1).
+
+Note: the nconc2 function destructively inserts the second list at the
+end of the first.
\begin{verbatim}
nextInterpreterFrame() ==
updateCurrentInterpreterFrame()
@@ -4308,18 +4434,11 @@ nextInterpreterFrame() ==
\end{verbatim}
<<defun nextInterpreterFrame>>=
(defun |nextInterpreterFrame| ()
- (progn
-  (|updateCurrentInterpreterFrame|)
-  (cond
-    ((null (cdr |$interpreterFrameRing|)) - nil) - (t - (spadlet |$interpreterFrameRing|
-       (nconc2
-        (cdr |$interpreterFrameRing|) - (cons - (car |$interpreterFrameRing|) nil)))
-      (|updateFromCurrentInterpreterFrame|)))))
+  (when (cdr |$interpreterFrameRing|) + (setq |$interpreterFrameRing|
+    (nconc2 (cdr |$interpreterFrameRing|) + (list (car |$interpreterFrameRing|))))
+   (|updateFromCurrentInterpreterFrame|)))

@
\subsection{defun changeToNamedInterpreterFrame}
@@ -4402,7 +4521,7 @@ addNewInterpreterFrame(name) ==
nil)
(seq
(exit
-         (when (boot-equal name (|frameName| f))
+         (when (boot-equal name (frameName f))
(exit
(|throwKeyedMsg| 'S2IZ0019 ; existing frame with same name
(cons name nil)))))))
@@ -4457,7 +4576,7 @@ closeInterpreterFrame(name) ==
(seq
(exit
(cond
-              ((or found (nequal name (|frameName| f)))
+              ((or found (nequal name (frameName f)))
(spadlet ifr (cons f ifr)))
(t
(spadlet found t))))))
@@ -4495,7 +4614,7 @@ displayFrameNames() ==
(exit
(setq tmp0
(append tmp0 (cons '|%l|
-              (cons (makestring "     ") (|bright| (|frameName| f))))))))))))
+              (cons (makestring "     ") (|bright| (frameName f))))))))))))
(|sayKeyedMsg| 'S2IZ0024 (cons fs nil))))))) ; frame names are ...

@
@@ -4551,7 +4670,7 @@ importFromFrame args ==
(cond
((null (|member| fname (|frameNames|)))
(|throwKeyedMsg| 'S2IZ0074 (cons fname nil))) ; not frame name
-         ((boot-equal fname (|frameName| (car |$interpreterFrameRing|))) + ((boot-equal fname (frameName (car |$interpreterFrameRing|)))
(|throwKeyedMsg| 'S2IZ0075 NIL)) ; cannot import from curr frame
(t
(spadlet fenv (|frameEnvironment| fname))
@@ -5934,6 +6053,15 @@ load the file \verb|exposed.lsp| to set up the exposure
group information.
<<defun findFrameInRing>>
<<defun frame>>
<<defun frameEnvironment>>
+<<defun frameExposureData>>
+<<defun frameHiFiAccess>>
+<<defun frameHistList>>
+<<defun frameHistListAct>>
+<<defun frameHistListLen>>
+<<defun frameHistoryTable>>
+<<defun frameHistRecord>>
+<<defun frameInteractive>>
+<<defun frameIOIndex>>
<<defun frameName>>
<<defun frameNames>>
<<defun frameSpad2Cmd>>
diff --git a/changelog b/changelog
index 1eb750a..416cdb6 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,18 @@
+20090212 tpd src/axiom-website/patches.html 20090220.01.tpd.patch
+20090220 tpd src/input/Makefile add dop.input, frame.input
+20090220 tpd src/input/frame.input regression test )frame
+20090220 tpd src/input/dop.input regression test )d op documentation
+20090220 tpd books/bookvol10.4 fix comments
+20090220 tpd books/bookvol5 fixup sayExample
+20090220 tpd books/bookvol5 fixup frameName
+20090220 tpd src/interp/i-map.boot.pamphlet fix frameName
+20090212 tpd src/axiom-website/patches.html 20090212.03.tpd.patch
+20090212 tpd readme add Zeilberger quote
+20090212 tpd src/interp/format.boot move sayExample, cleanupLine
+20090212 tpd books/bookvol5 move sayExample, cleanupLine
+20090212 tpd books/bookvol10.4 make rm forceful
+20090212 tpd books/bookvol10.3 make rm forceful
+20090212 tpd books/bookvol5 fixup restart
20090212 tpd src/axiom-website/patches.html 20090212.02.tpd.patch
20090212 tpd src/Makefile.pamphlet copy bookvol5
20090212 tpd books/ps/v5restart.ps added
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 140c90c..93fa5c5 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -945,5 +945,9 @@ bookvol10.4 add exports<br/>
remove unused code<br/>
<a href="patches/20090212.02.tpd.patch">20090212.02.tpd.patch</a>
rewrite restart<br/>
+<a href="patches/20090212.03.tpd.patch">20090212.03.tpd.patch</a>
+rewrite sayExample, frame<br/>
+<a href="patches/20090220.01.tpd.patch">20090220.01.tpd.patch</a>
+regression test )d op, )frame<br/>
</body>
</html>
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index b341753..eb8cbf6 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -294,7 +294,8 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress
alist.regress  \
decimal.regress   defintef.regress defintrf.regress \
derham.regress    dfloat.regress   dhmatrix.regress \
dhtri.regress     directproduct.regress divisor.regress \
-    dmp.regress       dpol.regress     e1.regress       ei.regress \
+    dmp.regress       dop.regress      dpol.regress     \
+    e1.regress        ei.regress \
easter.regress    efi.regress \
eigen.regress     elemfun.regress  elemnum.regress  elfuts.regress \
elt.regress       en.regress \
@@ -308,7 +309,8 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress
alist.regress  \
fib.regress       file.regress     fixed.regress \
float1.regress    float2.regress \
float.regress     fname1.regress   fname.regress    fnla.regress \
-    fns.regress       fparfrac.regress fparfrc.regress  fr1.regress \
+    fns.regress       fparfrac.regress fparfrc.regress  \
+    frame.regress     fr1.regress \
fr2.regress       frac.regress     fr.regress       free.regress \
function.regress  galois.regress    gamma.regress \
gbf.regress       genups.regress   gonshor.regress  grpthry.regress \
@@ -553,7 +555,8 @@ FILES= ${OUT}/algaggr.input${OUT}/algbrbf.input
${OUT}/algfacob.input \${OUT}/dfloat.input   ${OUT}/dhmatrix.input \${OUT}/dhtri.input  ${OUT}/directproduct.input \${OUT}/divisor.input \
-       ${OUT}/dmp.input${OUT}/dpol.input       ${OUT}/draw2dsf.input \ +${OUT}/dmp.input      ${OUT}/dop.input \ +${OUT}/dpol.input     ${OUT}/draw2dsf.input \${OUT}/drawalg.input  ${OUT}/drawcfn.input \${OUT}/drawcfun.input ${OUT}/drawcurv.input \${OUT}/draw.input     ${OUT}/drawcx.input${OUT}/drawex.input \
@@ -577,7 +580,8 @@ FILES= ${OUT}/algaggr.input${OUT}/algbrbf.input
${OUT}/algfacob.input \${OUT}/fname1.input   ${OUT}/fnla.input${OUT}/folium.input   \
${OUT}/fparfrac.input \${OUT}/fparfrc.input  ${OUT}/fr2.input${OUT}/frac.input \
-       ${OUT}/fr.input${OUT}/fr1.input        ${OUT}/gary1.input \ +${OUT}/fr.input       ${OUT}/frame.input \ +${OUT}/fr1.input      ${OUT}/gary1.input \${OUT}/gbf.input      ${OUT}/genups.input${OUT}/gnarly1.input \
${OUT}/gonshor.input${OUT}/grdef.input    \
${OUT}/gstbl.input \ @@ -791,7 +795,7 @@ DOCFILES= \${DOC}/dhtri.input.dvi      \
${DOC}/directproduct.input.dvi \${DOC}/divisor.input.dvi     ${DOC}/dmp.input.dvi \ -${DOC}/dpol.input.dvi        \
+  ${DOC}/dop.input.dvi${DOC}/dpol.input.dvi       \
${DOC}/draw2dsf.input.dvi${DOC}/drawalg.input.dvi    \
${DOC}/drawcfn.input.dvi${DOC}/drawcfun.input.dvi   \
${DOC}/drawcurv.input.dvi${DOC}/drawcx.input.dvi     \
@@ -863,6 +867,7 @@ DOCFILES= \
${DOC}/fname.input.dvi${DOC}/fnla.input.dvi       \
${DOC}/fns.input.dvi${DOC}/folium.input.dvi     \
${DOC}/fparfrac.input.dvi${DOC}/fparfrc.input.dvi    \
+  ${DOC}/frame.input.dvi \${DOC}/fr1.input.dvi         ${DOC}/fr2.input.dvi \${DOC}/frac.input.dvi        ${DOC}/fr.input.dvi \${DOC}/free.input.dvi        \
diff --git a/src/input/dop.input.pamphlet b/src/input/dop.input.pamphlet
new file mode 100644
index 0000000..887f4bc
--- /dev/null
+++ b/src/input/dop.input.pamphlet
@@ -0,0 +1,6163 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input dop.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +<<license>>= +--Copyright The Numerical Algorithms Group Limited 1991. +@ +<<*>>= +)spool dop.output +)set message test on +)set message auto off +)clear all + +--S 1 of 127 +)d op binaryTree +--R +--R +--RThere are 2 exposed functions called binaryTree : +--R  (BinaryTree D1,D1,BinaryTree D1) -> BinaryTree D1 from +--R BinaryTree D1 +--R if D1 has SETCAT +--R  D1 -> BinaryTree D1 from BinaryTree D1 if D1 has SETCAT +--R +--RExamples of binaryTree from BinaryTree +--R +--Rt1:=binaryTree([1,2,3]) +--Rt2:=binaryTree([4,5,6]) +--RbinaryTree(t1,[7,8,9],t2) +--R +--Rt1:=binaryTree([1,2,3]) +--R +--E 1 + +--S 2 of 127 +)d op rationalPoint? +--R +--R +--RThere is one exposed function called rationalPoint? : +--R  (D2,D2) -> Boolean from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC +--R D2 and D4 has UPOLYC FRAC D3 +--R +--RThere is one unexposed function called rationalPoint? : +--R  (D2,D2) -> Boolean from FunctionFieldCategory&(D3,D2,D4,D5) +--R if D2 has UFD and D4 has UPOLYC D2 and D5 has UPOLYC FRAC +--R D4 and D3 has FFCAT(D2,D4,D5) +--R +--RExamples of rationalPoint? from FunctionFieldCategory& +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RrationalPoint?(0,0)$R
+--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4)
+--RrationalPoint?(0,0)$R2 +--R +--R +--RExamples of rationalPoint? from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RrationalPoint?(0,0)$R
+--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4)
+--RrationalPoint?(0,0)$R2 +--R +--E 2 + +--S 3 of 127 +--R)d op nthFactor +--R +--R +--RThere are 2 exposed functions called nthFactor : +--R  (D,Integer) -> D1 from D +--R if D has FAMONC(D1,D3) and D3 has CABMON and D1 has SETCAT +--R +--R  (Factored D1,Integer) -> D1 from Factored D1 if D1 has INTDOM +--R +--R +--RThere are 4 unexposed functions called nthFactor : +--R  (FreeGroup D1,Integer) -> D1 from FreeGroup D1 if D1 has SETCAT +--R +--R  (FreeMonoid D1,Integer) -> D1 from FreeMonoid D1 if D1 has +--R SETCAT +--R  (ListMonoidOps(D1,D3,D4),Integer) -> D1 from ListMonoidOps(D1,D3 +--R ,D4) +--R if D1 has SETCAT and D3 has ABELMON and D4: D3 +--R  (OrderedFreeMonoid D1,Integer) -> D1 from OrderedFreeMonoid D1 +--R if D1 has ORDSET +--R +--RExamples of nthFactor from FreeAbelianMonoidCategory +--R +--R +--RExamples of nthFactor from FreeGroup +--R +--R +--RExamples of nthFactor from FreeMonoid +--R +--R +--RExamples of nthFactor from Factored +--R +--Ra:=factor 9720000 +--RnthFactor(a,2) +--R +--R +--RExamples of nthFactor from ListMonoidOps +--R +--R +--RExamples of nthFactor from OrderedFreeMonoid +--R +--E 3 + +--S 4 of 127 +--R)d op qsetelt! +--R +--R +--RThere are 2 exposed functions called qsetelt! : +--R  (D,Integer,Integer,D1) -> D1 from D +--R if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG +--R D1 and D4 has FLAGG D1 +--R  (D,D2,D1) -> D1 from D +--R if D has shallowlyMutable and D has ELTAGG(D2,D1) and D2 +--R has SETCAT and D1 has TYPE +--R +--RExamples of qsetelt! from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,0) +--Rqsetelt!(arr,1,1,17) +--R +--R +--RExamples of qsetelt! from EltableAggregate +--R +--E 4 + +--S 5 of 127 +--R)d op cycleElt +--R +--R +--RThere is one unexposed function called cycleElt : +--R  D1 -> Union(D1,"failed") from CyclicStreamTools(D2,D1) +--R if D2 has TYPE and D1 has LZSTAGG D2 +--R +--RExamples of cycleElt from CyclicStreamTools +--R +--Rp:=repeating([1,2,3]) +--Rq:=cons(4,p) +--RcycleElt q +--Rr:=[1,2,3]::Stream(Integer) +--RcycleElt r +--R +--E 5 + +--S 6 of 127 +--R)d op cyclicEntries +--R +--R +--RThere is one exposed function called cyclicEntries : +--R  Tree D2 -> List Tree D2 from Tree D2 if D2 has SETCAT +--R +--RExamples of cyclicEntries from Tree +--R +--Rt1:=tree [1,2,3,4] +--RcyclicEntries t1 +--R +--E 6 + +--S 7 of 127 +--R)d op oneDimensionalArray +--R +--R +--RThere are 2 exposed functions called oneDimensionalArray : +--R  (NonNegativeInteger,D2) -> OneDimensionalArray D2 +--R from OneDimensionalArray D2 if D2 has TYPE +--R  List D2 -> OneDimensionalArray D2 from OneDimensionalArray D2 +--R if D2 has TYPE +--R +--RExamples of oneDimensionalArray from OneDimensionalArray +--R +--RoneDimensionalArray(10,0.0) +--R +--RoneDimensionalArray [i**2 for i in 1..10] +--R +--E 7 + +--S 8 of 127 +--R)d op alphanumeric? +--R +--R +--RThere is one exposed function called alphanumeric? : +--R  Character -> Boolean from Character +--R +--RExamples of alphanumeric? from Character +--R +--Rchars := [char "a", char "A", char "X", char "8", char "+"] +--R[alphanumeric? c for c in chars] +--R +--E 8 + +--S 9 of 127 +--R)d op digit? +--R +--R +--RThere is one exposed function called digit? : +--R  Character -> Boolean from Character +--R +--RExamples of digit? from Character +--R +--Rchars := [char "a", char "A", char "X", char "8", char "+"] +--R[digit? c for c in chars] +--R +--E 9 + +--S 10 of 127 +--R)d op sqfrFactor +--R +--R +--RThere is one exposed function called sqfrFactor : +--R  (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM +--R +--R +--RExamples of sqfrFactor from Factored +--R +--Ra:=sqfrFactor(3,5) +--RnthFlag(a,1) +--R +--E 10 + +--S 11 of 127 +--R)d op integralMatrix +--R +--R +--RThere is one exposed function called integralMatrix : +--R  -> Matrix Fraction D3 from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC +--R D2 and D4 has UPOLYC FRAC D3 +--R +--RExamples of integralMatrix from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RintegralMatrix()$R
+--R
+--E 11
+
+--S 12 of 127
+--R)d op ptree
+--R
+--R
+--RThere are 2 exposed functions called ptree :
+--R    (PendantTree D1,PendantTree D1) -> PendantTree D1 from
+--R            PendantTree D1
+--R            if D1 has SETCAT
+--R    D1 -> PendantTree D1 from PendantTree D1 if D1 has SETCAT
+--R
+--RExamples of ptree from PendantTree
+--R
+--Rt1:=ptree([1,2,3])
+--Rptree(t1,ptree([1,2,3]))
+--R
+--Rt1:=ptree([1,2,3])
+--R
+--E 12
+
+--S 13 of 127
+--R)d op insert!
+--R
+--R
+--RThere are 8 exposed functions called insert! :
+--R    (D1,D) -> D from D if D has BGAGG D1 and D1 has TYPE
+--R    (D1,BinarySearchTree D1) -> BinarySearchTree D1
+--R            from BinarySearchTree D1 if D1 has ORDSET
+--R    (D1,BinaryTournament D1) -> BinaryTournament D1
+--R            from BinaryTournament D1 if D1 has ORDSET
+--R    (D,D,Integer) -> D from D if D has ELAGG D2 and D2 has TYPE
+--R    (D1,D,Integer) -> D from D if D has ELAGG D1 and D1 has TYPE
+--R    Record(key: Record(var: Symbol,fn: Expression DoubleFloat,range
+--R            : Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,
+--R            relerr: DoubleFloat),entry: Record(endPointContinuity: Union(
+--R            continuous: Continuous at the end points,lowerSingular:
+--R            There is a singularity at the lower end point,upperSingular:
+--R            There is a singularity at the upper end point,bothSingular:
+--R            There are singularities at both end points,notEvaluated:
+--R            End point continuity not yet evaluated),singularitiesStream:
+--R            Union(str: Stream DoubleFloat,notEvaluated:
+--R            Internal singularities not yet evaluated),range: Union(finite:
+--R            The range is finite,lowerInfinite:
+--R            The bottom of range is infinite,upperInfinite:
+--R            The top of range is infinite,bothInfinite:
+--R            Both top and bottom points are infinite,notEvaluated:
+--R            Range not yet evaluated))) -> IntegrationFunctionsTable
+--R            from IntegrationFunctionsTable
+--R    (D1,D,NonNegativeInteger) -> D from D
+--R            if D has MDAGG D1 and D1 has SETCAT
+--R    Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn:
+--R            Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals:
+--R            List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,
+--R            relerr: DoubleFloat),entry: Record(stiffness: Float,stability:
+--R            Float,expense: Float,accuracy: Float,intermediateResults:
Float))
+--R             -> ODEIntensityFunctionsTable
+--R            from ODEIntensityFunctionsTable
+--R
+--RThere is one unexposed function called insert! :
+--R    (D2,D3) -> Void from TabulatedComputationPackage(D2,D3)
+--R            if D2 has SETCAT and D3 has SETCAT
+--R
+--RExamples of insert! from BagAggregate
+--R
+--R
+--RExamples of insert! from BinarySearchTree
+--R
+--Rt1:=binarySearchTree [1,2,3,4]
+--Rinsert!(5,t1)
+--R
+--R
+--RExamples of insert! from BinaryTournament
+--R
+--Rt1:=binaryTournament [1,2,3,4]
+--Rinsert!(5,t1)
+--Rt1
+--R
+--R
+--RExamples of insert! from ExtensibleLinearAggregate
+--R
+--R
+--RExamples of insert! from IntegrationFunctionsTable
+--R
+--R
+--RExamples of insert! from MultiDictionary
+--R
+--R
+--RExamples of insert! from ODEIntensityFunctionsTable
+--R
+--R
+--RExamples of insert! from TabulatedComputationPackage
+--R
+--E 13
+
+--S 14 of 127
+--R)d op genus
+--R
+--R
+--RThere is one exposed function called genus :
+--R     -> NonNegativeInteger from D
+--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC
+--R            D2 and D4 has UPOLYC FRAC D3
+--R
+--RThere is one unexposed function called genus :
+--R     -> NonNegativeInteger from FunctionFieldCategory&(D2,D3,D4,D5)
+--R            if D3 has UFD and D4 has UPOLYC D3 and D5 has UPOLYC FRAC
+--R            D4 and D2 has FFCAT(D3,D4,D5)
+--R
+--RExamples of genus from FunctionFieldCategory&
+--R
+--RP0 := UnivariatePolynomial(x, Integer)
+--RP1 := UnivariatePolynomial(y, Fraction P0)
+--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
+--Rgenus()$R +--R +--R +--RExamples of genus from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--Rgenus()$R
+--R
+--E 14
+
+--S 15 of 127
+--R)d op hexDigit?
+--R
+--R
+--RThere is one exposed function called hexDigit? :
+--R    Character -> Boolean from Character
+--R
+--RExamples of hexDigit? from Character
+--R
+--Rchars := [char "a", char "A", char "X", char "8", char "+"]
+--R[hexDigit? c for c in chars]
+--R
+--E 15
+
+--S 16 of 127
+--R)d op computeCycleLength
+--R
+--R
+--RThere is one unexposed function called computeCycleLength :
+--R    D2 -> NonNegativeInteger from CyclicStreamTools(D3,D2)
+--R            if D3 has TYPE and D2 has LZSTAGG D3
+--R
+--RExamples of computeCycleLength from CyclicStreamTools
+--R
+--Rp:=repeating([1,2,3])
+--Rq:=cons(4,p)
+--RcomputeCycleLength(cycleElt(q))
+--R
+--E 16
+
+--S 17 of 127
+--R)d op findCycle
+--R
+--R
+--RThere is one exposed function called findCycle :
+--R    (NonNegativeInteger,Stream D3) -> Record(cycle?: Boolean,prefix
+--R            : NonNegativeInteger,period: NonNegativeInteger)
+--R            from Stream D3 if D3 has TYPE
+--R
+--RExamples of findCycle from Stream
+--R
+--Rm:=[1,2,3]
+--Rn:=repeating(m)
+--RfindCycle(3,n)
+--RfindCycle(2,n)
+--R
+--E 17
+
+--S 18 of 127
+--R)d op draw
+--R
+--R
+--RThere are 31 exposed functions called draw :
+--R    ((DoubleFloat -> DoubleFloat),Segment Float,List DrawOption) ->
+--R            TwoDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    ((DoubleFloat -> DoubleFloat),Segment Float) ->
+--R            TwoDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    (ParametricPlaneCurve (DoubleFloat -> DoubleFloat),Segment Float
+--R            ,List DrawOption) -> TwoDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    (ParametricPlaneCurve (DoubleFloat -> DoubleFloat),Segment Float
+--R            ) -> TwoDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    (ParametricSpaceCurve (DoubleFloat -> DoubleFloat),Segment Float
+--R            ,List DrawOption) -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    (ParametricSpaceCurve (DoubleFloat -> DoubleFloat),Segment Float
+--R            ) -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    ((DoubleFloat -> Point DoubleFloat),Segment Float,List
+--R            DrawOption) -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    ((DoubleFloat -> Point DoubleFloat),Segment Float) ->
+--R            ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment Float,
+--R            Segment Float,List DrawOption) -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment Float,
+--R            Segment Float) -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    (((DoubleFloat,DoubleFloat) -> Point DoubleFloat),Segment Float
+--R            ,Segment Float,List DrawOption) -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    (((DoubleFloat,DoubleFloat) -> Point DoubleFloat),Segment Float
+--R            ,Segment Float) -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    (ParametricSurface ((DoubleFloat,DoubleFloat) -> DoubleFloat),
+--R            Segment Float,Segment Float,List DrawOption) ->
+--R            ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    (ParametricSurface ((DoubleFloat,DoubleFloat) -> DoubleFloat),
+--R            Segment Float,Segment Float) -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForCompiledFunctions
+--R    (Equation D6,Symbol,Symbol,List DrawOption) ->
+--R            TwoDimensionalViewport
+--R            from TopLevelDrawFunctionsForAlgebraicCurves(D5,D6)
+--R            if D6 has FS D5 and D5 has Join(IntegralDomain,OrderedSet,
+--R            RetractableTo Integer)
+--R    (D2,SegmentBinding Float,List DrawOption) ->
+--R            TwoDimensionalViewport
+--R            from TopLevelDrawFunctions D2
+--R            if D2 has Join(ConvertibleTo InputForm,SetCategory)
+--R    (D2,SegmentBinding Float) -> TwoDimensionalViewport
+--R            from TopLevelDrawFunctions D2
+--R            if D2 has Join(ConvertibleTo InputForm,SetCategory)
+--R    (ParametricPlaneCurve D5,SegmentBinding Float,List DrawOption)
+--R             -> TwoDimensionalViewport
+--R            from TopLevelDrawFunctions D5
+--R            if D5 has Join(ConvertibleTo InputForm,SetCategory)
+--R    (ParametricPlaneCurve D4,SegmentBinding Float) ->
+--R            TwoDimensionalViewport
+--R            from TopLevelDrawFunctions D4
+--R            if D4 has Join(ConvertibleTo InputForm,SetCategory)
+--R    (ParametricSpaceCurve D5,SegmentBinding Float,List DrawOption)
+--R             -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctions D5
+--R            if D5 has Join(ConvertibleTo InputForm,SetCategory)
+--R    (ParametricSpaceCurve D4,SegmentBinding Float) ->
+--R            ThreeDimensionalViewport
+--R            from TopLevelDrawFunctions D4
+--R            if D4 has Join(ConvertibleTo InputForm,SetCategory)
+--R    (D2,SegmentBinding Float,SegmentBinding Float,List DrawOption)
+--R             -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctions D2
+--R            if D2 has Join(ConvertibleTo InputForm,SetCategory)
+--R    (D2,SegmentBinding Float,SegmentBinding Float) ->
+--R            ThreeDimensionalViewport
+--R            from TopLevelDrawFunctions D2
+--R            if D2 has Join(ConvertibleTo InputForm,SetCategory)
+--R    (ParametricSurface D5,SegmentBinding Float,SegmentBinding Float
+--R            ,List DrawOption) -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctions D5
+--R            if D5 has Join(ConvertibleTo InputForm,SetCategory)
+--R    (ParametricSurface D4,SegmentBinding Float,SegmentBinding Float
+--R            ) -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctions D4
+--R            if D4 has Join(ConvertibleTo InputForm,SetCategory)
+--R    (List DoubleFloat,List DoubleFloat) -> TwoDimensionalViewport
+--R            from TopLevelDrawFunctionsForPoints
+--R    (List DoubleFloat,List DoubleFloat,List DrawOption) ->
+--R            TwoDimensionalViewport
+--R            from TopLevelDrawFunctionsForPoints
+--R    List Point DoubleFloat -> TwoDimensionalViewport
+--R            from TopLevelDrawFunctionsForPoints
+--R    (List Point DoubleFloat,List DrawOption) ->
+--R            TwoDimensionalViewport
+--R            from TopLevelDrawFunctionsForPoints
+--R    (List DoubleFloat,List DoubleFloat,List DoubleFloat) ->
+--R            ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForPoints
+--R    (List DoubleFloat,List DoubleFloat,List DoubleFloat,List
+--R            DrawOption) -> ThreeDimensionalViewport
+--R            from TopLevelDrawFunctionsForPoints
+--R
+--RExamples of draw from TopLevelDrawFunctionsForCompiledFunctions
+--R
+--R
+--RExamples of draw from TopLevelDrawFunctionsForAlgebraicCurves
+--R
+--R
+--RExamples of draw from TopLevelDrawFunctions
+--R
+--R
+--RExamples of draw from TopLevelDrawFunctionsForPoints
+--R
+--E 18
+
+--S 19 of 127
+--R)d op repeating
+--R
+--R
+--RThere is one exposed function called repeating :
+--R    List D2 -> Stream D2 from Stream D2 if D2 has TYPE
+--R
+--RExamples of repeating from Stream
+--R
+--Rm:=repeating([-1,0,1,2,3])
+--R
+--E 19
+
+--S 20 of 127
+--R)d op cons
+--R
+--R
+--RThere are 2 exposed functions called cons :
+--R    (D1,List D1) -> List D1 from List D1 if D1 has TYPE
+--R    (D1,Stream D1) -> Stream D1 from Stream D1 if D1 has TYPE
+--R
+--RExamples of cons from List
+--R
+--R
+--RExamples of cons from Stream
+--R
+--Rm:=[1,2,3]
+--Rn:=repeating(m)
+--Rcons(4,n)
+--R
+--E 20
+
+--S 21 of 127
+--R)d op map
+--R
+--R
+--RThere are 80 exposed functions called map :
+--R    ((D2 -> D2),D) -> D from D
+--R            if D has AMR(D2,D3) and D2 has RING and D3 has OAMON
+--R    (((D2,D2) -> D2),D,D,D2) -> D from D
+--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
+--R            D2 and D4 has FLAGG D2
+--R    (((D2,D2) -> D2),D,D) -> D from D
+--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
+--R            D2 and D4 has FLAGG D2
+--R    ((D2 -> D2),D) -> D from D
+--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
+--R            D2 and D4 has FLAGG D2
+--R    ((D4 -> D5),OneDimensionalArray D4) -> OneDimensionalArray D5
+--R            from OneDimensionalArrayFunctions2(D4,D5)
+--R            if D4 has TYPE and D5 has TYPE
+--R    ((D6 -> D7),CartesianTensor(D4,D5,D6)) -> CartesianTensor(D4,D5,
+--R            D7)
+--R            from CartesianTensorFunctions2(D4,D5,D6,D7)
+--R            if D4: INT and D5: NNI and D6 has COMRING and D7 has
+--R            COMRING
+--R    ((D4 -> D5),Complex D4) -> Complex D5 from ComplexFunctions2(D4,
+--R            D5)
+--R            if D4 has COMRING and D5 has COMRING
+--R    ((D5 -> D6),DirectProduct(D4,D5)) -> DirectProduct(D4,D6)
+--R            from DirectProductFunctions2(D4,D5,D6)
+--R            if D4: NNI and D5 has TYPE and D6 has TYPE
+--R    ((D4 -> D5),Equation D4) -> Equation D5 from EquationFunctions2(
+--R            D4,D5)
+--R            if D4 has TYPE and D5 has TYPE
+--R    ((D2 -> D2),Equation D2) -> Equation D2 from Equation D2 if D2
+--R            has TYPE
+--R    ((D4 -> D1),Kernel D4) -> D1 from ExpressionSpaceFunctions2(D4,
+--R            D1)
+--R            if D4 has ES and D1 has ES
+--R    ((D -> D),Kernel D) -> D from D if D has ES
+--R    ((D4 -> D5),Matrix D4) -> Matrix D5
+--R            from ExpertSystemToolsPackage2(D4,D5)
+--R            if D4 has RING and D5 has RING
+--R    ((D4 -> D5),Expression D4) -> Expression D5
+--R            from ExpressionFunctions2(D4,D5)
+--R            if D4 has ORDSET and D5 has ORDSET
+--R    ((D7 -> D11),FiniteDivisor(D7,D8,D9,D10)) -> FiniteDivisor(D11,
+--R            D1,D2,D3)
+--R            from FiniteDivisorFunctions2(D7,D8,D9,D10,D11,D1,D2,D3)
+--R            if D7 has FIELD and D8 has UPOLYC D7 and D9 has UPOLYC FRAC
+--R            D8 and D10 has FFCAT(D7,D8,D9) and D11 has FIELD and D1 has
+--R            UPOLYC D11 and D2 has UPOLYC FRAC D1 and D3 has FFCAT(D11,
+--R            D1,D2)
+--R    ((D2 -> D2),D) -> D from D if D has FEVALAB D2 and D2 has
+--R            SETCAT
+--R    ((D5 -> D8),D4) -> D2
+--R            from FunctionFieldCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,
+--R            D2)
+--R            if D5 has UFD and D8 has UFD and D6 has UPOLYC D5 and D7
+--R            has UPOLYC FRAC D6 and D9 has UPOLYC D8 and D2 has FFCAT(D8
+--R            ,D9,D1) and D4 has FFCAT(D5,D6,D7) and D1 has UPOLYC FRAC
+--R            D9
+--R    ((D4 -> D5),D3) -> D1 from FiniteLinearAggregateFunctions2(D4,
+--R            D3,D5,D1)
+--R            if D4 has TYPE and D5 has TYPE and D1 has FLAGG D5 and D3
+--R            has FLAGG D4
+--R    ((D2 -> D2),D) -> D from D
+--R            if D has FMCAT(D2,D3) and D2 has RING and D3 has SETCAT
+--R    ((D4 -> D5),Factored D4) -> Factored D5 from FactoredFunctions2
+--R            (D4,D5)
+--R            if D4 has INTDOM and D5 has INTDOM
+--R    ((D4 -> D5),Fraction D4) -> Fraction D5 from FractionFunctions2
+--R            (D4,D5)
+--R            if D4 has INTDOM and D5 has INTDOM
+--R    ((D7 -> D11),FractionalIdeal(D7,D8,D9,D10)) -> FractionalIdeal(
+--R            D11,D1,D2,D3)
+--R            from FractionalIdealFunctions2(D7,D8,D9,D10,D11,D1,D2,D3)
+--R            if D7 has EUCDOM and D8 has QFCAT D7 and D9 has UPOLYC D8
+--R            and D10 has Join(FramedAlgebra(D8,D9),RetractableTo D8) and
+--R            D11 has EUCDOM and D1 has QFCAT D11 and D2 has UPOLYC D1
+--R            and D3 has Join(FramedAlgebra(D1,D2),RetractableTo D1)
+--R    ((D4 -> D5),D3) -> D1
+--R            from FramedNonAssociativeAlgebraFunctions2(D3,D4,D1,D5)
+--R            if D4 has COMRING and D5 has COMRING and D1 has FRNAALG D5
+--R            and D3 has FRNAALG D4
+--R    ((D2 -> D2),Factored D2) -> Factored D2 from Factored D2
+--R            if D2 has INTDOM
+--R    ((D4 -> D5),D3) -> D1 from FunctionSpaceFunctions2(D4,D3,D5,D1)
+--R            if D4 has Join(Ring,OrderedSet) and D5 has Join(Ring,
+--R            OrderedSet) and D1 has FS D5 and D3 has FS D4
+--R    ((D4 -> D5),D3) -> D1 from FiniteSetAggregateFunctions2(D4,D3,
+--R            D5,D1)
+--R            if D4 has SETCAT and D5 has SETCAT and D1 has FSAGG D5 and
+--R            D3 has FSAGG D4
+--R    ((D2 -> D2),D) -> D from D if D has HOAGG D2 and D2 has TYPE
+--R
+--R    ((D2 -> D2),D) -> D from D
+--R            if D has IDPC(D2,D3) and D2 has SETCAT and D3 has ORDSET
+--R
+--R    ((D4 -> D5),IntegrationResult D4) -> IntegrationResult D5
+--R            from IntegrationResultFunctions2(D4,D5)
+--R            if D4 has FIELD and D5 has FIELD
+--R    ((D4 -> D5),Union(Record(ratpart: D4,coeff: D4),"failed")) ->
+--R            Union(Record(ratpart: D5,coeff: D5),"failed")
+--R            from IntegrationResultFunctions2(D4,D5)
+--R            if D4 has FIELD and D5 has FIELD
+--R    ((D4 -> D1),Union(D4,"failed")) -> Union(D1,"failed")
+--R            from IntegrationResultFunctions2(D4,D1)
+--R            if D4 has FIELD and D1 has FIELD
+--R    ((D4 -> D5),Union(Record(mainpart: D4,limitedlogs: List Record(
+--R            coeff: D4,logand: D4)),"failed")) -> Union(Record(mainpart: D5,
+--R            limitedlogs: List Record(coeff: D5,logand: D5)),"failed")
+--R            from IntegrationResultFunctions2(D4,D5)
+--R            if D4 has FIELD and D5 has FIELD
+--R    ((D4 -> D5),InfiniteTuple D4) -> InfiniteTuple D5
+--R            from InfiniteTupleFunctions2(D4,D5)
+--R            if D4 has TYPE and D5 has TYPE
+--R    (((D5,D6) -> D7),InfiniteTuple D5,InfiniteTuple D6) ->
+--R            InfiniteTuple D7
+--R            from InfiniteTupleFunctions3(D5,D6,D7)
+--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
+--R    (((D5,D6) -> D7),Stream D5,InfiniteTuple D6) -> Stream D7
+--R            from InfiniteTupleFunctions3(D5,D6,D7)
+--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
+--R    (((D5,D6) -> D7),InfiniteTuple D5,Stream D6) -> Stream D7
+--R            from InfiniteTupleFunctions3(D5,D6,D7)
+--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
+--R    ((D2 -> D2),InfiniteTuple D2) -> InfiniteTuple D2 from
+--R            InfiniteTuple D2
+--R            if D2 has TYPE
+--R    ((D4 -> D5),List D4) -> List D5 from ListFunctions2(D4,D5)
+--R            if D4 has TYPE and D5 has TYPE
+--R    (((D5,D6) -> D7),List D5,List D6) -> List D7
+--R            from ListFunctions3(D5,D6,D7)
+--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
+--R    (((D2,D2) -> D2),D,D) -> D from D if D has LNAGG D2 and D2 has
+--R            TYPE
+--R    ((D5 -> D8),D4) -> D2
+--R            from MatrixCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,D2)
+--R            if D5 has RING and D8 has RING and D6 has FLAGG D5 and D7
+--R            has FLAGG D5 and D2 has MATCAT(D8,D9,D1) and D4 has MATCAT(
+--R            D5,D6,D7) and D9 has FLAGG D8 and D1 has FLAGG D8
+--R    ((D5 -> Union(D8,"failed")),D4) -> Union(D2,"failed")
+--R            from MatrixCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,D2)
+--R            if D5 has RING and D8 has RING and D6 has FLAGG D5 and D7
+--R            has FLAGG D5 and D2 has MATCAT(D8,D9,D1) and D4 has MATCAT(
+--R            D5,D6,D7) and D9 has FLAGG D8 and D1 has FLAGG D8
+--R    ((D7 -> D8),D3) -> D1 from MPolyCatFunctions2(D4,D5,D6,D7,D8,D3
+--R            ,D1)
+--R            if D7 has RING and D8 has RING and D4 has ORDSET and D5 has
+--R            OAMONS and D1 has POLYCAT(D8,D6,D4) and D6 has OAMONS and
+--R            D3 has POLYCAT(D7,D5,D4)
+--R    ((D4 -> D5),MonoidRing(D4,D6)) -> MonoidRing(D5,D6)
+--R            from MonoidRingFunctions2(D4,D5,D6)
+--R            if D4 has RING and D5 has RING and D6 has MONOID
+--R    ((D4 -> D5),D3) -> D1 from OctonionCategoryFunctions2(D3,D4,D1,
+--R            D5)
+--R            if D4 has COMRING and D5 has COMRING and D1 has OC D5 and
+--R            D3 has OC D4
+--R    ((D4 -> D5),OnePointCompletion D4) -> OnePointCompletion D5
+--R            from OnePointCompletionFunctions2(D4,D5)
+--R            if D4 has SETCAT and D5 has SETCAT
+--R    ((D4 -> D5),OnePointCompletion D4,OnePointCompletion D5) ->
+--R            OnePointCompletion D5
+--R            from OnePointCompletionFunctions2(D4,D5)
+--R            if D4 has SETCAT and D5 has SETCAT
+--R    ((D4 -> D5),OrderedCompletion D4) -> OrderedCompletion D5
+--R            from OrderedCompletionFunctions2(D4,D5)
+--R            if D4 has SETCAT and D5 has SETCAT
+--R    ((D4 -> D5),OrderedCompletion D4,OrderedCompletion D5,
+--R            OrderedCompletion D5) -> OrderedCompletion D5
+--R            from OrderedCompletionFunctions2(D4,D5)
+--R            if D4 has SETCAT and D5 has SETCAT
+--R    ((D4 -> D5),ParametricPlaneCurve D4) -> ParametricPlaneCurve D5
+--R            from ParametricPlaneCurveFunctions2(D4,D5)
+--R            if D4 has TYPE and D5 has TYPE
+--R    ((D4 -> D5),ParametricSpaceCurve D4) -> ParametricSpaceCurve D5
+--R            from ParametricSpaceCurveFunctions2(D4,D5)
+--R            if D4 has TYPE and D5 has TYPE
+--R    ((D4 -> D5),ParametricSurface D4) -> ParametricSurface D5
+--R            from ParametricSurfaceFunctions2(D4,D5)
+--R            if D4 has TYPE and D5 has TYPE
+--R    ((D5 -> D6),PatternMatchResult(D4,D5)) -> PatternMatchResult(D4
+--R            ,D6)
+--R            from PatternMatchResultFunctions2(D4,D5,D6)
+--R            if D4 has SETCAT and D5 has SETCAT and D6 has SETCAT
+--R    ((D4 -> D5),Pattern D4) -> Pattern D5 from PatternFunctions2(D4
+--R            ,D5)
+--R            if D4 has SETCAT and D5 has SETCAT
+--R    ((D4 -> D5),Polynomial D4) -> Polynomial D5
+--R            from PolynomialFunctions2(D4,D5)
+--R            if D4 has RING and D5 has RING
+--R    ((D4 -> D5),PrimitiveArray D4) -> PrimitiveArray D5
+--R            from PrimitiveArrayFunctions2(D4,D5)
+--R            if D4 has TYPE and D5 has TYPE
+--R    ((D4 -> D5),Point D4) -> Point D5 from PointFunctions2(D4,D5)
+--R            if D4 has RING and D5 has RING
+--R    ((D4 -> D5),D3) -> D1 from QuotientFieldCategoryFunctions2(D4,
+--R            D5,D3,D1)
+--R            if D4 has INTDOM and D5 has INTDOM and D1 has QFCAT D5 and
+--R            D3 has QFCAT D4
+--R    ((D4 -> D5),D3) -> D1 from QuaternionCategoryFunctions2(D3,D4,
+--R            D1,D5)
+--R            if D4 has COMRING and D5 has COMRING and D1 has QUATCAT D5
+--R            and D3 has QUATCAT D4
+--R    (((D4,D4) -> D4),D,D) -> D from D
+--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
+--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
+--R    ((D4 -> D4),D) -> D from D
+--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
+--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
+--R    ((D9 -> D1),D6) -> D4
+--R            from RectangularMatrixCategoryFunctions2(D7,D8,D9,D10,D11,
+--R            D6,D1,D2,D3,D4)
+--R            if D9 has RING and D1 has RING and D7: NNI and D8: NNI and
+--R            D10 has DIRPCAT(D8,D9) and D11 has DIRPCAT(D7,D9) and D4
+--R            has RMATCAT(D7,D8,D1,D2,D3) and D6 has RMATCAT(D7,D8,D9,D10
+--R            ,D11) and D2 has DIRPCAT(D8,D1) and D3 has DIRPCAT(D7,D1)
+--R
+--R    ((D4 -> D5),Segment D4) -> Segment D5 from SegmentFunctions2(D4
+--R            ,D5)
+--R            if D4 has TYPE and D5 has TYPE
+--R    ((D4 -> D5),Segment D4) -> List D5 from SegmentFunctions2(D4,D5
+--R            )
+--R            if D4 has ORDRING and D4 has TYPE and D5 has TYPE
+--R    ((D4 -> D5),SegmentBinding D4) -> SegmentBinding D5
+--R            from SegmentBindingFunctions2(D4,D5)
+--R            if D4 has TYPE and D5 has TYPE
+--R    ((D3 -> D3),D) -> D1 from D
+--R            if D has SEGXCAT(D3,D1) and D3 has ORDRING and D1 has STAGG
+--R            D3
+--R    ((D4 -> D5),Stream D4) -> Stream D5 from StreamFunctions2(D4,D5
+--R            )
+--R            if D4 has TYPE and D5 has TYPE
+--R    (((D5,D6) -> D7),Stream D5,Stream D6) -> Stream D7
+--R            from StreamFunctions3(D5,D6,D7)
+--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
+--R    ((D4 -> D5),SparseUnivariatePolynomial D4) ->
+--R            SparseUnivariatePolynomial D5
+--R            from SparseUnivariatePolynomialFunctions2(D4,D5)
+--R            if D4 has RING and D5 has RING
+--R    (((D3,D3) -> D3),D,D) -> D from D
+--R            if D has TBAGG(D2,D3) and D2 has SETCAT and D3 has SETCAT
+--R
+--R    ((D5 -> D6),UnivariateLaurentSeries(D5,D7,D9)) ->
+--R            UnivariateLaurentSeries(D6,D8,D1)
+--R            from UnivariateLaurentSeriesFunctions2(D5,D6,D7,D8,D9,D1)
+--R            if D5 has RING and D6 has RING and D7: SYMBOL and D9: D5
+--R            and D1: D6 and D8: SYMBOL
+--R    ((D4 -> D5),UniversalSegment D4) -> UniversalSegment D5
+--R            from UniversalSegmentFunctions2(D4,D5)
+--R            if D4 has TYPE and D5 has TYPE
+--R    ((D4 -> D5),UniversalSegment D4) -> Stream D5
+--R            from UniversalSegmentFunctions2(D4,D5)
+--R            if D4 has ORDRING and D4 has TYPE and D5 has TYPE
+--R    ((D5 -> D7),UnivariatePolynomial(D4,D5)) ->
+--R            UnivariatePolynomial(D6,D7)
+--R            from UnivariatePolynomialFunctions2(D4,D5,D6,D7)
+--R            if D4: SYMBOL and D5 has RING and D7 has RING and D6:
+--R            SYMBOL
+--R    ((D4 -> D5),D3) -> D1
+--R            from UnivariatePolynomialCategoryFunctions2(D4,D3,D5,D1)
+--R            if D4 has RING and D5 has RING and D1 has UPOLYC D5 and D3
+--R            has UPOLYC D4
+--R    ((D5 -> D6),UnivariatePuiseuxSeries(D5,D7,D9)) ->
+--R            UnivariatePuiseuxSeries(D6,D8,D1)
+--R            from UnivariatePuiseuxSeriesFunctions2(D5,D6,D7,D8,D9,D1)
+--R            if D5 has RING and D6 has RING and D7: SYMBOL and D9: D5
+--R            and D1: D6 and D8: SYMBOL
+--R    ((D4 -> D5),D3) -> D1
+--R            from UnivariateTaylorSeriesFunctions2(D4,D5,D3,D1)
+--R            if D4 has RING and D5 has RING and D1 has UTSCAT D5 and D3
+--R            has UTSCAT D4
+--R    ((D4 -> D5),Vector D4) -> Vector D5 from VectorFunctions2(D4,D5
+--R            )
+--R            if D4 has TYPE and D5 has TYPE
+--R    ((D4 -> Union(D5,"failed")),Vector D4) -> Union(Vector D5,
+--R            "failed")
+--R            from VectorFunctions2(D4,D5) if D4 has TYPE and D5 has TYPE
+--R
+--R    ((D3 -> D3),D) -> D from D
+--R            if D has XFALG(D2,D3) and D2 has ORDSET and D3 has RING
+--R
+--RThere are 11 unexposed functions called map :
+--R    ((D2 -> D2),AntiSymm(D2,D3)) -> AntiSymm(D2,D3) from AntiSymm(D2
+--R            ,D3)
+--R            if D2 has RING and D3: LIST SYMBOL
+--R    ((Expression D2 -> Expression D2),DeRhamComplex(D2,D3)) ->
+--R            DeRhamComplex(D2,D3)
+--R            from DeRhamComplex(D2,D3)
+--R            if D2 has Join(Ring,OrderedSet) and D3: LIST SYMBOL
+--R    ((D5 -> D1),String,Kernel D5) -> D1
+--R            from ExpressionSpaceFunctions1(D5,D1)
+--R            if D5 has ES and D1 has TYPE
+--R    ((D5 -> D6),D3) -> D1
+--R            from FiniteAbelianMonoidRingFunctions2(D4,D5,D3,D6,D1)
+--R            if D5 has RING and D6 has RING and D4 has OAMON and D1 has
+--R            FAMR(D6,D4) and D3 has FAMR(D5,D4)
+--R    ((D4 -> D6),D3) -> D1 from MultipleMap(D4,D5,D3,D6,D7,D1)
+--R            if D4 has INTDOM and D6 has INTDOM and D5 has UPOLYC D4 and
+--R            D1 has UPOLYC FRAC D7 and D3 has UPOLYC FRAC D5 and D7 has
+--R            UPOLYC D6
+--R    ((D4 -> D5),D3) -> D1 from MPolyCatFunctions3(D4,D5,D6,D7,D8,D3,
+--R            D1)
+--R            if D4 has ORDSET and D5 has ORDSET and D6 has OAMONS and D8
+--R            has RING and D1 has POLYCAT(D8,D7,D5) and D7 has OAMONS and
+--R            D3 has POLYCAT(D8,D6,D4)
+--R    ((D2 -> D2),MonoidRing(D2,D3)) -> MonoidRing(D2,D3)
+--R            from MonoidRing(D2,D3) if D2 has RING and D3 has MONOID
+--R    ((D4 -> D5),NewSparseUnivariatePolynomial D4) ->
+--R            NewSparseUnivariatePolynomial D5
+--R            from NewSparseUnivariatePolynomialFunctions2(D4,D5)
+--R            if D4 has RING and D5 has RING
+--R    ((D7 -> D2),(D8 -> D2),D5) -> D2
+--R            from PolynomialCategoryLifting(D6,D7,D8,D5,D2)
+--R            if D7 has ORDSET and D8 has RING and D6 has OAMONS and D2
+--R            has SetCategory with
+--R               ?+? : (%,%) -> %
+--R               ?*? : (%,%) -> %
+--R               D : (%,NonNegativeInteger) -> % and D5 has POLYCAT(
+--R            D8,D6,D7)
+--R    ((Polynomial D3 -> D1),D1) -> D1 from PushVariables(D3,D4,D5,D1
+--R            )
+--R            if D3 has RING and D1 has POLYCAT(POLY D3,D4,D5) and D4 has
+--R            OAMONS and D5 has OrderedSet with
+--R               convert : % -> Symbol
+--R               variable : Symbol -> Union(%,"failed")
+--R    ((D2 -> D2),XPolynomialRing(D2,D3)) -> XPolynomialRing(D2,D3)
+--R            from XPolynomialRing(D2,D3) if D2 has RING and D3 has
+--R            ORDMON
+--R
+--RExamples of map from AbelianMonoidRing
+--R
+--R
+--RExamples of map from AntiSymm
+--R
+--R
+--RExamples of map from TwoDimensionalArrayCategory
+--R
+--Radder(a:Integer,b:Integer):Integer == a+b
+--Rarr1 : ARRAY2 INT := new(5,4,10)
+--Rarr2 : ARRAY2 INT := new(3,3,10)
+--Rmap(adder,arr1,arr2,17)
+--R
+--Radder(a:Integer,b:Integer):Integer == a+b
+--Rarr : ARRAY2 INT := new(5,4,10)
+--Rmap(adder,arr,arr)
+--R
+--Rarr : ARRAY2 INT := new(5,4,10)
+--Rmap(-,arr)
+--Rmap((x +-> x + x),arr)
+--R
+--R
+--RExamples of map from OneDimensionalArrayFunctions2
+--R
+--RT1:=OneDimensionalArrayFunctions2(Integer,Integer)
+--Rmap(x+->x+2,[i for i in 1..10])$T1 +--R +--R +--RExamples of map from CartesianTensorFunctions2 +--R +--R +--RExamples of map from ComplexFunctions2 +--R +--R +--RExamples of map from DeRhamComplex +--R +--R +--RExamples of map from DirectProductFunctions2 +--R +--R +--RExamples of map from EquationFunctions2 +--R +--R +--RExamples of map from Equation +--R +--R +--RExamples of map from ExpressionSpaceFunctions1 +--R +--R +--RExamples of map from ExpressionSpaceFunctions2 +--R +--R +--RExamples of map from ExpressionSpace +--R +--R +--RExamples of map from ExpertSystemToolsPackage2 +--R +--R +--RExamples of map from ExpressionFunctions2 +--R +--R +--RExamples of map from FiniteAbelianMonoidRingFunctions2 +--R +--R +--RExamples of map from FiniteDivisorFunctions2 +--R +--R +--RExamples of map from FullyEvalableOver +--R +--R +--RExamples of map from FunctionFieldCategoryFunctions2 +--R +--R +--RExamples of map from FiniteLinearAggregateFunctions2 +--R +--R +--RExamples of map from FreeModuleCat +--R +--R +--RExamples of map from FactoredFunctions2 +--R +--R +--RExamples of map from FractionFunctions2 +--R +--R +--RExamples of map from FractionalIdealFunctions2 +--R +--R +--RExamples of map from FramedNonAssociativeAlgebraFunctions2 +--R +--R +--RExamples of map from Factored +--R +--Rm(a:Factored Polynomial Integer):Factored Polynomial Integer == a^2 +--Rf:=x*y^3-3*x^2*y^2+3*x^3*y-x^4 +--Rmap(m,f) +--Rg:=makeFR(z,factorList f) +--Rmap(m,g) +--R +--R +--RExamples of map from FunctionSpaceFunctions2 +--R +--R +--RExamples of map from FiniteSetAggregateFunctions2 +--R +--R +--RExamples of map from HomogeneousAggregate +--R +--R +--RExamples of map from IndexedDirectProductCategory +--R +--R +--RExamples of map from IntegrationResultFunctions2 +--R +--R +--RExamples of map from InfiniteTupleFunctions2 +--R +--R +--RExamples of map from InfiniteTupleFunctions3 +--R +--R +--RExamples of map from InfiniteTuple +--R +--R +--RExamples of map from ListFunctions2 +--R +--R +--RExamples of map from ListFunctions3 +--R +--R +--RExamples of map from LinearAggregate +--R +--R +--RExamples of map from MatrixCategoryFunctions2 +--R +--R +--RExamples of map from MultipleMap +--R +--R +--RExamples of map from MPolyCatFunctions2 +--R +--R +--RExamples of map from MPolyCatFunctions3 +--R +--R +--RExamples of map from MonoidRingFunctions2 +--R +--R +--RExamples of map from MonoidRing +--R +--R +--RExamples of map from NewSparseUnivariatePolynomialFunctions2 +--R +--R +--RExamples of map from OctonionCategoryFunctions2 +--R +--R +--RExamples of map from OnePointCompletionFunctions2 +--R +--R +--RExamples of map from OrderedCompletionFunctions2 +--R +--R +--RExamples of map from ParametricPlaneCurveFunctions2 +--R +--R +--RExamples of map from ParametricSpaceCurveFunctions2 +--R +--R +--RExamples of map from ParametricSurfaceFunctions2 +--R +--R +--RExamples of map from PatternMatchResultFunctions2 +--R +--R +--RExamples of map from PatternFunctions2 +--R +--R +--RExamples of map from PolynomialFunctions2 +--R +--R +--RExamples of map from PolynomialCategoryLifting +--R +--R +--RExamples of map from PrimitiveArrayFunctions2 +--R +--RT1:=PrimitiveArrayFunctions2(Integer,Integer) +--Rmap(x+->x+2,[i for i in 1..10])$T1
+--R
+--R
+--RExamples of map from PointFunctions2
+--R
+--R
+--RExamples of map from PushVariables
+--R
+--R
+--RExamples of map from QuotientFieldCategoryFunctions2
+--R
+--R
+--RExamples of map from QuaternionCategoryFunctions2
+--R
+--R
+--RExamples of map from RectangularMatrixCategory
+--R
+--R
+--RExamples of map from RectangularMatrixCategoryFunctions2
+--R
+--R
+--RExamples of map from SegmentFunctions2
+--R
+--R
+--RExamples of map from SegmentBindingFunctions2
+--R
+--R
+--RExamples of map from SegmentExpansionCategory
+--R
+--R
+--RExamples of map from StreamFunctions2
+--R
+--Rm:=[i for i in 1..]
+--Rf(i:PositiveInteger):PositiveInteger==i**2
+--Rmap(f,m)
+--R
+--R
+--RExamples of map from StreamFunctions3
+--R
+--Rm:=[i for i in 1..]::Stream(Integer)
+--Rn:=[i for i in 1..]::Stream(Integer)
+--Rf(i:Integer,j:Integer):Integer == i+j
+--Rmap(f,m,n)
+--R
+--R
+--RExamples of map from SparseUnivariatePolynomialFunctions2
+--R
+--R
+--RExamples of map from TableAggregate
+--R
+--R
+--RExamples of map from UnivariateLaurentSeriesFunctions2
+--R
+--R
+--RExamples of map from UniversalSegmentFunctions2
+--R
+--R
+--RExamples of map from UnivariatePolynomialFunctions2
+--R
+--R
+--RExamples of map from UnivariatePolynomialCategoryFunctions2
+--R
+--R
+--RExamples of map from UnivariatePuiseuxSeriesFunctions2
+--R
+--R
+--RExamples of map from UnivariateTaylorSeriesFunctions2
+--R
+--R
+--RExamples of map from VectorFunctions2
+--R
+--R
+--RExamples of map from XFreeAlgebra
+--R
+--R
+--RExamples of map from XPolynomialRing
+--R
+--E 21
+
+--S 22 of 127
+--R)d op complete
+--R
+--R
+--RThere are 5 exposed functions called complete :
+--R    ContinuedFraction D1 -> ContinuedFraction D1 from
+--R            ContinuedFraction D1
+--R            if D1 has EUCDOM
+--R    Integer -> SymmetricPolynomial Fraction Integer from
+--R            CycleIndicators
+--R    D -> D from D if D has LZSTAGG D1 and D1 has TYPE
+--R    D -> D from D if D has PADICCT D1
+--R    D -> D from D
+--R            if D has PSCAT(D1,D2,D3) and D1 has RING and D2 has OAMON
+--R            and D3 has ORDSET
+--R
+--RExamples of complete from ContinuedFraction
+--R
+--R
+--RExamples of complete from CycleIndicators
+--R
+--R
+--RExamples of complete from LazyStreamAggregate
+--R
+--Rm:=[i for i in 1..]
+--Rn:=filterUntil(i+->i>100,m)
+--RnumberOfComputedEntries n
+--Rcomplete n
+--RnumberOfComputedEntries n
+--R
+--R
+--RExamples of complete from PAdicIntegerCategory
+--R
+--R
+--RExamples of complete from PowerSeriesCategory
+--R
+--E 22
+
+--S 23 of 127
+--R)d op cyclicEqual?
+--R
+--R
+--RThere is one exposed function called cyclicEqual? :
+--R    (Tree D2,Tree D2) -> Boolean from Tree D2 if D2 has SETCAT
+--R
+--RExamples of cyclicEqual? from Tree
+--R
+--Rt1:=tree [1,2,3,4]
+--Rt2:=tree [1,2,3,4]
+--RcyclicEqual?(t1,t2)
+--R
+--E 23
+
+--S 24 of 127
+--R)d op ncols
+--R
+--R
+--RThere are 2 exposed functions called ncols :
+--R    D -> NonNegativeInteger from D
+--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
+--R            D2 and D4 has FLAGG D2
+--R    D -> NonNegativeInteger from D
+--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
+--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
+--R
+--RExamples of ncols from TwoDimensionalArrayCategory
+--R
+--Rarr : ARRAY2 INT := new(5,4,10)
+--Rncols(arr)
+--R
+--R
+--RExamples of ncols from RectangularMatrixCategory
+--R
+--E 24
+
+--S 25 of 127
+--R)d op inverseIntegralMatrixAtInfinity
+--R
+--R
+--RThere is one exposed function called inverseIntegralMatrixAtInfinity :
+--R     -> Matrix Fraction D3 from D
+--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC
+--R            D2 and D4 has UPOLYC FRAC D3
+--R
+--RExamples of inverseIntegralMatrixAtInfinity from FunctionFieldCategory
+--R
+--RP0 := UnivariatePolynomial(x, Integer)
+--RP1 := UnivariatePolynomial(y, Fraction P0)
+--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
+--RinverseIntegralMatrixAtInfinity()$R +--R +--E 25 + +--S 26 of 127 +--R)d op generalizedContinuumHypothesisAssumed +--R +--R +--RThere is one exposed function called generalizedContinuumHypothesisAssumed : +--R  Boolean -> Boolean from CardinalNumber +--R +--RExamples of generalizedContinuumHypothesisAssumed from CardinalNumber +--R +--RgeneralizedContinuumHypothesisAssumed true +--Ra:=Aleph 0 +--Rc:=2**a +--Rf:=2**c +--R +--E 26 + +--S 27 of 127 +--R)d op cyclic? +--R +--R +--RThere are 2 exposed functions called cyclic? : +--R  D -> Boolean from D if D has RCAGG D2 and D2 has TYPE +--R  Tree D2 -> Boolean from Tree D2 if D2 has SETCAT +--R +--RExamples of cyclic? from RecursiveAggregate +--R +--R +--RExamples of cyclic? from Tree +--R +--Rt1:=tree [1,2,3,4] +--Rcyclic? t1 +--R +--E 27 + +--S 28 of 127 +--R)d op nilFactor +--R +--R +--RThere is one exposed function called nilFactor : +--R  (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM +--R +--R +--RExamples of nilFactor from Factored +--R +--RnilFactor(24,2) +--RnilFactor(x-y,3) +--R +--E 28 + +--S 29 of 127 +--R)d op quote +--R +--R +--RThere is one exposed function called quote : +--R  -> Character from Character +--R +--RThere is one unexposed function called quote : +--R  OutputForm -> OutputForm from OutputForm +--R +--RExamples of quote from Character +--R +--Rquote() +--R +--R +--RExamples of quote from OutputForm +--R +--E 29 + +--S 30 of 127 +--R)d op balancedBinaryTree +--R +--R +--RThere is one exposed function called balancedBinaryTree : +--R  (NonNegativeInteger,D2) -> BalancedBinaryTree D2 +--R from BalancedBinaryTree D2 if D2 has SETCAT +--R +--RExamples of balancedBinaryTree from BalancedBinaryTree +--R +--RbalancedBinaryTree(4, 0) +--R +--E 30 + +--S 31 of 127 +--R)d op integralBasisAtInfinity +--R +--R +--RThere is one exposed function called integralBasisAtInfinity : +--R  -> Vector D from D +--R if D2 has UFD and D3 has UPOLYC D2 and D4 has UPOLYC FRAC +--R D3 and D has FFCAT(D2,D3,D4) +--R +--RExamples of integralBasisAtInfinity from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RintegralBasisAtInfinity()$R
+--R
+--E 31
+
+--S 32 of 127
+--R)d op branchPointAtInfinity?
+--R
+--R
+--RThere is one exposed function called branchPointAtInfinity? :
+--R     -> Boolean from D
+--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC
+--R            D2 and D4 has UPOLYC FRAC D3
+--R
+--RExamples of branchPointAtInfinity? from FunctionFieldCategory
+--R
+--RP0 := UnivariatePolynomial(x, Integer)
+--RP1 := UnivariatePolynomial(y, Fraction P0)
+--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
+--RbranchPointAtInfinity?()$R +--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) +--RbranchPointAtInfinity?()$R
+--R
+--E 32
+
+--S 33 of 127
+--R)d op transpose
+--R
+--R
+--RThere are 4 exposed functions called transpose :
+--R    (CartesianTensor(D2,D3,D4),Integer,Integer) -> CartesianTensor(
+--R            D2,D3,D4)
+--R            from CartesianTensor(D2,D3,D4)
+--R            if D2: INT and D3: NNI and D4 has COMRING
+--R    CartesianTensor(D1,D2,D3) -> CartesianTensor(D1,D2,D3)
+--R            from CartesianTensor(D1,D2,D3)
+--R            if D1: INT and D2: NNI and D3 has COMRING
+--R    D -> D from D
+--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG
+--R            D1 and D3 has FLAGG D1
+--R    D1 -> D from D
+--R            if D2 has RING and D has MATCAT(D2,D1,D3) and D1 has FLAGG
+--R            D2 and D3 has FLAGG D2
+--R
+--RThere is one unexposed function called transpose :
+--R    SquareMatrix(D1,D2) -> SquareMatrix(D1,D2) from SquareMatrix(D1,
+--R            D2)
+--R            if D1: NNI and D2 has RING
+--R
+--RExamples of transpose from CartesianTensor
+--R
+--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]]
+--Rtm:CartesianTensor(1,2,Integer):=m
+--Rtn:CartesianTensor(1,2,Integer):=[tm,tm]
+--Rtranspose(tn,1,2)
+--R
+--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]]
+--RTm:CartesianTensor(1,2,Integer):=m
+--Rtranspose(Tm)
+--R
+--R
+--RExamples of transpose from MatrixCategory
+--R
+--R
+--RExamples of transpose from SquareMatrix
+--R
+--E 33
+
+--S 34 of 127
+--R)d op setrest!
+--R
+--R
+--RThere are 2 exposed functions called setrest! :
+--R    (Stream D2,Integer,Stream D2) -> Stream D2 from Stream D2 if D2
+--R            has TYPE
+--R    (D,D) -> D from D
+--R            if D has shallowlyMutable and D has URAGG D1 and D1 has
+--R            TYPE
+--R
+--RExamples of setrest! from Stream
+--R
+--Rp:=[i for i in 1..]
+--Rq:=[i for i in 9..]
+--Rsetrest!(p,4,q)
+--Rp
+--R
+--R
+--RExamples of setrest! from UnaryRecursiveAggregate
+--R
+--E 34
+
+--S 35 of 127
+--R)d op **
+--R
+--R
+--RThere are 20 exposed functions called ** :
+--R    (CardinalNumber,CardinalNumber) -> CardinalNumber from
+--R            CardinalNumber
+--R    (DoubleFloat,DoubleFloat) -> DoubleFloat from DoubleFloat
+--R    (D,Integer) -> D from D if D has DIVRING
+--R    (D,D) -> D from D if D has ELEMFUN
+--R    (Float,Float) -> Float from Float
+--R    (D,NonNegativeInteger) -> D from D
+--R            if D has FS D2 and D2 has ORDSET and D2 has SGROUP
+--R    (D,Integer) -> D from D if D has GROUP
+--R    (PolynomialIdeals(D2,D3,D4,D5),NonNegativeInteger) ->
+--R            PolynomialIdeals(D2,D3,D4,D5)
+--R            from PolynomialIdeals(D2,D3,D4,D5)
+--R            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5
+--R            has POLYCAT(D2,D3,D4)
+--R    ((D3 -> D3),NonNegativeInteger) -> (D3 -> D3) from
+--R            MappingPackage1 D3
+--R            if D3 has SETCAT
+--R    (D,Integer) -> D from D
+--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG
+--R            D2 and D4 has FLAGG D2 and D2 has FIELD
+--R    (D,NonNegativeInteger) -> D from D
+--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG
+--R            D2 and D4 has FLAGG D2
+--R    (ModuleOperator(D2,D3),Integer) -> ModuleOperator(D2,D3)
+--R            from ModuleOperator(D2,D3)
+--R            if D2 has RING and D3 has LMODULE D2
+--R    (BasicOperator,Integer) -> ModuleOperator(D3,D4)
+--R            from ModuleOperator(D3,D4)
+--R            if D3 has RING and D4 has LMODULE D3
+--R    (D,PositiveInteger) -> D from D if D has MONAD
+--R    (D,NonNegativeInteger) -> D from D if D has MONADWU
+--R    (D,NonNegativeInteger) -> D from D if D has MONOID
+--R    (D,Fraction Integer) -> D from D if D has RADCAT
+--R    (D,PositiveInteger) -> D from D if D has SGROUP
+--R    (D,Integer) -> D from D
+--R            if D has SMATCAT(D2,D3,D4,D5) and D3 has RING and D4 has
+--R            DIRPCAT(D2,D3) and D5 has DIRPCAT(D2,D3) and D3 has FIELD
+--R
+--R    (D,D1) -> D from D
+--R            if D has UTSCAT D1 and D1 has RING and D1 has FIELD
+--R
+--RThere are 19 unexposed functions called ** :
+--R    (D1,Fraction Integer) -> D1 from AlgebraicFunction(D3,D1)
+--R            if D3 has RETRACT INT and D3 has Join(OrderedSet,
+--R            IntegralDomain) and D1 has FS D3
+--R    (D1,D1) -> D1 from CombinatorialFunction(D2,D1)
+--R            if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS D2
+--R
+--R    (D1,Fraction Integer) -> D1
+--R            from ElementaryFunctionsUnivariateLaurentSeries(D3,D4,D1)
+--R            if D3 has FIELD and D3 has ALGEBRA FRAC INT and D4 has
+--R            UTSCAT D3 and D1 has ULSCCAT(D3,D4)
+--R    (D1,Fraction Integer) -> D1
+--R            from ElementaryFunctionsUnivariatePuiseuxSeries(D3,D4,D1,D5
+--R            )
+--R            if D3 has FIELD and D3 has ALGEBRA FRAC INT and D4 has
+--R            ULSCAT D3 and D1 has UPXSCCA(D3,D4) and D5 has PTRANFN D4
+--R
+--R    (D1,Integer) -> FreeGroup D1 from FreeGroup D1 if D1 has SETCAT
+--R
+--R    (D1,NonNegativeInteger) -> FreeMonoid D1 from FreeMonoid D1
+--R            if D1 has SETCAT
+--R    (Vector D3,Integer) -> Vector D3 from
+--R            InnerNormalBasisFieldFunctions D3
+--R            if D3 has FFIELDC
+--R    (InputForm,Integer) -> InputForm from InputForm
+--R    (InputForm,NonNegativeInteger) -> InputForm from InputForm
+--R    (Matrix D3,NonNegativeInteger) -> Matrix D3
+--R            from StorageEfficientMatrixOperations D3 if D3 has RING
+--R    (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2
+--R            )
+--R            from MyExpression(D1,D2)
+--R            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
+--R            IntegralDomain)
+--R    (D1,NonNegativeInteger) -> OrderedFreeMonoid D1
+--R            from OrderedFreeMonoid D1 if D1 has ORDSET
+--R    (Operator D2,Integer) -> Operator D2 from Operator D2 if D2 has
+--R            RING
+--R    (BasicOperator,Integer) -> Operator D3 from Operator D3 if D3
+--R            has RING
+--R    (OutputForm,OutputForm) -> OutputForm from OutputForm
+--R    (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
+--R            SETCAT
+--R    (Pattern D2,NonNegativeInteger) -> Pattern D2 from Pattern D2
+--R            if D2 has SETCAT
+--R    (Stream D2,Stream D2) -> Stream D2
+--R            from StreamTranscendentalFunctionsNonCommutative D2
+--R            if D2 has ALGEBRA FRAC INT
+--R    (Stream D2,Stream D2) -> Stream D2
+--R            from StreamTranscendentalFunctions D2 if D2 has ALGEBRA
+--R            FRAC INT
+--R
+--RExamples of ** from AlgebraicFunction
+--R
+--R
+--RExamples of ** from CardinalNumber
+--R
+--Rc2:=2::CardinalNumber
+--Rc2**c2
+--RA1:=Aleph 1
+--RA1**c2
+--RgeneralizedContinuumHypothesisAssumed true
+--RA1**A1
+--R
+--R
+--RExamples of ** from CombinatorialFunction
+--R
+--R
+--RExamples of ** from DoubleFloat
+--R
+--R
+--RExamples of ** from DivisionRing
+--R
+--R
+--RExamples of ** from ElementaryFunctionsUnivariateLaurentSeries
+--R
+--R
+--RExamples of ** from ElementaryFunctionsUnivariatePuiseuxSeries
+--R
+--R
+--RExamples of ** from ElementaryFunctionCategory
+--R
+--R
+--RExamples of ** from FreeGroup
+--R
+--R
+--RExamples of ** from Float
+--R
+--R
+--RExamples of ** from FreeMonoid
+--R
+--R
+--RExamples of ** from FunctionSpace
+--R
+--R
+--RExamples of ** from Group
+--R
+--R
+--RExamples of ** from PolynomialIdeals
+--R
+--R
+--RExamples of ** from InnerNormalBasisFieldFunctions
+--R
+--R
+--RExamples of ** from InputForm
+--R
+--R
+--RExamples of ** from MappingPackage1
+--R
+--R
+--RExamples of ** from MatrixCategory
+--R
+--R
+--RExamples of ** from StorageEfficientMatrixOperations
+--R
+--R
+--RExamples of ** from ModuleOperator
+--R
+--R
+--RExamples of ** from Monad
+--R
+--R
+--RExamples of ** from MonadWithUnit
+--R
+--R
+--RExamples of ** from Monoid
+--R
+--R
+--RExamples of ** from MyExpression
+--R
+--R
+--RExamples of ** from OrderedFreeMonoid
+--R
+--R
+--RExamples of ** from Operator
+--R
+--R
+--RExamples of ** from OutputForm
+--R
+--R
+--RExamples of ** from Pattern
+--R
+--R
+--RExamples of ** from RadicalCategory
+--R
+--R
+--RExamples of ** from SemiGroup
+--R
+--R
+--RExamples of ** from SquareMatrixCategory
+--R
+--R
+--RExamples of ** from StreamTranscendentalFunctionsNonCommutative
+--R
+--R
+--RExamples of ** from StreamTranscendentalFunctions
+--R
+--R
+--RExamples of ** from UnivariateTaylorSeriesCategory
+--R
+--E 35
+
+--S 36 of 127
+--R)d op plot
+--R
+--R
+--RThere are 12 unexposed functions called plot :
+--R    (D2,Symbol,Segment DoubleFloat) -> Plot from PlotFunctions1 D2
+--R            if D2 has KONVERT INFORM
+--R    (D2,D2,Symbol,Segment DoubleFloat) -> Plot from PlotFunctions1
+--R            D2
+--R            if D2 has KONVERT INFORM
+--R    (Plot3D,Segment DoubleFloat) -> Plot3D from Plot3D
+--R    ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(
+--R            DoubleFloat -> DoubleFloat),(DoubleFloat ->
DoubleFloat),Segment
+--R            DoubleFloat,Segment DoubleFloat,Segment DoubleFloat,Segment
+--R            DoubleFloat) -> Plot3D
+--R            from Plot3D
+--R    ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(
+--R            DoubleFloat -> DoubleFloat),(DoubleFloat ->
DoubleFloat),Segment
+--R            DoubleFloat) -> Plot3D
+--R            from Plot3D
+--R    (Plot,Segment DoubleFloat) -> Plot from Plot
+--R    ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),
+--R            Segment DoubleFloat,Segment DoubleFloat,Segment DoubleFloat) ->
+--R            Plot
+--R            from Plot
+--R    ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),
+--R            Segment DoubleFloat) -> Plot
+--R            from Plot
+--R    (List (DoubleFloat -> DoubleFloat),Segment DoubleFloat,Segment
+--R            DoubleFloat) -> Plot
+--R            from Plot
+--R    (List (DoubleFloat -> DoubleFloat),Segment DoubleFloat) -> Plot
+--R            from Plot
+--R    ((DoubleFloat -> DoubleFloat),Segment DoubleFloat,Segment
+--R            DoubleFloat) -> Plot
+--R            from Plot
+--R    ((DoubleFloat -> DoubleFloat),Segment DoubleFloat) -> Plot from
+--R            Plot
+--R
+--RExamples of plot from PlotFunctions1
+--R
+--R
+--RExamples of plot from Plot3D
+--R
+--R
+--RExamples of plot from Plot
+--R
+--Rfp:=(t:DFLOAT):DFLOAT +-> sin(t)
+--Rplot(fp,-1.0..1.0)$PLOT +--R +--E 36 + +--S 37 of 127 +--R)d op factorList +--R +--R +--RThere is one exposed function called factorList : +--R  Factored D2 -> List Record(flg: Union("nil","sqfr","irred", +--R "prime"),fctr: D2,xpnt: Integer) +--R from Factored D2 if D2 has INTDOM +--R +--RThere is one unexposed function called factorList : +--R  (D2,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger) +--R -> List SparseUnivariatePolynomial D2 +--R from ChineseRemainderToolsForIntegralBases(D2,D4,D5) +--R if D2 has FFIELDC and D4 has UPOLYC D2 and D5 has UPOLYC D4 +--R +--R +--RExamples of factorList from Factored +--R +--Rf:=nilFactor(x-y,3) +--RfactorList f +--R +--R +--RExamples of factorList from ChineseRemainderToolsForIntegralBases +--R +--E 37 + +--S 38 of 127 +--R)d op physicalLength +--R +--R +--RThere is one exposed function called physicalLength : +--R  FlexibleArray D2 -> NonNegativeInteger from FlexibleArray D2 +--R if D2 has TYPE +--R +--RThere is one unexposed function called physicalLength : +--R  IndexedFlexibleArray(D2,D3) -> NonNegativeInteger +--R from IndexedFlexibleArray(D2,D3) if D2 has TYPE and D3: INT +--R +--R +--RExamples of physicalLength from FlexibleArray +--R +--R +--RExamples of physicalLength from IndexedFlexibleArray +--R +--RT1:=IndexedFlexibleArray(Integer,20) +--Rt2:=flexibleArray([i for i in 1..10])$T1
+--RphysicalLength t2
+--R
+--E 38
+
+--S 39 of 127
+--R)d op absolutelyIrreducible?
+--R
+--R
+--RThere is one exposed function called absolutelyIrreducible? :
+--R     -> Boolean from D
+--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC
+--R            D2 and D4 has UPOLYC FRAC D3
+--R
+--RThere is one unexposed function called absolutelyIrreducible? :
+--R     -> Boolean from FunctionFieldCategory&(D2,D3,D4,D5)
+--R            if D3 has UFD and D4 has UPOLYC D3 and D5 has UPOLYC FRAC
+--R            D4 and D2 has FFCAT(D3,D4,D5)
+--R
+--RExamples of absolutelyIrreducible? from FunctionFieldCategory&
+--R
+--RP0 := UnivariatePolynomial(x, Integer)
+--RP1 := UnivariatePolynomial(y, Fraction P0)
+--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4)
+--RabsolutelyIrreducible?()$R2 +--R +--R +--RExamples of absolutelyIrreducible? from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) +--RabsolutelyIrreducible?()$R2
+--R
+--E 39
+
+--S 40 of 127
+--R)d op repeating?
+--R
+--R
+--RThere is one exposed function called repeating? :
+--R    (List D3,Stream D3) -> Boolean from Stream D3
+--R            if D3 has SETCAT and D3 has TYPE
+--R
+--RExamples of repeating? from Stream
+--R
+--Rm:=[1,2,3]
+--Rn:=repeating(m)
+--Rrepeating?(m,n)
+--R
+--E 40
+
+--S 41 of 127
+--R)d op lazy?
+--R
+--R
+--RThere is one exposed function called lazy? :
+--R    D -> Boolean from D if D has LZSTAGG D2 and D2 has TYPE
+--R
+--RExamples of lazy? from LazyStreamAggregate
+--R
+--Rm:=[i for i in 0..]
+--Rlazy? m
+--R
+--E 41
+
+--S 42 of 127
+--R)d op ord
+--R
+--R
+--RThere is one exposed function called ord :
+--R    Character -> Integer from Character
+--R
+--RExamples of ord from Character
+--R
+--Rchars := [char "a", char "A", char "X", char "8", char "+"]
+--R[ord c for c in chars]
+--R
+--E 42
+
+--S 43 of 127
+--R)d op setColumn!
+--R
+--R
+--RThere is one exposed function called setColumn! :
+--R    (D,Integer,D2) -> D from D
+--R            if D has ARR2CAT(D3,D4,D2) and D3 has TYPE and D4 has FLAGG
+--R            D3 and D2 has FLAGG D3
+--R
+--RExamples of setColumn! from TwoDimensionalArrayCategory
+--R
+--RT1:=TwoDimensionalArray Integer
+--Rarr:T1:= new(5,4,0)
+--RT2:=OneDimensionalArray Integer
+--Racol:=construct([1,2,3,4,5]::List(INT))$T2 +--RsetColumn!(arr,1,acol)$T1
+--R
+--E 43
+
+--S 44 of 127
+--R)d op lowerCase?
+--R
+--R
+--RThere is one exposed function called lowerCase? :
+--R    Character -> Boolean from Character
+--R
+--RExamples of lowerCase? from Character
+--R
+--Rchars := [char "a", char "A", char "X", char "8", char "+"]
+--R[lowerCase? c for c in chars]
+--R
+--E 44
+
+--S 45 of 127
+--R)d op physicalLength!
+--R
+--R
+--RThere is one exposed function called physicalLength! :
+--R    (FlexibleArray D2,Integer) -> FlexibleArray D2 from
+--R            FlexibleArray D2
+--R            if D2 has TYPE
+--R
+--RThere is one unexposed function called physicalLength! :
+--R    (IndexedFlexibleArray(D2,D3),Integer) -> IndexedFlexibleArray(D2
+--R            ,D3)
+--R            from IndexedFlexibleArray(D2,D3) if D2 has TYPE and D3: INT
+--R
+--R
+--RExamples of physicalLength! from FlexibleArray
+--R
+--R
+--RExamples of physicalLength! from IndexedFlexibleArray
+--R
+--RT1:=IndexedFlexibleArray(Integer,20)
+--Rt2:=flexibleArray([i for i in 1..10])$T1 +--RphysicalLength!(t2,15) +--R +--E 45 + +--S 46 of 127 +--R)d op countable? +--R +--R +--RThere is one exposed function called countable? : +--R  CardinalNumber -> Boolean from CardinalNumber +--R +--RExamples of countable? from CardinalNumber +--R +--Rc2:=2::CardinalNumber +--Rcountable? c2 +--RA0:=Aleph 0 +--Rcountable? A0 +--RA1:=Aleph 1 +--Rcountable? A1 +--R +--E 46 + +--S 47 of 127 +--R)d op extend +--R +--R +--RThere are 11 exposed functions called extend : +--R  (ContinuedFraction D2,Integer) -> ContinuedFraction D2 +--R from ContinuedFraction D2 if D2 has EUCDOM +--R  (D,Integer) -> D from D if D has LZSTAGG D2 and D2 has TYPE +--R  (D,NonNegativeInteger) -> D from D +--R if D has MTSCAT(D2,D3) and D2 has RING and D3 has ORDSET +--R +--R  (D,Integer) -> D from D if D has PADICCT D2 +--R  (D,List D2) -> D from D if D has PTCAT D2 and D2 has RING +--R  (List D6,List D) -> List D from D +--R if D has RSETCAT(D3,D4,D5,D6) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D6 has RPOLCAT(D3,D4,D5) +--R  (List D6,D) -> List D from D +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D has RSETCAT(D3,D4,D5,D6) +--R  (D2,List D) -> List D from D +--R if D has RSETCAT(D3,D4,D5,D2) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5) +--R  (D2,D) -> List D from D +--R if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and D2 +--R has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2) +--R  (D,D1) -> D from D +--R if D has TSETCAT(D2,D3,D4,D1) and D2 has INTDOM and D3 has +--R OAMONS and D4 has ORDSET and D1 has RPOLCAT(D2,D3,D4) +--R  (D,D1) -> D from D +--R if D has UPSCAT(D2,D1) and D2 has RING and D1 has OAMON +--R +--RExamples of extend from ContinuedFraction +--R +--R +--RExamples of extend from LazyStreamAggregate +--R +--Rm:=[i for i in 0..] +--RnumberOfComputedEntries m +--Rextend(m,20) +--RnumberOfComputedEntries m +--R +--R +--RExamples of extend from MultivariateTaylorSeriesCategory +--R +--R +--RExamples of extend from PAdicIntegerCategory +--R +--R +--RExamples of extend from PointCategory +--R +--R +--RExamples of extend from RegularTriangularSetCategory +--R +--R +--RExamples of extend from TriangularSetCategory +--R +--R +--RExamples of extend from UnivariatePowerSeriesCategory +--R +--E 47 + +--S 48 of 127 +--R)d op length +--R +--R +--RThere are 3 exposed functions called length : +--R  D -> D from D if D has INS +--R  D -> NonNegativeInteger from D if D has QUAGG D2 and D2 has TYPE +--R +--R  D -> D1 from D +--R if D has VECTCAT D1 and D1 has TYPE and D1 has RADCAT and +--R D1 has RING +--R +--RThere are 6 unexposed functions called length : +--R  D2 -> D1 from GaloisGroupFactorizationUtilities(D3,D2,D1) +--R if D3 has RING and D1 has Join(FloatingPointSystem, +--R RetractableTo D3,Field,TranscendentalFunctionCategory, +--R ElementaryFunctionCategory) and D2 has UPOLYC D3 +--R  LyndonWord D2 -> PositiveInteger from LyndonWord D2 if D2 has +--R ORDSET +--R  Magma D2 -> PositiveInteger from Magma D2 if D2 has ORDSET +--R  OrderedFreeMonoid D2 -> NonNegativeInteger from +--R OrderedFreeMonoid D2 +--R if D2 has ORDSET +--R  PoincareBirkhoffWittLyndonBasis D2 -> NonNegativeInteger +--R from PoincareBirkhoffWittLyndonBasis D2 if D2 has ORDSET +--R +--R  Tuple D2 -> NonNegativeInteger from Tuple D2 if D2 has TYPE +--R +--RExamples of length from GaloisGroupFactorizationUtilities +--R +--R +--RExamples of length from IntegerNumberSystem +--R +--R +--RExamples of length from LyndonWord +--R +--R +--RExamples of length from Magma +--R +--R +--RExamples of length from OrderedFreeMonoid +--R +--R +--RExamples of length from PoincareBirkhoffWittLyndonBasis +--R +--R +--RExamples of length from QueueAggregate +--R +--R +--RExamples of length from Tuple +--R +--Rt1:PrimitiveArray(Integer):= [i for i in 1..10] +--Rt2:=coerce(t1)$Tuple(Integer)
+--Rlength(t2)
+--R
+--R
+--RExamples of length from VectorCategory
+--R
+--E 48
+
+--S 49 of 127
+--R)d op viewPosDefault
+--R
+--R
+--RThere are 2 exposed functions called viewPosDefault :
+--R     -> List NonNegativeInteger from ViewDefaultsPackage
+--R    List NonNegativeInteger -> List NonNegativeInteger
+--R            from ViewDefaultsPackage
+--R
+--RExamples of viewPosDefault from ViewDefaultsPackage
+--R
+--Rand Y position of a viewport window unless overriden explicityly, newly
created viewports will have th
+--Rand Y coordinates x, y.
+--R
+--Rand Y position of a viewport window unless overriden explicityly, newly
created viewports will have this
+--Rand Y coordinate.
+--R
+--E 49
+
+--S 50 of 127
+--R)d op groebner
+--R
+--R
+--RThere are 4 exposed functions called groebner :
+--R    List D5 -> List D5 from GroebnerPackage(D2,D3,D4,D5)
+--R            if D5 has POLYCAT(D2,D3,D4) and D2 has GCDDOM and D3 has
+--R            OAMONS and D4 has ORDSET
+--R    (List D6,String) -> List D6 from GroebnerPackage(D3,D4,D5,D6)
+--R            if D6 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has
+--R            OAMONS and D5 has ORDSET
+--R    (List D6,String,String) -> List D6 from GroebnerPackage(D3,D4,D5
+--R            ,D6)
+--R            if D6 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has
+--R            OAMONS and D5 has ORDSET
+--R    PolynomialIdeals(D1,D2,D3,D4) -> PolynomialIdeals(D1,D2,D3,D4)
+--R            from PolynomialIdeals(D1,D2,D3,D4)
+--R            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4
+--R            has POLYCAT(D1,D2,D3)
+--R
+--RThere are 2 unexposed functions called groebner :
+--R    List Polynomial D2 -> List Polynomial D2 from FGLMIfCanPackage(
+--R            D2,D3)
+--R            if D2 has GCDDOM and D3: LIST SYMBOL
+--R    List NewSparseMultivariatePolynomial(D2,OrderedVariableList D3)
+--R             -> List NewSparseMultivariatePolynomial(D2,OrderedVariableList
+--R            D3)
+--R            from LexTriangularPackage(D2,D3)
+--R            if D2 has GCDDOM and D3: LIST SYMBOL
+--R
+--RExamples of groebner from FGLMIfCanPackage
+--R
+--R
+--RExamples of groebner from GroebnerPackage
+--R
+--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36
+--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s
+--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2
+--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s
+--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3
+--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2
+--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000
+--Rsn7:=[s1,s2,s3,s4,s5,s6,s7]
+--Rgroebner(sn7,"info","redcrit")
+--R
+--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36
+--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s
+--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2
+--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s
+--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3
+--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2
+--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000
+--Rsn7:=[s1,s2,s3,s4,s5,s6,s7]
+--Rgroebner(sn7,"info")
+--Rgroebner(sn7,"redcrit")
+--R
+--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36
+--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s
+--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2
+--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s
+--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3
+--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2
+--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000
+--Rsn7:=[s1,s2,s3,s4,s5,s6,s7]
+--Rgroebner(sn7)
+--R
+--R
+--RExamples of groebner from PolynomialIdeals
+--R
+--R
+--RExamples of groebner from LexTriangularPackage
+--R
+--E 50
+
+--S 51 of 127
+--R)d op primeFactor
+--R
+--R
+--RThere is one exposed function called primeFactor :
+--R    (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM
+--R
+--R
+--RExamples of primeFactor from Factored
+--R
+--Ra:=primeFactor(3,4)
+--RnthFlag(a,1)
+--R
+--E 51
+
+--S 52 of 127
+--R)d op map!
+--R
+--R
+--RThere are 2 exposed functions called map! :
+--R    ((D2 -> D2),D) -> D from D
+--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
+--R            D2 and D4 has FLAGG D2
+--R    ((D2 -> D2),D) -> D from D
+--R            if D has shallowlyMutable and D has HOAGG D2 and D2 has
+--R            TYPE
+--R
+--RExamples of map! from TwoDimensionalArrayCategory
+--R
+--Rarr : ARRAY2 INT := new(5,4,10)
+--Rmap!(-,arr)
+--R
+--R
+--RExamples of map! from HomogeneousAggregate
+--R
+--E 52
+
+--S 53 of 127
+--R)d op setleaves!
+--R
+--R
+--RThere is one exposed function called setleaves! :
+--R    (BalancedBinaryTree D2,List D2) -> BalancedBinaryTree D2
+--R            from BalancedBinaryTree D2 if D2 has SETCAT
+--R
+--RExamples of setleaves! from BalancedBinaryTree
+--R
+--Rt1:=balancedBinaryTree(4, 0)
+--Rsetleaves!(t1,[1,2,3,4])
+--R
+--E 53
+
+--S 54 of 127
+--R)d op scan
+--R
+--R
+--RThere are 8 exposed functions called scan :
+--R    (((D5,D4) -> D4),OneDimensionalArray D5,D4) ->
+--R            OneDimensionalArray D4
+--R            from OneDimensionalArrayFunctions2(D5,D4)
+--R            if D5 has TYPE and D4 has TYPE
+--R    (((D6,D4) -> D4),DirectProduct(D5,D6),D4) -> DirectProduct(D5,D4
+--R            )
+--R            from DirectProductFunctions2(D5,D6,D4)
+--R            if D5: NNI and D6 has TYPE and D4 has TYPE
+--R    (((D5,D4) -> D4),D3,D4) -> D1
+--R            from FiniteLinearAggregateFunctions2(D5,D3,D4,D1)
+--R            if D5 has TYPE and D4 has TYPE and D1 has FLAGG D4 and D3
+--R            has FLAGG D5
+--R    (((D5,D4) -> D4),D3,D4) -> D1
+--R            from FiniteSetAggregateFunctions2(D5,D3,D4,D1)
+--R            if D5 has SETCAT and D4 has SETCAT and D1 has FSAGG D4 and
+--R            D3 has FSAGG D5
+--R    (((D5,D4) -> D4),List D5,D4) -> List D4 from ListFunctions2(D5,
+--R            D4)
+--R            if D5 has TYPE and D4 has TYPE
+--R    (((D5,D4) -> D4),PrimitiveArray D5,D4) -> PrimitiveArray D4
+--R            from PrimitiveArrayFunctions2(D5,D4)
+--R            if D5 has TYPE and D4 has TYPE
+--R    (D2,((D5,D2) -> D2),Stream D5) -> Stream D2
+--R            from StreamFunctions2(D5,D2) if D5 has TYPE and D2 has TYPE
+--R
+--R    (((D5,D4) -> D4),Vector D5,D4) -> Vector D4
+--R            from VectorFunctions2(D5,D4) if D5 has TYPE and D4 has TYPE
+--R
+--R
+--RExamples of scan from OneDimensionalArrayFunctions2
+--R
+--RT1:=OneDimensionalArrayFunctions2(Integer,Integer)
+--Radder(a:Integer,b:Integer):Integer == a+b
+--Rscan(adder,[i for i in 1..10],0)$T1 +--R +--R +--RExamples of scan from DirectProductFunctions2 +--R +--R +--RExamples of scan from FiniteLinearAggregateFunctions2 +--R +--R +--RExamples of scan from FiniteSetAggregateFunctions2 +--R +--R +--RExamples of scan from ListFunctions2 +--R +--R +--RExamples of scan from PrimitiveArrayFunctions2 +--R +--RT1:=PrimitiveArrayFunctions2(Integer,Integer) +--Radder(a:Integer,b:Integer):Integer == a+b +--Rscan(adder,[i for i in 1..10],0)$T1
+--R
+--R
+--RExamples of scan from StreamFunctions2
+--R
+--Rm:=[i for i in 1..]::Stream(Integer)
+--Rf(i:Integer,j:Integer):Integer==i+j
+--Rscan(1,f,m)
+--R
+--R
+--RExamples of scan from VectorFunctions2
+--R
+--E 54
+
+--S 55 of 127
+--R)d op alphabetic?
+--R
+--R
+--RThere is one exposed function called alphabetic? :
+--R    Character -> Boolean from Character
+--R
+--RExamples of alphabetic? from Character
+--R
+--Rchars := [char "a", char "A", char "X", char "8", char "+"]
+--R[alphabetic? c for c in chars]
+--R
+--E 55
+
+--S 56 of 127
+--R)d op +
+--R
+--R
+--RThere are 12 exposed functions called + :
+--R    (D,D) -> D from D if D has ABELSG
+--R    (Color,Color) -> Color from Color
+--R    (Database D1,Database D1) -> Database D1 from Database D1
+--R            if D1 has OrderedSet with
+--R               ?.? : (%,Symbol) -> String
+--R               display : % -> Void
+--R               fullDisplay : % -> Void
+--R    (Equation D1,D1) -> Equation D1 from Equation D1
+--R            if D1 has ABELSG and D1 has TYPE
+--R    (D1,Equation D1) -> Equation D1 from Equation D1
+--R            if D1 has ABELSG and D1 has TYPE
+--R    (D1,D) -> D from D
+--R            if D has FAMONC(D1,D2) and D1 has SETCAT and D2 has CABMON
+--R
+--R    (D1,FullPartialFractionExpansion(D2,D1)) ->
+--R            FullPartialFractionExpansion(D2,D1)
+--R            from FullPartialFractionExpansion(D2,D1)
+--R            if D2 has Join(Field,CharacteristicZero) and D1 has UPOLYC
+--R            D2
+--R    (D,D) -> D from D
+--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
+--R
+--R    (PolynomialIdeals(D1,D2,D3,D4),PolynomialIdeals(D1,D2,D3,D4))
+--R             -> PolynomialIdeals(D1,D2,D3,D4)
+--R            from PolynomialIdeals(D1,D2,D3,D4)
+--R            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4
+--R            has POLYCAT(D1,D2,D3)
+--R    ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,
+--R            D3)
+--R            if D2 has SETCAT and D3 has RING
+--R    (D,D) -> D from D
+--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG
+--R            D1 and D3 has FLAGG D1
+--R    (D,D) -> D from D
+--R            if D has VECTCAT D1 and D1 has TYPE and D1 has ABELSG
+--R
+--RThere are 5 unexposed functions called + :
+--R    (InputForm,InputForm) -> InputForm from InputForm
+--R    (OutputForm,OutputForm) -> OutputForm from OutputForm
+--R    (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
+--R            SETCAT
+--R    (Stream D2,Stream D2) -> Stream D2 from
+--R            StreamTaylorSeriesOperations D2
+--R            if D2 has RING
+--R    (Point DoubleFloat,Point DoubleFloat) -> Point DoubleFloat
+--R            from TubePlotTools
+--R
+--RExamples of + from AbelianSemiGroup
+--R
+--R
+--RExamples of + from Color
+--R
+--R
+--RExamples of + from Database
+--R
+--R
+--RExamples of + from Equation
+--R
+--R
+--RExamples of + from FreeAbelianMonoidCategory
+--R
+--R
+--RExamples of + from FullPartialFractionExpansion
+--R
+--R
+--RExamples of + from GradedModule
+--R
+--R
+--RExamples of + from PolynomialIdeals
+--R
+--R
+--RExamples of + from InputForm
+--R
+--R
+--RExamples of + from MappingPackage4
+--R
+--Rf:=(x:INT):INT +-> 3*x
+--Rg:=(x:INT):INT +-> 2*x+3
+--R(f+g)(4)
+--R
+--R
+--RExamples of + from MatrixCategory
+--R
+--R
+--RExamples of + from OutputForm
+--R
+--R
+--RExamples of + from Pattern
+--R
+--R
+--RExamples of + from StreamTaylorSeriesOperations
+--R
+--R
+--RExamples of + from TubePlotTools
+--R
+--R
+--RExamples of + from VectorCategory
+--R
+--E 56
+
+--S 57 of 127
+--R)d op -
+--R
+--R
+--RThere are 13 exposed functions called - :
+--R    (D,D) -> D from D if D has ABELGRP
+--R    D -> D from D if D has ABELGRP
+--R    (CardinalNumber,CardinalNumber) -> Union(CardinalNumber,"failed"
+--R            )
+--R            from CardinalNumber
+--R    (Database D1,Database D1) -> Database D1 from Database D1
+--R            if D1 has OrderedSet with
+--R               ?.? : (%,Symbol) -> String
+--R               display : % -> Void
+--R               fullDisplay : % -> Void
+--R    (Equation D1,D1) -> Equation D1 from Equation D1
+--R            if D1 has ABELGRP and D1 has TYPE
+--R    (D1,Equation D1) -> Equation D1 from Equation D1
+--R            if D1 has ABELGRP and D1 has TYPE
+--R    (D,D) -> D from D
+--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
+--R
+--R    D -> D from D
+--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
+--R
+--R    ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,D3
+--R            )
+--R            if D2 has SETCAT and D3 has RING
+--R    D -> D from D
+--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG
+--R            D1 and D3 has FLAGG D1
+--R    (D,D) -> D from D
+--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG
+--R            D1 and D3 has FLAGG D1
+--R    (D,D) -> D from D
+--R            if D has VECTCAT D1 and D1 has TYPE and D1 has ABELGRP
+--R    D -> D from D
+--R            if D has VECTCAT D1 and D1 has TYPE and D1 has ABELGRP
+--R
+--RThere are 5 unexposed functions called - :
+--R    OutputForm -> OutputForm from OutputForm
+--R    (OutputForm,OutputForm) -> OutputForm from OutputForm
+--R    (Stream D2,Stream D2) -> Stream D2 from
+--R            StreamTaylorSeriesOperations D2
+--R            if D2 has RING
+--R    Stream D2 -> Stream D2 from StreamTaylorSeriesOperations D2
+--R            if D2 has RING
+--R    (Point DoubleFloat,Point DoubleFloat) -> Point DoubleFloat
+--R            from TubePlotTools
+--R
+--RExamples of - from AbelianGroup
+--R
+--R
+--RExamples of - from CardinalNumber
+--R
+--Rc2:=2::CardinalNumber
+--Rc2-c2
+--RA1:=Aleph 1
+--RA1-c2
+--R
+--R
+--RExamples of - from Database
+--R
+--R
+--RExamples of - from Equation
+--R
+--R
+--RExamples of - from GradedModule
+--R
+--R
+--RExamples of - from MappingPackage4
+--R
+--Rf:=(x:INT):INT +-> 3*x
+--Rg:=(x:INT):INT +-> 2*x+3
+--R(f-g)(4)
+--R
+--R
+--RExamples of - from MatrixCategory
+--R
+--R
+--RExamples of - from OutputForm
+--R
+--R
+--RExamples of - from StreamTaylorSeriesOperations
+--R
+--R
+--RExamples of - from TubePlotTools
+--R
+--R
+--RExamples of - from VectorCategory
+--R
+--E 57
+
+--S 58 of 127
+--R)d op /
+--R
+--R
+--RThere are 13 exposed functions called / :
+--R    (D,D1) -> D from D
+--R            if D has AMR(D1,D2) and D1 has RING and D2 has OAMON and D1
+--R            has FIELD
+--R    (DoubleFloat,Integer) -> DoubleFloat from DoubleFloat
+--R    (D,D) -> D from D
+--R            if D = EQ D1 and D1 has FIELD and D1 has TYPE or D = EQ D1
+--R            and D1 has GROUP and D1 has TYPE
+--R    (D,D) -> D from D if D has FIELD
+--R    (Float,Integer) -> Float from Float
+--R    (SparseMultivariatePolynomial(D2,Kernel D),
+--R            SparseMultivariatePolynomial(D2,Kernel D)) -> D
+--R            from D if D2 has INTDOM and D2 has ORDSET and D has FS D2
+--R
+--R    (D,D) -> D from D if D has GROUP
+--R    (D,D1) -> D from D
+--R            if D has LIECAT D1 and D1 has COMRING and D1 has FIELD
+--R    ((D2 -> Expression Integer),(D2 -> Expression Integer)) -> (D2
+--R             -> Expression Integer)
+--R            from MappingPackage4(D2,D3) if D2 has SETCAT and D3 has
+--R            RING
+--R    (D,D1) -> D from D
+--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG
+--R            D1 and D3 has FLAGG D1 and D1 has FIELD
+--R    (D1,D1) -> D from D if D has QFCAT D1 and D1 has INTDOM
+--R    (D,D1) -> D from D
+--R            if D has RMATCAT(D2,D3,D1,D4,D5) and D1 has RING and D4 has
+--R            DIRPCAT(D3,D1) and D5 has DIRPCAT(D2,D1) and D1 has FIELD
+--R
+--R    (D,D1) -> D from D if D has VSPACE D1 and D1 has FIELD
+--R
+--RThere are 13 unexposed functions called / :
+--R    (Vector D2,Vector D2) -> Vector D2
+--R            from InnerNormalBasisFieldFunctions D2 if D2 has FFIELDC
+--R
+--R    (InputForm,InputForm) -> InputForm from InputForm
+--R    (D1,D2) -> LocalAlgebra(D1,D3,D2) from LocalAlgebra(D1,D3,D2)
+--R            if D3 has COMRING and D1 has ALGEBRA D3 and D2 has
+--R            SubsetCategory(Monoid,D3)
+--R    (LocalAlgebra(D2,D3,D1),D1) -> LocalAlgebra(D2,D3,D1)
+--R            from LocalAlgebra(D2,D3,D1)
+--R            if D3 has COMRING and D2 has ALGEBRA D3 and D1 has
+--R            SubsetCategory(Monoid,D3)
+--R    (D1,D2) -> Localize(D1,D3,D2) from Localize(D1,D3,D2)
+--R            if D3 has COMRING and D1 has MODULE D3 and D2 has
+--R            SubsetCategory(Monoid,D3)
+--R    (Localize(D2,D3,D1),D1) -> Localize(D2,D3,D1) from Localize(D2,
+--R            D3,D1)
+--R            if D3 has COMRING and D2 has MODULE D3 and D1 has
+--R            SubsetCategory(Monoid,D3)
+--R    (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2)
+--R            from MyExpression(D1,D2)
+--R            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
+--R            IntegralDomain)
+--R    (OutputForm,OutputForm) -> OutputForm from OutputForm
+--R    (OrdinaryWeightedPolynomials(D1,D2,D3,D4),
+--R            OrdinaryWeightedPolynomials(D1,D2,D3,D4)) -> Union(
+--R            OrdinaryWeightedPolynomials(D1,D2,D3,D4),"failed")
+--R            from OrdinaryWeightedPolynomials(D1,D2,D3,D4)
+--R            if D1 has FIELD and D1 has RING and D2: LIST SYMBOL and D3
+--R            : LIST NNI and D4: NNI
+--R    (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
+--R            SETCAT
+--R    (Stream D2,Stream D2) -> Stream D2 from
+--R            StreamTaylorSeriesOperations D2
+--R            if D2 has RING
+--R    (WeightedPolynomials(D1,D2,D3,D4,D5,D6,D7),WeightedPolynomials(
+--R            D1,D2,D3,D4,D5,D6,D7)) -> Union(WeightedPolynomials(D1,D2,D3,D4,
+--R            D5,D6,D7),"failed")
+--R            from WeightedPolynomials(D1,D2,D3,D4,D5,D6,D7)
+--R            if D1 has FIELD and D1 has RING and D2 has ORDSET and D3
+--R            has OAMONS and D5: LIST D2 and D4 has POLYCAT(D1,D3,D2) and
+--R            D6: LIST NNI and D7: NNI
+--R    (XPolynomialRing(D1,D2),D1) -> XPolynomialRing(D1,D2)
+--R            from XPolynomialRing(D1,D2)
+--R            if D1 has FIELD and D1 has RING and D2 has ORDMON
+--R
+--RExamples of / from AbelianMonoidRing
+--R
+--R
+--RExamples of / from DoubleFloat
+--R
+--R
+--RExamples of / from Equation
+--R
+--R
+--RExamples of / from Field
+--R
+--R
+--RExamples of / from Float
+--R
+--R
+--RExamples of / from FunctionSpace
+--R
+--R
+--RExamples of / from Group
+--R
+--R
+--RExamples of / from InnerNormalBasisFieldFunctions
+--R
+--R
+--RExamples of / from InputForm
+--R
+--R
+--RExamples of / from LocalAlgebra
+--R
+--R
+--RExamples of / from LieAlgebra
+--R
+--R
+--RExamples of / from Localize
+--R
+--R
+--RExamples of / from MappingPackage4
+--R
+--Rp:=(x:EXPR(INT)):EXPR(INT)+->3*x
+--Rq:=(x:EXPR(INT)):EXPR(INT)+->2*x+3
+--R(p/q)(4)
+--R(p/q)(x)
+--R
+--R
+--RExamples of / from MatrixCategory
+--R
+--R
+--RExamples of / from MyExpression
+--R
+--R
+--RExamples of / from OutputForm
+--R
+--R
+--RExamples of / from OrdinaryWeightedPolynomials
+--R
+--R
+--RExamples of / from Pattern
+--R
+--R
+--RExamples of / from QuotientFieldCategory
+--R
+--R
+--RExamples of / from RectangularMatrixCategory
+--R
+--R
+--RExamples of / from StreamTaylorSeriesOperations
+--R
+--R
+--RExamples of / from VectorSpace
+--R
+--R
+--RExamples of / from WeightedPolynomials
+--R
+--R
+--RExamples of / from XPolynomialRing
+--R
+--E 58
+
+--S 59 of 127
+--R)d op integralBasis
+--R
+--R
+--RThere is one exposed function called integralBasis :
+--R     -> Vector D from D
+--R            if D2 has UFD and D3 has UPOLYC D2 and D4 has UPOLYC FRAC
+--R            D3 and D has FFCAT(D2,D3,D4)
+--R
+--RThere are 4 unexposed functions called integralBasis :
+--R     -> Record(basis: Matrix D2,basisDen: D2,basisInv: Matrix D2)
+--R            from FunctionFieldIntegralBasis(D2,D3,D4)
+--R            if D2 has EuclideanDomain with
+--R               squareFree : % -> Factored % and D3 has UPOLYC D2
+--R            and D4 has FRAMALG(D2,D3)
+--R     -> Record(basis: Matrix Integer,basisDen: Integer,basisInv:
+--R            Matrix Integer)
+--R            from NumberFieldIntegralBasis(D2,D3)
+--R            if D2 has UPOLYC INT and D3 has FRAMALG(INT,D2)
+--R     -> Record(basis: Matrix D3,basisDen: D3,basisInv: Matrix D3)
+--R            from PAdicWildFunctionFieldIntegralBasis(D2,D3,D4,D5)
+--R            if D2 has FFIELDC and D3 has UPOLYC D2 and D4 has UPOLYC D3
+--R            and D5 has MONOGEN(D3,D4)
+--R     -> Record(basis: Matrix D3,basisDen: D3,basisInv: Matrix D3)
+--R            from WildFunctionFieldIntegralBasis(D2,D3,D4,D5)
+--R            if D2 has FFIELDC and D3 has UPOLYC D2 and D4 has UPOLYC D3
+--R            and D5 has FRAMALG(D3,D4)
+--R
+--RExamples of integralBasis from FunctionFieldCategory
+--R
+--RP0 := UnivariatePolynomial(x, Integer)
+--RP1 := UnivariatePolynomial(y, Fraction P0)
+--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
+--RintegralBasis()$R +--R +--R +--RExamples of integralBasis from FunctionFieldIntegralBasis +--R +--R +--RExamples of integralBasis from NumberFieldIntegralBasis +--R +--R +--RExamples of integralBasis from PAdicWildFunctionFieldIntegralBasis +--R +--R +--RExamples of integralBasis from WildFunctionFieldIntegralBasis +--R +--E 59 + +--S 60 of 127 +--R)d op split +--R +--R +--RThere are 8 exposed functions called split : +--R  D2 -> Factored D2 from AlgFactor D2 if D2 has UPOLYC AN +--R  (D2,BinarySearchTree D2) -> Record(less: BinarySearchTree D2, +--R greater: BinarySearchTree D2) +--R from BinarySearchTree D2 if D2 has ORDSET +--R  IntegrationResult D3 -> IntegrationResult D3 +--R from IntegrationResultToFunction(D2,D3) +--R if D3 has Join(AlgebraicallyClosedFunctionSpace D2, +--R TranscendentalFunctionCategory) and D2 has Join(GcdDomain, +--R RetractableTo Integer,OrderedSet,LinearlyExplicitRingOver +--R Integer) +--R  IntegrationResult Fraction Polynomial D2 -> IntegrationResult +--R Fraction Polynomial D2 +--R from IntegrationResultRFToFunction D2 +--R if D2 has Join(GcdDomain,RetractableTo Integer,OrderedSet, +--R LinearlyExplicitRingOver Integer) +--R  (List Matrix D4,Vector D4) -> List List Matrix D4 +--R from RepresentationPackage2 D4 if D4 has FIELD and D4 has +--R RING +--R  (List Matrix D4,Vector Vector D4) -> List List Matrix D4 +--R from RepresentationPackage2 D4 if D4 has FIELD and D4 has +--R RING +--R  (D,CharacterClass) -> List D from D if D has SRAGG +--R  (D,Character) -> List D from D if D has SRAGG +--R +--RThere is one unexposed function called split : +--R  (D2,(D2 -> D2)) -> Record(normal: D2,special: D2) +--R from MonomialExtensionTools(D4,D2) +--R if D2 has UPOLYC D4 and D4 has FIELD +--R +--RExamples of split from AlgFactor +--R +--R +--RExamples of split from BinarySearchTree +--R +--Rt1:=binarySearchTree [1,2,3,4] +--Rsplit(3,t1) +--R +--R +--RExamples of split from IntegrationResultToFunction +--R +--R +--RExamples of split from IntegrationResultRFToFunction +--R +--R +--RExamples of split from MonomialExtensionTools +--R +--R +--RExamples of split from RepresentationPackage2 +--R +--R +--RExamples of split from StringAggregate +--R +--E 60 + +--S 61 of 127 +--R)d op qelt +--R +--R +--RThere are 3 exposed functions called qelt : +--R  (D,Integer,Integer) -> D1 from D +--R if D has ARR2CAT(D1,D3,D4) and D3 has FLAGG D1 and D4 has +--R FLAGG D1 and D1 has TYPE +--R  (D,D2) -> D1 from D +--R if D has ELTAGG(D2,D1) and D2 has SETCAT and D1 has TYPE +--R +--R  (D,Integer,Integer) -> D1 from D +--R if D has RMATCAT(D3,D4,D1,D5,D6) and D5 has DIRPCAT(D4,D1) +--R and D6 has DIRPCAT(D3,D1) and D1 has RING +--R +--RExamples of qelt from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--Rqelt(arr,1,1) +--R +--R +--RExamples of qelt from EltableAggregate +--R +--R +--RExamples of qelt from RectangularMatrixCategory +--R +--E 61 + +--S 62 of 127 +--R)d op mapUp! +--R +--R +--RThere are 2 exposed functions called mapUp! : +--R  (BalancedBinaryTree D2,BalancedBinaryTree D2,((D2,D2,D2,D2) -> +--R D2)) -> BalancedBinaryTree D2 +--R from BalancedBinaryTree D2 if D2 has SETCAT +--R  (BalancedBinaryTree D1,((D1,D1) -> D1)) -> D1 +--R from BalancedBinaryTree D1 if D1 has SETCAT +--R +--RExamples of mapUp! from BalancedBinaryTree +--R +--RT1:=BalancedBinaryTree Integer +--Rt2:=balancedBinaryTree(4, 0)$T1
+--Rsetleaves!(t2,[1,2,3,4]::List(Integer))
+--Radder4(i:INT,j:INT,k:INT,l:INT):INT == i+j+k+l
+--RmapUp!(t2,t2,adder4)
+--Rt2
+--R
+--RT1:=BalancedBinaryTree Integer
+--Rt2:=balancedBinaryTree(4, 0)$T1 +--Rsetleaves!(t2,[1,2,3,4]::List(Integer)) +--Radder(a:Integer,b:Integer):Integer == a+b +--RmapUp!(t2,adder) +--Rt2 +--R +--E 62 + +--S 63 of 127 +--R)d op reindex +--R +--R +--RThere is one exposed function called reindex : +--R  (CartesianTensor(D2,D3,D4),List Integer) -> CartesianTensor(D2, +--R D3,D4) +--R from CartesianTensor(D2,D3,D4) +--R if D2: INT and D3: NNI and D4 has COMRING +--R +--RExamples of reindex from CartesianTensor +--R +--Rn:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]] +--Rtn:CartesianTensor(1,2,Integer):=n +--Rp:=product(tn,tn) +--Rreindex(p,[4,3,2,1]) +--R +--E 63 + +--S 64 of 127 +--R)d op mapDown! +--R +--R +--RThere are 2 exposed functions called mapDown! : +--R  (BalancedBinaryTree D1,D1,((D1,D1,D1) -> List D1)) -> +--R BalancedBinaryTree D1 +--R from BalancedBinaryTree D1 if D1 has SETCAT +--R  (BalancedBinaryTree D1,D1,((D1,D1) -> D1)) -> BalancedBinaryTree +--R D1 +--R from BalancedBinaryTree D1 if D1 has SETCAT +--R +--RExamples of mapDown! from BalancedBinaryTree +--R +--RT1:=BalancedBinaryTree Integer +--Rt2:=balancedBinaryTree(4, 0)$T1
+--Rsetleaves!(t2,[1,2,3,4]::List(Integer))
+--Radder3(i:Integer,j:Integer,k:Integer):List Integer == [i+j,j+k]
+--RmapDown!(t2,4::INT,adder3)
+--Rt2
+--R
+--RT1:=BalancedBinaryTree Integer
+--Rt2:=balancedBinaryTree(4, 0)$T1 +--Rsetleaves!(t2,[1,2,3,4]::List(Integer)) +--Radder(i:Integer,j:Integer):Integer == i+j +--RmapDown!(t2,4::INT,adder) +--Rt2 +--R +--E 64 + +--S 65 of 127 +--R)d op nrows +--R +--R +--RThere are 2 exposed functions called nrows : +--R  D -> NonNegativeInteger from D +--R if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG +--R D2 and D4 has FLAGG D2 +--R  D -> NonNegativeInteger from D +--R if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has +--R DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4) +--R +--RExamples of nrows from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--Rnrows(arr) +--R +--R +--RExamples of nrows from RectangularMatrixCategory +--R +--E 65 + +--S 66 of 127 +--R)d op row +--R +--R +--RThere are 2 exposed functions called row : +--R  (D,Integer) -> D1 from D +--R if D has ARR2CAT(D3,D1,D4) and D3 has TYPE and D4 has FLAGG +--R D3 and D1 has FLAGG D3 +--R  (D,Integer) -> D1 from D +--R if D has RMATCAT(D3,D4,D5,D1,D6) and D5 has RING and D6 has +--R DIRPCAT(D3,D5) and D1 has DIRPCAT(D4,D5) +--R +--RExamples of row from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--Rrow(arr,1) +--R +--R +--RExamples of row from RectangularMatrixCategory +--R +--E 66 + +--S 67 of 127 +--R)d op ravel +--R +--R +--RThere is one exposed function called ravel : +--R  CartesianTensor(D2,D3,D4) -> List D4 from CartesianTensor(D2,D3, +--R D4) +--R if D2: INT and D3: NNI and D4 has COMRING +--R +--RExamples of ravel from CartesianTensor +--R +--Rn:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]] +--Rtn:CartesianTensor(1,2,Integer):=n +--Rravel tn +--R +--E 67 + +--S 68 of 127 +--R)d op inverseIntegralMatrix +--R +--R +--RThere is one exposed function called inverseIntegralMatrix : +--R  -> Matrix Fraction D3 from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC +--R D2 and D4 has UPOLYC FRAC D3 +--R +--RExamples of inverseIntegralMatrix from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RinverseIntegralMatrix()$R
+--R
+--E 68
+
+--S 69 of 127
+--R)d op coerce
+--R
+--R
+--RThere are 169 exposed functions called coerce :
+--R    D1 -> D from D if D has ALGEBRA D1 and D1 has COMRING
+--R    Vector D2 -> AlgebraGivenByStructuralConstants(D2,D3,D4,D5)
+--R            from AlgebraGivenByStructuralConstants(D2,D3,D4,D5)
+--R            if D2 has FIELD and D5: VECTOR MATRIX D2 and D3: PI and D4
+--R            : LIST SYMBOL
+--R    SparseMultivariatePolynomial(Integer,Kernel AlgebraicNumber) ->
+--R            AlgebraicNumber
+--R            from AlgebraicNumber
+--R    D2 -> Any from AnyFunctions1 D2 if D2 has TYPE
+--R    Vector FortranExpression([construct,QUOTEJINT,QUOTEX,QUOTEELAM],
+--R            [construct],MachineFloat) -> Asp10 D2
+--R            from Asp10 D2 if D2: SYMBOL
+--R    Vector FortranExpression([construct],[construct,QUOTEXC],
+--R            MachineFloat) -> Asp19 D2
+--R            from Asp19 D2 if D2: SYMBOL
+--R    FortranExpression([construct,QUOTEX],[construct],MachineFloat)
+--R             -> Asp1 D2
+--R            from Asp1 D2 if D2: SYMBOL
+--R    Matrix FortranExpression([construct],[construct,QUOTEX,QUOTEHESS
+--R            ],MachineFloat) -> Asp20 D2
+--R            from Asp20 D2 if D2: SYMBOL
+--R    FortranExpression([construct],[construct,QUOTEXC],MachineFloat)
+--R             -> Asp24 D2
+--R            from Asp24 D2 if D2: SYMBOL
+--R    Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],
+--R            MachineFloat) -> Asp31 D2
+--R            from Asp31 D2 if D2: SYMBOL
+--R    Vector FortranExpression([construct],[construct,QUOTEX],
+--R            MachineFloat) -> Asp35 D2
+--R            from Asp35 D2 if D2: SYMBOL
+--R    Vector FortranExpression([construct,QUOTEX,QUOTEEPS],[construct
+--R            ,QUOTEY],MachineFloat) -> Asp41(D2,D3,D4)
+--R            from Asp41(D2,D3,D4) if D2: SYMBOL and D3: SYMBOL and D4:
+--R            SYMBOL
+--R    Vector FortranExpression([construct,QUOTEEPS],[construct,QUOTE
+--R            YA,QUOTEYB],MachineFloat) -> Asp42(D2,D3,D4)
+--R            from Asp42(D2,D3,D4) if D2: SYMBOL and D3: SYMBOL and D4:
+--R            SYMBOL
+--R    FortranExpression([construct],[construct,QUOTEX],MachineFloat)
+--R             -> Asp49 D2
+--R            from Asp49 D2 if D2: SYMBOL
+--R    FortranExpression([construct],[construct,QUOTEX],MachineFloat)
+--R             -> Asp4 D2
+--R            from Asp4 D2 if D2: SYMBOL
+--R    Vector FortranExpression([construct],[construct,QUOTEXC],
+--R            MachineFloat) -> Asp50 D2
+--R            from Asp50 D2 if D2: SYMBOL
+--R    Vector FortranExpression([construct],[construct,QUOTEX],
+--R            MachineFloat) -> Asp55 D2
+--R            from Asp55 D2 if D2: SYMBOL
+--R    Vector FortranExpression([construct],[construct,QUOTEX],
+--R            MachineFloat) -> Asp6 D2
+--R            from Asp6 D2 if D2: SYMBOL
+--R    Vector FortranExpression([construct,QUOTEX,QUOTEY],[construct],
+--R            MachineFloat) -> Asp73 D2
+--R            from Asp73 D2 if D2: SYMBOL
+--R    Matrix FortranExpression([construct,QUOTEX,QUOTEY],[construct],
+--R            MachineFloat) -> Asp74 D2
+--R            from Asp74 D2 if D2: SYMBOL
+--R    Matrix FortranExpression([construct,QUOTEX],[construct],
+--R            MachineFloat) -> Asp77 D2
+--R            from Asp77 D2 if D2: SYMBOL
+--R    Vector FortranExpression([construct,QUOTEX],[construct],
+--R            MachineFloat) -> Asp78 D2
+--R            from Asp78 D2 if D2: SYMBOL
+--R    Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],
+--R            MachineFloat) -> Asp7 D2
+--R            from Asp7 D2 if D2: SYMBOL
+--R    Matrix FortranExpression([construct,QUOTEXL,QUOTEXR,QUOTEELAM],
+--R            [construct],MachineFloat) -> Asp80 D2
+--R            from Asp80 D2 if D2: SYMBOL
+--R    FortranExpression([construct,QUOTEX],[construct,QUOTEY],
+--R            MachineFloat) -> Asp9 D2
+--R            from Asp9 D2 if D2: SYMBOL
+--R    BinaryExpansion -> RadixExpansion 2 from BinaryExpansion
+--R    BinaryExpansion -> Fraction Integer from BinaryExpansion
+--R    List CartesianTensor(D2,D3,D4) -> CartesianTensor(D2,D3,D4)
+--R            from CartesianTensor(D2,D3,D4)
+--R            if D2: INT and D3: NNI and D4 has COMRING
+--R    List D4 -> CartesianTensor(D2,D3,D4) from CartesianTensor(D2,D3
+--R            ,D4)
+--R            if D4 has COMRING and D2: INT and D3: NNI
+--R    SquareMatrix(D3,D4) -> CartesianTensor(D2,D3,D4)
+--R            from CartesianTensor(D2,D3,D4)
+--R            if D3: NNI and D4 has COMRING and D2: INT
+--R    DirectProduct(D3,D4) -> CartesianTensor(D2,D3,D4)
+--R            from CartesianTensor(D2,D3,D4)
+--R            if D3: NNI and D4 has COMRING and D2: INT
+--R    List D2 -> Database D2 from Database D2
+--R            if D2 has OrderedSet with
+--R               ?.? : (%,Symbol) -> String
+--R               display : % -> Void
+--R               fullDisplay : % -> Void
+--R    DecimalExpansion -> RadixExpansion 10 from DecimalExpansion
+--R    DecimalExpansion -> Fraction Integer from DecimalExpansion
+--R    DataList D2 -> List D2 from DataList D2 if D2 has ORDSET
+--R    List D2 -> DataList D2 from DataList D2 if D2 has ORDSET
+--R    SegmentBinding Expression D3 -> SegmentBinding Float
+--R            from DrawNumericHack D3
+--R            if D3 has Join(OrderedSet,IntegralDomain,ConvertibleTo
+--R            Float)
+--R    D1 -> D from D if D has DVARCAT D1 and D1 has ORDSET
+--R    FortranCode -> OutputForm from FortranCode
+--R    FortranExpression(D2,D3,D4) -> Expression D4
+--R            from FortranExpression(D2,D3,D4)
+--R            if D2: LIST SYMBOL and D3: LIST SYMBOL and D4 has FMTC
+--R    D2 -> D1 from FiniteFieldHomomorphisms(D2,D3,D1)
+--R            if D3 has FFIELDC and D1 has FAXF D3 and D2 has FAXF D3
+--R    D2 -> D1 from FiniteFieldHomomorphisms(D1,D3,D2)
+--R            if D3 has FFIELDC and D1 has FAXF D3 and D2 has FAXF D3
+--R    D -> XRecursivePolynomial(D2,D3) from D
+--R            if D has FLALG(D2,D3) and D2 has ORDSET and D3 has COMRING
+--R
+--R    D -> XDistributedPolynomial(D2,D3) from D
+--R            if D has FLALG(D2,D3) and D2 has ORDSET and D3 has COMRING
+--R
+--R    D1 -> D from D
+--R            if D has FLALG(D1,D2) and D1 has ORDSET and D2 has COMRING
+--R
+--R    Record(localSymbols: SymbolTable,code: List FortranCode) -> D
+--R            from D
+--R            if D has FMC
+--R    FortranCode -> D from D if D has FMC
+--R    List FortranCode -> D from D if D has FMC
+--R    Matrix MachineFloat -> D from D if D has FMC
+--R    Record(localSymbols: SymbolTable,code: List FortranCode) -> D
+--R            from D
+--R            if D has FMFUN
+--R    FortranCode -> D from D if D has FMFUN
+--R    List FortranCode -> D from D if D has FMFUN
+--R    D -> String from D if D has FNCAT
+--R    String -> D from D if D has FNCAT
+--R    D2 -> ScriptFormulaFormat from ScriptFormulaFormat1 D2 if D2
+--R            has SETCAT
+--R    OutputForm -> ScriptFormulaFormat from ScriptFormulaFormat
+--R    Record(localSymbols: SymbolTable,code: List FortranCode) -> D
+--R            from D
+--R            if D has FORTFN
+--R    FortranCode -> D from D if D has FORTFN
+--R    List FortranCode -> D from D if D has FORTFN
+--R    Equation Expression Complex Float -> FortranProgram(D2,D3,D4,D5
+--R            )
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Equation Expression Float -> FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Equation Expression Integer -> FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Expression Complex Float -> FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Expression Float -> FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Expression Integer -> FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Equation Expression MachineComplex -> FortranProgram(D2,D3,D4,
+--R            D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Equation Expression MachineFloat -> FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Equation Expression MachineInteger -> FortranProgram(D2,D3,D4,
+--R            D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Expression MachineComplex -> FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Expression MachineFloat -> FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Expression MachineInteger -> FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    Record(localSymbols: SymbolTable,code: List FortranCode) ->
+--R            FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    List FortranCode -> FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    FortranCode -> FortranProgram(D2,D3,D4,D5)
+--R            from FortranProgram(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
+--R            void) and D4: LIST SYMBOL and D5: SYMTAB
+--R    FourierComponent D3 -> FourierSeries(D2,D3) from FourierSeries(
+--R            D2,D3)
+--R            if D3 has Join(OrderedSet,AbelianGroup) and D2 has Join(
+--R            CommutativeRing,Algebra Fraction Integer)
+--R    D1 -> FourierSeries(D1,D2) from FourierSeries(D1,D2)
+--R            if D1 has Join(CommutativeRing,Algebra Fraction Integer)
+--R            and D2 has Join(OrderedSet,AbelianGroup)
+--R    Fraction Polynomial Fraction D2 -> D from D
+--R            if D2 has INTDOM and D2 has ORDSET and D has FS D2
+--R    Polynomial Fraction D2 -> D from D
+--R            if D2 has INTDOM and D2 has ORDSET and D has FS D2
+--R    Fraction D2 -> D from D
+--R            if D2 has INTDOM and D2 has ORDSET and D has FS D2
+--R    SparseMultivariatePolynomial(D2,Kernel D) -> D from D
+--R            if D2 has RING and D2 has ORDSET and D has FS D2
+--R    FortranScalarType -> SExpression from FortranScalarType
+--R    FortranScalarType -> Symbol from FortranScalarType
+--R    Symbol -> FortranScalarType from FortranScalarType
+--R    String -> FortranScalarType from FortranScalarType
+--R    FortranScalarType -> FortranType from FortranType
+--R    FortranType -> OutputForm from FortranType
+--R    Record(localSymbols: SymbolTable,code: List FortranCode) -> D
+--R            from D
+--R            if D has FVC
+--R    FortranCode -> D from D if D has FVC
+--R    List FortranCode -> D from D if D has FVC
+--R    Vector MachineFloat -> D from D if D has FVC
+--R    Record(localSymbols: SymbolTable,code: List FortranCode) -> D
+--R            from D
+--R            if D has FVFUN
+--R    FortranCode -> D from D if D has FVFUN
+--R    List FortranCode -> D from D if D has FVFUN
+--R    UnivariatePuiseuxSeries(D2,D3,D4) ->
+--R            GeneralUnivariatePowerSeries(D2,D3,D4)
+--R            from GeneralUnivariatePowerSeries(D2,D3,D4)
+--R            if D2 has RING and D3: SYMBOL and D4: D2
+--R    Variable D3 -> GeneralUnivariatePowerSeries(D2,D3,D4)
+--R            from GeneralUnivariatePowerSeries(D2,D3,D4)
+--R            if D3: SYMBOL and D2 has RING and D4: D2
+--R    HexadecimalExpansion -> RadixExpansion 16 from
+--R            HexadecimalExpansion
+--R    HexadecimalExpansion -> Fraction Integer from
+--R            HexadecimalExpansion
+--R    String -> IndexCard from IndexCard
+--R    List D5 -> PolynomialIdeals(D2,D3,D4,D5)
+--R            from PolynomialIdeals(D2,D3,D4,D5)
+--R            if D5 has POLYCAT(D2,D3,D4) and D2 has FIELD and D3 has
+--R            OAMONS and D4 has ORDSET
+--R    D1 -> AssociatedJordanAlgebra(D2,D1)
+--R            from AssociatedJordanAlgebra(D2,D1)
+--R            if D2 has COMRING and D1 has NAALG D2
+--R    D -> D1 from D if D has KOERCE D1 and D1 has TYPE
+--R    D1 -> D from D if D has LALG D1 and D1 has RING
+--R    D1 -> AssociatedLieAlgebra(D2,D1) from AssociatedLieAlgebra(D2
+--R            ,D1)
+--R            if D2 has COMRING and D1 has NAALG D2
+--R    ThreeDimensionalMatrix D2 -> PrimitiveArray PrimitiveArray
+--R            PrimitiveArray D2
+--R            from ThreeDimensionalMatrix D2 if D2 has SETCAT
+--R    PrimitiveArray PrimitiveArray PrimitiveArray D2 ->
+--R            ThreeDimensionalMatrix D2
+--R            from ThreeDimensionalMatrix D2 if D2 has SETCAT
+--R    D2 -> (() -> D2) from MappingPackage1 D2 if D2 has SETCAT
+--R    D1 -> D from D
+--R            if D2 has RING and D has MATCAT(D2,D3,D1) and D3 has FLAGG
+--R            D2 and D1 has FLAGG D2
+--R    MachineComplex -> Complex Float from MachineComplex
+--R    Complex MachineInteger -> MachineComplex from MachineComplex
+--R
+--R    Complex MachineFloat -> MachineComplex from MachineComplex
+--R    Complex Integer -> MachineComplex from MachineComplex
+--R    Complex Float -> MachineComplex from MachineComplex
+--R    MachineInteger -> MachineFloat from MachineFloat
+--R    MachineFloat -> Float from MachineFloat
+--R    Expression Integer -> Expression MachineInteger from
+--R            MachineInteger
+--R    OutputForm -> String from MathMLFormat
+--R    Integer -> D from D if D has NASRING
+--R    Union(nia: Record(var: Symbol,fn: Expression DoubleFloat,range
+--R            : Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,
+--R            relerr: DoubleFloat),mdnia: Record(fn: Expression DoubleFloat,
+--R            range: List Segment OrderedCompletion DoubleFloat,abserr:
+--R            DoubleFloat,relerr: DoubleFloat)) -> NumericalIntegrationProblem
+--R            from NumericalIntegrationProblem
+--R    Record(fn: Expression DoubleFloat,range: List Segment
+--R            OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr:
+--R            DoubleFloat) -> NumericalIntegrationProblem
+--R            from NumericalIntegrationProblem
+--R    Record(var: Symbol,fn: Expression DoubleFloat,range: Segment
+--R            OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr:
+--R            DoubleFloat) -> NumericalIntegrationProblem
+--R            from NumericalIntegrationProblem
+--R    NumericalIntegrationProblem -> OutputForm
+--R            from NumericalIntegrationProblem
+--R    D2 -> None from NoneFunctions1 D2 if D2 has TYPE
+--R    Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector
+--R            Expression DoubleFloat,yinit: List DoubleFloat,intvals: List
+--R            DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr
+--R            : DoubleFloat) -> NumericalODEProblem
+--R            from NumericalODEProblem
+--R    NumericalODEProblem -> OutputForm from NumericalODEProblem
+--R    OrdinaryDifferentialRing(D2,D1,D3) -> D1
+--R            from OrdinaryDifferentialRing(D2,D1,D3)
+--R            if D1 has PDRING D2 and D2 has SETCAT and D3: D2
+--R    D1 -> OrdinaryDifferentialRing(D2,D1,D3)
+--R            from OrdinaryDifferentialRing(D2,D1,D3)
+--R            if D2 has SETCAT and D3: D2 and D1 has PDRING D2
+--R    Symbol -> OpenMathErrorKind from OpenMathErrorKind
+--R    Union(noa: Record(fn: Expression DoubleFloat,init: List
+--R            DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List
+--R            Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat),
+--R            lsa: Record(lfn: List Expression DoubleFloat,init: List
+--R            DoubleFloat)) -> NumericalOptimizationProblem
+--R            from NumericalOptimizationProblem
+--R    Record(lfn: List Expression DoubleFloat,init: List DoubleFloat
+--R            ) -> NumericalOptimizationProblem
+--R            from NumericalOptimizationProblem
+--R    Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb:
+--R            List OrderedCompletion DoubleFloat,cf: List Expression
+--R            DoubleFloat,ub: List OrderedCompletion DoubleFloat) ->
+--R            NumericalOptimizationProblem
+--R            from NumericalOptimizationProblem
+--R    NumericalOptimizationProblem -> OutputForm
+--R            from NumericalOptimizationProblem
+--R    Integer -> OrdSetInts from OrdSetInts
+--R    Color -> Palette from Palette
+--R    Polynomial AlgebraicNumber -> Expression Integer
+--R            from PolynomialAN2Expression
+--R    Fraction Polynomial AlgebraicNumber -> Expression Integer
+--R            from PolynomialAN2Expression
+--R    Record(pde: List Expression DoubleFloat,constraints: List
+--R            Record(start: DoubleFloat,finish: DoubleFloat,grid:
+--R            NonNegativeInteger,boundaryType: Integer,dStart: Matrix
+--R            DoubleFloat,dFinish: Matrix DoubleFloat),f: List List
Expression
+--R            DoubleFloat,st: String,tol: DoubleFloat) -> NumericalPDEProblem
+--R            from NumericalPDEProblem
+--R    NumericalPDEProblem -> OutputForm from NumericalPDEProblem
+--R    PendantTree D2 -> Tree D2 from PendantTree D2 if D2 has SETCAT
+--R
+--R    List Permutation D2 -> PermutationGroup D2 from
+--R            PermutationGroup D2
+--R            if D2 has SETCAT
+--R    PermutationGroup D2 -> List Permutation D2 from
+--R            PermutationGroup D2
+--R            if D2 has SETCAT
+--R    List D2 -> Permutation D2 from Permutation D2 if D2 has SETCAT
+--R
+--R    List List D2 -> Permutation D2 from Permutation D2 if D2 has
+--R            SETCAT
+--R    Fraction Factored D2 -> PartialFraction D2 from
+--R            PartialFraction D2
+--R            if D2 has EUCDOM
+--R    PartialFraction D2 -> Fraction D2 from PartialFraction D2
+--R            if D2 has EUCDOM
+--R    Pi -> Expression D3 from PiCoercions D3
+--R            if D3 has Join(OrderedSet,IntegralDomain)
+--R    RadixExpansion D2 -> Fraction Integer from RadixExpansion D2
+--R            if D2: INT
+--R    D2 -> Void from ResolveLatticeCompletion D2 if D2 has TYPE
+--R    Exit -> D1 from ResolveLatticeCompletion D1 if D1 has TYPE
+--R    D1 -> D from D if D has RETRACT D1 and D1 has TYPE
+--R    D2 -> Fraction Polynomial D2 from RationalFunction D2 if D2
+--R            has INTDOM
+--R    Integer -> D from D if D has RING
+--R    D -> OutputForm from D if D has SPACEC D2 and D2 has RING
+--R    Character -> D from D if D has SRAGG
+--R    List D2 -> Stream D2 from Stream D2 if D2 has TYPE
+--R    Symbol -> Switch from Switch
+--R    String -> Symbol from Symbol
+--R    SymbolTable -> Table(Symbol,FortranType) from SymbolTable
+--R    Tableau D2 -> OutputForm from Tableau D2 if D2 has SETCAT
+--R    D2 -> TexFormat from TexFormat1 D2 if D2 has SETCAT
+--R    OutputForm -> TexFormat from TexFormat
+--R    Polynomial D2 -> TaylorSeries D2 from TaylorSeries D2 if D2
+--R            has RING
+--R    Symbol -> TaylorSeries D2 from TaylorSeries D2 if D2 has RING
+--R
+--R    D1 -> D from D
+--R            if D2 has RING and D has ULSCCAT(D2,D1) and D1 has UTSCAT
+--R            D2
+--R    Segment D2 -> UniversalSegment D2 from UniversalSegment D2
+--R            if D2 has TYPE
+--R    Variable D2 -> UnivariatePolynomial(D2,D3)
+--R            from UnivariatePolynomial(D2,D3) if D2: SYMBOL and D3 has
+--R            RING
+--R    D1 -> D from D
+--R            if D2 has RING and D has UPXSCCA(D2,D1) and D1 has ULSCAT
+--R            D2
+--R    Void -> OutputForm from Void
+--R    D1 -> D from D if D has XALG D1 and D1 has RING
+--R    D1 -> D from D
+--R            if D has XFALG(D1,D2) and D1 has ORDSET and D2 has RING
+--R
+--RThere are 56 unexposed functions called coerce :
+--R    Vector Matrix D3 -> Vector Matrix Fraction Polynomial D3
+--R            from CoerceVectorMatrixPackage D3 if D3 has COMRING
+--R    List Integer -> ExtAlgBasis from ExtAlgBasis
+--R    EuclideanModularRing(D2,D1,D3,D4,D5,D6) -> D1
+--R            from EuclideanModularRing(D2,D1,D3,D4,D5,D6)
+--R            if D1 has UPOLYC D2 and D2 has COMRING and D3 has ABELMON
+--R            and D4: ((D1,D3) -> D1) and D5: ((D3,D3) -> Union(D3,
+--R            "failed")) and D6: ((D1,D1,D3) -> Union(D1,"failed"))
+--R    UnivariatePuiseuxSeries(D3,D4,D5) -> ExponentialExpansion(D2,D3,
+--R            D4,D5)
+--R            from ExponentialExpansion(D2,D3,D4,D5)
+--R            if D3 has Join(AlgebraicallyClosedField,
+--R            TranscendentalFunctionCategory,FunctionSpace D2) and D4:
+--R            SYMBOL and D5: D3 and D2 has Join(OrderedSet,RetractableTo
+--R            Integer,LinearlyExplicitRingOver Integer,GcdDomain)
+--R    Vector Fraction Polynomial D2 -> GenericNonAssociativeAlgebra(D2
+--R            ,D3,D4,D5)
+--R            from GenericNonAssociativeAlgebra(D2,D3,D4,D5)
+--R            if D2 has COMRING and D5: VECTOR MATRIX D2 and D3: PI and
+--R            D4: LIST SYMBOL
+--R    List List Point DoubleFloat -> GraphImage from GraphImage
+--R    GraphImage -> OutputForm from GraphImage
+--R    SparseMultivariatePolynomial(Integer,Kernel InnerAlgebraicNumber
+--R            ) -> InnerAlgebraicNumber
+--R            from InnerAlgebraicNumber
+--R    LieExponentials(D2,D3,D4) -> XPBWPolynomial(D2,D3)
+--R            from LieExponentials(D2,D3,D4)
+--R            if D2 has ORDSET and D3 has Join(CommutativeRing,Module
+--R            Fraction Integer) and D4: PI
+--R    LieExponentials(D2,D3,D4) -> XDistributedPolynomial(D2,D3)
+--R            from LieExponentials(D2,D3,D4)
+--R            if D2 has ORDSET and D3 has Join(CommutativeRing,Module
+--R            Fraction Integer) and D4: PI
+--R    LyndonWord D2 -> Magma D2 from LyndonWord D2 if D2 has ORDSET
+--R
+--R    LyndonWord D2 -> OrderedFreeMonoid D2 from LyndonWord D2
+--R            if D2 has ORDSET
+--R    Magma D2 -> OrderedFreeMonoid D2 from Magma D2 if D2 has ORDSET
+--R
+--R    D1 -> MakeCachableSet D1 from MakeCachableSet D1 if D1 has
+--R            SETCAT
+--R    ModularField(D1,D2,D3,D4,D5) -> D1 from ModularField(D1,D2,D3,
+--R            D4,D5)
+--R            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
+--R            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
+--R            D2) -> Union(D1,"failed"))
+--R    D1 -> ModMonic(D2,D1) from ModMonic(D2,D1)
+--R            if D2 has RING and D1 has UPOLYC D2
+--R    ModuleMonomial(D2,D3,D4) -> Record(index: D2,exponent: D3)
+--R            from ModuleMonomial(D2,D3,D4)
+--R            if D2 has ORDSET and D3 has SETCAT and D4: ((Record(index:
+--R            D2,exponent: D3),Record(index: D2,exponent: D3)) -> Boolean
+--R            )
+--R    Record(index: D2,exponent: D3) -> ModuleMonomial(D2,D3,D4)
+--R            from ModuleMonomial(D2,D3,D4)
+--R            if D2 has ORDSET and D3 has SETCAT and D4: ((Record(index:
+--R            D2,exponent: D3),Record(index: D2,exponent: D3)) -> Boolean
+--R            )
+--R    ModularRing(D1,D2,D3,D4,D5) -> D1 from ModularRing(D1,D2,D3,D4,
+--R            D5)
+--R            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
+--R            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
+--R            D2) -> Union(D1,"failed"))
+--R    List Record(coef: D2,monom: D3) -> MonoidRing(D2,D3)
+--R            from MonoidRing(D2,D3) if D2 has RING and D3 has MONOID
+--R    Fraction MyUnivariatePolynomial(D2,D3) -> MyExpression(D2,D3)
+--R            from MyExpression(D2,D3)
+--R            if D2: SYMBOL and D3 has Join(Ring,OrderedSet,
+--R            IntegralDomain)
+--R    Polynomial D3 -> MyUnivariatePolynomial(D2,D3)
+--R            from MyUnivariatePolynomial(D2,D3) if D3 has RING and D2:
+--R            SYMBOL
+--R    Variable D2 -> MyUnivariatePolynomial(D2,D3)
+--R            from MyUnivariatePolynomial(D2,D3) if D2: SYMBOL and D3 has
+--R            RING
+--R    D1 -> MyUnivariatePolynomial(D2,D1) from MyUnivariatePolynomial
+--R            (D2,D1)
+--R            if D2: SYMBOL and D1 has RING
+--R    Variable D2 -> UnivariateSkewPolynomial(D2,D3,D4,D5)
+--R            from UnivariateSkewPolynomial(D2,D3,D4,D5)
+--R            if D2: SYMBOL and D3 has RING and D4: AUTOMOR D3 and D5: (
+--R            D3 -> D3)
+--R    Polynomial D2 -> OrdinaryWeightedPolynomials(D2,D3,D4,D5)
+--R            from OrdinaryWeightedPolynomials(D2,D3,D4,D5)
+--R            if D2 has RING and D3: LIST SYMBOL and D4: LIST NNI and D5
+--R            : NNI
+--R    OrdinaryWeightedPolynomials(D2,D3,D4,D5) -> Polynomial D2
+--R            from OrdinaryWeightedPolynomials(D2,D3,D4,D5)
+--R            if D2 has RING and D3: LIST SYMBOL and D4: LIST NNI and D5
+--R            : NNI
+--R    D1 -> PoincareBirkhoffWittLyndonBasis D1
+--R            from PoincareBirkhoffWittLyndonBasis D1 if D1 has ORDSET
+--R
+--R    PoincareBirkhoffWittLyndonBasis D2 -> OrderedFreeMonoid D2
+--R            from PoincareBirkhoffWittLyndonBasis D2 if D2 has ORDSET
+--R
+--R    Partition -> List Integer from Partition
+--R    D1 -> ResidueRing(D2,D3,D4,D1,D5) from ResidueRing(D2,D3,D4,D1,
+--R            D5)
+--R            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D1
+--R            has POLYCAT(D2,D3,D4) and D5: LIST D1
+--R    RectangularMatrix(D2,D3,D4) -> Matrix D4
+--R            from RectangularMatrix(D2,D3,D4)
+--R            if D2: NNI and D3: NNI and D4 has RING
+--R    D1 -> SparseMultivariateTaylorSeries(D2,D3,D1)
+--R            from SparseMultivariateTaylorSeries(D2,D3,D1)
+--R            if D2 has RING and D3 has ORDSET and D1 has POLYCAT(D2,INDE
+--R            D3,D3)
+--R    D1 -> SparseMultivariateTaylorSeries(D2,D1,D3)
+--R            from SparseMultivariateTaylorSeries(D2,D1,D3)
+--R            if D2 has RING and D1 has ORDSET and D3 has POLYCAT(D2,INDE
+--R            D1,D1)
+--R    SquareMatrix(D2,D3) -> Matrix D3 from SquareMatrix(D2,D3)
+--R            if D2: NNI and D3 has RING
+--R    D2 -> Stream D2 from StreamTaylorSeriesOperations D2 if D2 has
+--R            RING
+--R    Variable D3 -> SparseUnivariateLaurentSeries(D2,D3,D4)
+--R            from SparseUnivariateLaurentSeries(D2,D3,D4)
+--R            if D3: SYMBOL and D2 has RING and D4: D2
+--R    Variable D3 -> SparseUnivariatePuiseuxSeries(D2,D3,D4)
+--R            from SparseUnivariatePuiseuxSeries(D2,D3,D4)
+--R            if D3: SYMBOL and D2 has RING and D4: D2
+--R    Variable D3 -> SparseUnivariateTaylorSeries(D2,D3,D4)
+--R            from SparseUnivariateTaylorSeries(D2,D3,D4)
+--R            if D3: SYMBOL and D2 has RING and D4: D2
+--R    UnivariatePolynomial(D3,D2) -> SparseUnivariateTaylorSeries(D2,
+--R            D3,D4)
+--R            from SparseUnivariateTaylorSeries(D2,D3,D4)
+--R            if D2 has RING and D3: SYMBOL and D4: D2
+--R    PrimitiveArray D2 -> Tuple D2 from Tuple D2 if D2 has TYPE
+--R    Variable QUOTE x -> UnivariateFormalPowerSeries D2
+--R            from UnivariateFormalPowerSeries D2 if D2 has RING
+--R    UnivariatePolynomial(QUOTE x,D2) -> UnivariateFormalPowerSeries
+--R            D2
+--R            from UnivariateFormalPowerSeries D2 if D2 has RING
+--R    Variable D3 -> UnivariateLaurentSeries(D2,D3,D4)
+--R            from UnivariateLaurentSeries(D2,D3,D4)
+--R            if D3: SYMBOL and D2 has RING and D4: D2
+--R    Variable D3 -> UnivariatePuiseuxSeries(D2,D3,D4)
+--R            from UnivariatePuiseuxSeries(D2,D3,D4)
+--R            if D3: SYMBOL and D2 has RING and D4: D2
+--R    Variable D3 -> UnivariateTaylorSeries(D2,D3,D4)
+--R            from UnivariateTaylorSeries(D2,D3,D4)
+--R            if D3: SYMBOL and D2 has RING and D4: D2
+--R    UnivariatePolynomial(D3,D2) -> UnivariateTaylorSeries(D2,D3,D4)
+--R            from UnivariateTaylorSeries(D2,D3,D4)
+--R            if D2 has RING and D3: SYMBOL and D4: D2
+--R    Variable D2 -> Symbol from Variable D2 if D2: SYMBOL
+--R    TwoDimensionalViewport -> OutputForm from
+--R            TwoDimensionalViewport
+--R    GraphImage -> TwoDimensionalViewport from ViewportPackage
+--R    D1 -> WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
+--R            from WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
+--R            if D2 has RING and D3 has ORDSET and D4 has OAMONS and D5:
+--R            LIST D3 and D1 has POLYCAT(D2,D4,D3) and D6: LIST NNI and
+--R            D7: NNI
+--R    WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7) -> D1
+--R            from WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
+--R            if D1 has POLYCAT(D2,D4,D3) and D2 has RING and D3 has
+--R            ORDSET and D4 has OAMONS and D5: LIST D3 and D6: LIST NNI
+--R            and D7: NNI
+--R    XPBWPolynomial(D2,D3) -> XRecursivePolynomial(D2,D3)
+--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has
+--R            COMRING
+--R    XPBWPolynomial(D2,D3) -> XDistributedPolynomial(D2,D3)
+--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has
+--R            COMRING
+--R    LiePolynomial(D2,D3) -> XPBWPolynomial(D2,D3)
+--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has
+--R            COMRING
+--R    D1 -> XPolynomialRing(D2,D1) from XPolynomialRing(D2,D1)
+--R            if D2 has RING and D1 has ORDMON
+--R
+--RExamples of coerce from Algebra
+--R
+--R
+--RExamples of coerce from AlgebraGivenByStructuralConstants
+--R
+--R
+--RExamples of coerce from AlgebraicNumber
+--R
+--R
+--RExamples of coerce from AnyFunctions1
+--R
+--R
+--RExamples of coerce from Asp10
+--R
+--R
+--RExamples of coerce from Asp19
+--R
+--R
+--RExamples of coerce from Asp1
+--R
+--R
+--RExamples of coerce from Asp20
+--R
+--R
+--RExamples of coerce from Asp24
+--R
+--R
+--RExamples of coerce from Asp31
+--R
+--R
+--RExamples of coerce from Asp35
+--R
+--R
+--RExamples of coerce from Asp41
+--R
+--R
+--RExamples of coerce from Asp42
+--R
+--R
+--RExamples of coerce from Asp49
+--R
+--R
+--RExamples of coerce from Asp4
+--R
+--R
+--RExamples of coerce from Asp50
+--R
+--R
+--RExamples of coerce from Asp55
+--R
+--R
+--RExamples of coerce from Asp6
+--R
+--R
+--RExamples of coerce from Asp73
+--R
+--R
+--RExamples of coerce from Asp74
+--R
+--R
+--RExamples of coerce from Asp77
+--R
+--R
+--RExamples of coerce from Asp78
+--R
+--R
+--RExamples of coerce from Asp7
+--R
+--R
+--RExamples of coerce from Asp80
+--R
+--R
+--RExamples of coerce from Asp9
+--R
+--R
+--RExamples of coerce from BinaryExpansion
+--R
+--R
+--RExamples of coerce from CartesianTensor
+--R
+--Rv:=[2,3]
+--Rtv:CartesianTensor(1,2,Integer):=v
+--Rtm:CartesianTensor(1,2,Integer):=[tv,tv]
+--R
+--Rv:=[2,3]
+--Rtv:CartesianTensor(1,2,Integer):=v
+--R
+--Rv:SquareMatrix(2,Integer):=[[1,2],[3,4]]
+--Rtv:CartesianTensor(1,2,Integer):=v
+--R
+--Rv:DirectProduct(2,Integer):=directProduct [3,4]
+--Rtv:CartesianTensor(1,2,Integer):=v
+--R
+--R
+--RExamples of coerce from CoerceVectorMatrixPackage
+--R
+--R
+--RExamples of coerce from Database
+--R
+--R
+--RExamples of coerce from DecimalExpansion
+--R
+--R
+--RExamples of coerce from DataList
+--R
+--R
+--RExamples of coerce from DrawNumericHack
+--R
+--R
+--RExamples of coerce from DifferentialVariableCategory
+--R
+--R
+--RExamples of coerce from ExtAlgBasis
+--R
+--R
+--RExamples of coerce from EuclideanModularRing
+--R
+--R
+--RExamples of coerce from ExponentialExpansion
+--R
+--R
+--RExamples of coerce from FortranCode
+--R
+--R
+--RExamples of coerce from FortranExpression
+--R
+--R
+--RExamples of coerce from FiniteFieldHomomorphisms
+--R
+--R
+--RExamples of coerce from FreeLieAlgebra
+--R
+--R
+--RExamples of coerce from FortranMatrixCategory
+--R
+--R
+--RExamples of coerce from FortranMatrixFunctionCategory
+--R
+--R
+--RExamples of coerce from FileNameCategory
+--R
+--R
+--RExamples of coerce from ScriptFormulaFormat1
+--R
+--R
+--RExamples of coerce from ScriptFormulaFormat
+--R
+--R
+--RExamples of coerce from FortranFunctionCategory
+--R
+--R
+--RExamples of coerce from FortranProgram
+--R
+--R
+--RExamples of coerce from FourierSeries
+--R
+--R
+--RExamples of coerce from FunctionSpace
+--R
+--R
+--RExamples of coerce from FortranScalarType
+--R
+--R
+--RExamples of coerce from FortranType
+--R
+--R
+--RExamples of coerce from FortranVectorCategory
+--R
+--R
+--RExamples of coerce from FortranVectorFunctionCategory
+--R
+--R
+--RExamples of coerce from GenericNonAssociativeAlgebra
+--R
+--R
+--RExamples of coerce from GraphImage
+--R
+--R
+--RExamples of coerce from GeneralUnivariatePowerSeries
+--R
+--R
+--RExamples of coerce from HexadecimalExpansion
+--R
+--R
+--RExamples of coerce from InnerAlgebraicNumber
+--R
+--R
+--RExamples of coerce from IndexCard
+--R
+--R
+--RExamples of coerce from PolynomialIdeals
+--R
+--R
+--RExamples of coerce from AssociatedJordanAlgebra
+--R
+--R
+--RExamples of coerce from CoercibleTo
+--R
+--R
+--RExamples of coerce from LeftAlgebra
+--R
+--R
+--RExamples of coerce from LieExponentials
+--R
+--R
+--RExamples of coerce from AssociatedLieAlgebra
+--R
+--R
+--RExamples of coerce from LyndonWord
+--R
+--R
+--RExamples of coerce from ThreeDimensionalMatrix
+--R
+--R
+--RExamples of coerce from Magma
+--R
+--R
+--RExamples of coerce from MappingPackage1
+--R
+--R
+--RExamples of coerce from MatrixCategory
+--R
+--R
+--RExamples of coerce from MachineComplex
+--R
+--R
+--RExamples of coerce from MachineFloat
+--R
+--R
+--RExamples of coerce from MachineInteger
+--R
+--R
+--RExamples of coerce from MakeCachableSet
+--R
+--R
+--RExamples of coerce from MathMLFormat
+--R
+--R
+--RExamples of coerce from ModularField
+--R
+--R
+--RExamples of coerce from ModMonic
+--R
+--R
+--RExamples of coerce from ModuleMonomial
+--R
+--R
+--RExamples of coerce from ModularRing
+--R
+--R
+--RExamples of coerce from MonoidRing
+--R
+--R
+--RExamples of coerce from MyExpression
+--R
+--R
+--RExamples of coerce from MyUnivariatePolynomial
+--R
+--R
+--RExamples of coerce from NonAssociativeRing
+--R
+--R
+--RExamples of coerce from NumericalIntegrationProblem
+--R
+--R
+--RExamples of coerce from NoneFunctions1
+--R
+--R
+--RExamples of coerce from NumericalODEProblem
+--R
+--R
+--RExamples of coerce from OrdinaryDifferentialRing
+--R
+--R
+--RExamples of coerce from OpenMathErrorKind
+--R
+--R
+--RExamples of coerce from NumericalOptimizationProblem
+--R
+--R
+--RExamples of coerce from UnivariateSkewPolynomial
+--R
+--R
+--RExamples of coerce from OrdSetInts
+--R
+--R
+--RExamples of coerce from OrdinaryWeightedPolynomials
+--R
+--R
+--RExamples of coerce from Palette
+--R
+--R
+--RExamples of coerce from PolynomialAN2Expression
+--R
+--R
+--RExamples of coerce from PoincareBirkhoffWittLyndonBasis
+--R
+--R
+--RExamples of coerce from NumericalPDEProblem
+--R
+--R
+--RExamples of coerce from PendantTree
+--R
+--Rt1:=ptree([1,2,3])
+--Rt2:=ptree(t1,ptree([1,2,3]))
+--Rt2::Tree List PositiveInteger
+--R
+--R
+--RExamples of coerce from PermutationGroup
+--R
+--R
+--RExamples of coerce from Permutation
+--R
+--R
+--RExamples of coerce from PartialFraction
+--R
+--R
+--RExamples of coerce from PiCoercions
+--R
+--R
+--RExamples of coerce from Partition
+--R
+--R
+--RExamples of coerce from RadixExpansion
+--R
+--R
+--RExamples of coerce from ResolveLatticeCompletion
+--R
+--R
+--RExamples of coerce from ResidueRing
+--R
+--R
+--RExamples of coerce from RetractableTo
+--R
+--R
+--RExamples of coerce from RationalFunction
+--R
+--R
+--RExamples of coerce from Ring
+--R
+--R
+--RExamples of coerce from RectangularMatrix
+--R
+--R
+--RExamples of coerce from SparseMultivariateTaylorSeries
+--R
+--R
+--RExamples of coerce from ThreeSpaceCategory
+--R
+--R
+--RExamples of coerce from SquareMatrix
+--R
+--R
+--RExamples of coerce from StringAggregate
+--R
+--R
+--RExamples of coerce from Stream
+--R
+--Rm:=[1,2,3,4,5,6,7,8,9,10,11,12]
+--Rcoerce(m)@Stream(Integer)
+--Rm::Stream(Integer)
+--R
+--R
+--RExamples of coerce from StreamTaylorSeriesOperations
+--R
+--R
+--RExamples of coerce from SparseUnivariateLaurentSeries
+--R
+--R
+--RExamples of coerce from SparseUnivariatePuiseuxSeries
+--R
+--R
+--RExamples of coerce from SparseUnivariateTaylorSeries
+--R
+--R
+--RExamples of coerce from Switch
+--R
+--R
+--RExamples of coerce from Symbol
+--R
+--R
+--RExamples of coerce from SymbolTable
+--R
+--R
+--RExamples of coerce from Tableau
+--R
+--R
+--RExamples of coerce from TexFormat1
+--R
+--R
+--RExamples of coerce from TexFormat
+--R
+--R
+--RExamples of coerce from TaylorSeries
+--R
+--R
+--RExamples of coerce from Tuple
+--R
+--Rt1:PrimitiveArray(Integer):= [i for i in 1..10]
+--Rt2:=coerce(t1)$Tuple(Integer) +--R +--R +--RExamples of coerce from UnivariateFormalPowerSeries +--R +--R +--RExamples of coerce from UnivariateLaurentSeriesConstructorCategory +--R +--R +--RExamples of coerce from UnivariateLaurentSeries +--R +--R +--RExamples of coerce from UniversalSegment +--R +--R +--RExamples of coerce from UnivariatePolynomial +--R +--R +--RExamples of coerce from UnivariatePuiseuxSeriesConstructorCategory +--R +--R +--RExamples of coerce from UnivariatePuiseuxSeries +--R +--R +--RExamples of coerce from UnivariateTaylorSeries +--R +--R +--RExamples of coerce from Variable +--R +--R +--RExamples of coerce from TwoDimensionalViewport +--R +--R +--RExamples of coerce from ViewportPackage +--R +--R +--RExamples of coerce from Void +--R +--R +--RExamples of coerce from WeightedPolynomials +--R +--R +--RExamples of coerce from XAlgebra +--R +--R +--RExamples of coerce from XFreeAlgebra +--R +--R +--RExamples of coerce from XPBWPolynomial +--R +--R +--RExamples of coerce from XPolynomialRing +--R +--E 69 + +--S 70 of 127 +--R)d op contract +--R +--R +--RThere are 3 exposed functions called contract : +--R  (CartesianTensor(D2,D3,D4),Integer,Integer) -> CartesianTensor( +--R D2,D3,D4) +--R from CartesianTensor(D2,D3,D4) +--R if D2: INT and D3: NNI and D4 has COMRING +--R  (CartesianTensor(D2,D3,D4),Integer,CartesianTensor(D2,D3,D4), +--R Integer) -> CartesianTensor(D2,D3,D4) +--R from CartesianTensor(D2,D3,D4) +--R if D2: INT and D3: NNI and D4 has COMRING +--R  (PolynomialIdeals(Fraction Integer,DirectProduct(D4, +--R NonNegativeInteger),OrderedVariableList D3, +--R DistributedMultivariatePolynomial(D3,Fraction Integer)),List +--R OrderedVariableList D3) -> PolynomialIdeals(Fraction Integer, +--R DirectProduct(D4,NonNegativeInteger),OrderedVariableList D3, +--R DistributedMultivariatePolynomial(D3,Fraction Integer)) +--R from IdealDecompositionPackage(D3,D4) +--R if D3: LIST SYMBOL and D4: NNI +--R +--RExamples of contract from CartesianTensor +--R +--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] +--RTm:CartesianTensor(1,2,Integer):=m +--Rv:DirectProduct(2,Integer):=directProduct [3,4] +--RTv:CartesianTensor(1,2,Integer):=v +--RTmv:=contract(Tm,2,1) +--R +--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] +--RTm:CartesianTensor(1,2,Integer):=m +--Rv:DirectProduct(2,Integer):=directProduct [3,4] +--RTv:CartesianTensor(1,2,Integer):=v +--RTmv:=contract(Tm,2,Tv,1) +--R +--R +--RExamples of contract from IdealDecompositionPackage +--R +--E 70 + +--S 71 of 127 +--R)d op irreducibleFactor +--R +--R +--RThere is one exposed function called irreducibleFactor : +--R  (D1,Integer) -> Factored D1 from Factored D1 if D1 has INTDOM +--R +--R +--RExamples of irreducibleFactor from Factored +--R +--Ra:=irreducibleFactor(3,1) +--RnthFlag(a,1) +--R +--E 71 + +--S 72 of 127 +--R)d op concat +--R +--R +--RThere are 10 exposed functions called concat : +--R  (Result,Result) -> Result from ExpertSystemToolsPackage +--R  List Result -> Result from ExpertSystemToolsPackage +--R  List D -> D from D if D has LNAGG D2 and D2 has TYPE +--R  (D,D) -> D from D if D has LNAGG D1 and D1 has TYPE +--R  (D1,D) -> D from D if D has LNAGG D1 and D1 has TYPE +--R  (D,D1) -> D from D if D has LNAGG D1 and D1 has TYPE +--R  (RoutinesTable,RoutinesTable) -> RoutinesTable from +--R RoutinesTable +--R  Stream Stream D3 -> Stream D3 from StreamFunctions1 D3 if D3 has +--R TYPE +--R  (D1,D) -> D from D if D has URAGG D1 and D1 has TYPE +--R  (D,D) -> D from D if D has URAGG D1 and D1 has TYPE +--R +--RExamples of concat from ExpertSystemToolsPackage +--R +--R +--RExamples of concat from LinearAggregate +--R +--R +--RExamples of concat from RoutinesTable +--R +--R +--RExamples of concat from StreamFunctions1 +--R +--Rm:=[i for i in 10..] +--Rn:=[j for j in 1.. | prime? j] +--Rp:=[m,n]::Stream(Stream(PositiveInteger)) +--Rconcat(p) +--R +--R +--RExamples of concat from UnaryRecursiveAggregate +--R +--E 72 + +--S 73 of 127 +--R)d op binaryTournament +--R +--R +--RThere is one exposed function called binaryTournament : +--R  List D2 -> BinaryTournament D2 from BinaryTournament D2 if D2 +--R has ORDSET +--R +--RExamples of binaryTournament from BinaryTournament +--R +--RbinaryTournament [1,2,3,4] +--R +--E 73 + +--S 74 of 127 +--R)d op upperCase +--R +--R +--RThere are 3 exposed functions called upperCase : +--R  -> CharacterClass from CharacterClass +--R  Character -> Character from Character +--R  D -> D from D if D has SRAGG +--R +--RExamples of upperCase from CharacterClass +--R +--R +--RExamples of upperCase from Character +--R +--Rchars := [char "a", char "A", char "X", char "8", char "+"] +--R[upperCase c for c in chars] +--R +--R +--RExamples of upperCase from StringAggregate +--R +--E 74 + +--S 75 of 127 +--R)d op exponent +--R +--R +--RThere are 3 exposed functions called exponent : +--R  D -> Integer from D if D has FPS +--R  Factored D2 -> Integer from Factored D2 if D2 has INTDOM +--R  MachineFloat -> Integer from MachineFloat +--R +--RThere are 2 unexposed functions called exponent : +--R  ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4) -> +--R UnivariatePuiseuxSeries(D2,D3,D4) +--R from ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4) +--R if D2 has Join(Field,OrderedSet) and D3: SYMBOL and D4: D2 +--R +--R  ModuleMonomial(D2,D1,D3) -> D1 from ModuleMonomial(D2,D1,D3) +--R if D1 has SETCAT and D2 has ORDSET and D3: ((Record(index: +--R D2,exponent: D1),Record(index: D2,exponent: D1)) -> Boolean +--R ) +--R +--RExamples of exponent from ExponentialOfUnivariatePuiseuxSeries +--R +--R +--RExamples of exponent from FloatingPointSystem +--R +--R +--RExamples of exponent from Factored +--R +--Rf:=nilFactor(y-x,3) +--Rexponent(f) +--R +--R +--RExamples of exponent from MachineFloat +--R +--R +--RExamples of exponent from ModuleMonomial +--R +--E 75 + +--S 76 of 127 +--R)d op setRow! +--R +--R +--RThere is one exposed function called setRow! : +--R  (D,Integer,D2) -> D from D +--R if D has ARR2CAT(D3,D2,D4) and D3 has TYPE and D2 has FLAGG +--R D3 and D4 has FLAGG D3 +--R +--RExamples of setRow! from TwoDimensionalArrayCategory +--R +--RT1:=TwoDimensionalArray Integer +--Rarr:T1:= new(5,4,0) +--RT2:=OneDimensionalArray Integer +--Rarow:=construct([1,2,3,4]::List(INT))$T2
+--RsetRow!(arr,1,arow)$T1 +--R +--E 76 + +--S 77 of 127 +--R)d op generate +--R +--R +--RThere are 4 exposed functions called generate : +--R  (NonNegativeInteger,NonNegativeInteger) -> Vector List Integer +--R from HallBasis +--R  ((D2 -> D2),D2) -> InfiniteTuple D2 from InfiniteTuple D2 if D2 +--R has TYPE +--R  ((D2 -> D2),D2) -> Stream D2 from Stream D2 if D2 has TYPE +--R  (() -> D2) -> Stream D2 from Stream D2 if D2 has TYPE +--R +--RExamples of generate from HallBasis +--R +--R +--RExamples of generate from InfiniteTuple +--R +--R +--RExamples of generate from Stream +--R +--Rf(x:Integer):Integer == x+10 +--Rgenerate(f,10) +--R +--Rf():Integer == 1 +--Rgenerate(f) +--R +--E 77 + +--S 78 of 127 +--R)d op gcd +--R +--R +--RThere are 6 exposed functions called gcd : +--R  List D -> D from D if D has GCDDOM +--R  (D,D) -> D from D if D has GCDDOM +--R  (D1,D1,Integer) -> D1 from ModularDistinctDegreeFactorizer D1 +--R if D1 has UPOLYC INT +--R  (NonNegativeInteger,NonNegativeInteger) -> NonNegativeInteger +--R from NonNegativeInteger +--R  (PositiveInteger,PositiveInteger) -> PositiveInteger +--R from PositiveInteger +--R  (D1,D) -> D1 from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET and D1 has GCDDOM +--R +--RThere are 6 unexposed functions called gcd : +--R  List D1 -> D1 from HeuGcd D1 if D1 has UPOLYC INT +--R  (D1,D1) -> D1 from PolynomialGcdPackage(D2,D3,D4,D1) +--R if D2 has OAMONS and D3 has ORDSET and D4 has EUCDOM and D1 +--R has POLYCAT(D4,D2,D3) +--R  List D1 -> D1 from PolynomialGcdPackage(D3,D4,D5,D1) +--R if D1 has POLYCAT(D5,D3,D4) and D3 has OAMONS and D4 has +--R ORDSET and D5 has EUCDOM +--R  (SparseUnivariatePolynomial D5,SparseUnivariatePolynomial D5) +--R -> SparseUnivariatePolynomial D5 +--R from PolynomialGcdPackage(D2,D3,D4,D5) +--R if D5 has POLYCAT(D4,D2,D3) and D2 has OAMONS and D3 has +--R ORDSET and D4 has EUCDOM +--R  List SparseUnivariatePolynomial D6 -> SparseUnivariatePolynomial +--R D6 +--R from PolynomialGcdPackage(D3,D4,D5,D6) +--R if D3 has OAMONS and D4 has ORDSET and D5 has EUCDOM and D6 +--R has POLYCAT(D5,D3,D4) +--R  (D1,D1) -> D1 from PseudoRemainderSequence(D2,D1) +--R if D2 has GCDDOM and D2 has INTDOM and D1 has UPOLYC D2 +--R +--RExamples of gcd from GcdDomain +--R +--R +--RExamples of gcd from HeuGcd +--R +--Rgcd([671*671*x^2-1,671*671*x^2+2*671*x+1]) +--Rgcd([7*x^2+1,(7*x^2+1)^2]) +--R +--R +--RExamples of gcd from ModularDistinctDegreeFactorizer +--R +--R +--RExamples of gcd from NonNegativeInteger +--R +--R +--RExamples of gcd from PolynomialGcdPackage +--R +--R +--RExamples of gcd from PositiveInteger +--R +--R +--RExamples of gcd from PseudoRemainderSequence +--R +--R +--RExamples of gcd from RecursivePolynomialCategory +--R +--E 78 + +--S 79 of 127 +--R)d op binary +--R +--R +--RThere is one exposed function called binary : +--R  Fraction Integer -> BinaryExpansion from BinaryExpansion +--R +--RThere is one unexposed function called binary : +--R  (InputForm,List InputForm) -> InputForm from InputForm +--R +--RExamples of binary from BinaryExpansion +--R +--Rbinary(22/7) +--R +--R +--RExamples of binary from InputForm +--R +--Ra:=[1,2,3]::List(InputForm) +--Rbinary(_+::InputForm,a) +--R +--E 79 + +--S 80 of 127 +--R)d op expand +--R +--R +--RThere are 6 exposed functions called expand : +--R  Factored D1 -> D1 from Factored D1 if D1 has INTDOM +--R  IntegrationResult D4 -> List D4 from IntegrationResultToFunction +--R (D3,D4) +--R if D4 has Join(AlgebraicallyClosedFunctionSpace D3, +--R TranscendentalFunctionCategory) and D3 has Join(GcdDomain, +--R RetractableTo Integer,OrderedSet,LinearlyExplicitRingOver +--R Integer) +--R  IntegrationResult Fraction Polynomial D3 -> List Expression D3 +--R from IntegrationResultRFToFunction D3 +--R if D3 has Join(GcdDomain,RetractableTo Integer,OrderedSet, +--R LinearlyExplicitRingOver Integer) +--R  D -> D1 from D +--R if D has SEGXCAT(D2,D1) and D2 has ORDRING and D1 has STAGG +--R D2 +--R  List D -> D1 from D +--R if D has SEGXCAT(D3,D1) and D3 has ORDRING and D1 has STAGG +--R D3 +--R  D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace D2,TranscendentalFunctionCategory) +--R +--RThere are 3 unexposed functions called expand : +--R  (Expression D5,PositiveInteger) -> List Expression D5 +--R from DegreeReductionPackage(D4,D5) +--R if D5 has Join(IntegralDomain,OrderedSet) and D4 has RING +--R +--R  XPolynomial D2 -> XDistributedPolynomial(Symbol,D2) from +--R XPolynomial D2 +--R if D2 has RING +--R  XRecursivePolynomial(D2,D3) -> XDistributedPolynomial(D2,D3) +--R from XRecursivePolynomial(D2,D3) +--R if D2 has ORDSET and D3 has RING +--R +--RExamples of expand from DegreeReductionPackage +--R +--R +--RExamples of expand from Factored +--R +--Rf:=nilFactor(y-x,3) +--Rexpand(f) +--R +--R +--RExamples of expand from IntegrationResultToFunction +--R +--R +--RExamples of expand from IntegrationResultRFToFunction +--R +--R +--RExamples of expand from SegmentExpansionCategory +--R +--R +--RExamples of expand from TranscendentalManipulations +--R +--R +--RExamples of expand from XPolynomial +--R +--R +--RExamples of expand from XRecursivePolynomial +--R +--E 80 + +--S 81 of 127 +--R)d op filterWhile +--R +--R +--RThere are 2 exposed functions called filterWhile : +--R  ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2 +--R from InfiniteTuple D2 if D2 has TYPE +--R  ((D2 -> Boolean),Stream D2) -> Stream D2 from Stream D2 if D2 +--R has TYPE +--R +--RExamples of filterWhile from InfiniteTuple +--R +--R +--RExamples of filterWhile from Stream +--R +--Rm:=[i for i in 1..] +--Rf(x:PositiveInteger):Boolean == x < 5 +--RfilterWhile(f,m) +--R +--E 81 + +--S 82 of 127 +--R)d op filterUntil +--R +--R +--RThere are 2 exposed functions called filterUntil : +--R  ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2 +--R from InfiniteTuple D2 if D2 has TYPE +--R  ((D2 -> Boolean),Stream D2) -> Stream D2 from Stream D2 if D2 +--R has TYPE +--R +--RExamples of filterUntil from InfiniteTuple +--R +--R +--RExamples of filterUntil from Stream +--R +--Rm:=[i for i in 1..] +--Rf(x:PositiveInteger):Boolean == x < 5 +--RfilterUntil(f,m) +--R +--E 82 + +--S 83 of 127 +--R)d op select +--R +--R +--RThere are 4 exposed functions called select : +--R  ((D2 -> Boolean),D) -> D from D +--R if D has finiteAggregate and D has CLAGG D2 and D2 has TYPE +--R +--R  ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2 +--R from InfiniteTuple D2 if D2 has TYPE +--R  ((D2 -> Boolean),D) -> D from D if D has LZSTAGG D2 and D2 has +--R TYPE +--R  (D,D2) -> Union(D1,"failed") from D +--R if D has TSETCAT(D3,D4,D2,D1) and D3 has INTDOM and D4 has +--R OAMONS and D2 has ORDSET and D1 has RPOLCAT(D3,D4,D2) +--R +--RThere is one unexposed function called select : +--R  (Tuple D1,NonNegativeInteger) -> D1 from Tuple D1 if D1 has TYPE +--R +--R +--RExamples of select from Collection +--R +--R +--RExamples of select from InfiniteTuple +--R +--R +--RExamples of select from LazyStreamAggregate +--R +--Rm:=[i for i in 0..] +--Rselect(x+->prime? x,m) +--R +--R +--RExamples of select from TriangularSetCategory +--R +--R +--RExamples of select from Tuple +--R +--Rt1:PrimitiveArray(Integer):= [i for i in 1..10] +--Rt2:=coerce(t1)$Tuple(Integer)
+--Rselect(t2,3)
+--R
+--E 83
+
+--S 84 of 127
+--R)d op nthFlag
+--R
+--R
+--RThere is one exposed function called nthFlag :
+--R    (Factored D3,Integer) -> Union("nil","sqfr","irred","prime")
+--R            from Factored D3 if D3 has INTDOM
+--R
+--RExamples of nthFlag from Factored
+--R
+--Ra:=factor 9720000
+--RnthFlag(a,2)
+--R
+--E 84
+
+--S 85 of 127
+--R)d op makeFR
+--R
+--R
+--RThere is one exposed function called makeFR :
+--R    (D1,List Record(flg: Union("nil","sqfr","irred","prime"),fctr:
+--R            D1,xpnt: Integer)) -> Factored D1
+--R            from Factored D1 if D1 has INTDOM
+--R
+--RThere is one unexposed function called makeFR :
+--R    Record(contp: Integer,factors: List Record(irr: D3,pow: Integer)
+--R            ) -> Factored D3
+--R            from GaloisGroupFactorizer D3 if D3 has UPOLYC INT
+--R
+--RExamples of makeFR from Factored
+--R
+--Rf:=nilFactor(x-y,3)
+--Rg:=factorList f
+--RmakeFR(z,g)
+--R
+--R
+--RExamples of makeFR from GaloisGroupFactorizer
+--R
+--E 85
+
+--S 86 of 127
+--R)d op *
+--R
+--R
+--RThere are 33 exposed functions called * :
+--R    (Integer,D) -> D from D if D has ABELGRP
+--R    (NonNegativeInteger,D) -> D from D if D has ABELMON
+--R    (PositiveInteger,D) -> D from D if D has ABELSG
+--R    (CartesianTensor(D1,D2,D3),CartesianTensor(D1,D2,D3)) ->
+--R            CartesianTensor(D1,D2,D3)
+--R            from CartesianTensor(D1,D2,D3)
+--R            if D1: INT and D2: NNI and D3 has COMRING
+--R    (DoubleFloat,Color) -> Color from Color
+--R    (PositiveInteger,Color) -> Color from Color
+--R    (DenavitHartenbergMatrix D2,Point D2) -> Point D2
+--R            from DenavitHartenbergMatrix D2
+--R            if D2 has Join(Field,TranscendentalFunctionCategory)
+--R    (D1,Equation D1) -> Equation D1 from Equation D1
+--R            if D1 has SGROUP and D1 has TYPE
+--R    (Equation D1,D1) -> Equation D1 from Equation D1
+--R            if D1 has SGROUP and D1 has TYPE
+--R    (D1,D2) -> D from D
+--R            if D has FAMONC(D2,D1) and D2 has SETCAT and D1 has CABMON
+--R
+--R    (D1,D2) -> D from D
+--R            if D has FMCAT(D1,D2) and D1 has RING and D2 has SETCAT
+--R    (D,D1) -> D from D
+--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
+--R
+--R    (D1,D) -> D from D
+--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
+--R
+--R    (PolynomialIdeals(D1,D2,D3,D4),PolynomialIdeals(D1,D2,D3,D4))
+--R             -> PolynomialIdeals(D1,D2,D3,D4)
+--R            from PolynomialIdeals(D1,D2,D3,D4)
+--R            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4
+--R            has POLYCAT(D1,D2,D3)
+--R    (D1,D) -> D from D if D has LMODULE D1 and D1 has RNG
+--R    ((D5 -> D6),(D4 -> D5)) -> (D4 -> D6) from MappingPackage3(D4,
+--R            D5,D6)
+--R            if D4 has SETCAT and D5 has SETCAT and D6 has SETCAT
+--R    ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,
+--R            D3)
+--R            if D2 has SETCAT and D3 has RING
+--R    (D1,D) -> D1 from D
+--R            if D has MATCAT(D2,D1,D3) and D2 has RING and D1 has FLAGG
+--R            D2 and D3 has FLAGG D2
+--R    (D,D1) -> D1 from D
+--R            if D has MATCAT(D2,D3,D1) and D2 has RING and D3 has FLAGG
+--R            D2 and D1 has FLAGG D2
+--R    (Integer,D) -> D from D
+--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG
+--R            D2 and D4 has FLAGG D2
+--R    (D,D1) -> D from D
+--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG
+--R            D1 and D3 has FLAGG D1
+--R    (D1,D) -> D from D
+--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG
+--R            D1 and D3 has FLAGG D1
+--R    (D,D) -> D from D
+--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG
+--R            D1 and D3 has FLAGG D1
+--R    (D,D) -> D from D if D has MONAD
+--R    (D,D1) -> D from D if D has RMODULE D1 and D1 has RNG
+--R    (D,D) -> D from D if D has SGROUP
+--R    (D1,D) -> D1 from D
+--R            if D has SMATCAT(D2,D3,D1,D4) and D3 has RING and D1 has
+--R            DIRPCAT(D2,D3) and D4 has DIRPCAT(D2,D3)
+--R    (D,D1) -> D1 from D
+--R            if D has SMATCAT(D2,D3,D4,D1) and D3 has RING and D4 has
+--R            DIRPCAT(D2,D3) and D1 has DIRPCAT(D2,D3)
+--R    (D,D1) -> D from D
+--R            if D has VECTCAT D1 and D1 has TYPE and D1 has MONOID
+--R    (D1,D) -> D from D
+--R            if D has VECTCAT D1 and D1 has TYPE and D1 has MONOID
+--R    (Integer,D) -> D from D
+--R            if D has VECTCAT D2 and D2 has TYPE and D2 has ABELGRP
+--R    (D1,D) -> D from D
+--R            if D has XFALG(D1,D2) and D1 has ORDSET and D2 has RING
+--R    (D,D1) -> D from D
+--R            if D has XFALG(D2,D1) and D2 has ORDSET and D1 has RING
+--R
+--RThere are 24 unexposed functions called * :
+--R    (FreeGroup D1,D1) -> FreeGroup D1 from FreeGroup D1 if D1 has
+--R            SETCAT
+--R    (D1,FreeGroup D1) -> FreeGroup D1 from FreeGroup D1 if D1 has
+--R            SETCAT
+--R    (D1,D2) -> FreeModule1(D2,D1) from FreeModule1(D2,D1)
+--R            if D2 has RING and D1 has ORDSET
+--R    (FreeMonoid D1,D1) -> FreeMonoid D1 from FreeMonoid D1 if D1 has
+--R            SETCAT
+--R    (D1,FreeMonoid D1) -> FreeMonoid D1 from FreeMonoid D1 if D1 has
+--R            SETCAT
+--R    (D1,GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)) ->
+--R            GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)
+--R            from GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)
+--R            if D2: LIST SYMBOL and D3 has COMRING and D5 has DIRPCAT(#
+--R            D2,NNI) and D6: ((Record(index: D4,exponent: D5),Record(
+--R            index: D4,exponent: D5)) -> Boolean) and D4 has ORDSET and
+--R            D1 has POLYCAT(D3,D5,OVAR D2)
+--R    (Vector D2,Vector D2) -> Vector D2
+--R            from InnerNormalBasisFieldFunctions D2 if D2 has FFIELDC
+--R
+--R    (InputForm,InputForm) -> InputForm from InputForm
+--R    (InnerTaylorSeries D2,Integer) -> InnerTaylorSeries D2
+--R            from InnerTaylorSeries D2 if D2 has RING
+--R    (InnerTaylorSeries D1,D1) -> InnerTaylorSeries D1
+--R            from InnerTaylorSeries D1 if D1 has RING
+--R    (D1,InnerTaylorSeries D1) -> InnerTaylorSeries D1
+--R            from InnerTaylorSeries D1 if D1 has RING
+--R    (Magma D1,Magma D1) -> Magma D1 from Magma D1 if D1 has ORDSET
+--R
+--R    (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2
+--R            )
+--R            from MyExpression(D1,D2)
+--R            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
+--R            IntegralDomain)
+--R    (OrderedFreeMonoid D1,D1) -> OrderedFreeMonoid D1
+--R            from OrderedFreeMonoid D1 if D1 has ORDSET
+--R    (D1,OrderedFreeMonoid D1) -> OrderedFreeMonoid D1
+--R            from OrderedFreeMonoid D1 if D1 has ORDSET
+--R    (OutputForm,OutputForm) -> OutputForm from OutputForm
+--R    (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
+--R            SETCAT
+--R    (D2,Vector D3) -> Vector D3 from PseudoRemainderSequence(D2,D3)
+--R            if D3 has UPOLYC D2 and D2 has INTDOM
+--R    (D1,SparseMultivariateTaylorSeries(D2,D3,D1)) ->
+--R            SparseMultivariateTaylorSeries(D2,D3,D1)
+--R            from SparseMultivariateTaylorSeries(D2,D3,D1)
+--R            if D2 has RING and D3 has ORDSET and D1 has POLYCAT(D2,INDE
+--R            D3,D3)
+--R    (Stream D2,Stream D2) -> Stream D2 from
+--R            StreamTaylorSeriesOperations D2
+--R            if D2 has RING
+--R    (D2,Stream D2) -> Stream D2 from StreamTaylorSeriesOperations
+--R            D2
+--R            if D2 has RING
+--R    (Stream D2,D2) -> Stream D2 from StreamTaylorSeriesOperations
+--R            D2
+--R            if D2 has RING
+--R    (DoubleFloat,Point DoubleFloat) -> Point DoubleFloat from
+--R            TubePlotTools
+--R    (XPolynomialRing(D1,D2),D1) -> XPolynomialRing(D1,D2)
+--R            from XPolynomialRing(D1,D2) if D1 has RING and D2 has
+--R            ORDMON
+--R
+--RExamples of * from AbelianGroup
+--R
+--R
+--RExamples of * from AbelianMonoid
+--R
+--R
+--RExamples of * from AbelianSemiGroup
+--R
+--R
+--RExamples of * from CartesianTensor
+--R
+--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]]
+--RTm:CartesianTensor(1,2,Integer):=m
+--Rv:DirectProduct(2,Integer):=directProduct [3,4]
+--RTv:CartesianTensor(1,2,Integer):=v
+--RTm*Tv
+--R
+--R
+--RExamples of * from Color
+--R
+--R
+--RExamples of * from DenavitHartenbergMatrix
+--R
+--R
+--RExamples of * from Equation
+--R
+--R
+--RExamples of * from FreeAbelianMonoidCategory
+--R
+--R
+--RExamples of * from FreeGroup
+--R
+--R
+--RExamples of * from FreeModule1
+--R
+--R
+--RExamples of * from FreeModuleCat
+--R
+--R
+--RExamples of * from FreeMonoid
+--R
+--R
+--RExamples of * from GeneralModulePolynomial
+--R
+--R
+--RExamples of * from GradedModule
+--R
+--R
+--RExamples of * from PolynomialIdeals
+--R
+--R
+--RExamples of * from InnerNormalBasisFieldFunctions
+--R
+--R
+--RExamples of * from InputForm
+--R
+--R
+--RExamples of * from InnerTaylorSeries
+--R
+--R
+--RExamples of * from LeftModule
+--R
+--R
+--RExamples of * from Magma
+--R
+--R
+--RExamples of * from MappingPackage3
+--R
+--R
+--RExamples of * from MappingPackage4
+--R
+--Rf:=(x:INT):INT +-> 3*x
+--Rg:=(x:INT):INT +-> 2*x+3
+--R(f*g)(4)
+--R
+--R
+--RExamples of * from MatrixCategory
+--R
+--R
+--RExamples of * from Monad
+--R
+--R
+--RExamples of * from MyExpression
+--R
+--R
+--RExamples of * from OrderedFreeMonoid
+--R
+--R
+--RExamples of * from OutputForm
+--R
+--R
+--RExamples of * from Pattern
+--R
+--R
+--RExamples of * from PseudoRemainderSequence
+--R
+--R
+--RExamples of * from RightModule
+--R
+--R
+--RExamples of * from SemiGroup
+--R
+--R
+--RExamples of * from SquareMatrixCategory
+--R
+--R
+--RExamples of * from SparseMultivariateTaylorSeries
+--R
+--R
+--RExamples of * from StreamTaylorSeriesOperations
+--R
+--R
+--RExamples of * from TubePlotTools
+--R
+--R
+--RExamples of * from VectorCategory
+--R
+--R
+--RExamples of * from XFreeAlgebra
+--R
+--R
+--RExamples of * from XPolynomialRing
+--R
+--E 86
+
+--S 87 of 127
+--R)d op numberOfComponents
+--R
+--R
+--RThere are 2 exposed functions called numberOfComponents :
+--R     -> NonNegativeInteger from D
+--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC
+--R            D2 and D4 has UPOLYC FRAC D3
+--R    D -> NonNegativeInteger from D if D has SPACEC D2 and D2 has
+--R            RING
+--R
+--RThere is one unexposed function called numberOfComponents :
+--R     -> NonNegativeInteger from FunctionFieldCategory&(D2,D3,D4,D5)
+--R            if D3 has UFD and D4 has UPOLYC D3 and D5 has UPOLYC FRAC
+--R            D4 and D2 has FFCAT(D3,D4,D5)
+--R
+--RExamples of numberOfComponents from FunctionFieldCategory&
+--R
+--RP0 := UnivariatePolynomial(x, Integer)
+--RP1 := UnivariatePolynomial(y, Fraction P0)
+--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
+--RnumberOfComponents()$R +--R +--R +--RExamples of numberOfComponents from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RnumberOfComponents()$R
+--R
+--R
+--RExamples of numberOfComponents from ThreeSpaceCategory
+--R
+--E 87
+
+--S 88 of 127
+--R)d op tree
+--R
+--R
+--RThere are 3 exposed functions called tree :
+--R    D1 -> Tree D1 from Tree D1 if D1 has SETCAT
+--R    List D2 -> Tree D2 from Tree D2 if D2 has SETCAT
+--R    (D1,List Tree D1) -> Tree D1 from Tree D1 if D1 has SETCAT
+--R
+--RExamples of tree from Tree
+--R
+--Rtree 6
+--R
+--Rtree [1,2,3,4]
+--R
+--Rt1:=tree [1,2,3,4]
+--Rtree(5,[t1])
+--R
+--E 88
+
+--S 89 of 127
+--R)d op Aleph
+--R
+--R
+--RThere is one exposed function called Aleph :
+--R    NonNegativeInteger -> CardinalNumber from CardinalNumber
+--R
+--RExamples of Aleph from CardinalNumber
+--R
+--RA0:=Aleph 0
+--R
+--E 89
+
+--S 90 of 127
+--R)d op unit
+--R
+--R
+--RThere are 3 exposed functions called unit :
+--R    List Float -> DrawOption from DrawOption
+--R     -> Union(D,"failed") from D
+--R            if D has FINAALG D1 and D1 has INTDOM and D1 has COMRING
+--R
+--R    Factored D1 -> D1 from Factored D1 if D1 has INTDOM
+--R
+--RExamples of unit from DrawOption
+--R
+--R
+--RExamples of unit from FiniteRankNonAssociativeAlgebra
+--R
+--R
+--RExamples of unit from Factored
+--R
+--Rf:=x*y^3-3*x^2*y^2+3*x^3*y-x^4
+--Runit f
+--Rg:=makeFR(z,factorList f)
+--Runit g
+--R
+--E 90
+
+--S 91 of 127
+--R)d op frst
+--R
+--R
+--RThere is one exposed function called frst :
+--R    D -> D1 from D if D has LZSTAGG D1 and D1 has TYPE
+--R
+--RExamples of frst from LazyStreamAggregate
+--R
+--Rm:=[i for i in 0..]
+--Rfrst m
+--R
+--E 91
+
+--S 92 of 127
+--R)d op product
+--R
+--R
+--RThere are 4 exposed functions called product :
+--R    (CartesianTensor(D1,D2,D3),CartesianTensor(D1,D2,D3)) ->
+--R            CartesianTensor(D1,D2,D3)
+--R            from CartesianTensor(D1,D2,D3)
+--R            if D1: INT and D2: NNI and D3 has COMRING
+--R    (D,SegmentBinding D) -> D from D if D has COMBOPC
+--R    (D,Symbol) -> D from D if D has COMBOPC
+--R    (D,D) -> D from D
+--R            if D has GRALG(D1,D2) and D1 has COMRING and D2 has ABELMON
+--R
+--R
+--RThere are 3 unexposed functions called product :
+--R    (D1,Symbol) -> D1 from CombinatorialFunction(D3,D1)
+--R            if D3 has Join(OrderedSet,IntegralDomain) and D1 has FS D3
+--R
+--R    (D1,SegmentBinding D1) -> D1 from CombinatorialFunction(D3,D1)
+--R            if D1 has FS D3 and D3 has Join(OrderedSet,IntegralDomain)
+--R
+--R    (XPBWPolynomial(D2,D3),XPBWPolynomial(D2,D3),NonNegativeInteger)
+--R             -> XPBWPolynomial(D2,D3)
+--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has
+--R            COMRING
+--R
+--RExamples of product from CartesianTensor
+--R
+--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]]
+--RTm:CartesianTensor(1,2,Integer):=m
+--Rn:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]]
+--RTn:CartesianTensor(1,2,Integer):=n
+--RTmn:=product(Tm,Tn)
+--R
+--R
+--RExamples of product from CombinatorialFunction
+--R
+--R
+--RExamples of product from CombinatorialOpsCategory
+--R
+--R
+--RExamples of product from GradedAlgebra
+--R
+--R
+--RExamples of product from XPBWPolynomial
+--R
+--E 92
+
+--S 93 of 127
+--R)d op fill!
+--R
+--R
+--RThere are 2 exposed functions called fill! :
+--R    (D,D1) -> D from D
+--R            if D has ARR2CAT(D1,D2,D3) and D1 has TYPE and D2 has FLAGG
+--R            D1 and D3 has FLAGG D1
+--R    (D,D1) -> D from D
+--R            if D has shallowlyMutable and D has IXAGG(D2,D1) and D2 has
+--R            SETCAT and D1 has TYPE
+--R
+--RExamples of fill! from TwoDimensionalArrayCategory
+--R
+--Rarr : ARRAY2 INT := new(5,4,0)
+--Rfill!(arr,10)
+--R
+--R
+--RExamples of fill! from IndexedAggregate
+--R
+--E 93
+
+--S 94 of 127
+--R)d op upperCase?
+--R
+--R
+--RThere is one exposed function called upperCase? :
+--R    Character -> Boolean from Character
+--R
+--RExamples of upperCase? from Character
+--R
+--Rchars := [char "a", char "A", char "X", char "8", char "+"]
+--R[upperCase? c for c in chars]
+--R
+--E 94
+
+--S 95 of 127
+--R)d op integralMatrixAtInfinity
+--R
+--R
+--RThere is one exposed function called integralMatrixAtInfinity :
+--R     -> Matrix Fraction D3 from D
+--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC
+--R            D2 and D4 has UPOLYC FRAC D3
+--R
+--RExamples of integralMatrixAtInfinity from FunctionFieldCategory
+--R
+--RP0 := UnivariatePolynomial(x, Integer)
+--RP1 := UnivariatePolynomial(y, Fraction P0)
+--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
+--RintegralMatrixAtInfinity()$R +--R +--E 95 + +--S 96 of 127 +--R)d op finite? +--R +--R +--RThere are 3 exposed functions called finite? : +--R  CardinalNumber -> Boolean from CardinalNumber +--R  OnePointCompletion D2 -> Boolean from OnePointCompletion D2 +--R if D2 has SETCAT +--R  OrderedCompletion D2 -> Boolean from OrderedCompletion D2 +--R if D2 has SETCAT +--R +--RExamples of finite? from CardinalNumber +--R +--Rc2:=2::CardinalNumber +--Rfinite? c2 +--RA0:=Aleph 0 +--Rfinite? A0 +--R +--R +--RExamples of finite? from OnePointCompletion +--R +--R +--RExamples of finite? from OrderedCompletion +--R +--E 96 + +--S 97 of 127 +--R)d op rank +--R +--R +--RThere are 8 exposed functions called rank : +--R  CartesianTensor(D2,D3,D4) -> NonNegativeInteger +--R from CartesianTensor(D2,D3,D4) +--R if D2: INT and D3: NNI and D4 has COMRING +--R  -> PositiveInteger from D if D has FINAALG D2 and D2 has +--R COMRING +--R  -> PositiveInteger from D +--R if D has FINRALG(D2,D3) and D2 has COMRING and D3 has +--R UPOLYC D2 +--R  (Matrix D4,Vector D4) -> NonNegativeInteger +--R from LinearSystemMatrixPackage1 D4 if D4 has FIELD +--R  (D2,D3) -> NonNegativeInteger +--R from LinearSystemMatrixPackage(D4,D5,D3,D2) +--R if D4 has FIELD and D5 has FiniteLinearAggregate D4 with +--R shallowlyMutable and D3 has FiniteLinearAggregate D4 +--R with +--R shallowlyMutable and D2 has MATCAT(D4,D5,D3) +--R  D -> NonNegativeInteger from D +--R if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG +--R D2 and D4 has FLAGG D2 and D2 has INTDOM +--R  D2 -> NonNegativeInteger from MatrixLinearAlgebraFunctions(D3,D4 +--R ,D5,D2) +--R if D3 has INTDOM and D3 has COMRING and D4 has FLAGG D3 and +--R D5 has FLAGG D3 and D2 has MATCAT(D3,D4,D5) +--R  D -> NonNegativeInteger from D +--R if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has +--R DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4) and D4 has INTDOM +--R +--R +--RThere are 2 unexposed functions called rank : +--R  -> PositiveInteger from ComplexCategory&(D2,D3) +--R if D3 has COMRING and D2 has COMPCAT D3 +--R  D2 -> NonNegativeInteger +--R from InnerMatrixLinearAlgebraFunctions(D3,D4,D5,D2) +--R if D3 has FIELD and D4 has FLAGG D3 and D5 has FLAGG D3 and +--R D2 has MATCAT(D3,D4,D5) +--R +--RExamples of rank from CartesianTensor +--R +--RCT:=CARTEN(1,2,Integer) +--Rt0:CT:=8 +--Rrank t0 +--R +--R +--RExamples of rank from ComplexCategory& +--R +--R +--RExamples of rank from FiniteRankNonAssociativeAlgebra +--R +--R +--RExamples of rank from FiniteRankAlgebra +--R +--R +--RExamples of rank from InnerMatrixLinearAlgebraFunctions +--R +--R +--RExamples of rank from LinearSystemMatrixPackage1 +--R +--R +--RExamples of rank from LinearSystemMatrixPackage +--R +--R +--RExamples of rank from MatrixCategory +--R +--R +--RExamples of rank from MatrixLinearAlgebraFunctions +--R +--R +--RExamples of rank from RectangularMatrixCategory +--R +--E 97 + +--S 98 of 127 +--R)d op numberOfComputedEntries +--R +--R +--RThere is one exposed function called numberOfComputedEntries : +--R  D -> NonNegativeInteger from D if D has LZSTAGG D2 and D2 has +--R TYPE +--R +--RExamples of numberOfComputedEntries from LazyStreamAggregate +--R +--Rm:=[i for i in 0..] +--RnumberOfComputedEntries m +--R +--E 98 + +--S 99 of 127 +--R)d op groebnerFactorize +--R +--R +--RThere are 4 exposed functions called groebnerFactorize : +--R  (List D6,List D6) -> List List D6 +--R from GroebnerFactorizationPackage(D3,D4,D5,D6) +--R if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has OAMONS and D5 has ORDSET and D6 has POLYCAT(D3,D4,D5) +--R +--R  (List D7,List D7,Boolean) -> List List D7 +--R from GroebnerFactorizationPackage(D4,D5,D6,D7) +--R if D4 has Join(EuclideanDomain,CharacteristicZero) and D5 +--R has OAMONS and D6 has ORDSET and D7 has POLYCAT(D4,D5,D6) +--R +--R  List D6 -> List List D6 from GroebnerFactorizationPackage(D3,D4, +--R D5,D6) +--R if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has OAMONS and D5 has ORDSET and D6 has POLYCAT(D3,D4,D5) +--R +--R  (List D7,Boolean) -> List List D7 +--R from GroebnerFactorizationPackage(D4,D5,D6,D7) +--R if D4 has Join(EuclideanDomain,CharacteristicZero) and D5 +--R has OAMONS and D6 has ORDSET and D7 has POLYCAT(D4,D5,D6) +--R +--R +--RExamples of groebnerFactorize from GroebnerFactorizationPackage +--R +--Rmfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := ++X [ [0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], ++X [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0] ] +--Req := determinant mfzn +--RgroebnerFactorize ++X [eq,eval(eq, [x,y,z],[y,z,x]), eval(eq,[x,y,z],[z,x,y])] +--R +--E 99 + +--S 100 of 127 +--R)d op lowerCase +--R +--R +--RThere are 3 exposed functions called lowerCase : +--R  -> CharacterClass from CharacterClass +--R  Character -> Character from Character +--R  D -> D from D if D has SRAGG +--R +--RExamples of lowerCase from CharacterClass +--R +--R +--RExamples of lowerCase from Character +--R +--Rchars := [char "a", char "A", char "X", char "8", char "+"] +--R[lowerCase c for c in chars] +--R +--R +--RExamples of lowerCase from StringAggregate +--R +--E 100 + +--S 101 of 127 +--R)d op showAllElements +--R +--R +--RThere is one exposed function called showAllElements : +--R  Stream D2 -> OutputForm from Stream D2 +--R if D2 has SETCAT and D2 has TYPE +--R +--RExamples of showAllElements from Stream +--R +--Rm:=[1,2,3,4,5,6,7,8,9,10,11,12] +--Rn:=m::Stream(PositiveInteger) +--RshowAllElements n +--R +--E 101 + +--S 102 of 127 +--R)d op maxColIndex +--R +--R +--RThere are 2 exposed functions called maxColIndex : +--R  D -> Integer from D +--R if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG +--R D2 and D4 has FLAGG D2 +--R  D -> Integer from D +--R if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has +--R DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4) +--R +--RExamples of maxColIndex from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--RmaxColIndex(arr) +--R +--R +--RExamples of maxColIndex from RectangularMatrixCategory +--R +--E 102 + +--S 103 of 127 +--R)d op minRowIndex +--R +--R +--RThere are 2 exposed functions called minRowIndex : +--R  D -> Integer from D +--R if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG +--R D2 and D4 has FLAGG D2 +--R  D -> Integer from D +--R if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has +--R DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4) +--R +--RExamples of minRowIndex from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--RminRowIndex(arr) +--R +--R +--RExamples of minRowIndex from RectangularMatrixCategory +--R +--E 103 + +--S 104 of 127 +--R)d op space +--R +--R +--RThere are 2 exposed functions called space : +--R  -> Character from Character +--R  ThreeSpace DoubleFloat -> DrawOption from DrawOption +--R +--RThere is one unexposed function called space : +--R  List DrawOption -> ThreeSpace DoubleFloat from +--R DrawOptionFunctions0 +--R +--RExamples of space from Character +--R +--Rspace() +--R +--R +--RExamples of space from DrawOptionFunctions0 +--R +--R +--RExamples of space from DrawOption +--R +--E 104 + +--S 105 of 127 +--R)d op remove +--R +--R +--RThere are 5 exposed functions called remove : +--R  (D1,D) -> D from D +--R if D has finiteAggregate and D has CLAGG D1 and D1 has TYPE +--R and D1 has SETCAT +--R  ((D2 -> Boolean),D) -> D from D +--R if D has finiteAggregate and D has CLAGG D2 and D2 has TYPE +--R +--R  ((D2 -> Boolean),D) -> D from D if D has LZSTAGG D2 and D2 has +--R TYPE +--R  ((D3 -> Boolean),Multiset D3,Integer) -> Multiset D3 from +--R Multiset D3 +--R if D3 has SETCAT +--R  (D1,Multiset D1,Integer) -> Multiset D1 from Multiset D1 +--R if D1 has SETCAT +--R +--RThere is one unexposed function called remove : +--R  (SplittingNode(D2,D3),SplittingTree(D2,D3)) -> SplittingTree(D2, +--R D3) +--R from SplittingTree(D2,D3) +--R if D2 has Join(SetCategory,Aggregate) and D3 has Join( +--R SetCategory,Aggregate) +--R +--RExamples of remove from Collection +--R +--R +--RExamples of remove from LazyStreamAggregate +--R +--Rm:=[i for i in 1..] +--Rf(i:PositiveInteger):Boolean == even? i +--Rremove(f,m) +--R +--R +--RExamples of remove from Multiset +--R +--R +--RExamples of remove from SplittingTree +--R +--E 105 + +--S 106 of 127 +--R)d op factors +--R +--R +--RThere is one exposed function called factors : +--R  Factored D2 -> List Record(factor: D2,exponent: Integer) +--R from Factored D2 if D2 has INTDOM +--R +--RThere are 3 unexposed functions called factors : +--R  FreeGroup D2 -> List Record(gen: D2,exp: Integer) from FreeGroup +--R D2 +--R if D2 has SETCAT +--R  FreeMonoid D2 -> List Record(gen: D2,exp: NonNegativeInteger) +--R from FreeMonoid D2 if D2 has SETCAT +--R  OrderedFreeMonoid D2 -> List Record(gen: D2,exp: +--R NonNegativeInteger) +--R from OrderedFreeMonoid D2 if D2 has ORDSET +--R +--RExamples of factors from FreeGroup +--R +--R +--RExamples of factors from FreeMonoid +--R +--R +--RExamples of factors from Factored +--R +--Rf:=x*y^3-3*x^2*y^2+3*x^3*y-x^4 +--Rfactors f +--Rg:=makeFR(z,factorList f) +--Rfactors g +--R +--R +--RExamples of factors from OrderedFreeMonoid +--R +--E 106 + +--S 107 of 127 +--R)d op output +--R +--R +--RThere are 4 exposed functions called output : +--R  String -> Void from OutputPackage +--R  OutputForm -> Void from OutputPackage +--R  (String,OutputForm) -> Void from OutputPackage +--R  (Integer,Stream D3) -> Void from Stream D3 +--R if D3 has SETCAT and D3 has TYPE +--R +--RExamples of output from OutputPackage +--R +--R +--RExamples of output from Stream +--R +--Rm:=[1,2,3] +--Rn:=repeating(m) +--Routput(5,n) +--R +--E 107 + +--S 108 of 127 +--R)d op binarySearchTree +--R +--R +--RThere is one exposed function called binarySearchTree : +--R  List D2 -> BinarySearchTree D2 from BinarySearchTree D2 if D2 +--R has ORDSET +--R +--RExamples of binarySearchTree from BinarySearchTree +--R +--RbinarySearchTree [1,2,3,4] +--R +--E 108 + +--S 109 of 127 +--R)d op char +--R +--R +--RThere are 2 exposed functions called char : +--R  String -> Character from Character +--R  Integer -> Character from Character +--R +--RExamples of char from Character +--R +--R[char c for c in ["a","A","X","8","+"]] +--R +--R[char c for c in [97,65,88,56,43]] +--R +--E 109 + +--S 110 of 127 +--R)d op shrinkable +--R +--R +--RThere is one exposed function called shrinkable : +--R  Boolean -> Boolean from FlexibleArray D2 if D2 has TYPE +--R +--RThere is one unexposed function called shrinkable : +--R  Boolean -> Boolean from IndexedFlexibleArray(D2,D3) +--R if D2 has TYPE and D3: INT +--R +--RExamples of shrinkable from FlexibleArray +--R +--R +--RExamples of shrinkable from IndexedFlexibleArray +--R +--RT1:=IndexedFlexibleArray(Integer,20) +--Rshrinkable(false)$T1
+--R
+--E 110
+
+--S 111 of 127
+--R)d op rst
+--R
+--R
+--RThere is one exposed function called rst :
+--R    D -> D from D if D has LZSTAGG D1 and D1 has TYPE
+--R
+--RExamples of rst from LazyStreamAggregate
+--R
+--Rm:=[i for i in 0..]
+--Rrst m
+--R
+--E 111
+
+--S 112 of 127
+--R)d op flexibleArray
+--R
+--R
+--RThere is one exposed function called flexibleArray :
+--R    List D2 -> FlexibleArray D2 from FlexibleArray D2 if D2 has TYPE
+--R
+--R
+--RThere is one unexposed function called flexibleArray :
+--R    List D2 -> IndexedFlexibleArray(D2,D3) from IndexedFlexibleArray
+--R            (D2,D3)
+--R            if D2 has TYPE and D3: INT
+--R
+--RExamples of flexibleArray from FlexibleArray
+--R
+--R
+--RExamples of flexibleArray from IndexedFlexibleArray
+--R
+--RT1:=IndexedFlexibleArray(Integer,20)
+--RflexibleArray([i for i in 1..10])$T1 +--R +--E 112 + +--S 113 of 127 +--R)d op setelt +--R +--R +--RThere are 12 exposed functions called setelt : +--R  (D,Integer,Integer,D1) -> D1 from D +--R if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG +--R D1 and D4 has FLAGG D1 +--R  (D,right,D) -> D from D +--R if D has shallowlyMutable and D has BRAGG D2 and D2 has +--R TYPE +--R  (D,left,D) -> D from D +--R if D has shallowlyMutable and D has BRAGG D2 and D2 has +--R TYPE +--R  (D,D2,D1) -> D1 from D +--R if D has shallowlyMutable and D has ELTAGG(D2,D1) and D2 +--R has SETCAT and D1 has TYPE +--R  (Library,Symbol,Any) -> Any from Library +--R  (D,UniversalSegment Integer,D1) -> D1 from D +--R if D has shallowlyMutable and D has LNAGG D1 and D1 has +--R TYPE +--R  (D,List Integer,List Integer,D) -> D from D +--R if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG +--R D2 and D4 has FLAGG D2 +--R  (D,value,D1) -> D1 from D +--R if D has shallowlyMutable and D has RCAGG D1 and D1 has +--R TYPE +--R  (D,D2,D1) -> D1 from D +--R if D has TBAGG(D2,D1) and D2 has SETCAT and D1 has SETCAT +--R +--R  (D,last,D1) -> D1 from D +--R if D has shallowlyMutable and D has URAGG D1 and D1 has +--R TYPE +--R  (D,rest,D) -> D from D +--R if D has shallowlyMutable and D has URAGG D2 and D2 has +--R TYPE +--R  (D,first,D1) -> D1 from D +--R if D has shallowlyMutable and D has URAGG D1 and D1 has +--R TYPE +--R +--RThere is one unexposed function called setelt : +--R  (Reference D1,D1) -> D1 from Reference D1 if D1 has TYPE +--R +--RExamples of setelt from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,0) +--Rsetelt(arr,1,1,17) +--R +--R +--RExamples of setelt from BinaryRecursiveAggregate +--R +--R +--RExamples of setelt from EltableAggregate +--R +--R +--RExamples of setelt from Library +--R +--R +--RExamples of setelt from LinearAggregate +--R +--R +--RExamples of setelt from MatrixCategory +--R +--R +--RExamples of setelt from RecursiveAggregate +--R +--R +--RExamples of setelt from Reference +--R +--R +--RExamples of setelt from TableAggregate +--R +--R +--RExamples of setelt from UnaryRecursiveAggregate +--R +--E 113 + +--S 114 of 127 +--R)d op cyclicParents +--R +--R +--RThere is one exposed function called cyclicParents : +--R  Tree D2 -> List Tree D2 from Tree D2 if D2 has SETCAT +--R +--RExamples of cyclicParents from Tree +--R +--Rt1:=tree [1,2,3,4] +--RcyclicParents t1 +--R +--E 114 + +--S 115 of 127 +--R)d op explicitEntries? +--R +--R +--RThere is one exposed function called explicitEntries? : +--R  D -> Boolean from D if D has LZSTAGG D2 and D2 has TYPE +--R +--RExamples of explicitEntries? from LazyStreamAggregate +--R +--Rm:=[i for i in 0..] +--RexplicitEntries? m +--R +--E 115 + +--S 116 of 127 +--R)d op column +--R +--R +--RThere are 2 exposed functions called column : +--R  (D,Integer) -> D1 from D +--R if D has ARR2CAT(D3,D4,D1) and D3 has TYPE and D4 has FLAGG +--R D3 and D1 has FLAGG D3 +--R  (D,Integer) -> D1 from D +--R if D has RMATCAT(D3,D4,D5,D6,D1) and D5 has RING and D6 has +--R DIRPCAT(D4,D5) and D1 has DIRPCAT(D3,D5) +--R +--RExamples of column from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--Rcolumn(arr,1) +--R +--R +--RExamples of column from RectangularMatrixCategory +--R +--E 116 + +--S 117 of 127 +--R)d op reduce +--R +--R +--RThere are 19 exposed functions called reduce : +--R  AlgebraicNumber -> AlgebraicNumber from AlgebraicNumber +--R  (((D4,D1) -> D1),OneDimensionalArray D4,D1) -> D1 +--R from OneDimensionalArrayFunctions2(D4,D1) +--R if D4 has TYPE and D1 has TYPE +--R  (((D1,D1) -> D1),D,D1,D1) -> D1 from D +--R if D1 has SETCAT and D has finiteAggregate and D has CLAGG +--R D1 and D1 has TYPE +--R  (((D1,D1) -> D1),D,D1) -> D1 from D +--R if D has finiteAggregate and D has CLAGG D1 and D1 has TYPE +--R +--R  (((D1,D1) -> D1),D) -> D1 from D +--R if D has finiteAggregate and D has CLAGG D1 and D1 has TYPE +--R +--R  (((D5,D1) -> D1),DirectProduct(D4,D5),D1) -> D1 +--R from DirectProductFunctions2(D4,D5,D1) +--R if D4: NNI and D5 has TYPE and D1 has TYPE +--R  Expression D1 -> Expression D1 from Expression D1 +--R if D1 has INTDOM and D1 has ORDSET +--R  D -> D from D +--R if D has FDIVCAT(D1,D2,D3,D4) and D1 has FIELD and D2 has +--R UPOLYC D1 and D3 has UPOLYC FRAC D2 and D4 has FFCAT(D1,D2, +--R D3) +--R  (((D4,D1) -> D1),D3,D1) -> D1 +--R from FiniteLinearAggregateFunctions2(D4,D3,D1,D5) +--R if D4 has TYPE and D1 has TYPE and D3 has FLAGG D4 and D5 +--R has FLAGG D1 +--R  (((D4,D1) -> D1),D3,D1) -> D1 +--R from FiniteSetAggregateFunctions2(D4,D3,D1,D5) +--R if D4 has SETCAT and D1 has SETCAT and D3 has FSAGG D4 and +--R D5 has FSAGG D1 +--R  (((D4,D1) -> D1),List D4,D1) -> D1 from ListFunctions2(D4,D1) +--R if D4 has TYPE and D1 has TYPE +--R  (((D5,D2) -> D2),D4,D2) -> D2 +--R from MatrixCategoryFunctions2(D5,D6,D7,D4,D2,D8,D9,D1) +--R if D5 has RING and D2 has RING and D6 has FLAGG D5 and D7 +--R has FLAGG D5 and D8 has FLAGG D2 and D9 has FLAGG D2 and D4 +--R has MATCAT(D5,D6,D7) and D1 has MATCAT(D2,D8,D9) +--R  Fraction D3 -> Union(D,"failed") from D +--R if D3 has UPOLYC D2 and D2 has FIELD and D2 has COMRING and +--R D has MONOGEN(D2,D3) +--R  D1 -> D from D +--R if D2 has COMRING and D has MONOGEN(D2,D1) and D1 has +--R UPOLYC D2 +--R  (((D4,D1) -> D1),PrimitiveArray D4,D1) -> D1 +--R from PrimitiveArrayFunctions2(D4,D1) +--R if D4 has TYPE and D1 has TYPE +--R  (((D9,D4) -> D4),D6,D4) -> D4 +--R from RectangularMatrixCategoryFunctions2(D7,D8,D9,D10,D11, +--R D6,D4,D1,D2,D3) +--R if D9 has RING and D4 has RING and D7: NNI and D8: NNI and +--R D10 has DIRPCAT(D8,D9) and D11 has DIRPCAT(D7,D9) and D1 +--R has DIRPCAT(D8,D4) and D2 has DIRPCAT(D7,D4) and D6 has +--R RMATCAT(D7,D8,D9,D10,D11) and D3 has RMATCAT(D7,D8,D4,D1,D2 +--R ) +--R  (D1,((D4,D1) -> D1),Stream D4) -> D1 from StreamFunctions2(D4, +--R D1) +--R if D4 has TYPE and D1 has TYPE +--R  (D1,D,((D1,D1) -> D1),((D1,D1) -> Boolean)) -> D1 from D +--R if D has TSETCAT(D4,D5,D6,D1) and D4 has INTDOM and D5 has +--R OAMONS and D6 has ORDSET and D1 has RPOLCAT(D4,D5,D6) +--R  (((D4,D1) -> D1),Vector D4,D1) -> D1 from VectorFunctions2(D4, +--R D1) +--R if D4 has TYPE and D1 has TYPE +--R +--RThere are 7 unexposed functions called reduce : +--R  SparseUnivariatePolynomial D3 -> Record(pol: +--R SparseUnivariatePolynomial D3,deg: PositiveInteger) +--R from DegreeReductionPackage(D3,D4) +--R if D3 has RING and D4 has Join(IntegralDomain,OrderedSet) +--R +--R  (D1,D2) -> EuclideanModularRing(D3,D1,D2,D4,D5,D6) +--R from EuclideanModularRing(D3,D1,D2,D4,D5,D6) +--R if D3 has COMRING and D1 has UPOLYC D3 and D2 has ABELMON +--R and D4: ((D1,D2) -> D1) and D5: ((D2,D2) -> Union(D2, +--R "failed")) and D6: ((D1,D1,D2) -> Union(D1,"failed")) +--R  InnerAlgebraicNumber -> InnerAlgebraicNumber from +--R InnerAlgebraicNumber +--R  (D1,D2) -> ModularField(D1,D2,D3,D4,D5) +--R from ModularField(D1,D2,D3,D4,D5) +--R if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1 +--R ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1, +--R D2) -> Union(D1,"failed")) +--R  D1 -> ModMonic(D2,D1) from ModMonic(D2,D1) +--R if D2 has RING and D1 has UPOLYC D2 +--R  (D1,D2) -> ModularRing(D1,D2,D3,D4,D5) from ModularRing(D1,D2,D3 +--R ,D4,D5) +--R if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1 +--R ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1, +--R D2) -> Union(D1,"failed")) +--R  D1 -> ResidueRing(D2,D3,D4,D1,D5) from ResidueRing(D2,D3,D4,D1, +--R D5) +--R if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D1 +--R has POLYCAT(D2,D3,D4) and D5: LIST D1 +--R +--RExamples of reduce from AlgebraicNumber +--R +--R +--RExamples of reduce from OneDimensionalArrayFunctions2 +--R +--RT1:=OneDimensionalArrayFunctions2(Integer,Integer) +--Radder(a:Integer,b:Integer):Integer == a+b +--Rreduce(adder,[i for i in 1..10],0)$T1
+--R
+--R
+--RExamples of reduce from Collection
+--R
+--Rreduce(+,[C[i]*x**i for i in 1..5])
+--R
+--R
+--RExamples of reduce from DegreeReductionPackage
+--R
+--R
+--RExamples of reduce from DirectProductFunctions2
+--R
+--R
+--RExamples of reduce from EuclideanModularRing
+--R
+--R
+--RExamples of reduce from Expression
+--R
+--R
+--RExamples of reduce from FiniteDivisorCategory
+--R
+--R
+--RExamples of reduce from FiniteLinearAggregateFunctions2
+--R
+--R
+--RExamples of reduce from FiniteSetAggregateFunctions2
+--R
+--R
+--RExamples of reduce from InnerAlgebraicNumber
+--R
+--R
+--RExamples of reduce from ListFunctions2
+--R
+--R
+--RExamples of reduce from MatrixCategoryFunctions2
+--R
+--R
+--RExamples of reduce from ModularField
+--R
+--R
+--RExamples of reduce from ModMonic
+--R
+--R
+--RExamples of reduce from ModularRing
+--R
+--R
+--RExamples of reduce from MonogenicAlgebra
+--R
+--R
+--RExamples of reduce from PrimitiveArrayFunctions2
+--R
+--RT1:=PrimitiveArrayFunctions2(Integer,Integer)
+--Radder(a:Integer,b:Integer):Integer == a+b
+--Rreduce(adder,[i for i in 1..10],0)$T1 +--R +--R +--RExamples of reduce from ResidueRing +--R +--R +--RExamples of reduce from RectangularMatrixCategoryFunctions2 +--R +--R +--RExamples of reduce from StreamFunctions2 +--R +--Rm:=[i for i in 1..300]::Stream(Integer) +--Rf(i:Integer,j:Integer):Integer==i+j +--Rreduce(1,f,m) +--R +--R +--RExamples of reduce from TriangularSetCategory +--R +--R +--RExamples of reduce from VectorFunctions2 +--R +--E 117 + +--S 118 of 127 +--R)d op new +--R +--R +--RThere are 7 exposed functions called new : +--R  (NonNegativeInteger,NonNegativeInteger,D2) -> D from D +--R if D2 has TYPE and D has ARR2CAT(D2,D3,D4) and D3 has FLAGG +--R D2 and D4 has FLAGG D2 +--R  (String,String,String) -> D from D if D has FNCAT +--R  -> ScriptFormulaFormat from ScriptFormulaFormat +--R  (NonNegativeInteger,D2) -> D from D +--R if D has LNAGG D2 and D2 has TYPE +--R  Symbol -> Symbol from Symbol +--R  -> Symbol from Symbol +--R  -> TexFormat from TexFormat +--R +--RThere are 4 unexposed functions called new : +--R  -> SubSpaceComponentProperty from SubSpaceComponentProperty +--R  -> PatternMatchListResult(D1,D2,D3) +--R from PatternMatchListResult(D1,D2,D3) +--R if D2 has SETCAT and D1 has SETCAT and D3 has LSAGG D2 +--R  -> PatternMatchResult(D1,D2) from PatternMatchResult(D1,D2) +--R if D1 has SETCAT and D2 has SETCAT +--R  -> SubSpace(D1,D2) from SubSpace(D1,D2) if D1: PI and D2 has +--R RING +--R +--RExamples of new from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,0) +--R +--R +--RExamples of new from SubSpaceComponentProperty +--R +--R +--RExamples of new from FileNameCategory +--R +--R +--RExamples of new from ScriptFormulaFormat +--R +--R +--RExamples of new from LinearAggregate +--R +--R +--RExamples of new from PatternMatchListResult +--R +--R +--RExamples of new from PatternMatchResult +--R +--R +--RExamples of new from SubSpace +--R +--R +--RExamples of new from Symbol +--R +--R +--RExamples of new from TexFormat +--R +--E 118 + +--S 119 of 127 +--R)d op insertRoot! +--R +--R +--RThere is one exposed function called insertRoot! : +--R  (D1,BinarySearchTree D1) -> BinarySearchTree D1 +--R from BinarySearchTree D1 if D1 has ORDSET +--R +--RExamples of insertRoot! from BinarySearchTree +--R +--Rt1:=binarySearchTree [1,2,3,4] +--RinsertRoot!(5,t1) +--R +--E 119 + +--S 120 of 127 +--R)d op maxRowIndex +--R +--R +--RThere are 2 exposed functions called maxRowIndex : +--R  D -> Integer from D +--R if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG +--R D2 and D4 has FLAGG D2 +--R  D -> Integer from D +--R if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has +--R DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4) +--R +--RExamples of maxRowIndex from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--RmaxRowIndex(arr) +--R +--R +--RExamples of maxRowIndex from RectangularMatrixCategory +--R +--E 120 + +--S 121 of 127 +--R)d op escape +--R +--R +--RThere is one exposed function called escape : +--R  -> Character from Character +--R +--RExamples of escape from Character +--R +--Rescape() +--R +--E 121 + +--S 122 of 127 +--R)d op nthExponent +--R +--R +--RThere is one exposed function called nthExponent : +--R  (Factored D2,Integer) -> Integer from Factored D2 if D2 has +--R INTDOM +--R +--RExamples of nthExponent from Factored +--R +--Ra:=factor 9720000 +--RnthExponent(a,2) +--R +--E 122 + +--S 123 of 127 +--R)d op parts +--R +--R +--RThere are 2 exposed functions called parts : +--R  D -> List D2 from D +--R if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG +--R D2 and D4 has FLAGG D2 +--R  D -> List D2 from D +--R if D has finiteAggregate and D has HOAGG D2 and D2 has TYPE +--R +--R +--RExamples of parts from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--Rparts(arr) +--R +--R +--RExamples of parts from HomogeneousAggregate +--R +--E 123 + +--S 124 of 127 +--R)d op elt +--R +--R +--RThere are 47 exposed functions called elt : +--R  (D,Integer,Integer,D1) -> D1 from D +--R if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG +--R D1 and D4 has FLAGG D1 +--R  (D,Integer,Integer) -> D1 from D +--R if D has ARR2CAT(D1,D3,D4) and D3 has FLAGG D1 and D4 has +--R FLAGG D1 and D1 has TYPE +--R  (D,right) -> D from D if D has BRAGG D2 and D2 has TYPE +--R  (D,left) -> D from D if D has BRAGG D2 and D2 has TYPE +--R  (CartesianTensor(D3,D4,D1),List Integer) -> D1 +--R from CartesianTensor(D3,D4,D1) +--R if D1 has COMRING and D3: INT and D4: NNI +--R  (CartesianTensor(D3,D4,D1),Integer,Integer,Integer,Integer) -> +--R D1 +--R from CartesianTensor(D3,D4,D1) +--R if D1 has COMRING and D3: INT and D4: NNI +--R  (CartesianTensor(D3,D4,D1),Integer,Integer,Integer) -> D1 +--R from CartesianTensor(D3,D4,D1) +--R if D1 has COMRING and D3: INT and D4: NNI +--R  (CartesianTensor(D3,D4,D1),Integer,Integer) -> D1 +--R from CartesianTensor(D3,D4,D1) +--R if D1 has COMRING and D3: INT and D4: NNI +--R  (CartesianTensor(D3,D4,D1),Integer) -> D1 +--R from CartesianTensor(D3,D4,D1) +--R if D1 has COMRING and D3: INT and D4: NNI +--R  CartesianTensor(D2,D3,D1) -> D1 from CartesianTensor(D2,D3,D1) +--R if D1 has COMRING and D2: INT and D3: NNI +--R  (Database D3,Symbol) -> DataList String from Database D3 +--R if D3 has OrderedSet with +--R ?.? : (%,Symbol) -> String +--R display : % -> Void +--R fullDisplay : % -> Void +--R  (Database D2,QueryEquation) -> Database D2 from Database D2 +--R if D2 has OrderedSet with +--R ?.? : (%,Symbol) -> String +--R display : % -> Void +--R fullDisplay : % -> Void +--R  (DataList D3,count) -> NonNegativeInteger from DataList D3 +--R if D3 has ORDSET +--R  (DataList D2,sort) -> DataList D2 from DataList D2 if D2 has +--R ORDSET +--R  (DataList D2,unique) -> DataList D2 from DataList D2 if D2 has +--R ORDSET +--R  (D,D2) -> D1 from D +--R if D has ELTAB(D2,D1) and D2 has SETCAT and D1 has TYPE +--R  (D,D2,D1) -> D1 from D +--R if D has ELTAGG(D2,D1) and D2 has SETCAT and D1 has TYPE +--R +--R  (BasicOperator,List D) -> D from D if D has ES +--R  (BasicOperator,D,D,D,D) -> D from D if D has ES +--R  (BasicOperator,D,D,D) -> D from D if D has ES +--R  (BasicOperator,D,D) -> D from D if D has ES +--R  (BasicOperator,D) -> D from D if D has ES +--R  (D,D1,D1) -> D1 from D +--R if D has FFCAT(D1,D2,D3) and D1 has UFD and D2 has UPOLYC +--R D1 and D3 has UPOLYC FRAC D2 +--R  (D,Integer) -> D1 from D if D has FRNAALG D1 and D1 has COMRING +--R +--R  (IndexCard,Symbol) -> String from IndexCard +--R  (Library,Symbol) -> Any from Library +--R  (D,UniversalSegment Integer) -> D from D +--R if D has LNAGG D2 and D2 has TYPE +--R  (ThreeDimensionalMatrix D1,NonNegativeInteger, +--R NonNegativeInteger,NonNegativeInteger) -> D1 +--R from ThreeDimensionalMatrix D1 if D1 has SETCAT +--R  (D,List Integer,List Integer) -> D from D +--R if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG +--R D2 and D4 has FLAGG D2 +--R  (D,D1) -> D1 from D if D has PERMCAT D1 and D1 has SETCAT +--R  (PermutationGroup D3,NonNegativeInteger) -> Permutation D3 +--R from PermutationGroup D3 if D3 has SETCAT +--R  (QuadraticForm(D3,D1),DirectProduct(D3,D1)) -> D1 +--R from QuadraticForm(D3,D1) if D3: PI and D1 has FIELD +--R  (D,value) -> D1 from D if D has RCAGG D1 and D1 has TYPE +--R  (D,Integer,Integer,D1) -> D1 from D +--R if D has RMATCAT(D3,D4,D1,D5,D6) and D1 has RING and D5 has +--R DIRPCAT(D4,D1) and D6 has DIRPCAT(D3,D1) +--R  (D,Integer,Integer) -> D1 from D +--R if D has RMATCAT(D3,D4,D1,D5,D6) and D5 has DIRPCAT(D4,D1) +--R and D6 has DIRPCAT(D3,D1) and D1 has RING +--R  (RewriteRule(D3,D4,D1),D1,PositiveInteger) -> D1 +--R from RewriteRule(D3,D4,D1) +--R if D3 has SETCAT and D4 has Join(Ring,PatternMatchable D3, +--R OrderedSet,ConvertibleTo Pattern D3) and D1 has Join( +--R FunctionSpace D4,PatternMatchable D3,ConvertibleTo Pattern +--R D3) +--R  (Ruleset(D3,D4,D1),D1,PositiveInteger) -> D1 from Ruleset(D3,D4 +--R ,D1) +--R if D3 has SETCAT and D4 has Join(Ring,PatternMatchable D3, +--R OrderedSet,ConvertibleTo Pattern D3) and D1 has Join( +--R FunctionSpace D4,PatternMatchable D3,ConvertibleTo Pattern +--R D3) +--R  (D,List Integer) -> D from D +--R if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has +--R SETCAT +--R  (D,Integer) -> D from D +--R if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has +--R SETCAT +--R  (D,D) -> D from D if D has SRAGG +--R  (Symbol,List OutputForm) -> Symbol from Symbol +--R  (Fraction D,D1) -> D1 from D +--R if D has UPOLYC D1 and D1 has RING and D1 has FIELD +--R  (Fraction D,Fraction D) -> Fraction D from D +--R if D has UPOLYC D2 and D2 has RING and D2 has INTDOM +--R  (D,D2) -> D1 from D +--R if D has UPSCAT(D1,D2) and D2 has OAMON and D1 has RING +--R  (D,last) -> D1 from D if D has URAGG D1 and D1 has TYPE +--R  (D,rest) -> D from D if D has URAGG D2 and D2 has TYPE +--R  (D,first) -> D1 from D if D has URAGG D1 and D1 has TYPE +--R +--RThere are 4 unexposed functions called elt : +--R  (EuclideanModularRing(D2,D1,D3,D4,D5,D6),D1) -> D1 +--R from EuclideanModularRing(D2,D1,D3,D4,D5,D6) +--R if D2 has COMRING and D1 has UPOLYC D2 and D3 has ABELMON +--R and D4: ((D1,D3) -> D1) and D5: ((D3,D3) -> Union(D3, +--R "failed")) and D6: ((D1,D1,D3) -> Union(D1,"failed")) +--R  (OutputForm,List OutputForm) -> OutputForm from OutputForm +--R  (BasicOperator,List Pattern D3) -> Pattern D3 from Pattern D3 +--R if D3 has SETCAT +--R  Reference D1 -> D1 from Reference D1 if D1 has TYPE +--R +--RExamples of elt from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--Relt(arr,1,1,6) +--Relt(arr,1,10,6) +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--Relt(arr,1,1) +--R +--R +--RExamples of elt from BinaryRecursiveAggregate +--R +--R +--RExamples of elt from CartesianTensor +--R +--Rv:=[2,3] +--Rtv:CartesianTensor(1,2,Integer):=v +--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] +--Rtn:CartesianTensor(1,2,Integer):=[tm,tm] +--Rtp:CartesianTensor(1,2,Integer):=[tn,tn] +--Rtq:CartesianTensor(1,2,Integer):=[tp,tp] +--Relt(tq,[2,2,2,2,2]) +--R +--Rv:=[2,3] +--Rtv:CartesianTensor(1,2,Integer):=v +--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] +--Rtn:CartesianTensor(1,2,Integer):=[tm,tm] +--Rtp:CartesianTensor(1,2,Integer):=[tn,tn] +--Relt(tp,2,2,2,2) +--Rtp[2,2,2,2] +--R +--Rv:=[2,3] +--Rtv:CartesianTensor(1,2,Integer):=v +--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] +--Rtn:CartesianTensor(1,2,Integer):=[tm,tm] +--Relt(tn,2,2,2) +--Rtn[2,2,2] +--R +--Rv:=[2,3] +--Rtv:CartesianTensor(1,2,Integer):=v +--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] +--Relt(tm,2,2) +--Rtm[2,2] +--R +--Rv:=[2,3] +--Rtv:CartesianTensor(1,2,Integer):=v +--Relt(tv,2) +--Rtv +--R +--Rtv:CartesianTensor(1,2,Integer):=8 +--Relt(tv) +--Rtv[] +--R +--R +--RExamples of elt from Database +--R +--R +--RExamples of elt from DataList +--R +--R +--RExamples of elt from Eltable +--R +--R +--RExamples of elt from EltableAggregate +--R +--R +--RExamples of elt from EuclideanModularRing +--R +--R +--RExamples of elt from ExpressionSpace +--R +--R +--RExamples of elt from FunctionFieldCategory +--R +--R +--RExamples of elt from FramedNonAssociativeAlgebra +--R +--R +--RExamples of elt from IndexCard +--R +--R +--RExamples of elt from Library +--R +--R +--RExamples of elt from LinearAggregate +--R +--R +--RExamples of elt from ThreeDimensionalMatrix +--R +--R +--RExamples of elt from MatrixCategory +--R +--R +--RExamples of elt from OutputForm +--R +--R +--RExamples of elt from Pattern +--R +--R +--RExamples of elt from PermutationCategory +--R +--R +--RExamples of elt from PermutationGroup +--R +--R +--RExamples of elt from QuadraticForm +--R +--R +--RExamples of elt from RecursiveAggregate +--R +--R +--RExamples of elt from Reference +--R +--R +--RExamples of elt from RectangularMatrixCategory +--R +--R +--RExamples of elt from RewriteRule +--R +--R +--RExamples of elt from Ruleset +--R +--R +--RExamples of elt from SExpressionCategory +--R +--R +--RExamples of elt from StringAggregate +--R +--R +--RExamples of elt from Symbol +--R +--R +--RExamples of elt from UnivariatePolynomialCategory +--R +--R +--RExamples of elt from UnivariatePowerSeriesCategory +--R +--R +--RExamples of elt from UnaryRecursiveAggregate +--R +--E 123 + +--S 125 of 127 +--R)d op minColIndex +--R +--R +--RThere are 2 exposed functions called minColIndex : +--R  D -> Integer from D +--R if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG +--R D2 and D4 has FLAGG D2 +--R  D -> Integer from D +--R if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has +--R DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4) +--R +--RExamples of minColIndex from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--RminColIndex(arr) +--R +--R +--RExamples of minColIndex from RectangularMatrixCategory +--R +--E 125 + +--S 126 of 127 +--R)d op numberOfFactors +--R +--R +--RThere is one exposed function called numberOfFactors : +--R  Factored D2 -> NonNegativeInteger from Factored D2 if D2 has +--R INTDOM +--R +--RThere is one unexposed function called numberOfFactors : +--R  List Record(factor: D3,degree: Integer) -> NonNegativeInteger +--R from GaloisGroupFactorizer D3 if D3 has UPOLYC INT +--R +--RExamples of numberOfFactors from Factored +--R +--Ra:=factor 9720000 +--RnumberOfFactors a +--R +--R +--RExamples of numberOfFactors from GaloisGroupFactorizer +--R +--E 126 + +--S 127 of 127 +--R)d op cyclicCopy +--R +--R +--RThere is one exposed function called cyclicCopy : +--R  Tree D1 -> Tree D1 from Tree D1 if D1 has SETCAT +--R +--RExamples of cyclicCopy from Tree +--R +--Rt1:=tree [1,2,3,4] +--RcyclicCopy t1 +--R +--E 127 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/frame.input.pamphlet b/src/input/frame.input.pamphlet new file mode 100644 index 0000000..75ce1a2 --- /dev/null +++ b/src/input/frame.input.pamphlet @@ -0,0 +1,212 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input frame.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1991.
+@
+<<*>>=
+)spool frame.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 24
+)frame new testframe
+--R
+--E 1
+
+--S 2 of 24
+)frame names
+--R
+--R   The names of the existing frames are:
+--R            testframe
+--R            initial
+--R      The current frame is the first one listed.
+--E 2
+
+--S 3 of 24
+)frame next
+--R
+--E 3
+
+--S 4 of 24
+)frame names
+--R
+--R   The names of the existing frames are:
+--R            initial
+--R            testframe
+--R      The current frame is the first one listed.
+--E 4
+
+--S 5 of 24
+)frame next
+--R
+--E 5
+
+--S 6 of 24
+)frame names
+--R
+--R   The names of the existing frames are:
+--R            testframe
+--R            initial
+--R      The current frame is the first one listed.
+--E 6
+
+--S 7 of 24
+)frame next
+--R
+--E 7
+
+--S 8 of 24
+)frame drop
+--R
+--E 8
+
+--S 9 of 24
+)frame names
+--R
+--R   The names of the existing frames are:
+--R            testframe
+--R      The current frame is the first one listed.
+--E 9
+
+--S 10 of 24
+)frame new testframe2
+--R
+--E 10
+
+--S 11 of 24
+a:=1
+--R
+--R
+--R   (1)  1
+--R                                                        Type:
PositiveInteger
+--E 11
+
+--S 12 of 24
+)frame names
+--R
+--R   The names of the existing frames are:
+--R            testframe2
+--R            testframe
+--R      The current frame is the first one listed.
+--E 12
+
+--S 13 of 24
+)frame next
+--R
+--E 13
+
+--S 14 of 24
+a
+--R
+--R
+--R   (1)  a
+--R                                                             Type: Variable
a
+--E 14
+
+--S 15 of 24
+)frame import testframe2 a
+--R
+--R   Import from frame testframe2 is complete. Please issue )display all
+--R      if you wish to see the contents of the current frame.
+--E 15
+
+--S 16 of 24
+)display all
+--R
+--RProperties of % :
+--R   Value (has type Variable a):  a
+--RProperties of %e :
+--R   This is a system-defined macro.
+--R   macro %e () == exp(1)
+--RProperties of %i :
+--R   This is a system-defined macro.
+--R   macro %i () == complex(0,1)
+--RProperties of %infinity :
+--R   This is a system-defined macro.
+--R   macro %infinity () == infinity()
+--RProperties of %minusInfinity :
+--R   This is a system-defined macro.
+--R   macro %minusInfinity () == minusInfinity()
+--RProperties of %pi :
+--R   This is a system-defined macro.
+--R   macro %pi () == pi()
+--RProperties of %plusInfinity :
+--R   This is a system-defined macro.
+--R   macro %plusInfinity () == plusInfinity()
+--RProperties of SF :
+--R   This is a system-defined macro.
+--R   macro SF () == DoubleFloat()
+--RProperties of a :
+--R   Value (has type PositiveInteger):  1
+--E 16
+
+--S 17 of 24
+a
+--R
+--R
+--R   (2)  1
+--R                                                        Type:
PositiveInteger
+--E 17
+
+--S 18 of 24
+)set message prompt frame
+--R
+--E 18
+
+--S 19 of 24
+)frame next
+--R
+--E 19
+
+--S 20 of 24
+)frame next
+--R
+--E 20
+
+--S 21 of 24
+)frame next
+--R
+--E 21
+
+--S 22 of 24
+)frame names
+--R
+--R   The names of the existing frames are:
+--R            testframe2
+--R            testframe
+--R      The current frame is the first one listed.
+--E 22
+
+--S 23 of 24
+)frame drop testframe2
+--R
+--E 23
+
+--S 24 of 24
+)frame names
+--R
+--R   The names of the existing frames are:
+--R            testframe
+--R      The current frame is the first one listed.
+--E 24
+
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/interp/i-map.boot.pamphlet b/src/interp/i-map.boot.pamphlet
index cdfbef4..97c825b 100644
--- a/src/interp/i-map.boot.pamphlet
+++ b/src/interp/i-map.boot.pamphlet
@@ -62,7 +62,7 @@ SETANDFILEQ($specialMapNameSuffix, NIL) makeInternalMapName(userName,numArgs,numMms,extraPart) == name := CONCAT('"*",STRINGIMAGE numArgs,'";", object2String userName,'";",STRINGIMAGE numMms,'";", - object2String frameName first$interpreterFrameRing )
+      object2String FRAMENAME first $interpreterFrameRing ) if extraPart then name := CONCAT(name,'";",extraPart) if$specialMapNameSuffix then
name := CONCAT(name,'";",\$specialMapNameSuffix)



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