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| (frame) +(defun frameName (frame) (car frame)) @ +\subsection{1st Frame Component -- frameInteractive} +<>= +(defun frameInteractive (frame) + (nth 1 frame)) + +@ +\subsection{2nd Frame Component -- frameIOIndex} +<>= +(defun frameIOIndex (frame) + (nth 2 frame)) + +@ +\subsection{3rd Frame Component -- frameHiFiAccess} +<>= +(defun frameHiFiAccess (frame) + (nth 3 frame)) + +@ +\subsection{4th Frame Component -- frameHistList} +<>= +(defun frameHistList (frame) + (nth 4 frame)) + +@ +\subsection{5th Frame Component -- frameHistListLen} +<>= +(defun frameHistListLen (frame) + (nth 5 frame)) + +@ +\subsection{6th Frame Component -- frameHistListAct} +<>= +(defun frameHistListAct (frame) + (nth 6 frame)) + +@ +\subsection{7th Frame Component -- frameHistRecord} +<>= +(defun frameHistRecord (frame) + (nth 7 frame)) + +@ +\subsection{8th Frame Component -- frameHistoryTable} +<>= +(defun frameHistoryTable (frame) + (nth 8 frame)) + +@ +\subsection{9th Frame Component -- 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| () + (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 $interpreterFrameRing] \end{verbatim} <>= (defun |frameNames| () - (prog () - (return - (seq - (prog (tmp0) - (spadlet tmp0 nil) - (return - (do ((tmp1 |$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 |$interpreterFrameRing|)) @ + +\subsection{Get Named Frame Environment (aka Interactive)} +If the frame is found we return the environment portion of the frame +otherwise we construct an empty environment and return it. +The initial values of an empty frame are created here. This function +returns a single frame that will be placed in the frame ring. \subsection{defun frameEnvironment} \begin{verbatim} frameEnvironment fname == @@ -4106,29 +4242,10 @@ frameEnvironment fname == \end{verbatim} <>= (defun |frameEnvironment| (fname) - (prog - (tmp1 f e ifr) - (return - (seq - (cond - ((boot-equal fname (|frameName| (CAR |$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| () - (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| (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| () - (progn (rplaca |$interpreterFrameRing| (|createCurrentInterpreterFrame|)) (|updateFromCurrentInterpreterFrame|) - nil)) + nil) @ \subsection{defun initializeInterpreterFrameRing} @@ -4290,14 +4407,23 @@ initializeInterpreterFrameRing() == \end{verbatim} <>= (defun |initializeInterpreterFrameRing| () - (progn (spadlet |$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| () - (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. <> <> <> +<> +<> +<> +<> +<> +<> +<> +<> +<> <> <> <> 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
remove unused code
20090212.02.tpd.patch rewrite restart
+20090212.03.tpd.patch +rewrite sayExample, frame
+20090220.01.tpd.patch +regression test )d op, )frame
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index b341753..eb8cbf6 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -294,7 +294,8 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \ decimal.regress defintef.regress defintrf.regress \ derham.regress dfloat.regress dhmatrix.regress \ dhtri.regress directproduct.regress divisor.regress \ - dmp.regress dpol.regress e1.regress ei.regress \ + dmp.regress dop.regress dpol.regress \ + e1.regress ei.regress \ easter.regress efi.regress \ eigen.regress elemfun.regress elemnum.regress elfuts.regress \ elt.regress en.regress \ @@ -308,7 +309,8 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \ fib.regress file.regress fixed.regress \ float1.regress float2.regress \ float.regress fname1.regress fname.regress fnla.regress \ - fns.regress fparfrac.regress fparfrc.regress fr1.regress \ + fns.regress fparfrac.regress fparfrc.regress \ + frame.regress fr1.regress \ fr2.regress frac.regress fr.regress free.regress \ function.regress galois.regress gamma.regress \ gbf.regress genups.regress gonshor.regress grpthry.regress \ @@ -553,7 +555,8 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \ ${OUT}/dfloat.input ${OUT}/dhmatrix.input \ ${OUT}/dhtri.input ${OUT}/directproduct.input \ ${OUT}/divisor.input \ - ${OUT}/dmp.input ${OUT}/dpol.input ${OUT}/draw2dsf.input \ + ${OUT}/dmp.input ${OUT}/dop.input \ + ${OUT}/dpol.input ${OUT}/draw2dsf.input \ ${OUT}/drawalg.input ${OUT}/drawcfn.input \ ${OUT}/drawcfun.input ${OUT}/drawcurv.input \ ${OUT}/draw.input ${OUT}/drawcx.input ${OUT}/drawex.input \ @@ -577,7 +580,8 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \ ${OUT}/fname1.input ${OUT}/fnla.input ${OUT}/folium.input \ ${OUT}/fparfrac.input \ ${OUT}/fparfrc.input ${OUT}/fr2.input ${OUT}/frac.input \ - ${OUT}/fr.input ${OUT}/fr1.input ${OUT}/gary1.input \ + ${OUT}/fr.input ${OUT}/frame.input \ + ${OUT}/fr1.input ${OUT}/gary1.input \ ${OUT}/gbf.input ${OUT}/genups.input ${OUT}/gnarly1.input \ ${OUT}/gonshor.input ${OUT}/grdef.input \ ${OUT}/gstbl.input \ @@ -791,7 +795,7 @@ DOCFILES= \ ${DOC}/dhtri.input.dvi \ ${DOC}/directproduct.input.dvi \ ${DOC}/divisor.input.dvi ${DOC}/dmp.input.dvi \ - ${DOC}/dpol.input.dvi \ + ${DOC}/dop.input.dvi ${DOC}/dpol.input.dvi \ ${DOC}/draw2dsf.input.dvi ${DOC}/drawalg.input.dvi \ ${DOC}/drawcfn.input.dvi ${DOC}/drawcfun.input.dvi \ ${DOC}/drawcurv.input.dvi ${DOC}/drawcx.input.dvi \ @@ -863,6 +867,7 @@ DOCFILES= \ ${DOC}/fname.input.dvi ${DOC}/fnla.input.dvi \ ${DOC}/fns.input.dvi ${DOC}/folium.input.dvi \ ${DOC}/fparfrac.input.dvi ${DOC}/fparfrc.input.dvi \ + ${DOC}/frame.input.dvi \ ${DOC}/fr1.input.dvi ${DOC}/fr2.input.dvi \ ${DOC}/frac.input.dvi ${DOC}/fr.input.dvi \ ${DOC}/free.input.dvi \ diff --git a/src/input/dop.input.pamphlet b/src/input/dop.input.pamphlet new file mode 100644 index 0000000..887f4bc --- /dev/null +++ b/src/input/dop.input.pamphlet @@ -0,0 +1,6163 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input dop.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +<>= +--Copyright The Numerical Algorithms Group Limited 1991. +@ +<<*>>= +)spool dop.output +)set message test on +)set message auto off +)clear all + +--S 1 of 127 +)d op binaryTree +--R +--R +--RThere are 2 exposed functions called binaryTree : +--R [1] (BinaryTree D1,D1,BinaryTree D1) -> BinaryTree D1 from +--R BinaryTree D1 +--R if D1 has SETCAT +--R [2] D1 -> BinaryTree D1 from BinaryTree D1 if D1 has SETCAT +--R +--RExamples of binaryTree from BinaryTree +--R +--Rt1:=binaryTree([1,2,3]) +--Rt2:=binaryTree([4,5,6]) +--RbinaryTree(t1,[7,8,9],t2) +--R +--Rt1:=binaryTree([1,2,3]) +--R +--E 1 + +--S 2 of 127 +)d op rationalPoint? +--R +--R +--RThere is one exposed function called rationalPoint? : +--R [1] (D2,D2) -> Boolean from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC +--R D2 and D4 has UPOLYC FRAC D3 +--R +--RThere is one unexposed function called rationalPoint? : +--R [1] (D2,D2) -> Boolean from FunctionFieldCategory&(D3,D2,D4,D5) +--R if D2 has UFD and D4 has UPOLYC D2 and D5 has UPOLYC FRAC +--R D4 and D3 has FFCAT(D2,D4,D5) +--R +--RExamples of rationalPoint? from FunctionFieldCategory& +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RrationalPoint?(0,0)$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} +<>= +--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)