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Maxima Manual

3.2 Definitions for Command Line

Function: ALIAS (newname1, oldname1, newname2, oldname2, ...)

provides an alternate name for a (user or system) function, variable, array, etc. Any even number of arguments may be used.

Function: DEBUG ()

LISPDEBUGMODE(); DEBUGPRINTMODE(); and DEBUG(); make available to the user debugging features used by systems programmers. These tools are powerful, and although some conventions are different from the usual macsyma level it is felt their use is very intuitive. [Some printout may be verbose for slow terminals, there are switches for controlling this.] These commands were designed for the user who must debug translated macsyma code, as such they are a boon. See MACDOC;TRDEBG USAGE for more information. For more help, consult GJC.

Variable: DEBUGMODE

default: [FALSE] - causes MACSYMA to enter a MACSYMA break loop whenever a MACSYMA error occurs if it is TRUE and to terminate that mode if it is FALSE. If it is set to ALL then the user may examine BACKTRACE for the list of functions currently entered.

Function: DEBUGPRINTMODE ()

LISPDEBUGMODE(); DEBUGPRINTMODE(); and DEBUG(); make available to the user debugging features used by systems programmers. These tools are powerful, and although some conventions are different from the usual macsyma level it is felt their use is very intuitive. [Some printout may be verbose for slow terminals, there are switches for controlling this.] These commands were designed for the user who must debug translated macsyma code, as such they are a boon. See MACDOC;TRDEBG USAGE for more information. For more help, consult GJC.

Function: EV (exp, arg1, ..., argn)

is one of MACSYMA's most powerful and versatile commands. It evaluates the expression exp in the environment specified by the argi. This is done in steps, as follows:

• (1) First the environment is set up by scanning the argi which may be as follows: SIMP causes exp to be simplified regardless of the setting of the switch SIMP which inhibits simplification if FALSE. NOEVAL supresses the evaluation phase of EV (see step (4) below). This is useful in conjunction with the other switches and in causing exp to be resimplified without being reevaluated. EXPAND causes expansion. EXPAND(m,n) causes expansion, setting the values of MAXPOSEX and MAXNEGEX to m and n respectively. DETOUT causes any matrix inverses computed in exp to have their determinant kept outside of the inverse rather than dividing through each element. DIFF causes all differentiations indicated in exp to be performed. DERIVLIST(var1,...,vark) causes only differentiations with respect to the indicated variables. FLOAT causes non-integral rational numbers to be converted to floating point. NUMER causes some mathematical functions (including exponentiation) with numerical arguments to be evaluated in floating point. It causes variables in exp which have been given numervals to be replaced by their values. It also sets the FLOAT switch on. PRED causes predicates (expressions which evaluate to TRUE or FALSE) to be evaluated. EVAL causes an extra post-evaluation of exp to occur. (See step (5) below.) E where E is an atom declared to be an EVFLAG causes E to be bound to TRUE during the evaluation of exp. V:expression (or alternately V=expression) causes V to be bound to the value of expression during the evaluation of exp. Note that if V is a MACSYMA option, then expression is used for its value during the evaluation of exp. If more than one argument to EV is of this type then the binding is done in parallel. If V is a non-atomic expression then a substitution rather than a binding is performed. E where E, a function name, has been declared to be an EVFUN causes E to be applied to exp. Any other function names (e.g. SUM) cause evaluation of occurrences of those names in exp as though they were verbs. In addition a function occurring in exp (say F(args)) may be defined locally for the purpose of this evaluation of exp by giving F(args):=body as an argument to EV. If an atom not mentioned above or a subscripted variable or subscripted expression was given as an argument, it is evaluated and if the result is an equation or assignment then the indicated binding or substitution is performed. If the result is a list then the members of the list are treated as if they were additional arguments given to EV. This permits a list of equations to be given (e.g. [X=1, Y=A**2] ) or a list of names of equations (e.g. [E1,E2] where E1 and E2 are equations) such as that returned by SOLVE. The argi of EV may be given in any order with the exception of substitution equations which are handled in sequence, left to right, and EVFUNS which are composed, e.g. EV(exp,RATSIMP,REALPART) is handled as REALPART(RATSIMP(exp)). The SIMP, NUMER, FLOAT, and PRED switches may also be set locally in a block, or globally at the "top level" in MACSYMA so that they will remain in effect until being reset. If exp is in CRE form then EV will return a result in CRE form provided the NUMER and FLOAT switches are not both TRUE.

• (2) During step (1), a list is made of the non-subscripted variables appearing on the left side of equations in the argi or in the value of some argi if the value is an equation. The variables (both subscripted variables which do not have associated array functions, and non-subscripted variables) in the expression exp are replaced by their global values, except for those appearing in this list. Usually, exp is just a label or % (as in (C2) below), so this step simply retrieves the expression named by the label, so that EV may work on it.

• (3) If any substitutions are indicated by the argi, they are carried out now.

• (4) The resulting expression is then re-evaluated (unless one of the argi was NOEVAL) and simplified according the the argi. Note that any function calls in exp will be carried out after the variables in it are evaluated and that EV(F(X)) thus may behave like F(EV(X)).

• (5) If one of the argi was EVAL, steps (3) and (4) are repeated.

Examples (C1) SIN(X)+COS(Y)+(W+1)**2+'DIFF(SIN(W),W); d 2 (D1) COS(Y) + SIN(X) + -- SIN(W) + (W + 1) dW (C2) EV(%,SIN,EXPAND,DIFF,X=2,Y=1); 2 (D2) COS(W) + W + 2 W + COS(1) + 1.90929742

An alternate top level syntax has been provided for EV, whereby one may just type in its arguments, without the EV(). That is, one may write simply

exp, arg1, ...,argn.

This is not permitted as part of another expression, i.e. in functions, blocks, etc.

(C4) X+Y,X:A+Y,Y:2; (D4) Y + A + 2 (Notice the parallel binding process) (C5) 2*X-3*Y=3$ (C6) -3*X+2*Y=-4$ (C7) SOLVE([D5,D6]); SOLUTION 1 (E7) Y = - - 5 6 (E8) X = - 5 (D8) [E7, E8] (C9) D6,D8; (D9) - 4 = - 4 (C10) X+1/X > GAMMA(1/2); 1 (D10) X + - > SQRT(%PI) X (C11) %,NUMER,X=1/2; (D11) 2.5 > 1.7724539 (C12) %,PRED; (D12) TRUE

Variable: EVFLAG

default: [] - the list of things known to the EV function. An item will be bound to TRUE during the execution of EV if it is mentioned in the call to EV, e.g. EV(%,numer);. Initial evflags are

FLOAT, PRED, SIMP, NUMER, DETOUT, EXPONENTIALIZE, DEMOIVRE, KEEPFLOAT, LISTARITH, TRIGEXPAND, SIMPSUM, ALGEBRAIC, RATALGDENOM, FACTORFLAG, %EMODE, LOGARC, LOGNUMER, RADEXPAND, RATSIMPEXPONS, RATMX, RATFAC, INFEVAL, %ENUMER, PROGRAMMODE, LOGNEGINT, LOGABS, LETRAT, HALFANGLES, EXPTISOLATE, ISOLATE_WRT_TIMES, SUMEXPAND, CAUCHYSUM, NUMER_PBRANCH, M1PBRANCH, DOTSCRULES, and LOGEXPAND.

Variable: EVFUN

- the list of functions known to the EV function which will get applied if their name is mentioned. Initial evfuns are FACTOR, TRIGEXPAND, TRIGREDUCE, BFLOAT, RATSIMP, RATEXPAND, RADCAN, LOGCONTRACT, RECTFORM, and POLARFORM.

special symbol: INFEVAL

leads to an "infinite evaluation" mode. EV repeatedly evaluates an expression until it stops changing. To prevent a variable, say X, from being evaluated away in this mode, simply include X='X as an argument to EV. Of course expressions such as EV(X,X=X+1,INFEVAL); will generate an infinite loop. CAVEAT EVALUATOR.

Function: KILL (arg1, arg2, ...)

eliminates its arguments from the MACSYMA system. If argi is a variable (including a single array element), function, or array, the designated item with all of its properties is removed from core. If argi=LABELS then all input, intermediate, and output lines to date (but not other named items) are eliminated. If argi=CLABELS then only input lines will be eliminated; if argi=ELABELS then only intermediate E-lines will be eliminated; if argi=DLABELS only the output lines will be eliminated. If argi is the name of any of the other information lists (the elements of the MACSYMA variable INFOLISTS), then every item in that class (and its properties) is KILLed and if argi=ALL then every item on every information list previously defined as well as LABELS is KILLed. If argi=a number (say n), then the last n lines (i.e. the lines with the last n line numbers) are deleted. If argi is of the form [m,n] then all lines with numbers between m and n inclusive are killed. Note that KILL(VALUES) or KILL(variable) will not free the storage occupied unless the labels which are pointing to the same expressions are also KILLed. Thus if a large expression was assigned to X on line C7 one should do KILL(D7) as well as KILL(X) to release the storage occupied. KILL(ALLBUT(name1,...,namek) will do a KILL(ALL) except it will not KILL the names specified. (Note: namei means a name such as U, V, F, G, not an infolist such as FUNCTIONS.) KILL removes all properties from the given argument thus KILL(VALUES) will kill all properties associated with every item on the VALUES list whereas the REMOVE set of functions (REMVALUE,REMFUNCTION,REMARRAY,REMRULE) remove a specific property. Also the latter print out a list of names or FALSE if the specific argument doesn't exist whereas KILL always has value "DONE" even if the named item doesn't exist. Note that killing expressions will not help the problem which occurs on MC indicated by "NO CORE - FASLOAD" which results when either too many FASL files have been loaded in or when allocation level has gotten too high. In either of these cases, no amount of killing will cause the size of these spaces to decrease. Killing expressions only causes some spaces to get emptied out but not made smaller.

Function: LABELS (char)

takes a char C, D, or E as arg and generates a list of all C-labels, D-labels, or E- labels, respectively. If you've generated many E- labels via SOLVE, then

FIRST(REST(LABELS(C)))

reminds you what the last C-label was. LABELS will take as arg any symbolic name, so if you have reset INCHAR, OUTCHAR, or LINECHAR, it will return the list of labels whose first character matches the first character of the arg you give to LABELS. The variable, LABELS, default: [], is a list of C, D, and E lines which are bound.

Variable: LASTTIME

- the time to compute the last expression in milliseconds presented as a list of "time" and "gctime".

Variable: LINENUM

- the line number of the last expression.

Variable: MYOPTIONS

default: [] - all options ever reset by the user (whether or not they get reset to their default value).

Variable: NOLABELS

default: [FALSE] - if TRUE then no labels will be bound except for E lines generated by the solve functions. This is most useful in the "BATCH" mode where it eliminates the need to do KILL(LABELS) in order to free up storage.

Variable: OPTIONSET

default: [FALSE] - if TRUE, MACSYMA will print out a message whenever a MACSYMA option is reset. This is useful if the user is doubtful of the spelling of some option and wants to make sure that the variable he assigned a value to was truly an option variable.

Function: PLAYBACK (arg)

"plays back" input and output lines. If arg=n (a number) the last n expressions (Ci, Di, and Ei count as 1 each) are "played-back", while if arg is omitted, all lines are. If arg=INPUT then only input lines are played back. If arg=[m,n] then all lines with numbers from m to n inclusive are played-back. If m=n then [m] is sufficient for arg. Arg=SLOW places PLAYBACK in a slow-mode similar to DEMO's (as opposed to the "fast" BATCH). This is useful in conjunction with SAVE or STRINGOUT when creating a secondary-storage file in order to pick out useful expressions. If arg=TIME then the computation times are displayed as well as the expressions. If arg=GCTIME or TOTALTIME, then a complete breakdown of computation times are displayed, as with SHOWTIME:ALL;. Arg=STRING strings-out (see STRING function) all input lines when playing back rather than displaying them. If ARG=GRIND "grind" mode can also be turned on (for processing input lines) (see GRIND). One may include any number of options as in PLAYBACK([5,10],20,TIME,SLOW).

Function: PRINTPROPS (a, i)

will display the property with the indicator i associated with the atom a. a may also be a list of atoms or the atom ALL in which case all of the atoms with the given property will be used. For example, PRINTPROPS([F,G],ATVALUE). PRINTPROPS is for properties that cannot otherwise be displayed, i.e. for ATVALUE, ATOMGRAD, GRADEF, and MATCHDECLARE.

Variable: PROMPT

default: [_] is the prompt symbol of the DEMO function, PLAYBACK(SLOW) mode, and (MACSYMA-BREAK).

Function: QUIT ()

kills the current MACSYMA but doesn't affect the user's other jobs; equivalent to exiting to DCL and stopping the MACSYMA process. One may "quit" to MACSYMA top-level by typing Control-C Control-G; Control-C gets NIL's interrupt prompt, at which one types either Control-G or just G. Typing X at the Interrupt prompt will cause a quit in a computation started within a MACSYMA-BREAK without disrupting the suspended main computation.

Function: REMFUNCTION (f1, f2, ...)

removes the user defined functions f1,f2,... from MACSYMA. If there is only one argument of ALL then all functions are removed.

Function: RESET ()

causes all MACSYMA options to be set to their default values. (Please note that this does not include features of terminals such as LINEL which can only be changed by assignment as they are not considered to be computational features of MACSYMA.)

Function: RESTORE (file-specification)

reinitializes all quantities filed away by a use of the SAVE or STORE functions, in a prior MACSYMA session, from the file given by file-specification without bringing them into core.

Variable: SHOWTIME

default: [FALSE] - if TRUE then the computation time will be printed automatically with each output expression. By setting SHOWTIME:ALL, in addition to the cpu time MACSYMA now also prints out (when not zero) the amount of time spent in garbage collection (gc) in the course of a computation. This time is of course included in the time printed out as "time=" . (It should be noted that since the "time=" time only includes computation time and not any intermediate display time or time it takes to load in out-of-core files, and since it is difficult to ascribe "responsibility" for gc's, the gctime printed will include all gctime incurred in the course of the computation and hence may in rare cases even be larger than "time=").

Function: SSTATUS (feature,package)

- meaning SET STATUS. It can be used to SSTATUS( FEATURE, HACK_PACKAGE) so that STATUS( FEATURE, HACK_PACKAGE) will then return TRUE. This can be useful for package writers, to keep track of what FEATURES they have loaded in.

Function: TOBREAK ()

causes the MACSYMA break which was left by typing TOPLEVEL; to be re-entered. If TOBREAK is given any argument whatsoever, then the break will be exited, which is equivalent to typing TOBREAK() immediately followed by EXIT;.

Function: TOPLEVEL ()

During a break one may type TOPLEVEL;. This will cause top-level MACSYMA to be entered recursively. Labels will now be bound as usual. Everything will be identical to the previous top-level state except that the computation which was interrupted is saved. The function TOBREAK() will cause the break which was left by typing TOPLEVEL; to be re-entered. If TOBREAK is given any argument whatsoever, then the break will be exited, which is equivalent to typing TOBREAK() immediately followed by EXIT;.

Function: TO_LISP ()

enters the LISP system under MACSYMA. This is useful on those systems where control-uparrow is not available for this function.

Variable: TTYINTFUN

default: [FALSE] - Governs the function which will be run whenever the User-interrupt-character is typed. To use this feature, one sets TTYINTFUN (default FALSE meaning feature not in use) to a function of no arguments. Then whenever (e.g.) ^U (control-U) is typed, this function is run. E.g. suppose you have a FOR statement loop which increments I, and you want an easy way of checking on the value of I while the FOR statement is running. You can do: TTYINTFUN:PRINTI$ PRINTI():=PRINT(I)$ , then whenever you type (e.g.) ^U you get the check you want.

Variable: TTYINTNUM

default: [21] (the ascii value of Control-U (^U), U being the 21st letter of the alphabet). This controls what character becomes the User-interrupt-character. ^U was chosen for it mnemonic value. Most users should not reset TTYINTNUM unless they are already using ^U for something else.

Variable: VALUES

default:[] - all bound atoms, i.e. user variables, not MACSYMA Options or Switches, (set up by : , :: , or functional binding).