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[Axiom-developer] 20090220.01.tpd.patch (regression test )d op, )frame )
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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 :
[1] (BinaryTree D1,D1,BinaryTree D1) -> BinaryTree D1 from
BinaryTree D1
if D1 has SETCAT
[2] 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[1]'..y[n]' defined in terms of x,y[1]..y[n],
++ together with a starting value for x and y[1]..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 \
${DOC}/free.input.dvi \
diff --git a/src/input/dop.input.pamphlet b/src/input/dop.input.pamphlet
new file mode 100644
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input dop.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1991.
+@
+<<*>>=
+)spool dop.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 127
+)d op binaryTree
+--R
+--R
+--RThere are 2 exposed functions called binaryTree :
+--R [1] (BinaryTree D1,D1,BinaryTree D1) -> BinaryTree D1 from
+--R BinaryTree D1
+--R if D1 has SETCAT
+--R [2] D1 -> BinaryTree D1 from BinaryTree D1 if D1 has SETCAT
+--R
+--RExamples of binaryTree from BinaryTree
+--R
+--Rt1:=binaryTree([1,2,3])
+--Rt2:=binaryTree([4,5,6])
+--RbinaryTree(t1,[7,8,9],t2)
+--R
+--Rt1:=binaryTree([1,2,3])
+--R
+--E 1
+
+--S 2 of 127
+)d op rationalPoint?
+--R
+--R
+--RThere is one exposed function called rationalPoint? :
+--R [1] (D2,D2) -> Boolean from D
+--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC
+--R D2 and D4 has UPOLYC FRAC D3
+--R
+--RThere is one unexposed function called rationalPoint? :
+--R [1] (D2,D2) -> Boolean from FunctionFieldCategory&(D3,D2,D4,D5)
+--R if D2 has UFD and D4 has UPOLYC D2 and D5 has UPOLYC FRAC
+--R D4 and D3 has FFCAT(D2,D4,D5)
+--R
+--RExamples of rationalPoint? from FunctionFieldCategory&
+--R
+--RP0 := UnivariatePolynomial(x, Integer)
+--RP1 := UnivariatePolynomial(y, Fraction P0)
+--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
+--RrationalPoint?(0,0)$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 [1] (D,Integer) -> D1 from D
+--R if D has FAMONC(D1,D3) and D3 has CABMON and D1 has SETCAT
+--R
+--R [2] (Factored D1,Integer) -> D1 from Factored D1 if D1 has INTDOM
+--R
+--R
+--RThere are 4 unexposed functions called nthFactor :
+--R [1] (FreeGroup D1,Integer) -> D1 from FreeGroup D1 if D1 has SETCAT
+--R
+--R [2] (FreeMonoid D1,Integer) -> D1 from FreeMonoid D1 if D1 has
+--R SETCAT
+--R [3] (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 [4] (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 [1] (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 [2] (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 [1] 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 [1] 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 [1] (NonNegativeInteger,D2) -> OneDimensionalArray D2
+--R from OneDimensionalArray D2 if D2 has TYPE
+--R [2] 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 [1] 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 [1] 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 [1] (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 [1] -> 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 [1] (PendantTree D1,PendantTree D1) -> PendantTree D1 from
+--R PendantTree D1
+--R if D1 has SETCAT
+--R [2] 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 [1] (D1,D) -> D from D if D has BGAGG D1 and D1 has TYPE
+--R [2] (D1,BinarySearchTree D1) -> BinarySearchTree D1
+--R from BinarySearchTree D1 if D1 has ORDSET
+--R [3] (D1,BinaryTournament D1) -> BinaryTournament D1
+--R from BinaryTournament D1 if D1 has ORDSET
+--R [4] (D,D,Integer) -> D from D if D has ELAGG D2 and D2 has TYPE
+--R [5] (D1,D,Integer) -> D from D if D has ELAGG D1 and D1 has TYPE
+--R [6] 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 [7] (D1,D,NonNegativeInteger) -> D from D
+--R if D has MDAGG D1 and D1 has SETCAT
+--R [8] 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 [1] (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 [1] -> 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 [1] -> 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 [1] 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 [1] 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 [1] (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 [1] ((DoubleFloat -> DoubleFloat),Segment Float,List DrawOption) ->
+--R TwoDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [2] ((DoubleFloat -> DoubleFloat),Segment Float) ->
+--R TwoDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [3] (ParametricPlaneCurve (DoubleFloat -> DoubleFloat),Segment Float
+--R ,List DrawOption) -> TwoDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [4] (ParametricPlaneCurve (DoubleFloat -> DoubleFloat),Segment Float
+--R ) -> TwoDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [5] (ParametricSpaceCurve (DoubleFloat -> DoubleFloat),Segment Float
+--R ,List DrawOption) -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [6] (ParametricSpaceCurve (DoubleFloat -> DoubleFloat),Segment Float
+--R ) -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [7] ((DoubleFloat -> Point DoubleFloat),Segment Float,List
+--R DrawOption) -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [8] ((DoubleFloat -> Point DoubleFloat),Segment Float) ->
+--R ThreeDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [9] (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment Float,
+--R Segment Float,List DrawOption) -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [10] (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment Float,
+--R Segment Float) -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [11] (((DoubleFloat,DoubleFloat) -> Point DoubleFloat),Segment Float
+--R ,Segment Float,List DrawOption) -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [12] (((DoubleFloat,DoubleFloat) -> Point DoubleFloat),Segment Float
+--R ,Segment Float) -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [13] (ParametricSurface ((DoubleFloat,DoubleFloat) -> DoubleFloat),
+--R Segment Float,Segment Float,List DrawOption) ->
+--R ThreeDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [14] (ParametricSurface ((DoubleFloat,DoubleFloat) -> DoubleFloat),
+--R Segment Float,Segment Float) -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctionsForCompiledFunctions
+--R [15] (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 [16] (D2,SegmentBinding Float,List DrawOption) ->
+--R TwoDimensionalViewport
+--R from TopLevelDrawFunctions D2
+--R if D2 has Join(ConvertibleTo InputForm,SetCategory)
+--R [17] (D2,SegmentBinding Float) -> TwoDimensionalViewport
+--R from TopLevelDrawFunctions D2
+--R if D2 has Join(ConvertibleTo InputForm,SetCategory)
+--R [18] (ParametricPlaneCurve D5,SegmentBinding Float,List DrawOption)
+--R -> TwoDimensionalViewport
+--R from TopLevelDrawFunctions D5
+--R if D5 has Join(ConvertibleTo InputForm,SetCategory)
+--R [19] (ParametricPlaneCurve D4,SegmentBinding Float) ->
+--R TwoDimensionalViewport
+--R from TopLevelDrawFunctions D4
+--R if D4 has Join(ConvertibleTo InputForm,SetCategory)
+--R [20] (ParametricSpaceCurve D5,SegmentBinding Float,List DrawOption)
+--R -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctions D5
+--R if D5 has Join(ConvertibleTo InputForm,SetCategory)
+--R [21] (ParametricSpaceCurve D4,SegmentBinding Float) ->
+--R ThreeDimensionalViewport
+--R from TopLevelDrawFunctions D4
+--R if D4 has Join(ConvertibleTo InputForm,SetCategory)
+--R [22] (D2,SegmentBinding Float,SegmentBinding Float,List DrawOption)
+--R -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctions D2
+--R if D2 has Join(ConvertibleTo InputForm,SetCategory)
+--R [23] (D2,SegmentBinding Float,SegmentBinding Float) ->
+--R ThreeDimensionalViewport
+--R from TopLevelDrawFunctions D2
+--R if D2 has Join(ConvertibleTo InputForm,SetCategory)
+--R [24] (ParametricSurface D5,SegmentBinding Float,SegmentBinding Float
+--R ,List DrawOption) -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctions D5
+--R if D5 has Join(ConvertibleTo InputForm,SetCategory)
+--R [25] (ParametricSurface D4,SegmentBinding Float,SegmentBinding Float
+--R ) -> ThreeDimensionalViewport
+--R from TopLevelDrawFunctions D4
+--R if D4 has Join(ConvertibleTo InputForm,SetCategory)
+--R [26] (List DoubleFloat,List DoubleFloat) -> TwoDimensionalViewport
+--R from TopLevelDrawFunctionsForPoints
+--R [27] (List DoubleFloat,List DoubleFloat,List DrawOption) ->
+--R TwoDimensionalViewport
+--R from TopLevelDrawFunctionsForPoints
+--R [28] List Point DoubleFloat -> TwoDimensionalViewport
+--R from TopLevelDrawFunctionsForPoints
+--R [29] (List Point DoubleFloat,List DrawOption) ->
+--R TwoDimensionalViewport
+--R from TopLevelDrawFunctionsForPoints
+--R [30] (List DoubleFloat,List DoubleFloat,List DoubleFloat) ->
+--R ThreeDimensionalViewport
+--R from TopLevelDrawFunctionsForPoints
+--R [31] (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 [1] 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 [1] (D1,List D1) -> List D1 from List D1 if D1 has TYPE
+--R [2] (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 [1] ((D2 -> D2),D) -> D from D
+--R if D has AMR(D2,D3) and D2 has RING and D3 has OAMON
+--R [2] (((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 [3] (((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 [4] ((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 [5] ((D4 -> D5),OneDimensionalArray D4) -> OneDimensionalArray D5
+--R from OneDimensionalArrayFunctions2(D4,D5)
+--R if D4 has TYPE and D5 has TYPE
+--R [6] ((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 [7] ((D4 -> D5),Complex D4) -> Complex D5 from ComplexFunctions2(D4,
+--R D5)
+--R if D4 has COMRING and D5 has COMRING
+--R [8] ((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 [9] ((D4 -> D5),Equation D4) -> Equation D5 from EquationFunctions2(
+--R D4,D5)
+--R if D4 has TYPE and D5 has TYPE
+--R [10] ((D2 -> D2),Equation D2) -> Equation D2 from Equation D2 if D2
+--R has TYPE
+--R [11] ((D4 -> D1),Kernel D4) -> D1 from ExpressionSpaceFunctions2(D4,
+--R D1)
+--R if D4 has ES and D1 has ES
+--R [12] ((D -> D),Kernel D) -> D from D if D has ES
+--R [13] ((D4 -> D5),Matrix D4) -> Matrix D5
+--R from ExpertSystemToolsPackage2(D4,D5)
+--R if D4 has RING and D5 has RING
+--R [14] ((D4 -> D5),Expression D4) -> Expression D5
+--R from ExpressionFunctions2(D4,D5)
+--R if D4 has ORDSET and D5 has ORDSET
+--R [15] ((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 [16] ((D2 -> D2),D) -> D from D if D has FEVALAB D2 and D2 has
+--R SETCAT
+--R [17] ((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 [18] ((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 [19] ((D2 -> D2),D) -> D from D
+--R if D has FMCAT(D2,D3) and D2 has RING and D3 has SETCAT
+--R [20] ((D4 -> D5),Factored D4) -> Factored D5 from FactoredFunctions2
+--R (D4,D5)
+--R if D4 has INTDOM and D5 has INTDOM
+--R [21] ((D4 -> D5),Fraction D4) -> Fraction D5 from FractionFunctions2
+--R (D4,D5)
+--R if D4 has INTDOM and D5 has INTDOM
+--R [22] ((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 [23] ((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 [24] ((D2 -> D2),Factored D2) -> Factored D2 from Factored D2
+--R if D2 has INTDOM
+--R [25] ((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 [26] ((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 [27] ((D2 -> D2),D) -> D from D if D has HOAGG D2 and D2 has TYPE
+--R
+--R [28] ((D2 -> D2),D) -> D from D
+--R if D has IDPC(D2,D3) and D2 has SETCAT and D3 has ORDSET
+--R
+--R [29] ((D4 -> D5),IntegrationResult D4) -> IntegrationResult D5
+--R from IntegrationResultFunctions2(D4,D5)
+--R if D4 has FIELD and D5 has FIELD
+--R [30] ((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 [31] ((D4 -> D1),Union(D4,"failed")) -> Union(D1,"failed")
+--R from IntegrationResultFunctions2(D4,D1)
+--R if D4 has FIELD and D1 has FIELD
+--R [32] ((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 [33] ((D4 -> D5),InfiniteTuple D4) -> InfiniteTuple D5
+--R from InfiniteTupleFunctions2(D4,D5)
+--R if D4 has TYPE and D5 has TYPE
+--R [34] (((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 [35] (((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 [36] (((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 [37] ((D2 -> D2),InfiniteTuple D2) -> InfiniteTuple D2 from
+--R InfiniteTuple D2
+--R if D2 has TYPE
+--R [38] ((D4 -> D5),List D4) -> List D5 from ListFunctions2(D4,D5)
+--R if D4 has TYPE and D5 has TYPE
+--R [39] (((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 [40] (((D2,D2) -> D2),D,D) -> D from D if D has LNAGG D2 and D2 has
+--R TYPE
+--R [41] ((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 [42] ((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 [43] ((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 [44] ((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 [45] ((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 [46] ((D4 -> D5),OnePointCompletion D4) -> OnePointCompletion D5
+--R from OnePointCompletionFunctions2(D4,D5)
+--R if D4 has SETCAT and D5 has SETCAT
+--R [47] ((D4 -> D5),OnePointCompletion D4,OnePointCompletion D5) ->
+--R OnePointCompletion D5
+--R from OnePointCompletionFunctions2(D4,D5)
+--R if D4 has SETCAT and D5 has SETCAT
+--R [48] ((D4 -> D5),OrderedCompletion D4) -> OrderedCompletion D5
+--R from OrderedCompletionFunctions2(D4,D5)
+--R if D4 has SETCAT and D5 has SETCAT
+--R [49] ((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 [50] ((D4 -> D5),ParametricPlaneCurve D4) -> ParametricPlaneCurve D5
+--R from ParametricPlaneCurveFunctions2(D4,D5)
+--R if D4 has TYPE and D5 has TYPE
+--R [51] ((D4 -> D5),ParametricSpaceCurve D4) -> ParametricSpaceCurve D5
+--R from ParametricSpaceCurveFunctions2(D4,D5)
+--R if D4 has TYPE and D5 has TYPE
+--R [52] ((D4 -> D5),ParametricSurface D4) -> ParametricSurface D5
+--R from ParametricSurfaceFunctions2(D4,D5)
+--R if D4 has TYPE and D5 has TYPE
+--R [53] ((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 [54] ((D4 -> D5),Pattern D4) -> Pattern D5 from PatternFunctions2(D4
+--R ,D5)
+--R if D4 has SETCAT and D5 has SETCAT
+--R [55] ((D4 -> D5),Polynomial D4) -> Polynomial D5
+--R from PolynomialFunctions2(D4,D5)
+--R if D4 has RING and D5 has RING
+--R [56] ((D4 -> D5),PrimitiveArray D4) -> PrimitiveArray D5
+--R from PrimitiveArrayFunctions2(D4,D5)
+--R if D4 has TYPE and D5 has TYPE
+--R [57] ((D4 -> D5),Point D4) -> Point D5 from PointFunctions2(D4,D5)
+--R if D4 has RING and D5 has RING
+--R [58] ((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 [59] ((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 [60] (((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 [61] ((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 [62] ((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 [63] ((D4 -> D5),Segment D4) -> Segment D5 from SegmentFunctions2(D4
+--R ,D5)
+--R if D4 has TYPE and D5 has TYPE
+--R [64] ((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 [65] ((D4 -> D5),SegmentBinding D4) -> SegmentBinding D5
+--R from SegmentBindingFunctions2(D4,D5)
+--R if D4 has TYPE and D5 has TYPE
+--R [66] ((D3 -> D3),D) -> D1 from D
+--R if D has SEGXCAT(D3,D1) and D3 has ORDRING and D1 has STAGG
+--R D3
+--R [67] ((D4 -> D5),Stream D4) -> Stream D5 from StreamFunctions2(D4,D5
+--R )
+--R if D4 has TYPE and D5 has TYPE
+--R [68] (((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 [69] ((D4 -> D5),SparseUnivariatePolynomial D4) ->
+--R SparseUnivariatePolynomial D5
+--R from SparseUnivariatePolynomialFunctions2(D4,D5)
+--R if D4 has RING and D5 has RING
+--R [70] (((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 [71] ((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 [72] ((D4 -> D5),UniversalSegment D4) -> UniversalSegment D5
+--R from UniversalSegmentFunctions2(D4,D5)
+--R if D4 has TYPE and D5 has TYPE
+--R [73] ((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 [74] ((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 [75] ((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 [76] ((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 [77] ((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 [78] ((D4 -> D5),Vector D4) -> Vector D5 from VectorFunctions2(D4,D5
+--R )
+--R if D4 has TYPE and D5 has TYPE
+--R [79] ((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 [80] ((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 [1] ((D2 -> D2),AntiSymm(D2,D3)) -> AntiSymm(D2,D3) from AntiSymm(D2
+--R ,D3)
+--R if D2 has RING and D3: LIST SYMBOL
+--R [2] ((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 [3] ((D5 -> D1),String,Kernel D5) -> D1
+--R from ExpressionSpaceFunctions1(D5,D1)
+--R if D5 has ES and D1 has TYPE
+--R [4] ((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 [5] ((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 [6] ((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 [7] ((D2 -> D2),MonoidRing(D2,D3)) -> MonoidRing(D2,D3)
+--R from MonoidRing(D2,D3) if D2 has RING and D3 has MONOID
+--R [8] ((D4 -> D5),NewSparseUnivariatePolynomial D4) ->
+--R NewSparseUnivariatePolynomial D5
+--R from NewSparseUnivariatePolynomialFunctions2(D4,D5)
+--R if D4 has RING and D5 has RING
+--R [9] ((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 [10] ((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 [11] ((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 [1] ContinuedFraction D1 -> ContinuedFraction D1 from
+--R ContinuedFraction D1
+--R if D1 has EUCDOM
+--R [2] Integer -> SymmetricPolynomial Fraction Integer from
+--R CycleIndicators
+--R [3] D -> D from D if D has LZSTAGG D1 and D1 has TYPE
+--R [4] D -> D from D if D has PADICCT D1
+--R [5] 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 [1] (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 [1] 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 [2] 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 [1] -> 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 [1] 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 [1] D -> Boolean from D if D has RCAGG D2 and D2 has TYPE
+--R [2] 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 [1] (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 [1] -> Character from Character
+--R
+--RThere is one unexposed function called quote :
+--R [1] 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 [1] (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 [1] -> 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 [1] -> 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 [1] (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 [2] 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 [3] 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 [4] 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 [1] 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 [1] (Stream D2,Integer,Stream D2) -> Stream D2 from Stream D2 if D2
+--R has TYPE
+--R [2] (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 [1] (CardinalNumber,CardinalNumber) -> CardinalNumber from
+--R CardinalNumber
+--R [2] (DoubleFloat,DoubleFloat) -> DoubleFloat from DoubleFloat
+--R [3] (D,Integer) -> D from D if D has DIVRING
+--R [4] (D,D) -> D from D if D has ELEMFUN
+--R [5] (Float,Float) -> Float from Float
+--R [6] (D,NonNegativeInteger) -> D from D
+--R if D has FS D2 and D2 has ORDSET and D2 has SGROUP
+--R [7] (D,Integer) -> D from D if D has GROUP
+--R [8] (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 [9] ((D3 -> D3),NonNegativeInteger) -> (D3 -> D3) from
+--R MappingPackage1 D3
+--R if D3 has SETCAT
+--R [10] (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 [11] (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 [12] (ModuleOperator(D2,D3),Integer) -> ModuleOperator(D2,D3)
+--R from ModuleOperator(D2,D3)
+--R if D2 has RING and D3 has LMODULE D2
+--R [13] (BasicOperator,Integer) -> ModuleOperator(D3,D4)
+--R from ModuleOperator(D3,D4)
+--R if D3 has RING and D4 has LMODULE D3
+--R [14] (D,PositiveInteger) -> D from D if D has MONAD
+--R [15] (D,NonNegativeInteger) -> D from D if D has MONADWU
+--R [16] (D,NonNegativeInteger) -> D from D if D has MONOID
+--R [17] (D,Fraction Integer) -> D from D if D has RADCAT
+--R [18] (D,PositiveInteger) -> D from D if D has SGROUP
+--R [19] (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 [20] (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 [1] (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 [2] (D1,D1) -> D1 from CombinatorialFunction(D2,D1)
+--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS D2
+--R
+--R [3] (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 [4] (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 [5] (D1,Integer) -> FreeGroup D1 from FreeGroup D1 if D1 has SETCAT
+--R
+--R [6] (D1,NonNegativeInteger) -> FreeMonoid D1 from FreeMonoid D1
+--R if D1 has SETCAT
+--R [7] (Vector D3,Integer) -> Vector D3 from
+--R InnerNormalBasisFieldFunctions D3
+--R if D3 has FFIELDC
+--R [8] (InputForm,Integer) -> InputForm from InputForm
+--R [9] (InputForm,NonNegativeInteger) -> InputForm from InputForm
+--R [10] (Matrix D3,NonNegativeInteger) -> Matrix D3
+--R from StorageEfficientMatrixOperations D3 if D3 has RING
+--R [11] (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 [12] (D1,NonNegativeInteger) -> OrderedFreeMonoid D1
+--R from OrderedFreeMonoid D1 if D1 has ORDSET
+--R [13] (Operator D2,Integer) -> Operator D2 from Operator D2 if D2 has
+--R RING
+--R [14] (BasicOperator,Integer) -> Operator D3 from Operator D3 if D3
+--R has RING
+--R [15] (OutputForm,OutputForm) -> OutputForm from OutputForm
+--R [16] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
+--R SETCAT
+--R [17] (Pattern D2,NonNegativeInteger) -> Pattern D2 from Pattern D2
+--R if D2 has SETCAT
+--R [18] (Stream D2,Stream D2) -> Stream D2
+--R from StreamTranscendentalFunctionsNonCommutative D2
+--R if D2 has ALGEBRA FRAC INT
+--R [19] (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 [1] (D2,Symbol,Segment DoubleFloat) -> Plot from PlotFunctions1 D2
+--R if D2 has KONVERT INFORM
+--R [2] (D2,D2,Symbol,Segment DoubleFloat) -> Plot from PlotFunctions1
+--R D2
+--R if D2 has KONVERT INFORM
+--R [3] (Plot3D,Segment DoubleFloat) -> Plot3D from Plot3D
+--R [4] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(
+--R DoubleFloat -> DoubleFloat),(DoubleFloat ->
DoubleFloat),Segment
+--R DoubleFloat,Segment DoubleFloat,Segment DoubleFloat,Segment
+--R DoubleFloat) -> Plot3D
+--R from Plot3D
+--R [5] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(
+--R DoubleFloat -> DoubleFloat),(DoubleFloat ->
DoubleFloat),Segment
+--R DoubleFloat) -> Plot3D
+--R from Plot3D
+--R [6] (Plot,Segment DoubleFloat) -> Plot from Plot
+--R [7] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),
+--R Segment DoubleFloat,Segment DoubleFloat,Segment DoubleFloat) ->
+--R Plot
+--R from Plot
+--R [8] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),
+--R Segment DoubleFloat) -> Plot
+--R from Plot
+--R [9] (List (DoubleFloat -> DoubleFloat),Segment DoubleFloat,Segment
+--R DoubleFloat) -> Plot
+--R from Plot
+--R [10] (List (DoubleFloat -> DoubleFloat),Segment DoubleFloat) -> Plot
+--R from Plot
+--R [11] ((DoubleFloat -> DoubleFloat),Segment DoubleFloat,Segment
+--R DoubleFloat) -> Plot
+--R from Plot
+--R [12] ((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)$PLOT
+--R
+--E 36
+
+--S 37 of 127
+--R)d op factorList
+--R
+--R
+--RThere is one exposed function called factorList :
+--R [1] Factored D2 -> List Record(flg: Union("nil","sqfr","irred",
+--R "prime"),fctr: D2,xpnt: Integer)
+--R from Factored D2 if D2 has INTDOM
+--R
+--RThere is one unexposed function called factorList :
+--R [1] (D2,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger)
+--R -> List SparseUnivariatePolynomial D2
+--R from ChineseRemainderToolsForIntegralBases(D2,D4,D5)
+--R if D2 has FFIELDC and D4 has UPOLYC D2 and D5 has UPOLYC D4
+--R
+--R
+--RExamples of factorList from Factored
+--R
+--Rf:=nilFactor(x-y,3)
+--RfactorList f
+--R
+--R
+--RExamples of factorList from ChineseRemainderToolsForIntegralBases
+--R
+--E 37
+
+--S 38 of 127
+--R)d op physicalLength
+--R
+--R
+--RThere is one exposed function called physicalLength :
+--R [1] FlexibleArray D2 -> NonNegativeInteger from FlexibleArray D2
+--R if D2 has TYPE
+--R
+--RThere is one unexposed function called physicalLength :
+--R [1] IndexedFlexibleArray(D2,D3) -> NonNegativeInteger
+--R from IndexedFlexibleArray(D2,D3) if D2 has TYPE and D3: INT
+--R
+--R
+--RExamples of physicalLength from FlexibleArray
+--R
+--R
+--RExamples of physicalLength from IndexedFlexibleArray
+--R
+--RT1:=IndexedFlexibleArray(Integer,20)
+--Rt2:=flexibleArray([i for i in 1..10])$T1
+--RphysicalLength t2
+--R
+--E 38
+
+--S 39 of 127
+--R)d op absolutelyIrreducible?
+--R
+--R
+--RThere is one exposed function called absolutelyIrreducible? :
+--R [1] -> 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 [1] -> 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 [1] (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 [1] 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 [1] 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 [1] (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 [1] 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 [1] (FlexibleArray D2,Integer) -> FlexibleArray D2 from
+--R FlexibleArray D2
+--R if D2 has TYPE
+--R
+--RThere is one unexposed function called physicalLength! :
+--R [1] (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 [1] 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 [1] (ContinuedFraction D2,Integer) -> ContinuedFraction D2
+--R from ContinuedFraction D2 if D2 has EUCDOM
+--R [2] (D,Integer) -> D from D if D has LZSTAGG D2 and D2 has TYPE
+--R [3] (D,NonNegativeInteger) -> D from D
+--R if D has MTSCAT(D2,D3) and D2 has RING and D3 has ORDSET
+--R
+--R [4] (D,Integer) -> D from D if D has PADICCT D2
+--R [5] (D,List D2) -> D from D if D has PTCAT D2 and D2 has RING
+--R [6] (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 [7] (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 [8] (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 [9] (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 [10] (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 [11] (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 [1] D -> D from D if D has INS
+--R [2] D -> NonNegativeInteger from D if D has QUAGG D2 and D2 has TYPE
+--R
+--R [3] 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 [1] 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 [2] LyndonWord D2 -> PositiveInteger from LyndonWord D2 if D2 has
+--R ORDSET
+--R [3] Magma D2 -> PositiveInteger from Magma D2 if D2 has ORDSET
+--R [4] OrderedFreeMonoid D2 -> NonNegativeInteger from
+--R OrderedFreeMonoid D2
+--R if D2 has ORDSET
+--R [5] PoincareBirkhoffWittLyndonBasis D2 -> NonNegativeInteger
+--R from PoincareBirkhoffWittLyndonBasis D2 if D2 has ORDSET
+--R
+--R [6] 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 [1] -> List NonNegativeInteger from ViewDefaultsPackage
+--R [2] 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 [1] 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 [2] (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 [3] (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 [4] 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 [1] List Polynomial D2 -> List Polynomial D2 from FGLMIfCanPackage(
+--R D2,D3)
+--R if D2 has GCDDOM and D3: LIST SYMBOL
+--R [2] 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 [1] (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 [1] ((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 [2] ((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 [1] (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 [1] (((D5,D4) -> D4),OneDimensionalArray D5,D4) ->
+--R OneDimensionalArray D4
+--R from OneDimensionalArrayFunctions2(D5,D4)
+--R if D5 has TYPE and D4 has TYPE
+--R [2] (((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 [3] (((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 [4] (((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 [5] (((D5,D4) -> D4),List D5,D4) -> List D4 from ListFunctions2(D5,
+--R D4)
+--R if D5 has TYPE and D4 has TYPE
+--R [6] (((D5,D4) -> D4),PrimitiveArray D5,D4) -> PrimitiveArray D4
+--R from PrimitiveArrayFunctions2(D5,D4)
+--R if D5 has TYPE and D4 has TYPE
+--R [7] (D2,((D5,D2) -> D2),Stream D5) -> Stream D2
+--R from StreamFunctions2(D5,D2) if D5 has TYPE and D2 has TYPE
+--R
+--R [8] (((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 [1] 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 [1] (D,D) -> D from D if D has ABELSG
+--R [2] (Color,Color) -> Color from Color
+--R [3] (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 [4] (Equation D1,D1) -> Equation D1 from Equation D1
+--R if D1 has ABELSG and D1 has TYPE
+--R [5] (D1,Equation D1) -> Equation D1 from Equation D1
+--R if D1 has ABELSG and D1 has TYPE
+--R [6] (D1,D) -> D from D
+--R if D has FAMONC(D1,D2) and D1 has SETCAT and D2 has CABMON
+--R
+--R [7] (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 [8] (D,D) -> D from D
+--R if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
+--R
+--R [9] (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 [10] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,
+--R D3)
+--R if D2 has SETCAT and D3 has RING
+--R [11] (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 [12] (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 [1] (InputForm,InputForm) -> InputForm from InputForm
+--R [2] (OutputForm,OutputForm) -> OutputForm from OutputForm
+--R [3] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
+--R SETCAT
+--R [4] (Stream D2,Stream D2) -> Stream D2 from
+--R StreamTaylorSeriesOperations D2
+--R if D2 has RING
+--R [5] (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 [1] (D,D) -> D from D if D has ABELGRP
+--R [2] D -> D from D if D has ABELGRP
+--R [3] (CardinalNumber,CardinalNumber) -> Union(CardinalNumber,"failed"
+--R )
+--R from CardinalNumber
+--R [4] (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 [5] (Equation D1,D1) -> Equation D1 from Equation D1
+--R if D1 has ABELGRP and D1 has TYPE
+--R [6] (D1,Equation D1) -> Equation D1 from Equation D1
+--R if D1 has ABELGRP and D1 has TYPE
+--R [7] (D,D) -> D from D
+--R if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
+--R
+--R [8] D -> D from D
+--R if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
+--R
+--R [9] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,D3
+--R )
+--R if D2 has SETCAT and D3 has RING
+--R [10] 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 [11] (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 [12] (D,D) -> D from D
+--R if D has VECTCAT D1 and D1 has TYPE and D1 has ABELGRP
+--R [13] 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 [1] OutputForm -> OutputForm from OutputForm
+--R [2] (OutputForm,OutputForm) -> OutputForm from OutputForm
+--R [3] (Stream D2,Stream D2) -> Stream D2 from
+--R StreamTaylorSeriesOperations D2
+--R if D2 has RING
+--R [4] Stream D2 -> Stream D2 from StreamTaylorSeriesOperations D2
+--R if D2 has RING
+--R [5] (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 [1] (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 [2] (DoubleFloat,Integer) -> DoubleFloat from DoubleFloat
+--R [3] (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 [4] (D,D) -> D from D if D has FIELD
+--R [5] (Float,Integer) -> Float from Float
+--R [6] (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 [7] (D,D) -> D from D if D has GROUP
+--R [8] (D,D1) -> D from D
+--R if D has LIECAT D1 and D1 has COMRING and D1 has FIELD
+--R [9] ((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 [10] (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 [11] (D1,D1) -> D from D if D has QFCAT D1 and D1 has INTDOM
+--R [12] (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 [13] (D,D1) -> D from D if D has VSPACE D1 and D1 has FIELD
+--R
+--RThere are 13 unexposed functions called / :
+--R [1] (Vector D2,Vector D2) -> Vector D2
+--R from InnerNormalBasisFieldFunctions D2 if D2 has FFIELDC
+--R
+--R [2] (InputForm,InputForm) -> InputForm from InputForm
+--R [3] (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 [4] (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 [5] (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 [6] (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 [7] (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 [8] (OutputForm,OutputForm) -> OutputForm from OutputForm
+--R [9] (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 [10] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
+--R SETCAT
+--R [11] (Stream D2,Stream D2) -> Stream D2 from
+--R StreamTaylorSeriesOperations D2
+--R if D2 has RING
+--R [12] (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 [13] (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 [1] -> 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 [1] -> 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 [2] -> 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 [3] -> 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 [4] -> 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 [1] D2 -> Factored D2 from AlgFactor D2 if D2 has UPOLYC AN
+--R [2] (D2,BinarySearchTree D2) -> Record(less: BinarySearchTree D2,
+--R greater: BinarySearchTree D2)
+--R from BinarySearchTree D2 if D2 has ORDSET
+--R [3] 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 [4] 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 [5] (List Matrix D4,Vector D4) -> List List Matrix D4
+--R from RepresentationPackage2 D4 if D4 has FIELD and D4 has
+--R RING
+--R [6] (List Matrix D4,Vector Vector D4) -> List List Matrix D4
+--R from RepresentationPackage2 D4 if D4 has FIELD and D4 has
+--R RING
+--R [7] (D,CharacterClass) -> List D from D if D has SRAGG
+--R [8] (D,Character) -> List D from D if D has SRAGG
+--R
+--RThere is one unexposed function called split :
+--R [1] (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 [1] (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 [2] (D,D2) -> D1 from D
+--R if D has ELTAGG(D2,D1) and D2 has SETCAT and D1 has TYPE
+--R
+--R [3] (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 [1] (BalancedBinaryTree D2,BalancedBinaryTree D2,((D2,D2,D2,D2) ->
+--R D2)) -> BalancedBinaryTree D2
+--R from BalancedBinaryTree D2 if D2 has SETCAT
+--R [2] (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)$T1
+--Rsetleaves!(t2,[1,2,3,4]::List(Integer))
+--Radder(a:Integer,b:Integer):Integer == a+b
+--RmapUp!(t2,adder)
+--Rt2
+--R
+--E 62
+
+--S 63 of 127
+--R)d op reindex
+--R
+--R
+--RThere is one exposed function called reindex :
+--R [1] (CartesianTensor(D2,D3,D4),List Integer) -> CartesianTensor(D2,
+--R D3,D4)
+--R from CartesianTensor(D2,D3,D4)
+--R if D2: INT and D3: NNI and D4 has COMRING
+--R
+--RExamples of reindex from CartesianTensor
+--R
+--Rn:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]]
+--Rtn:CartesianTensor(1,2,Integer):=n
+--Rp:=product(tn,tn)
+--Rreindex(p,[4,3,2,1])
+--R
+--E 63
+
+--S 64 of 127
+--R)d op mapDown!
+--R
+--R
+--RThere are 2 exposed functions called mapDown! :
+--R [1] (BalancedBinaryTree D1,D1,((D1,D1,D1) -> List D1)) ->
+--R BalancedBinaryTree D1
+--R from BalancedBinaryTree D1 if D1 has SETCAT
+--R [2] (BalancedBinaryTree D1,D1,((D1,D1) -> D1)) -> BalancedBinaryTree
+--R D1
+--R from BalancedBinaryTree D1 if D1 has SETCAT
+--R
+--RExamples of mapDown! from BalancedBinaryTree
+--R
+--RT1:=BalancedBinaryTree Integer
+--Rt2:=balancedBinaryTree(4, 0)$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 [1] 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 [2] 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 [1] (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 [2] (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 [1] 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 [1] -> 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 [1] D1 -> D from D if D has ALGEBRA D1 and D1 has COMRING
+--R [2] 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 [3] SparseMultivariatePolynomial(Integer,Kernel AlgebraicNumber) ->
+--R AlgebraicNumber
+--R from AlgebraicNumber
+--R [4] D2 -> Any from AnyFunctions1 D2 if D2 has TYPE
+--R [5] Vector FortranExpression([construct,QUOTEJINT,QUOTEX,QUOTEELAM],
+--R [construct],MachineFloat) -> Asp10 D2
+--R from Asp10 D2 if D2: SYMBOL
+--R [6] Vector FortranExpression([construct],[construct,QUOTEXC],
+--R MachineFloat) -> Asp19 D2
+--R from Asp19 D2 if D2: SYMBOL
+--R [7] FortranExpression([construct,QUOTEX],[construct],MachineFloat)
+--R -> Asp1 D2
+--R from Asp1 D2 if D2: SYMBOL
+--R [8] Matrix FortranExpression([construct],[construct,QUOTEX,QUOTEHESS
+--R ],MachineFloat) -> Asp20 D2
+--R from Asp20 D2 if D2: SYMBOL
+--R [9] FortranExpression([construct],[construct,QUOTEXC],MachineFloat)
+--R -> Asp24 D2
+--R from Asp24 D2 if D2: SYMBOL
+--R [10] Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],
+--R MachineFloat) -> Asp31 D2
+--R from Asp31 D2 if D2: SYMBOL
+--R [11] Vector FortranExpression([construct],[construct,QUOTEX],
+--R MachineFloat) -> Asp35 D2
+--R from Asp35 D2 if D2: SYMBOL
+--R [12] 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 [13] 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 [14] FortranExpression([construct],[construct,QUOTEX],MachineFloat)
+--R -> Asp49 D2
+--R from Asp49 D2 if D2: SYMBOL
+--R [15] FortranExpression([construct],[construct,QUOTEX],MachineFloat)
+--R -> Asp4 D2
+--R from Asp4 D2 if D2: SYMBOL
+--R [16] Vector FortranExpression([construct],[construct,QUOTEXC],
+--R MachineFloat) -> Asp50 D2
+--R from Asp50 D2 if D2: SYMBOL
+--R [17] Vector FortranExpression([construct],[construct,QUOTEX],
+--R MachineFloat) -> Asp55 D2
+--R from Asp55 D2 if D2: SYMBOL
+--R [18] Vector FortranExpression([construct],[construct,QUOTEX],
+--R MachineFloat) -> Asp6 D2
+--R from Asp6 D2 if D2: SYMBOL
+--R [19] Vector FortranExpression([construct,QUOTEX,QUOTEY],[construct],
+--R MachineFloat) -> Asp73 D2
+--R from Asp73 D2 if D2: SYMBOL
+--R [20] Matrix FortranExpression([construct,QUOTEX,QUOTEY],[construct],
+--R MachineFloat) -> Asp74 D2
+--R from Asp74 D2 if D2: SYMBOL
+--R [21] Matrix FortranExpression([construct,QUOTEX],[construct],
+--R MachineFloat) -> Asp77 D2
+--R from Asp77 D2 if D2: SYMBOL
+--R [22] Vector FortranExpression([construct,QUOTEX],[construct],
+--R MachineFloat) -> Asp78 D2
+--R from Asp78 D2 if D2: SYMBOL
+--R [23] Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],
+--R MachineFloat) -> Asp7 D2
+--R from Asp7 D2 if D2: SYMBOL
+--R [24] Matrix FortranExpression([construct,QUOTEXL,QUOTEXR,QUOTEELAM],
+--R [construct],MachineFloat) -> Asp80 D2
+--R from Asp80 D2 if D2: SYMBOL
+--R [25] FortranExpression([construct,QUOTEX],[construct,QUOTEY],
+--R MachineFloat) -> Asp9 D2
+--R from Asp9 D2 if D2: SYMBOL
+--R [26] BinaryExpansion -> RadixExpansion 2 from BinaryExpansion
+--R [27] BinaryExpansion -> Fraction Integer from BinaryExpansion
+--R [28] 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 [29] List D4 -> CartesianTensor(D2,D3,D4) from CartesianTensor(D2,D3
+--R ,D4)
+--R if D4 has COMRING and D2: INT and D3: NNI
+--R [30] 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 [31] 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 [32] List D2 -> Database D2 from Database D2
+--R if D2 has OrderedSet with
+--R ?.? : (%,Symbol) -> String
+--R display : % -> Void
+--R fullDisplay : % -> Void
+--R [33] DecimalExpansion -> RadixExpansion 10 from DecimalExpansion
+--R [34] DecimalExpansion -> Fraction Integer from DecimalExpansion
+--R [35] DataList D2 -> List D2 from DataList D2 if D2 has ORDSET
+--R [36] List D2 -> DataList D2 from DataList D2 if D2 has ORDSET
+--R [37] SegmentBinding Expression D3 -> SegmentBinding Float
+--R from DrawNumericHack D3
+--R if D3 has Join(OrderedSet,IntegralDomain,ConvertibleTo
+--R Float)
+--R [38] D1 -> D from D if D has DVARCAT D1 and D1 has ORDSET
+--R [39] FortranCode -> OutputForm from FortranCode
+--R [40] 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 [41] D2 -> D1 from FiniteFieldHomomorphisms(D2,D3,D1)
+--R if D3 has FFIELDC and D1 has FAXF D3 and D2 has FAXF D3
+--R [42] D2 -> D1 from FiniteFieldHomomorphisms(D1,D3,D2)
+--R if D3 has FFIELDC and D1 has FAXF D3 and D2 has FAXF D3
+--R [43] D -> XRecursivePolynomial(D2,D3) from D
+--R if D has FLALG(D2,D3) and D2 has ORDSET and D3 has COMRING
+--R
+--R [44] D -> XDistributedPolynomial(D2,D3) from D
+--R if D has FLALG(D2,D3) and D2 has ORDSET and D3 has COMRING
+--R
+--R [45] D1 -> D from D
+--R if D has FLALG(D1,D2) and D1 has ORDSET and D2 has COMRING
+--R
+--R [46] Record(localSymbols: SymbolTable,code: List FortranCode) -> D
+--R from D
+--R if D has FMC
+--R [47] FortranCode -> D from D if D has FMC
+--R [48] List FortranCode -> D from D if D has FMC
+--R [49] Matrix MachineFloat -> D from D if D has FMC
+--R [50] Record(localSymbols: SymbolTable,code: List FortranCode) -> D
+--R from D
+--R if D has FMFUN
+--R [51] FortranCode -> D from D if D has FMFUN
+--R [52] List FortranCode -> D from D if D has FMFUN
+--R [53] D -> String from D if D has FNCAT
+--R [54] String -> D from D if D has FNCAT
+--R [55] D2 -> ScriptFormulaFormat from ScriptFormulaFormat1 D2 if D2
+--R has SETCAT
+--R [56] OutputForm -> ScriptFormulaFormat from ScriptFormulaFormat
+--R [57] Record(localSymbols: SymbolTable,code: List FortranCode) -> D
+--R from D
+--R if D has FORTFN
+--R [58] FortranCode -> D from D if D has FORTFN
+--R [59] List FortranCode -> D from D if D has FORTFN
+--R [60] 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 [61] 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 [62] 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 [63] 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 [64] 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 [65] 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 [66] 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 [67] 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 [68] 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 [69] 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 [70] 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 [71] 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 [72] 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 [73] 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 [74] 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 [75] 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 [76] 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 [77] Fraction Polynomial Fraction D2 -> D from D
+--R if D2 has INTDOM and D2 has ORDSET and D has FS D2
+--R [78] Polynomial Fraction D2 -> D from D
+--R if D2 has INTDOM and D2 has ORDSET and D has FS D2
+--R [79] Fraction D2 -> D from D
+--R if D2 has INTDOM and D2 has ORDSET and D has FS D2
+--R [80] SparseMultivariatePolynomial(D2,Kernel D) -> D from D
+--R if D2 has RING and D2 has ORDSET and D has FS D2
+--R [81] FortranScalarType -> SExpression from FortranScalarType
+--R [82] FortranScalarType -> Symbol from FortranScalarType
+--R [83] Symbol -> FortranScalarType from FortranScalarType
+--R [84] String -> FortranScalarType from FortranScalarType
+--R [85] FortranScalarType -> FortranType from FortranType
+--R [86] FortranType -> OutputForm from FortranType
+--R [87] Record(localSymbols: SymbolTable,code: List FortranCode) -> D
+--R from D
+--R if D has FVC
+--R [88] FortranCode -> D from D if D has FVC
+--R [89] List FortranCode -> D from D if D has FVC
+--R [90] Vector MachineFloat -> D from D if D has FVC
+--R [91] Record(localSymbols: SymbolTable,code: List FortranCode) -> D
+--R from D
+--R if D has FVFUN
+--R [92] FortranCode -> D from D if D has FVFUN
+--R [93] List FortranCode -> D from D if D has FVFUN
+--R [94] 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 [95] Variable D3 -> GeneralUnivariatePowerSeries(D2,D3,D4)
+--R from GeneralUnivariatePowerSeries(D2,D3,D4)
+--R if D3: SYMBOL and D2 has RING and D4: D2
+--R [96] HexadecimalExpansion -> RadixExpansion 16 from
+--R HexadecimalExpansion
+--R [97] HexadecimalExpansion -> Fraction Integer from
+--R HexadecimalExpansion
+--R [98] String -> IndexCard from IndexCard
+--R [99] 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 [100] D1 -> AssociatedJordanAlgebra(D2,D1)
+--R from AssociatedJordanAlgebra(D2,D1)
+--R if D2 has COMRING and D1 has NAALG D2
+--R [101] D -> D1 from D if D has KOERCE D1 and D1 has TYPE
+--R [102] D1 -> D from D if D has LALG D1 and D1 has RING
+--R [103] D1 -> AssociatedLieAlgebra(D2,D1) from AssociatedLieAlgebra(D2
+--R ,D1)
+--R if D2 has COMRING and D1 has NAALG D2
+--R [104] ThreeDimensionalMatrix D2 -> PrimitiveArray PrimitiveArray
+--R PrimitiveArray D2
+--R from ThreeDimensionalMatrix D2 if D2 has SETCAT
+--R [105] PrimitiveArray PrimitiveArray PrimitiveArray D2 ->
+--R ThreeDimensionalMatrix D2
+--R from ThreeDimensionalMatrix D2 if D2 has SETCAT
+--R [106] D2 -> (() -> D2) from MappingPackage1 D2 if D2 has SETCAT
+--R [107] 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 [108] MachineComplex -> Complex Float from MachineComplex
+--R [109] Complex MachineInteger -> MachineComplex from MachineComplex
+--R
+--R [110] Complex MachineFloat -> MachineComplex from MachineComplex
+--R [111] Complex Integer -> MachineComplex from MachineComplex
+--R [112] Complex Float -> MachineComplex from MachineComplex
+--R [113] MachineInteger -> MachineFloat from MachineFloat
+--R [114] MachineFloat -> Float from MachineFloat
+--R [115] Expression Integer -> Expression MachineInteger from
+--R MachineInteger
+--R [116] OutputForm -> String from MathMLFormat
+--R [117] Integer -> D from D if D has NASRING
+--R [118] 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 [119] Record(fn: Expression DoubleFloat,range: List Segment
+--R OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr:
+--R DoubleFloat) -> NumericalIntegrationProblem
+--R from NumericalIntegrationProblem
+--R [120] Record(var: Symbol,fn: Expression DoubleFloat,range: Segment
+--R OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr:
+--R DoubleFloat) -> NumericalIntegrationProblem
+--R from NumericalIntegrationProblem
+--R [121] NumericalIntegrationProblem -> OutputForm
+--R from NumericalIntegrationProblem
+--R [122] D2 -> None from NoneFunctions1 D2 if D2 has TYPE
+--R [123] 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 [124] NumericalODEProblem -> OutputForm from NumericalODEProblem
+--R [125] 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 [126] 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 [127] Symbol -> OpenMathErrorKind from OpenMathErrorKind
+--R [128] 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 [129] Record(lfn: List Expression DoubleFloat,init: List DoubleFloat
+--R ) -> NumericalOptimizationProblem
+--R from NumericalOptimizationProblem
+--R [130] 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 [131] NumericalOptimizationProblem -> OutputForm
+--R from NumericalOptimizationProblem
+--R [132] Integer -> OrdSetInts from OrdSetInts
+--R [133] Color -> Palette from Palette
+--R [134] Polynomial AlgebraicNumber -> Expression Integer
+--R from PolynomialAN2Expression
+--R [135] Fraction Polynomial AlgebraicNumber -> Expression Integer
+--R from PolynomialAN2Expression
+--R [136] 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 [137] NumericalPDEProblem -> OutputForm from NumericalPDEProblem
+--R [138] PendantTree D2 -> Tree D2 from PendantTree D2 if D2 has SETCAT
+--R
+--R [139] List Permutation D2 -> PermutationGroup D2 from
+--R PermutationGroup D2
+--R if D2 has SETCAT
+--R [140] PermutationGroup D2 -> List Permutation D2 from
+--R PermutationGroup D2
+--R if D2 has SETCAT
+--R [141] List D2 -> Permutation D2 from Permutation D2 if D2 has SETCAT
+--R
+--R [142] List List D2 -> Permutation D2 from Permutation D2 if D2 has
+--R SETCAT
+--R [143] Fraction Factored D2 -> PartialFraction D2 from
+--R PartialFraction D2
+--R if D2 has EUCDOM
+--R [144] PartialFraction D2 -> Fraction D2 from PartialFraction D2
+--R if D2 has EUCDOM
+--R [145] Pi -> Expression D3 from PiCoercions D3
+--R if D3 has Join(OrderedSet,IntegralDomain)
+--R [146] RadixExpansion D2 -> Fraction Integer from RadixExpansion D2
+--R if D2: INT
+--R [147] D2 -> Void from ResolveLatticeCompletion D2 if D2 has TYPE
+--R [148] Exit -> D1 from ResolveLatticeCompletion D1 if D1 has TYPE
+--R [149] D1 -> D from D if D has RETRACT D1 and D1 has TYPE
+--R [150] D2 -> Fraction Polynomial D2 from RationalFunction D2 if D2
+--R has INTDOM
+--R [151] Integer -> D from D if D has RING
+--R [152] D -> OutputForm from D if D has SPACEC D2 and D2 has RING
+--R [153] Character -> D from D if D has SRAGG
+--R [154] List D2 -> Stream D2 from Stream D2 if D2 has TYPE
+--R [155] Symbol -> Switch from Switch
+--R [156] String -> Symbol from Symbol
+--R [157] SymbolTable -> Table(Symbol,FortranType) from SymbolTable
+--R [158] Tableau D2 -> OutputForm from Tableau D2 if D2 has SETCAT
+--R [159] D2 -> TexFormat from TexFormat1 D2 if D2 has SETCAT
+--R [160] OutputForm -> TexFormat from TexFormat
+--R [161] Polynomial D2 -> TaylorSeries D2 from TaylorSeries D2 if D2
+--R has RING
+--R [162] Symbol -> TaylorSeries D2 from TaylorSeries D2 if D2 has RING
+--R
+--R [163] D1 -> D from D
+--R if D2 has RING and D has ULSCCAT(D2,D1) and D1 has UTSCAT
+--R D2
+--R [164] Segment D2 -> UniversalSegment D2 from UniversalSegment D2
+--R if D2 has TYPE
+--R [165] Variable D2 -> UnivariatePolynomial(D2,D3)
+--R from UnivariatePolynomial(D2,D3) if D2: SYMBOL and D3 has
+--R RING
+--R [166] D1 -> D from D
+--R if D2 has RING and D has UPXSCCA(D2,D1) and D1 has ULSCAT
+--R D2
+--R [167] Void -> OutputForm from Void
+--R [168] D1 -> D from D if D has XALG D1 and D1 has RING
+--R [169] 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 [1] Vector Matrix D3 -> Vector Matrix Fraction Polynomial D3
+--R from CoerceVectorMatrixPackage D3 if D3 has COMRING
+--R [2] List Integer -> ExtAlgBasis from ExtAlgBasis
+--R [3] 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 [4] 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 [5] 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 [6] List List Point DoubleFloat -> GraphImage from GraphImage
+--R [7] GraphImage -> OutputForm from GraphImage
+--R [8] SparseMultivariatePolynomial(Integer,Kernel InnerAlgebraicNumber
+--R ) -> InnerAlgebraicNumber
+--R from InnerAlgebraicNumber
+--R [9] 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 [10] 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 [11] LyndonWord D2 -> Magma D2 from LyndonWord D2 if D2 has ORDSET
+--R
+--R [12] LyndonWord D2 -> OrderedFreeMonoid D2 from LyndonWord D2
+--R if D2 has ORDSET
+--R [13] Magma D2 -> OrderedFreeMonoid D2 from Magma D2 if D2 has ORDSET
+--R
+--R [14] D1 -> MakeCachableSet D1 from MakeCachableSet D1 if D1 has
+--R SETCAT
+--R [15] 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 [16] D1 -> ModMonic(D2,D1) from ModMonic(D2,D1)
+--R if D2 has RING and D1 has UPOLYC D2
+--R [17] 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 [18] 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 [19] 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 [20] List Record(coef: D2,monom: D3) -> MonoidRing(D2,D3)
+--R from MonoidRing(D2,D3) if D2 has RING and D3 has MONOID
+--R [21] 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 [22] Polynomial D3 -> MyUnivariatePolynomial(D2,D3)
+--R from MyUnivariatePolynomial(D2,D3) if D3 has RING and D2:
+--R SYMBOL
+--R [23] Variable D2 -> MyUnivariatePolynomial(D2,D3)
+--R from MyUnivariatePolynomial(D2,D3) if D2: SYMBOL and D3 has
+--R RING
+--R [24] D1 -> MyUnivariatePolynomial(D2,D1) from MyUnivariatePolynomial
+--R (D2,D1)
+--R if D2: SYMBOL and D1 has RING
+--R [25] 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 [26] 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 [27] 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 [28] D1 -> PoincareBirkhoffWittLyndonBasis D1
+--R from PoincareBirkhoffWittLyndonBasis D1 if D1 has ORDSET
+--R
+--R [29] PoincareBirkhoffWittLyndonBasis D2 -> OrderedFreeMonoid D2
+--R from PoincareBirkhoffWittLyndonBasis D2 if D2 has ORDSET
+--R
+--R [30] Partition -> List Integer from Partition
+--R [31] 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 [32] RectangularMatrix(D2,D3,D4) -> Matrix D4
+--R from RectangularMatrix(D2,D3,D4)
+--R if D2: NNI and D3: NNI and D4 has RING
+--R [33] 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 [34] 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 [35] SquareMatrix(D2,D3) -> Matrix D3 from SquareMatrix(D2,D3)
+--R if D2: NNI and D3 has RING
+--R [36] D2 -> Stream D2 from StreamTaylorSeriesOperations D2 if D2 has
+--R RING
+--R [37] Variable D3 -> SparseUnivariateLaurentSeries(D2,D3,D4)
+--R from SparseUnivariateLaurentSeries(D2,D3,D4)
+--R if D3: SYMBOL and D2 has RING and D4: D2
+--R [38] Variable D3 -> SparseUnivariatePuiseuxSeries(D2,D3,D4)
+--R from SparseUnivariatePuiseuxSeries(D2,D3,D4)
+--R if D3: SYMBOL and D2 has RING and D4: D2
+--R [39] Variable D3 -> SparseUnivariateTaylorSeries(D2,D3,D4)
+--R from SparseUnivariateTaylorSeries(D2,D3,D4)
+--R if D3: SYMBOL and D2 has RING and D4: D2
+--R [40] 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 [41] PrimitiveArray D2 -> Tuple D2 from Tuple D2 if D2 has TYPE
+--R [42] Variable QUOTE x -> UnivariateFormalPowerSeries D2
+--R from UnivariateFormalPowerSeries D2 if D2 has RING
+--R [43] UnivariatePolynomial(QUOTE x,D2) -> UnivariateFormalPowerSeries
+--R D2
+--R from UnivariateFormalPowerSeries D2 if D2 has RING
+--R [44] Variable D3 -> UnivariateLaurentSeries(D2,D3,D4)
+--R from UnivariateLaurentSeries(D2,D3,D4)
+--R if D3: SYMBOL and D2 has RING and D4: D2
+--R [45] Variable D3 -> UnivariatePuiseuxSeries(D2,D3,D4)
+--R from UnivariatePuiseuxSeries(D2,D3,D4)
+--R if D3: SYMBOL and D2 has RING and D4: D2
+--R [46] Variable D3 -> UnivariateTaylorSeries(D2,D3,D4)
+--R from UnivariateTaylorSeries(D2,D3,D4)
+--R if D3: SYMBOL and D2 has RING and D4: D2
+--R [47] 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 [48] Variable D2 -> Symbol from Variable D2 if D2: SYMBOL
+--R [49] TwoDimensionalViewport -> OutputForm from
+--R TwoDimensionalViewport
+--R [50] GraphImage -> TwoDimensionalViewport from ViewportPackage
+--R [51] 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 [52] 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 [53] XPBWPolynomial(D2,D3) -> XRecursivePolynomial(D2,D3)
+--R from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has
+--R COMRING
+--R [54] XPBWPolynomial(D2,D3) -> XDistributedPolynomial(D2,D3)
+--R from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has
+--R COMRING
+--R [55] LiePolynomial(D2,D3) -> XPBWPolynomial(D2,D3)
+--R from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has
+--R COMRING
+--R [56] 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 [1] (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 [2] (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 [3] (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 [1] (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 [1] (Result,Result) -> Result from ExpertSystemToolsPackage
+--R [2] List Result -> Result from ExpertSystemToolsPackage
+--R [3] List D -> D from D if D has LNAGG D2 and D2 has TYPE
+--R [4] (D,D) -> D from D if D has LNAGG D1 and D1 has TYPE
+--R [5] (D1,D) -> D from D if D has LNAGG D1 and D1 has TYPE
+--R [6] (D,D1) -> D from D if D has LNAGG D1 and D1 has TYPE
+--R [7] (RoutinesTable,RoutinesTable) -> RoutinesTable from
+--R RoutinesTable
+--R [8] Stream Stream D3 -> Stream D3 from StreamFunctions1 D3 if D3 has
+--R TYPE
+--R [9] (D1,D) -> D from D if D has URAGG D1 and D1 has TYPE
+--R [10] (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 [1] 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 [1] -> CharacterClass from CharacterClass
+--R [2] Character -> Character from Character
+--R [3] 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 [1] D -> Integer from D if D has FPS
+--R [2] Factored D2 -> Integer from Factored D2 if D2 has INTDOM
+--R [3] MachineFloat -> Integer from MachineFloat
+--R
+--RThere are 2 unexposed functions called exponent :
+--R [1] 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 [2] 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 [1] (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 [1] (NonNegativeInteger,NonNegativeInteger) -> Vector List Integer
+--R from HallBasis
+--R [2] ((D2 -> D2),D2) -> InfiniteTuple D2 from InfiniteTuple D2 if D2
+--R has TYPE
+--R [3] ((D2 -> D2),D2) -> Stream D2 from Stream D2 if D2 has TYPE
+--R [4] (() -> 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 [1] List D -> D from D if D has GCDDOM
+--R [2] (D,D) -> D from D if D has GCDDOM
+--R [3] (D1,D1,Integer) -> D1 from ModularDistinctDegreeFactorizer D1
+--R if D1 has UPOLYC INT
+--R [4] (NonNegativeInteger,NonNegativeInteger) -> NonNegativeInteger
+--R from NonNegativeInteger
+--R [5] (PositiveInteger,PositiveInteger) -> PositiveInteger
+--R from PositiveInteger
+--R [6] (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 [1] List D1 -> D1 from HeuGcd D1 if D1 has UPOLYC INT
+--R [2] (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 [3] 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 [4] (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 [5] 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 [6] (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 [1] Fraction Integer -> BinaryExpansion from BinaryExpansion
+--R
+--RThere is one unexposed function called binary :
+--R [1] (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 [1] Factored D1 -> D1 from Factored D1 if D1 has INTDOM
+--R [2] 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 [3] IntegrationResult Fraction Polynomial D3 -> List Expression D3
+--R from IntegrationResultRFToFunction D3
+--R if D3 has Join(GcdDomain,RetractableTo Integer,OrderedSet,
+--R LinearlyExplicitRingOver Integer)
+--R [4] D -> D1 from D
+--R if D has SEGXCAT(D2,D1) and D2 has ORDRING and D1 has STAGG
+--R D2
+--R [5] List D -> D1 from D
+--R if D has SEGXCAT(D3,D1) and D3 has ORDRING and D1 has STAGG
+--R D3
+--R [6] 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 [1] (Expression D5,PositiveInteger) -> List Expression D5
+--R from DegreeReductionPackage(D4,D5)
+--R if D5 has Join(IntegralDomain,OrderedSet) and D4 has RING
+--R
+--R [2] XPolynomial D2 -> XDistributedPolynomial(Symbol,D2) from
+--R XPolynomial D2
+--R if D2 has RING
+--R [3] 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 [1] ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2
+--R from InfiniteTuple D2 if D2 has TYPE
+--R [2] ((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 [1] ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2
+--R from InfiniteTuple D2 if D2 has TYPE
+--R [2] ((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 [1] ((D2 -> Boolean),D) -> D from D
+--R if D has finiteAggregate and D has CLAGG D2 and D2 has TYPE
+--R
+--R [2] ((D2 -> Boolean),InfiniteTuple D2) -> InfiniteTuple D2
+--R from InfiniteTuple D2 if D2 has TYPE
+--R [3] ((D2 -> Boolean),D) -> D from D if D has LZSTAGG D2 and D2 has
+--R TYPE
+--R [4] (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 [1] (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 [1] (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 [1] (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 [1] 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 [1] (Integer,D) -> D from D if D has ABELGRP
+--R [2] (NonNegativeInteger,D) -> D from D if D has ABELMON
+--R [3] (PositiveInteger,D) -> D from D if D has ABELSG
+--R [4] (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 [5] (DoubleFloat,Color) -> Color from Color
+--R [6] (PositiveInteger,Color) -> Color from Color
+--R [7] (DenavitHartenbergMatrix D2,Point D2) -> Point D2
+--R from DenavitHartenbergMatrix D2
+--R if D2 has Join(Field,TranscendentalFunctionCategory)
+--R [8] (D1,Equation D1) -> Equation D1 from Equation D1
+--R if D1 has SGROUP and D1 has TYPE
+--R [9] (Equation D1,D1) -> Equation D1 from Equation D1
+--R if D1 has SGROUP and D1 has TYPE
+--R [10] (D1,D2) -> D from D
+--R if D has FAMONC(D2,D1) and D2 has SETCAT and D1 has CABMON
+--R
+--R [11] (D1,D2) -> D from D
+--R if D has FMCAT(D1,D2) and D1 has RING and D2 has SETCAT
+--R [12] (D,D1) -> D from D
+--R if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
+--R
+--R [13] (D1,D) -> D from D
+--R if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
+--R
+--R [14] (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 [15] (D1,D) -> D from D if D has LMODULE D1 and D1 has RNG
+--R [16] ((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 [17] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,
+--R D3)
+--R if D2 has SETCAT and D3 has RING
+--R [18] (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 [19] (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 [20] (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 [21] (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 [22] (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 [23] (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 [24] (D,D) -> D from D if D has MONAD
+--R [25] (D,D1) -> D from D if D has RMODULE D1 and D1 has RNG
+--R [26] (D,D) -> D from D if D has SGROUP
+--R [27] (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 [28] (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 [29] (D,D1) -> D from D
+--R if D has VECTCAT D1 and D1 has TYPE and D1 has MONOID
+--R [30] (D1,D) -> D from D
+--R if D has VECTCAT D1 and D1 has TYPE and D1 has MONOID
+--R [31] (Integer,D) -> D from D
+--R if D has VECTCAT D2 and D2 has TYPE and D2 has ABELGRP
+--R [32] (D1,D) -> D from D
+--R if D has XFALG(D1,D2) and D1 has ORDSET and D2 has RING
+--R [33] (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 [1] (FreeGroup D1,D1) -> FreeGroup D1 from FreeGroup D1 if D1 has
+--R SETCAT
+--R [2] (D1,FreeGroup D1) -> FreeGroup D1 from FreeGroup D1 if D1 has
+--R SETCAT
+--R [3] (D1,D2) -> FreeModule1(D2,D1) from FreeModule1(D2,D1)
+--R if D2 has RING and D1 has ORDSET
+--R [4] (FreeMonoid D1,D1) -> FreeMonoid D1 from FreeMonoid D1 if D1 has
+--R SETCAT
+--R [5] (D1,FreeMonoid D1) -> FreeMonoid D1 from FreeMonoid D1 if D1 has
+--R SETCAT
+--R [6] (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 [7] (Vector D2,Vector D2) -> Vector D2
+--R from InnerNormalBasisFieldFunctions D2 if D2 has FFIELDC
+--R
+--R [8] (InputForm,InputForm) -> InputForm from InputForm
+--R [9] (InnerTaylorSeries D2,Integer) -> InnerTaylorSeries D2
+--R from InnerTaylorSeries D2 if D2 has RING
+--R [10] (InnerTaylorSeries D1,D1) -> InnerTaylorSeries D1
+--R from InnerTaylorSeries D1 if D1 has RING
+--R [11] (D1,InnerTaylorSeries D1) -> InnerTaylorSeries D1
+--R from InnerTaylorSeries D1 if D1 has RING
+--R [12] (Magma D1,Magma D1) -> Magma D1 from Magma D1 if D1 has ORDSET
+--R
+--R [13] (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 [14] (OrderedFreeMonoid D1,D1) -> OrderedFreeMonoid D1
+--R from OrderedFreeMonoid D1 if D1 has ORDSET
+--R [15] (D1,OrderedFreeMonoid D1) -> OrderedFreeMonoid D1
+--R from OrderedFreeMonoid D1 if D1 has ORDSET
+--R [16] (OutputForm,OutputForm) -> OutputForm from OutputForm
+--R [17] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
+--R SETCAT
+--R [18] (D2,Vector D3) -> Vector D3 from PseudoRemainderSequence(D2,D3)
+--R if D3 has UPOLYC D2 and D2 has INTDOM
+--R [19] (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 [20] (Stream D2,Stream D2) -> Stream D2 from
+--R StreamTaylorSeriesOperations D2
+--R if D2 has RING
+--R [21] (D2,Stream D2) -> Stream D2 from StreamTaylorSeriesOperations
+--R D2
+--R if D2 has RING
+--R [22] (Stream D2,D2) -> Stream D2 from StreamTaylorSeriesOperations
+--R D2
+--R if D2 has RING
+--R [23] (DoubleFloat,Point DoubleFloat) -> Point DoubleFloat from
+--R TubePlotTools
+--R [24] (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 [1] -> 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 [2] D -> NonNegativeInteger from D if D has SPACEC D2 and D2 has
+--R RING
+--R
+--RThere is one unexposed function called numberOfComponents :
+--R [1] -> 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 [1] D1 -> Tree D1 from Tree D1 if D1 has SETCAT
+--R [2] List D2 -> Tree D2 from Tree D2 if D2 has SETCAT
+--R [3] (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 [1] 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 [1] List Float -> DrawOption from DrawOption
+--R [2] -> Union(D,"failed") from D
+--R if D has FINAALG D1 and D1 has INTDOM and D1 has COMRING
+--R
+--R [3] 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 [1] 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 [1] (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 [2] (D,SegmentBinding D) -> D from D if D has COMBOPC
+--R [3] (D,Symbol) -> D from D if D has COMBOPC
+--R [4] (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 [1] (D1,Symbol) -> D1 from CombinatorialFunction(D3,D1)
+--R if D3 has Join(OrderedSet,IntegralDomain) and D1 has FS D3
+--R
+--R [2] (D1,SegmentBinding D1) -> D1 from CombinatorialFunction(D3,D1)
+--R if D1 has FS D3 and D3 has Join(OrderedSet,IntegralDomain)
+--R
+--R [3] (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 [1] (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 [2] (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 [1] 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 [1] -> 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 [1] CardinalNumber -> Boolean from CardinalNumber
+--R [2] OnePointCompletion D2 -> Boolean from OnePointCompletion D2
+--R if D2 has SETCAT
+--R [3] 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 [1] CartesianTensor(D2,D3,D4) -> NonNegativeInteger
+--R from CartesianTensor(D2,D3,D4)
+--R if D2: INT and D3: NNI and D4 has COMRING
+--R [2] -> PositiveInteger from D if D has FINAALG D2 and D2 has
+--R COMRING
+--R [3] -> PositiveInteger from D
+--R if D has FINRALG(D2,D3) and D2 has COMRING and D3 has
+--R UPOLYC D2
+--R [4] (Matrix D4,Vector D4) -> NonNegativeInteger
+--R from LinearSystemMatrixPackage1 D4 if D4 has FIELD
+--R [5] (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 [6] 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 [7] 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 [8] 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 [1] -> PositiveInteger from ComplexCategory&(D2,D3)
+--R if D3 has COMRING and D2 has COMPCAT D3
+--R [2] 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 [1] 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 [1] (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 [2] (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 [3] 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 [4] (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 [1] -> CharacterClass from CharacterClass
+--R [2] Character -> Character from Character
+--R [3] 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 [1] 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 [1] 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 [2] 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 [1] 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 [2] 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 [1] -> Character from Character
+--R [2] ThreeSpace DoubleFloat -> DrawOption from DrawOption
+--R
+--RThere is one unexposed function called space :
+--R [1] 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 [1] (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 [2] ((D2 -> Boolean),D) -> D from D
+--R if D has finiteAggregate and D has CLAGG D2 and D2 has TYPE
+--R
+--R [3] ((D2 -> Boolean),D) -> D from D if D has LZSTAGG D2 and D2 has
+--R TYPE
+--R [4] ((D3 -> Boolean),Multiset D3,Integer) -> Multiset D3 from
+--R Multiset D3
+--R if D3 has SETCAT
+--R [5] (D1,Multiset D1,Integer) -> Multiset D1 from Multiset D1
+--R if D1 has SETCAT
+--R
+--RThere is one unexposed function called remove :
+--R [1] (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 [1] 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 [1] FreeGroup D2 -> List Record(gen: D2,exp: Integer) from FreeGroup
+--R D2
+--R if D2 has SETCAT
+--R [2] FreeMonoid D2 -> List Record(gen: D2,exp: NonNegativeInteger)
+--R from FreeMonoid D2 if D2 has SETCAT
+--R [3] 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 [1] String -> Void from OutputPackage
+--R [2] OutputForm -> Void from OutputPackage
+--R [3] (String,OutputForm) -> Void from OutputPackage
+--R [4] (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 [1] 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 [1] String -> Character from Character
+--R [2] 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 [1] Boolean -> Boolean from FlexibleArray D2 if D2 has TYPE
+--R
+--RThere is one unexposed function called shrinkable :
+--R [1] 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 [1] 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 [1] List D2 -> FlexibleArray D2 from FlexibleArray D2 if D2 has TYPE
+--R
+--R
+--RThere is one unexposed function called flexibleArray :
+--R [1] 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 [1] (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 [2] (D,right,D) -> D from D
+--R if D has shallowlyMutable and D has BRAGG D2 and D2 has
+--R TYPE
+--R [3] (D,left,D) -> D from D
+--R if D has shallowlyMutable and D has BRAGG D2 and D2 has
+--R TYPE
+--R [4] (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 [5] (Library,Symbol,Any) -> Any from Library
+--R [6] (D,UniversalSegment Integer,D1) -> D1 from D
+--R if D has shallowlyMutable and D has LNAGG D1 and D1 has
+--R TYPE
+--R [7] (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 [8] (D,value,D1) -> D1 from D
+--R if D has shallowlyMutable and D has RCAGG D1 and D1 has
+--R TYPE
+--R [9] (D,D2,D1) -> D1 from D
+--R if D has TBAGG(D2,D1) and D2 has SETCAT and D1 has SETCAT
+--R
+--R [10] (D,last,D1) -> D1 from D
+--R if D has shallowlyMutable and D has URAGG D1 and D1 has
+--R TYPE
+--R [11] (D,rest,D) -> D from D
+--R if D has shallowlyMutable and D has URAGG D2 and D2 has
+--R TYPE
+--R [12] (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 [1] (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 [1] 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 [1] 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 [1] (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 [2] (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 [1] AlgebraicNumber -> AlgebraicNumber from AlgebraicNumber
+--R [2] (((D4,D1) -> D1),OneDimensionalArray D4,D1) -> D1
+--R from OneDimensionalArrayFunctions2(D4,D1)
+--R if D4 has TYPE and D1 has TYPE
+--R [3] (((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 [4] (((D1,D1) -> D1),D,D1) -> D1 from D
+--R if D has finiteAggregate and D has CLAGG D1 and D1 has TYPE
+--R
+--R [5] (((D1,D1) -> D1),D) -> D1 from D
+--R if D has finiteAggregate and D has CLAGG D1 and D1 has TYPE
+--R
+--R [6] (((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 [7] Expression D1 -> Expression D1 from Expression D1
+--R if D1 has INTDOM and D1 has ORDSET
+--R [8] 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 [9] (((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 [10] (((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 [11] (((D4,D1) -> D1),List D4,D1) -> D1 from ListFunctions2(D4,D1)
+--R if D4 has TYPE and D1 has TYPE
+--R [12] (((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 [13] 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 [14] D1 -> D from D
+--R if D2 has COMRING and D has MONOGEN(D2,D1) and D1 has
+--R UPOLYC D2
+--R [15] (((D4,D1) -> D1),PrimitiveArray D4,D1) -> D1
+--R from PrimitiveArrayFunctions2(D4,D1)
+--R if D4 has TYPE and D1 has TYPE
+--R [16] (((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 [17] (D1,((D4,D1) -> D1),Stream D4) -> D1 from StreamFunctions2(D4,
+--R D1)
+--R if D4 has TYPE and D1 has TYPE
+--R [18] (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 [19] (((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 [1] 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 [2] (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 [3] InnerAlgebraicNumber -> InnerAlgebraicNumber from
+--R InnerAlgebraicNumber
+--R [4] (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 [5] D1 -> ModMonic(D2,D1) from ModMonic(D2,D1)
+--R if D2 has RING and D1 has UPOLYC D2
+--R [6] (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 [7] 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 [1] (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 [2] (String,String,String) -> D from D if D has FNCAT
+--R [3] -> ScriptFormulaFormat from ScriptFormulaFormat
+--R [4] (NonNegativeInteger,D2) -> D from D
+--R if D has LNAGG D2 and D2 has TYPE
+--R [5] Symbol -> Symbol from Symbol
+--R [6] -> Symbol from Symbol
+--R [7] -> TexFormat from TexFormat
+--R
+--RThere are 4 unexposed functions called new :
+--R [1] -> SubSpaceComponentProperty from SubSpaceComponentProperty
+--R [2] -> 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 [3] -> PatternMatchResult(D1,D2) from PatternMatchResult(D1,D2)
+--R if D1 has SETCAT and D2 has SETCAT
+--R [4] -> 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 [1] (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 [1] 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 [2] 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 [1] -> 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 [1] (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 [1] 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 [2] 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 [1] (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 [2] (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 [3] (D,right) -> D from D if D has BRAGG D2 and D2 has TYPE
+--R [4] (D,left) -> D from D if D has BRAGG D2 and D2 has TYPE
+--R [5] (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 [6] (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 [7] (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 [8] (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 [9] (CartesianTensor(D3,D4,D1),Integer) -> D1
+--R from CartesianTensor(D3,D4,D1)
+--R if D1 has COMRING and D3: INT and D4: NNI
+--R [10] CartesianTensor(D2,D3,D1) -> D1 from CartesianTensor(D2,D3,D1)
+--R if D1 has COMRING and D2: INT and D3: NNI
+--R [11] (Database D3,Symbol) -> DataList String from Database D3
+--R if D3 has OrderedSet with
+--R ?.? : (%,Symbol) -> String
+--R display : % -> Void
+--R fullDisplay : % -> Void
+--R [12] (Database D2,QueryEquation) -> Database D2 from Database D2
+--R if D2 has OrderedSet with
+--R ?.? : (%,Symbol) -> String
+--R display : % -> Void
+--R fullDisplay : % -> Void
+--R [13] (DataList D3,count) -> NonNegativeInteger from DataList D3
+--R if D3 has ORDSET
+--R [14] (DataList D2,sort) -> DataList D2 from DataList D2 if D2 has
+--R ORDSET
+--R [15] (DataList D2,unique) -> DataList D2 from DataList D2 if D2 has
+--R ORDSET
+--R [16] (D,D2) -> D1 from D
+--R if D has ELTAB(D2,D1) and D2 has SETCAT and D1 has TYPE
+--R [17] (D,D2,D1) -> D1 from D
+--R if D has ELTAGG(D2,D1) and D2 has SETCAT and D1 has TYPE
+--R
+--R [18] (BasicOperator,List D) -> D from D if D has ES
+--R [19] (BasicOperator,D,D,D,D) -> D from D if D has ES
+--R [20] (BasicOperator,D,D,D) -> D from D if D has ES
+--R [21] (BasicOperator,D,D) -> D from D if D has ES
+--R [22] (BasicOperator,D) -> D from D if D has ES
+--R [23] (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 [24] (D,Integer) -> D1 from D if D has FRNAALG D1 and D1 has COMRING
+--R
+--R [25] (IndexCard,Symbol) -> String from IndexCard
+--R [26] (Library,Symbol) -> Any from Library
+--R [27] (D,UniversalSegment Integer) -> D from D
+--R if D has LNAGG D2 and D2 has TYPE
+--R [28] (ThreeDimensionalMatrix D1,NonNegativeInteger,
+--R NonNegativeInteger,NonNegativeInteger) -> D1
+--R from ThreeDimensionalMatrix D1 if D1 has SETCAT
+--R [29] (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 [30] (D,D1) -> D1 from D if D has PERMCAT D1 and D1 has SETCAT
+--R [31] (PermutationGroup D3,NonNegativeInteger) -> Permutation D3
+--R from PermutationGroup D3 if D3 has SETCAT
+--R [32] (QuadraticForm(D3,D1),DirectProduct(D3,D1)) -> D1
+--R from QuadraticForm(D3,D1) if D3: PI and D1 has FIELD
+--R [33] (D,value) -> D1 from D if D has RCAGG D1 and D1 has TYPE
+--R [34] (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 [35] (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 [36] (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 [37] (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 [38] (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 [39] (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 [40] (D,D) -> D from D if D has SRAGG
+--R [41] (Symbol,List OutputForm) -> Symbol from Symbol
+--R [42] (Fraction D,D1) -> D1 from D
+--R if D has UPOLYC D1 and D1 has RING and D1 has FIELD
+--R [43] (Fraction D,Fraction D) -> Fraction D from D
+--R if D has UPOLYC D2 and D2 has RING and D2 has INTDOM
+--R [44] (D,D2) -> D1 from D
+--R if D has UPSCAT(D1,D2) and D2 has OAMON and D1 has RING
+--R [45] (D,last) -> D1 from D if D has URAGG D1 and D1 has TYPE
+--R [46] (D,rest) -> D from D if D has URAGG D2 and D2 has TYPE
+--R [47] (D,first) -> D1 from D if D has URAGG D1 and D1 has TYPE
+--R
+--RThere are 4 unexposed functions called elt :
+--R [1] (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 [2] (OutputForm,List OutputForm) -> OutputForm from OutputForm
+--R [3] (BasicOperator,List Pattern D3) -> Pattern D3 from Pattern D3
+--R if D3 has SETCAT
+--R [4] 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[2]
+--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 [1] 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 [2] 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 [1] Factored D2 -> NonNegativeInteger from Factored D2 if D2 has
+--R INTDOM
+--R
+--RThere is one unexposed function called numberOfFactors :
+--R [1] 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 [1] 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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- [Axiom-developer] 20090220.01.tpd.patch (regression test )d op, )frame ),
daly <=