From 86b2d0e3951398e4c9d6c2374901e379be61514c Mon Sep 17 00:00:00 2001 From: Eric Swenson Date: Sun, 15 Jul 2018 20:35:38 -0700 Subject: [PATCH] Add some macsyma documentation. Resolves #927. --- doc/info/macsym.12 | 262 ++++++++++++++++++++++++++++++++++++++++++ doc/macdoc/new.manual | 12 ++ doc/macdoc/update.10 | 142 +++++++++++++++++++++++ doc/macdoc/update.11 | 153 ++++++++++++++++++++++++ 4 files changed, 569 insertions(+) create mode 100755 doc/info/macsym.12 create mode 100755 doc/macdoc/new.manual create mode 100755 doc/macdoc/update.10 create mode 100755 doc/macdoc/update.11 diff --git a/doc/info/macsym.12 b/doc/info/macsym.12 new file mode 100755 index 00000000..cf3c7a94 --- /dev/null +++ b/doc/info/macsym.12 @@ -0,0 +1,262 @@ +[-*-Text-*-] +This file gives introductory material about MACSYMA. +It replaces the full manual which is useless in this mode. + +File: MACSYM, Node: Top, Up: (DIR), Next: Manual, + +MACSYMA is a large symbolic algebraic manipulation program. It runs +only on the MC machine. It is invoked by :MACSYMA or :A (for short). + +* Menu: + +* Manual:: How to obtain published documentation for MACSYMA. +* Primer:: How to invoke the MACSYMA Primer. +* Syntax:: A brief introduction to MACSYMA syntax. +* Commands:: Some useful commands for on-line documentation. +* Demo:: How to run DEMO files. +* Save:: How to save your work. +* Helpme:: How to request help on-line with MACSYMA. +* Helpers:: People to communicate with for help. + +File: MACSYM, Node: Manual, Previous: Top, Next: Primer, Up: Top + +The current version of the MACSYMA Reference Manual is version 10, +January 1983. + +The MACSYMA Reference Manual may be ordered from: + + Publications + Laboratory for Computer Science + 545 Technology Square + Cambridge, MA 02139 + +It costs $22.50. Prepayment or Purchase Order preferred. Checks or +money orders should be made payable to MIT Laboratory for Computer +Science. + +The file MACDOC;UPDATE > contains updates to MACSYMA since the publication +of version 10. DESCRIBE(UPDATE); will list them briefly. + +File: MACSYM, Node: Primer, Next: Syntax, Up: Top, Previous: Manual + +You may start up an on-line tutorial for MACSYMA by typing + +:TEACHMACSYMA + +Or, if you have already started up a MACSYMA you may call the Primer +from inside it by giving the command + +PRIMER(); + + +File: MACSYM, Node: Syntax, Next: Commands, Up: Top, Previous: Primer, + +Input to MACSYMA is done with a syntax somewhat like that of Fortran +or Algol. All input lines are terminated with a semi-colon (;). + +Input lines are labeled consecutively starting with (C1), and then +(C2), (C3) etc. MACSYMA results are labeled from (D1) on. Thus (D1) is +the result of the computations performed by MACSYMA on the user's +input string (C1). These line numbers may be used to refer to +expressions. + 2 +For example: The expression X + 2 X + 1 + +would be typed in as: x^2+2*x+1; + +Commands to MACSYMA take their arguments inside parentheses, e.g. + +FACTOR(x^2+2*x+1); + +Commands may be typed in upper or lower case. The symbol % may be used +to refer to the last expression MACSYMA computed. E.g. + +(C1) (x+3)^5; + 5 +(D1) (X + 3) + +(C2) expand(%); + 5 4 3 2 +(D2) X + 15 X + 90 X + 270 X + 405 X + 243 + +The Mathematical operators used by MACSYMA are: + ! for Factorial, + ^ or ** for Exponentiation, + * for Multiplication, + . for non-commutative multiplication (spaces must go on either + side of the dot) + / for Division, + + for Addition, and + - for Subtraction. + +For more details see the SYNTAX section in the Primer. + + +File: MACSYM, Node: Commands, Next: Demo, Up: Top, Previous: Syntax, + +MACSYMA itself provides some on-line help. Here are some useful commands +to get you started: + +APROPOS(string); takes a character string as argument and looks at all + the MACSYMA names for ones with that string appearing anywhere within + them. Thus, APROPOS(EXP); will return a long list of all the flags + and functions which have EXP as part of their names, such as EXPAND, + EXP, EXPONENTIALIZE. Thus if you can only remember part of the name + of something you can use this command to find the rest of the name. + +DESCRIBE(cmd); prints out information about "cmd", which may be any + MACSYMA command, switch or variable. Certain key words have also been + included, where they seem appropriate, thus DESCRIBE(TRIG); will print + out a list of the trig functions implemented in MACSYMA. See also + APROPOS(string) which allows you to locate command names even if you + aren't sure of the full name. + +OPTIONS(); enters the OPTIONS interpreter which is a structured list + of MACSYMA commands. You type the number of the subject of interest, + followed by a ";" to see the list of commands available for that + subject. To move back up the list the command BACK; will go back up + one level, and TOP; will get you back to the original entry list. + EXIT; will quit out of OPTIONS. DESCRIBE may be called inside OPTIONS + on the commands listed, either by number or by name. + OPTIONS(command); will give the various commands and switches + associated with command. + +EXAMPLE(command); will start up a demonstration of how command works + on some expressions. After each command line it will pause and wait + for a space to be typed, as in the DEMO command (type N to see the + DEMO command). + + + +File: MACSYM, Node: Demo, Previous: Commands, Next: Save, Up: Top + +There are two commands which are useful for finding out how MACSYMA +works on specific types of problems: DEMO and BATCH. BATCH is also +useful in programming. These two are essentially the same command, +except that the DEMO command pauses after each set of command/display +lines and waits for the user to indicate readiness for the next pair +by typing a space. Typing anything besides a space will terminate the +demonstration. (Note: on noisy phone lines, the phone line may type a +"rubout" (^? on some terminals) which terminates the demo. In this +case use the BATCH command to run demonstration files.) + +DEMO(name1,name2,device,directory); starts up a demonstration. + +To obtain a list of some interesting demonstrations, do +LISTFILES(DEMO); which will list the "DEMO" directory. To use the +DEMO command on a file from this directory, for instance, "BEGIN +DEMO", you proceed as follows: On the list printed out by +LISTFILES(DEMO); you will see the line: + +[BEGIN, DEMO, DSK, DEMO] 5/2/81 L=335 chars. + +The four words inside the square brackets are what you place inside +the parentheses as arguments to the DEMO command, e.g. + +DEMO(BEGIN,DEMO,DSK,DEMO); + +The remaining information on the line is the creation date of the file and +its length. + +To run this demonstration using the BATCH command, you would type: + +BATCH(BEGIN,DEMO,DSK,DEMO); + + +File: MACSYM, Node: Save, Previous: Demo, Next: Helpme, Up: Top + +There are several ways to store a MACSYMA calculation or partial +results on disk to return to at a later date: + +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]. 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 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. + +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. + +LOADFILE(fn1, fn2, DSK, directory) 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. + +STORE(args) same as SAVE but doesn't retain quantities in core. + +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. + + +File: MACSYM, Node: Helpme, Next: Helpers, Up: Top, Previous: Save, + +In MACSYMA there are a number of commands which will allow you to +communicate with the Mathlab Group or other MACSYMA Users: + +SEND("message"); - will send your message to some MACSYMA + system programmer who is logged in at that + time. Note that message must begin and end + with double quotes. + +SEND(username,"message"); - sends the message to a specified user. + +Expressions may be included by referring to them, outside double +quotes, e.g. + +SEND("I am trying to integrate",D3,"but it runs out of core."); + +MAIL("message"); - will send mail to MACSYMA. This may be used + to report problems or bugs. + +MAIL(username,"message"); - will send mail to a specific user. + +Expressions may be included outside double quotes, as with SEND. + +BUG("message"); - similar to mail, sends a message to MACSYMA + Mail. This may be used for reporting bugs or + suspected bugs in MACSYMA. Expressions may be + included by referring to them, outside double + quotes as with SEND and MAIL. + + +File: MACSYM, Node: Helpers, Up: Top, Previous: Helpme, + +To get help with problems in MACSYMA or with the system, these people +are useful to communicate with: + +Login name Full name Phone # Room # +---------------------------------------------------------------- +JPG Golden, Jeffrey (617)253-5891 832 +ELLEN Golden, Ellen " " -5891 832 +RWK Kerns, Bob " " -5217 835 +KMP Pitman, Kent " " -7838 352 +GJC Carrette, George " " -5887 833 + +U. S. Mail Address: + + Laboratory for Computer Science + Room + 545 Technology Square + Cambridge, MA 02139 + + +The WHO(); command will print out a list of people currently logged in. + + \ No newline at end of file diff --git a/doc/macdoc/new.manual b/doc/macdoc/new.manual new file mode 100755 index 00000000..9167bb1e --- /dev/null +++ b/doc/macdoc/new.manual @@ -0,0 +1,12 @@ +Version 10 of the MACSYMA Manual is now available. It may be +ordered from + +Publications +MIT Laboratory for Computer Science +545 Technology Square +Cambridge, MA 02139 + +It costs $22.50 and prepayment or official purchase order is preferred. +Checks, money orders, or Purchase Orders should be made out to: + +MIT Laboratory for Computer Science diff --git a/doc/macdoc/update.10 b/doc/macdoc/update.10 new file mode 100755 index 00000000..7022801d --- /dev/null +++ b/doc/macdoc/update.10 @@ -0,0 +1,142 @@ +JPG@MIT-MC 05/10/85 14:26:34-EST To: INFO-MACSYM +If you are interested in using new code which handles the differentiation +of unknown functions in MACSYMA, please read MC:JPG;NDIFF USAGE . +Comments to JPG. + +JGA@MIT-MC 10/20/84 11:25 Re.: divided differences +To: INFO-MACSYM +I put a divided difference function in SHARE2;DIVDIF . + +RWG@SPA-NIMBUS 01/07/84 21:23 PST Re.: new Share USAGE files +SHARE1;SPANGL USAGE for simplifying trigfun(rational*%PI). +SHARE2;SQDNST USAGE for denesting SQRTs of surds. + +JPG@MIT-MC 12/17/83 11:44 To: INFO-MACSYM +An EULERPOLY(v,n) function has been written by ASB. +It generates the nth Euler polynomial in the variable v. + +ELLEN@MIT-MC 08/13/83 16:11 To: INFO-MACSYM Re.: Updates to MACSYMA +A new entry has been added to DESCRIBE. DESCRIBE(UPDATE); will print +out a summary of the changes to MACSYMA since the most recent version +of the Manual was printed. (In this case, since January 1983.) + +JPG@MIT-MC 06/17/83 03:59 EDT To: INFO-MACSYM +Macsyma 304 has just been created in the newly released Lisp 2138. + +LPH@MIT-MC 05/12/83 17:59 EDT To: INFO-MACSYM +A set of rules for performing simplifications on inequalities is +available in SHARE1;INEQ FASL, and DEMO and USAGE files are provided. +Send comments and bugs to LPH@MIT-MC. + +GCOOK@MIT-MC 05/03/83 19:50 To: INFO-MACSYM +[1] A new function for generating FORTRAN: +The file DSK:SHARE1;CFORTR FASL contains the function CRAY_FORTRAN and +some other related functions (see the description file). CRAY_FORTRAN +generates FORTRAN suitable for the CRAY compilers. +A demo is available in DSK:SHARE1;CFORTR DEMO. +The function is described in DSK:SHARE1;CFORTR USAGE. + +[2] A code sequence optimization function: +The file DSK:SHARE1;SEQOPT FASL contains the function SEQUENCE_OPTIMIZE, a +function which optimizes a MACSYMA expression or code sequence (list of +MACSYMA equations). It knows slightly more about optimization than OPTIMIZE. +A demo is available in DSK:SHARE1;SEQOPT DEMO. +The function is described in DSK:SHARE1;SEQOPT USAGE. + +[3] A function which replaces constant subexpressions with new constants: +The file DSK:SHARE1;RDUCON FASL contains the function REDUCE_CONSTS, a +function which replaces constant subexpressions by newly-generated constant +atoms, and maintains a list of definitions of those atoms. +A demo is available in DSK:SHARE1;RDUCON DEMO. +The function is described in DSK:SHARE1;RDUCON USAGE. + +[4] A new factoring function: +The file DSK:SHARE1;SCIFAC FASL contains the function GCFAC, a new +factoring function which is capable of doing some "scientific" factoring. +A demo is available in DSK:SHARE1;SCIFAC DEMO. +The function is described in DSK:SHARE1;SCIFAC USAGE. + +ASB@MIT-MC 01/27/83 12:26 EST To: INFO-MACSYM +SHARE1;ATRIG1 FASL contains several additional simplification rules for +inverse trig functions. +A brief description can be found in SHARE1;ATRIG1 USAGE. +LOAD(ATRIG1) to use the rules. + +ASB@MIT-MC 01/15/83 13:02-EST To: INFO-MACSYM +There is a new function RNCOMBINE which is similar to COMBINE, but +unlike COMBINE it collects terms whose denominators may differ by +numerical factors. A more complete description is in SHARE1;RNCOMB USAGE +and a demo in SHARE1;RNCOMB DEMO. + +LCM, a function that finds the Least Common Multiple of a set of +expressions, has been added to SHARE;FUNCTS >. A brief description is in +SHARE;FUNCTS USAGE, and a line for LCM has been added to SHARE;FUNCTS DEMO. + +JPG@MIT-MC 01/12/83 06:31-EST To: INFO-MACSYM +MACSYMA 303 has just been created. + +GJC@MIT-MC 05/06/80 1816-EDT To: INFO-MACSYMA-TRANSLATION +The 4 argument version of ROMBERG, e.g. +F(A):=(MODEDECLARE(A,FLOAT),ROMBERG(SIN(A*X)*(X^2-A*X+1),X,0,%PI)); +now compiles well, actually better than the three argument version. +In this example F(3.3) takes 2.1 seconds to calculate uncompiled +but only 0.022 seconds compiled. Using a separate function for +SIN(A*X)*(X^2-A*X+1), and compiling it, gives a timing of 0.032 seconds. +P.S. the 4 argument version of INTERPOLATE works also. + +GJC@MIT-MC 03/09/80 0612-EST To: INFO-MACSYM +There is a version of CFFK's famous INTERPOLATE function on the NUMER +directory. The changes are that it now takes a macsyma (untranslated) +function as a functional argument in the 3 argument case. And a call +to it can be used in compiled code without loss of variable scoping. +These changes will also be made soon to PLOT2 and ROMBERG. If any users +have always wanted to write a function that took arguments in the neat +way that these functions do I can show you the package I used to convert +INTERPOLATE. A demo, NUMER;INTPOL DEMO highlights these changes. + +GJC@MIT-MC 01/12/80 0035-EST To: INFO-MACSYM +NUMER;BATCH FASL has some functions in it that may be useful to users +who run MACSYMA while not being logged in. Such things as checking +the status of a disowned running macsyma without stopping it. +See the file NUMER;BATCH INFO. + +JPG@MIT-MC 08/07/79 0716-EDT To: INFO-MACSYM, SPECIAL-FUNCTIONS +To aid in the introduction of polylogarithms, etc., when DIFF(F[N](X),X); +is done and F has a GRADEF defined for it, then DIFF(F(N,X),X); is +attempted. As an example, a GRADEF for the Bessel function %J[N](X) +has been set up, so e.g. RATSIMP(DIFF(%J[2](X),X,2)); may be done. +(The fact that this is implemented in terms of DIFF(%J(N,X),X) is +somewhat hidden here.) (Compare with the example given in the manual on +p.72. (Please note that the "RATSIMP" used there should be in line (C5), +not (C4).)) At this time, setting up the GRADEF via GRADEF(F[N](X),...); +cannot be done. The syntax GRADEF(F(N,X),...); must be used. + +GJC@MIT-MC 08/05/79 2134-EDT To: INFO-MACSYM +See the "SUPER WINNING EXAMPLE" in the documentation for the macsyma +COMPILE command for turning expressions derived with macsyma into +floating point function definitions that you will then use in GRAPH2, +RUNGEKUTTA, ROMBERG, or whatever. + +GJC@MIT-MC 08/04/79 0147-EDT To: INFO-MACSYM +To see an example of fast numerical methods in macsyma, do +DEMO(RGKTEST,MAC,GJC); . It shows the usage of the compiler from macsyma, +and two ways of calculating (GRAPH2'ing) the solution of a differential +equation, formal and RUNGEKUTTA. + +GJC@MIT-MC 07/26/79 02:56:58 To: INFO-MACSYM +A program RUNGEKUTTA(F,X,Y,D) that is fairly winning +when used in conjunction with GRAPH2 (X,Y, and D are arrays), +resides as NUMER;RUNGE FASL. Documentation is in the file RUNGE USAGE . +(*** For updated note on RUNGE_KUTTA, see this file, note of 06/07/81. ***) + +GJC@MIT-MC 07/08/79 15:47:02 To: INFO-MACSYM +I have just added to the share2 directory functions that I have been +using for a while that are both fast and convenient when working with +declared floating point arrays and translated functions. There are +functions for tabulating and mapping over declared arrays, a Gaussian +quadrature formula, a simpson's rule for functions and one for arrays. +If you tend to use PLOT2 and ROMBERG on the same functions, then these +can save you a lot of time. Please see the file SHARE2;NUMRCL INFO if +you are interested. + + \ No newline at end of file diff --git a/doc/macdoc/update.11 b/doc/macdoc/update.11 new file mode 100755 index 00000000..62113d11 --- /dev/null +++ b/doc/macdoc/update.11 @@ -0,0 +1,153 @@ +NCS@MIT-MC.ARPA 06/26/85 14:58:24-EDT To: INFO-MACSYM +There are new additions to the EIGEN package. Try load(eigen); while in +MACSYMA. This was written by Nicholas Strauss (NCS@MC). +Further documentation in SHARE; EIGEN DEMO and SHARE; EIGEN USAGE. + +Abstract: One addition allows automatic finding of eigenvalues over +finite fields. Merely set MODULUS to desired integer and type +EIGENVALUES(MAT). Also, there is a command JORDANFORM which automatically +returns the jordanform matrix over Complex or Finite Field. These are not +intended for large matrices, nor zero-equivalent ambiguous matrices. + +JPG@MIT-MC 05/10/85 14:26:34-EST To: INFO-MACSYM +If you are interested in using new code which handles the differentiation +of unknown functions in MACSYMA, please read MC:JPG;NDIFF USAGE . +Comments to JPG. + +JGA@MIT-MC 10/20/84 11:25 Re.: divided differences +To: INFO-MACSYM +I put a divided difference function in SHARE2;DIVDIF . + +RWG@SPA-NIMBUS 01/07/84 21:23 PST Re.: new Share USAGE files +SHARE1;SPANGL USAGE for simplifying trigfun(rational*%PI). +SHARE2;SQDNST USAGE for denesting SQRTs of surds. + +JPG@MIT-MC 12/17/83 11:44 To: INFO-MACSYM +An EULERPOLY(v,n) function has been written by ASB. +It generates the nth Euler polynomial in the variable v. + +ELLEN@MIT-MC 08/13/83 16:11 To: INFO-MACSYM Re.: Updates to MACSYMA +A new entry has been added to DESCRIBE. DESCRIBE(UPDATE); will print +out a summary of the changes to MACSYMA since the most recent version +of the Manual was printed. (In this case, since January 1983.) + +JPG@MIT-MC 06/17/83 03:59 EDT To: INFO-MACSYM +Macsyma 304 has just been created in the newly released Lisp 2138. + +LPH@MIT-MC 05/12/83 17:59 EDT To: INFO-MACSYM +A set of rules for performing simplifications on inequalities is +available in SHARE1;INEQ FASL, and DEMO and USAGE files are provided. +Send comments and bugs to LPH@MIT-MC. + +GCOOK@MIT-MC 05/03/83 19:50 To: INFO-MACSYM +[1] A new function for generating FORTRAN: +The file DSK:SHARE1;CFORTR FASL contains the function CRAY_FORTRAN and +some other related functions (see the description file). CRAY_FORTRAN +generates FORTRAN suitable for the CRAY compilers. +A demo is available in DSK:SHARE1;CFORTR DEMO. +The function is described in DSK:SHARE1;CFORTR USAGE. + +[2] A code sequence optimization function: +The file DSK:SHARE1;SEQOPT FASL contains the function SEQUENCE_OPTIMIZE, a +function which optimizes a MACSYMA expression or code sequence (list of +MACSYMA equations). It knows slightly more about optimization than OPTIMIZE. +A demo is available in DSK:SHARE1;SEQOPT DEMO. +The function is described in DSK:SHARE1;SEQOPT USAGE. + +[3] A function which replaces constant subexpressions with new constants: +The file DSK:SHARE1;RDUCON FASL contains the function REDUCE_CONSTS, a +function which replaces constant subexpressions by newly-generated constant +atoms, and maintains a list of definitions of those atoms. +A demo is available in DSK:SHARE1;RDUCON DEMO. +The function is described in DSK:SHARE1;RDUCON USAGE. + +[4] A new factoring function: +The file DSK:SHARE1;SCIFAC FASL contains the function GCFAC, a new +factoring function which is capable of doing some "scientific" factoring. +A demo is available in DSK:SHARE1;SCIFAC DEMO. +The function is described in DSK:SHARE1;SCIFAC USAGE. + +ASB@MIT-MC 01/27/83 12:26 EST To: INFO-MACSYM +SHARE1;ATRIG1 FASL contains several additional simplification rules for +inverse trig functions. +A brief description can be found in SHARE1;ATRIG1 USAGE. +LOAD(ATRIG1) to use the rules. + +ASB@MIT-MC 01/15/83 13:02-EST To: INFO-MACSYM +There is a new function RNCOMBINE which is similar to COMBINE, but +unlike COMBINE it collects terms whose denominators may differ by +numerical factors. A more complete description is in SHARE1;RNCOMB USAGE +and a demo in SHARE1;RNCOMB DEMO. + +LCM, a function that finds the Least Common Multiple of a set of +expressions, has been added to SHARE;FUNCTS >. A brief description is in +SHARE;FUNCTS USAGE, and a line for LCM has been added to SHARE;FUNCTS DEMO. + +JPG@MIT-MC 01/12/83 06:31-EST To: INFO-MACSYM +MACSYMA 303 has just been created. + +GJC@MIT-MC 05/06/80 1816-EDT To: INFO-MACSYMA-TRANSLATION +The 4 argument version of ROMBERG, e.g. +F(A):=(MODEDECLARE(A,FLOAT),ROMBERG(SIN(A*X)*(X^2-A*X+1),X,0,%PI)); +now compiles well, actually better than the three argument version. +In this example F(3.3) takes 2.1 seconds to calculate uncompiled +but only 0.022 seconds compiled. Using a separate function for +SIN(A*X)*(X^2-A*X+1), and compiling it, gives a timing of 0.032 seconds. +P.S. the 4 argument version of INTERPOLATE works also. + +GJC@MIT-MC 03/09/80 0612-EST To: INFO-MACSYM +There is a version of CFFK's famous INTERPOLATE function on the NUMER +directory. The changes are that it now takes a macsyma (untranslated) +function as a functional argument in the 3 argument case. And a call +to it can be used in compiled code without loss of variable scoping. +These changes will also be made soon to PLOT2 and ROMBERG. If any users +have always wanted to write a function that took arguments in the neat +way that these functions do I can show you the package I used to convert +INTERPOLATE. A demo, NUMER;INTPOL DEMO highlights these changes. + +GJC@MIT-MC 01/12/80 0035-EST To: INFO-MACSYM +NUMER;BATCH FASL has some functions in it that may be useful to users +who run MACSYMA while not being logged in. Such things as checking +the status of a disowned running macsyma without stopping it. +See the file NUMER;BATCH INFO. + +JPG@MIT-MC 08/07/79 0716-EDT To: INFO-MACSYM, SPECIAL-FUNCTIONS +To aid in the introduction of polylogarithms, etc., when DIFF(F[N](X),X); +is done and F has a GRADEF defined for it, then DIFF(F(N,X),X); is +attempted. As an example, a GRADEF for the Bessel function %J[N](X) +has been set up, so e.g. RATSIMP(DIFF(%J[2](X),X,2)); may be done. +(The fact that this is implemented in terms of DIFF(%J(N,X),X) is +somewhat hidden here.) (Compare with the example given in the manual on +p.72. (Please note that the "RATSIMP" used there should be in line (C5), +not (C4).)) At this time, setting up the GRADEF via GRADEF(F[N](X),...); +cannot be done. The syntax GRADEF(F(N,X),...); must be used. + +GJC@MIT-MC 08/05/79 2134-EDT To: INFO-MACSYM +See the "SUPER WINNING EXAMPLE" in the documentation for the macsyma +COMPILE command for turning expressions derived with macsyma into +floating point function definitions that you will then use in GRAPH2, +RUNGEKUTTA, ROMBERG, or whatever. + +GJC@MIT-MC 08/04/79 0147-EDT To: INFO-MACSYM +To see an example of fast numerical methods in macsyma, do +DEMO(RGKTEST,MAC,GJC); . It shows the usage of the compiler from macsyma, +and two ways of calculating (GRAPH2'ing) the solution of a differential +equation, formal and RUNGEKUTTA. + +GJC@MIT-MC 07/26/79 02:56:58 To: INFO-MACSYM +A program RUNGEKUTTA(F,X,Y,D) that is fairly winning +when used in conjunction with GRAPH2 (X,Y, and D are arrays), +resides as NUMER;RUNGE FASL. Documentation is in the file RUNGE USAGE . +(*** For updated note on RUNGE_KUTTA, see this file, note of 06/07/81. ***) + +GJC@MIT-MC 07/08/79 15:47:02 To: INFO-MACSYM +I have just added to the share2 directory functions that I have been +using for a while that are both fast and convenient when working with +declared floating point arrays and translated functions. There are +functions for tabulating and mapping over declared arrays, a Gaussian +quadrature formula, a simpson's rule for functions and one for arrays. +If you tend to use PLOT2 and ROMBERG on the same functions, then these +can save you a lot of time. Please see the file SHARE2;NUMRCL INFO if +you are interested. + + \ No newline at end of file