Maxima Manual. Node: Definitions for Input and Output

## 8.4: Definitions for Input and Output

Variable: %
The last D-line computed by MACSYMA (whether or not it was printed out). (See also %%.)
Variable: %%
The value of the last computation performed while in a (MACSYMA-BREAK). Also may be used in compound statements in the nth statement to refer to the value of the (n-1)th statement. E.g. F(N):=(INTEGRATE(X^N,X),SUBST(3,X,%%)-SUBST(2,X,%%)); is in essence equivalent to F(N):=BLOCK([%%], %%:INTEGRATE(X^N,X), SUBST(3,X,%%)-SUBST(2,X,%%)); This will also work for communicating between the (n-1)th and nth (non-atomic) BLOCK statements.
Variable: %EDISPFLAG
default: [FALSE] - if TRUE, MACSYMA displays %E to a negative exponent as a quotient, i.e. %E^-X as 1/%E^X.
Function: %TH (i)
is the ith previous computation. That is, if the next expression to be computed is D(j) this is D(j-i). This is useful in BATCH files or for referring to a group of D expressions. For example, if SUM is initialized to 0 then FOR I:1 THRU 10 DO SUM:SUM+%TH(I) will set SUM to the sum of the last ten D expressions.
special symbol: "?"
- As prefix to a function or variable name, signifies that the function or variable is a LISP token, not a MACSYMA token. Two question marks typed together, ??, will flush the current MACSYMA command line.
Variable: ABSBOXCHAR
default: [!] is the character used to draw absolute value signs around expressions which are more than a single line high.
Function: APPENDFILE (filename1, filename2, DSK, directory)
is like WRITEFILE(DSK,directory) but appends to the file whose name is specified by the first two arguments. A subsequent CLOSEFILE will delete the original file and rename the appended file.
Function: BACKUP ()
To "back up" and see what you did, see PLAYBACK.
Function: BATCH (file-specification)
reads in and evaluates MACSYMA command lines from a file - A facility for executing command lines stored on a disk file rather than in the usual on-line mode. This facility has several uses, namely to provide a reservoir for working command lines, for giving error-free demonstrations, or helping in organizing one's thinking in complex problem-solving situations where modifications may be done via a text editor. A batch file consists of a set of MACSYMA command lines, each with its terminating ; or \$, which may be further separated by spaces, carriage- returns, form-feeds, and the like. The BATCH function calls for reading in the command lines from the file one at a time, echoing them on the user console, and executing them in turn. Control is returned to the user console only when serious errors occur or when the end of the file is met. Of course, the user may quit out of the file-processing by typing control-G at any point. BATCH files may be created using a text editor or by use of the STRINGOUT command. Do DESCRIBE(STRINGOUT) for details DESCRIBE(FILE); and DESCRIBE(FILES); have additional information on how the file argument is interpreted, and files in general.
Variable: BATCHKILL
default: [FALSE] if TRUE then the effect of all previous BATCH files is nullified because a KILL(ALL) and a RESET() will be done automatically when the next one is read in. If BATCHKILL is bound to any other atom then a KILL of the value of BATCHKILL will be done.
Batches in the file silently without terminal output or labels.
Function: BATCON (argument)
continues BATCHing in a file which was interrupted.
Variable: BATCOUNT
default: [0] may be set to the number of the last expression BATCHed in from a file. Thus BATCON(BATCOUNT-1) will resume BATCHing from the expression before the last BATCHed in from before.
Variable: BOTHCASES
default: [FALSE] if TRUE will cause MACSYMA to retain lower case text as well as upper case. Note, however, that the names of any MACSYMA special variables or functions must be typed in upper case. (For historical reasons this is also a function, but it should be used as a switch. Please use it as described here, not as a function.)
Variable: CHANGE_FILEDEFAULTS
default: [TRUE] on PDP10 systems, and FALSE elsewhere. Controls whether the user doing a LOADFILE or BATCH has his file defaults changed to the file LOADFILEd or BATCHed. The TRUE setting is for people who like DDT-style file defaulting. The FALSE setting is for people who like the conventions of other operating systems, who like LISP-style file defaulting, or who write packages which do LOADFILEs or BATCHes which should not interfere with their user's file defaults.
Function: CLOSEFILE (filename1, filename2)
closes a file opened by WRITEFILE and gives it the name filename1 filename2. (On a Lisp Machine one need only say CLOSEFILE();.) Thus to save a file consisting of the display of all input and output during some part of a session with MACSYMA the user issues a WRITEFILE, transacts with MACSYMA, then issues a CLOSEFILE. The user can also issue the PLAYBACK function after a WRITEFILE to save the display of previous transactions. (Note that what is saved this way is a copy of the display of expressions not the expressions themselves). To save the actual expression in internal form the SAVE function may be used. The expression can then be brought back into MACSYMA via the LOADFILE function. To save the expression in a linear form which may then be BATCHed in later, the STRINGOUT function is used.
Function: COLLAPSE (expression)
collapses" its argument by causing all of its common (i.e. equal) subexpressions to share (i.e. use the same cells), thereby saving space. (COLLAPSE is a subroutine used by the OPTIMIZE command.) Thus, calling COLLAPSE may be useful before using FASSAVE or after loading in a SAVE file. You can collapse several expressions together by using COLLAPSE([expr1,...,exprN])\$. Similarly, you can collapse the elements of the array A by doing COLLAPSE(LISTARRAY('A))\$.
Function: CONCAT (arg1, arg2, ...)
evaluates its arguments and returns the concatenation of their values resulting in a name or a quoted string the type being given by that of the first argument. Thus if X is bound to 1 and D is unbound then CONCAT(X,2)="12" and CONCAT(D,X+1)=D2.
Function: SCONCAT (arg1, arg2, ...)

evaluates its arguments and concatenates them into a string. Unlike CONCAT, the arguments do NOT need to be atoms. The result is a Common Lisp String.

```(C5) sconcat("xx[",3,"]:",expand((x+y)^3));
(D5) 			 xx[3]:Y^3+3*X*Y^2+3*X^2*Y+X^3
```

The resulting string could be used in conjunction with print.

Variable: CURSORDISP
default: [TRUE] If TRUE, causes expressions to be drawn by the displayer in logical sequence. This only works with a console which can do cursor movement. If FALSE, expressions are simply printed line by line. CURSORDISP is FALSE when a WRITEFILE is in effect.
Variable: DIREC
- The value of this variable is the default file directory for SAVE, STORE, FASSAVE, and STRINGOUT. It is initialized to the user's login name, if he has a disk directory, and to one of the USERSi directories otherwise. DIREC determines to what directory disk files will be written.
Function: DISP (expr1,expr2, ...)
is like DISPLAY but only the value of the arguments are displayed rather than equations. This is useful for complicated arguments which don't have names or where only the value of the argument is of interest and not the name.
Function: DISPCON (tensor1,tensor2,...)
displays the contraction properties of the tensori as were given to DEFCON. DISPCON(ALL) displays all the contraction properties which were defined.
Function: DISPLAY (expr1, expr2, ...)
displays equations whose left side is expri unevaluated, and whose right side is the value of the expression centered on the line. This function is useful in blocks and FOR statements in order to have intermediate results displayed. The arguments to DISPLAY are usually atoms, subscripted variables, or function calls. (see the DISP function)
```(C1) DISPLAY(B[1,2]);
2
B     = X - X
1, 2
(D1)                            DONE

```
Variable: DISPLAY2D
default: [TRUE] - if set to FALSE will cause the standard display to be a string (1-dimensional) form rather than a display (2-dimensional) form. This may be of benefit for users on printing consoles who would like to conserve paper.
Variable: DISPLAY_FORMAT_INTERNAL
default: [FALSE] - if set to TRUE will cause expressions to be displayed without being transformed in ways that hide the internal mathematical representation. The display then corresponds to what the INPART command returns rather than the PART command. Examples:
```User     PART       INPART
a-b;      A - B     A + (- 1) B
A            - 1
a/b;       -         A B
B
1/2
sqrt(x);   SQRT(X)    X
4 X        4
X*4/3;    ---        - X
3         3

```
Function: DISPTERMS (expr)
displays its argument in parts one below the other. That is, first the operator of 'expr' is displayed, then each term in a sum, or factor in a product, or part of a more general expression is displayed separately. This is useful if expr is too large to be otherwise displayed. For example if P1, P2, ... are very large expressions then the display program may run out of storage space in trying to display P1+P2+... all at once. However, DISPTERMS(P1+P2+...) will display P1, then below it P2, etc. When not using DISPTERMS, if an exponential expression is too wide to be displayed as A**B it will appear as EXPT(A,B) (or as NCEXPT(A,B) in the case of A^^B).
Variable: DSKALL
default: [] If TRUE will cause values, functions, arrays, and rules to be written periodically onto the disk in addition to labelled expressions. TRUE is the default value whereas if DSKALL is FALSE then only labelled expresions will be written.
Variable: ERROR_SIZE
default: [20 for a display terminal, 10 for others]. controls the size of error messages. For example, let U:(C^D^E+B+A)/(COS(X-1)+1); . U has an error size of 24. So if ERROR_SIZE has value < 24 then
```(C1) ERROR("The function", FOO,"doesn't like", U,"as input.");
prints as:
The function FOO doesn't like ERREXP1 as input.
If ERROR_SIZE>24 then as:
E
D
C   + B + A
The function FOO doesn't like -------------- as input.
COS(X - 1) + 1

```

Expressions larger than ERROR_SIZE are replaced by symbols, and the symbols are set to the expressions. The symbols are taken from the user-settable list

```ERROR_SYMS:[ERREXP1,ERREXP2,ERREXP3]
```

. The default value of this switch might change depending on user experience. If you find the defaults either too big or two small for your tastes, send mail to MACSYMA.

Variable: ERROR_SYMS
default: [ERREXP1,ERREXP2,ERREXP3] - In error messages, expressions larger than ERROR_SIZE are replaced by symbols, and the symbols are set to the expressions. The symbols are taken from the list ERROR_SYMS, and are initially ERREXP1, ERREXP2, ERREXP3, etc. After an error message is printed, e.g. "The function FOO doesn't like ERREXP1 as input.", the user can type ERREXP1; to see the expression. ERROR_SYMS may be set by the user to a different set of symbols, if desired.
Function: EXPT (A,B)
if an exponential expression is too wide to be displayed as A^B it will appear as EXPT(A,B) (or as NCEXPT(A,B) in the case of A^^B).
Variable: EXPTDISPFLAG
default: [TRUE] - if TRUE, MACSYMA displays expressions with negative exponents using quotients e.g., X**(-1) as 1/X.
Function: FASSAVE (args)
is similar to SAVE but produces a FASL file in which the sharing of subexpressions which are shared in core is preserved in the file created. Hence, expressions which have common subexpressions will consume less space when loaded back from a file created by FASSAVE rather than by SAVE. Files created with FASSAVE are reloaded using LOADFILE, just as files created with SAVE. FASSAVE returns a list of the form [<name of file>,<size of file in blocks>,...] where ... are the things saved. Warnings are printed out in the case of large files. FASSAVE may be used while a WRITEFILE is in progress.
Function: FILEDEFAULTS ()
returns the current default filename, in whatever format is used by the specific Macsyma implementation. (See DESCRIBE(FILE) for what that format is.) This is the file specification used by LOADFILE, BATCH, and a number of other file-accessing commands. FILEDEFAULTS('file) - sets the current filedefaults to "file". The argument to FILEDEFAULTS is evaulated as it is anticipated that the command will be used mainly in programs. The "file" need not be a real file, so one can use this function e.g. if one's real purpose is to set only the "device" field to something, where one does not care about the settings of the other fields.
Variable: FILENAME
default: [] - The value of this variable is the first name of the files which are generated by the automatic disk storage scheme. The default value is the first three characters of the user's login name concatenated with the lowest unused integer, e.g. ECR1.
Function: FILENAME_MERGE ("filename1","filename2",...)
; merges together filenames. What this means is that it returns "filename1" except that missing components come from the corresponding components of "filename2", and if they are missing there, then from "filename3".
Variable: FILENUM
default: [0] - The default second file name for files generated by SAVE, STRINGOUT, or FASSAVE if no file names are specified by the user. It is an integer, and is incremented by one each time a new file is written.
Variable: FILE_SEARCH
- this is a list of files naming directories to search by LOAD and a number of other functions. The default value of this is a list of the various SHARE directories used by Macsyma. FILE_SEARCH("filename"); searches on those directories and devices specified by the FILE_SEARCH variable, and returns the name of the first file it finds. This function is invoked by the LOAD function, which is why LOAD("FFT") finds and loads DSK:SHARE;FFT FASL. You may do FILE_SEARCH:CONS("devdir",FILE_SEARCH); to add other directories to the search rules, where "devdir" is a file naming only a device and a directory. In NIL Macsyma, for instance, if one had a directory for a personal library of Macsyma routines, "devdir" would be something like "USRD\$:[myname.MAXLIB]".
Variable: FILE_STRING_PRINT
default: [FALSE] on MC, [TRUE] elsewhere. If TRUE, filenames are output as strings; if FALSE, as lists. For example, the message when an out of core file is loaded into MACSYMA (e.g. the LIMIT package), appears on MC in list format as LIMIT FASL DSK MACSYM being loaded and in string format as: DSK:MACSYM;LIMIT FASL being loaded The string format is like the top level (DDT) file specifications.
Function: FILE_TYPE ("filename")
; returns FASL, LISP, or MACSYMA, depending on what kind of file it is. FASL means a compiled Lisp file, which normally has an extension of .VAS in NIL.
Function: GRIND (arg)
prints out arg in a more readable format than the STRING command. It returns a D-line as value. The GRIND switch, default: [FALSE], if TRUE will cause the STRING, STRINGOUT, and PLAYBACK commands to use "grind" mode instead of "string" mode. For PLAYBACK, "grind" mode can also be turned on (for processing input lines) by specifying GRIND as an option.
Variable: IBASE
default: [10] - the base for inputting numbers.
Variable: INCHAR
default: [C] - the alphabetic prefix of the names of expressions typed by the user.
Function: LDISP (expr1,expr2,...)
is like DISP but also generates intermediate labels.
Function: LDISPLAY (expr1,expr2,...)
is like DISPLAY but also generates intermediate labels.
Variable: LINECHAR
default: [E] - the alphabetic prefix of the names of intermediate displayed expressions.
Variable: LINEDISP
default: [TRUE] - Allows the use of line graphics in the drawing of equations on those systems which support them (e.g. the Lisp Machine). This can be disabled by setting LINEDISP to FALSE. It is automatically disabled during WRITEFILE.
Variable: LINEL
default: [] - the number of characters which are printed on a line. It is initially set by MACSYMA to the line length of the type of terminal being used (as far as is known) but may be reset at any time by the user. The user may have to reset it in DDT with :TCTYP as well.
```(C4) load("eigen");
MACSYMA BUG: Unknown file type NIL

Error: macsyma error
Error signalled by MEVAL1.
Broken at \$LOAD.  Type :H for Help.
MAXIMA>>:q

By examining the file system we find the file is actually in
/public/maxima/share/eigen.mc.   So we add that to the file_search
path.   This can be done at start up (see sys-init.lsp in the
system directory or, else it can be done and then the system resaved
once it has been customized for local directories and pathnames.
At lisp level we would do
(in-package "MAXIMA")
(setq \$file_search (\$append (list '(mlist)
"/tmp/foo.mac" "/tmp/foo.mc") \$file_search))
and at maxima level:

(C5) file_search:append(["/public/maxima/share/foo.mc"],
file_search)\$

batching /usr/public/maxima/share/eigen.mc
(D6) 		        #/public/maxima/share/eigen.mc
(C7) eigenvalues(matrix([a,b],[c,d]));
2		    2
- SQRT(D  - 2 A D + 4 B C + A ) + D + A
(D7) [[---------------------------------------,
2

2			   2
SQRT(D  - 2 A D + 4 B C + A ) + D + A
-------------------------------------], [1, 1]]
2
(C8)

```
loads a file as designated by its arguments. This function may be used to bring back quantities that were stored from a prior MACSYMA session by use of the SAVE or STORE functions. Specify the pathname as on your operating system. For unix this would be "/home/wfs/foo.mc" for example.
default: [TRUE] - governs the printing of messages accompanying loading of files. The following options are available: TRUE means always print the message; 'LOADFILE means print only when the LOADFILE command is used; 'AUTOLOAD means print only when a file is automatically loaded in (e.g. the integration file SIN FASL); FALSE means never print the loading message.
Function: NOSTRING (arg)
displays all input lines when playing back rather than STRINGing them. If arg is GRIND then the display will be in a more readable format. One may include any number of options as in PLAYBACK([5,10],20,TIME,SLOW).
Variable: OBASE
default: [10] the base for display of numbers.
Variable: OUTCHAR
default: [D] - the alphabetic prefix of the names of outputted expressions.
Variable: PACKAGEFILE
default:[FALSE] - Package designers who use SAVE, FASSAVE, or TRANSLATE to create packages (files) for others to use may want to set PACKAGEFILE:TRUE\$ to prevent information from being added to MACSYMA's information-lists (e.g. VALUES, FUNCTIONS) except where necessary when the file is loaded in. In this way, the contents of the package will not get in the user's way when he adds his own data. Note that this will not solve the problem of possible name conflicts. Also note that the flag simply affects what is output to the package file. Setting the flag to TRUE is also useful for creating MACSYMA init files.
Variable: PARSEWINDOW
default:[10] - the maximum number of "lexical tokens" that are printed out on each side of the error-point when a syntax (parsing) error occurs. This option is especially useful on slow terminals. Setting it to -1 causes the entire input string to be printed out when an error occurs.
Variable: PFEFORMAT
default: [FALSE] - if TRUE will cause rational numbers to display in a linear form and denominators which are integers to display as rational number multipliers.
Function: PRINT (exp1, exp2, ...)
evaluates and displays its arguments one after the other "on a line" starting at the leftmost position. If expi is unbound or is preceded by a single quote or is enclosed in "s then it is printed literally. For example, PRINT("THE VALUE OF X IS ",X). The value returned by PRINT is the value of its last argument. No intermediate lines are generated. (For "printing" files, see the PRINTFILE function.)
prints its arguments, then reads in and evaluates one expression. For example: A:READ("ENTER THE NUMBER OF VALUES").
prints its arguments, then reads in an expression (which in contrast to READ is not evaluated).
Function: REVEAL (exp,depth)
will display exp to the specified integer depth with the length of each part indicated. Sums will be displayed as Sum(n) and products as Product(n) where n is the number of subparts of the sum or product. Exponentials will be displayed as Expt.
```(C1) INTEGRATE(1/(X^3+2),X)\$
(C2) REVEAL(%,2);
(D2)                    Negterm + Quotient + Quotient
(C3) REVEAL(D1,3);
ATAN         LOG
(D3)                 - Quotient + ---------- + ----------
Product(2)   Product(2)

```
Variable: RMXCHAR
default: []] - The character used to display the (right) delimiter of a matrix (see also LMXCHAR).
Function: SAVE ([optional file spec],arg1, arg2,...,argi)
saves quantities described by its arguments on disk and keeps them in core also. The optional file spec is in the form NAME1,NAME2,DSK,DIRECTORY and is enclosed in square brackets, e.g. [JAMU,FUNCS,DSK,USERS2]. Do DESCRIBE(FILES) for more details on file specifications. If you omit the file spec, MACSYMA will select a file name for you consisting of the first three letters of your login name followed by a digit (the lowest digit which will give a unique file name). The second file name will be a number. The arg's are the expressions to be SAVEd. ALL is the simplest, but note that saving ALL will save the entire contents of your MACSYMA, which in the case of a large computation may result in a file which is too large to be reloaded. VALUES, FUNCTIONS, or any other items on the INFOLISTS (do DESCRIBE(INFOLISTS); for the list) may be SAVEd, as may functions and variables by name. C and D lines may also be saved, but it is better to give them explicit names, which may be done in the command line, e.g. SAVE(RES1=D15); Files saved with SAVE should be reloaded with LOADFILE. SAVE returns a list of the form [<name of file>,<size of file in blocks>,...] where ... are the things saved. Warnings are printed out in the case of large files, or if an empty file is accidently generated. It is possible to do a SAVE when a WRITEFILE is in progress.
Variable: SAVEDEF
default: [TRUE] - if TRUE will cause the MACSYMA version of a user function to remain when the function is TRANSLATEd. This permits the definition to be displayed by DISPFUN and allows the function to be edited. If SAVEDEF is FALSE, the names of translated functions are removed from the FUNCTIONS list.
Function: SHOW (exp)
will display exp with the indexed objects in it shown having covariant indices as subscripts,contravariant indices as superscripts. The derivative indices will be displayed as subscripts, separated from the covariant indices by a comma.
Function: SHOWRATVARS (exp)
returns a list of the RATVARS (CRE variables) of exp.
Variable: STARDISP
default: [FALSE] - if TRUE will cause multiplication to be displayed explicitly with an * between operands.
Function: STRING (expr)
converts expr to MACSYMA's linear notation (similar to FORTRAN's) just as if it had been typed in and puts expr into the buffer for possible editing (in which case expr is usually Ci) The STRING'ed expression should not be used in a computation.
Function: STRINGOUT (args)
will output an expression to a file in a linear format. Such files are then used by the BATCH or DEMO commands. STRINGOUT(file-specification, A1, A2, ...) outputs to a file given by file-specification ([filename1,filename2,DSK, directory]) the values given by A1,A2,.. in a MACSYMA readable format. The file-specification may be omitted, in which case the default values will be used. The Ai are usually C labels or may be INPUT meaning the value of all C labels. Another option is to make ai FUNCTIONS which will cause all of the user's function definitions to be strungout (i.e. all those retrieved by DISPFUN(ALL)). Likewise the ai may be VALUES, and all the variables to which the user has assigned values will be strungout. ai may also be a list [m,n] which means to stringout all labels in the range m through n inclusive. This function may be used to create a file of FORTRAN statements by doing some simple editing on the strungout expressions. If the GRIND switch is set to TRUE, then STRINGOUT will use GRIND format instead of STRING format. Note: a STRINGOUT may be done while a WRITEFILE is in progress.
Function: SYSTEM(command)
Execute COMMAND as a subprocess. The command will be passed to the default shell for execution. System is not supported by all operating systems, but generally exists in the unix environment. if hist is a list of frequencies which you wish to plot as a bar graph using xgraph.
```      with_stdout("_hist.out",
for i:1 thru length(hist) do (
print(i,hist[i]))),
system("xgraph -bar -brw .7 -nl < _hist.out")
```

In order to make the plot be done in the background (returning control to maxima) and remove the temporary file after it is done do:

```system("(xgraph -bar -brw .7 -nl < _hist.out;  rm -f _hist.out)&")
```
Variable: TTYOFF
default: [FALSE] - if TRUE stops printing output to the console.
macro: WITH_STDOUT(file,stmt1,stmt2,...)
Opens file and then evaluates stmt1, stmt2, .... Any printing to standard output goes to the file instead of the terminal. It always returns FALSE.
```
mygnuplot(f,var,range,number_ticks):=
block([numer:true],
with_stdout("/tmp/gnu",
for x:range[1] thru range[2] step
(range[2]-range[1])/number_ticks
do (print(x,at(f,var=x)))),
system("echo \"set data style lines; set title '",
f,"' ;plot '/tmp/gnu'
;pause 10 \" | gnuplot"));

(C8) with_stdout("/home/wfs/joe",
n:10,
for i:8 thru n
do(print("factorial(",i,") gives ",i!)));
(D8) 				     FALSE
(C9) system("cat /home/wfs/joe");
factorial( 8 ) gives  40320
factorial( 9 ) gives  362880
factorial( 10 ) gives  3628800
(D9) 				       0
```
Function: WRITEFILE (DSK, directory)
opens up a file for writing. On a Lisp Machine one uses WRITEFILE("filename"). All interaction between the user and MACSYMA is then recorded in this file, just as it is on the console. Such a file is a transcript of the session, and is not reloadable or batchable into MACSYMA again. (See also CLOSEFILE.)
PLAYBACK Input and Output