DOCUMENTATION for CALCULUS DEMON (aka SYMBOLIX)
by Joseph K. Horn, 1042 Star Rt., Orange CA 92667, (714) 858-0222


"CALCULUS DEMON" is a BASIC program written by The Soft Warehouse (Honolulu HI)
for the Atari home computer.  The version presented here is called SYMBOLIX,
and was rewritten for the HP-71 by Joseph K. Horn from the Atari original.  It
is copyrighted by The Soft Warehouse.  It is to be used as is, and not modified
for use for other applications.  To insure this, SYMBOLIX is distributed only on
magnetic media in PRIVATE form.  Even if a clever user manages to remove the
PRIVATE status, the program still cannot be listed, because its line numbers
have been removed.  Any attempt to modify the program will result in immediate
decompiling of the GOTO's and GOSUB's, rendering the program inoperative. ***

SYMBOLIX is 20K long, so it requires at least one 32K RAM module.  It will not
run on a bare 16K HP-71.  The program also uses up to 8K of RAM for scratch.
It does not require any other files to run, but is ideally suited for use with
the HPIL ROM and a video interface (or printer, in DISPLAY IS PRINTER mode).


INSTRUCTIONS:

(1)  Copy SYMBOLIX into memory.  RUN SYMBOLIX.  It takes a moment to warm up.

(2)  The ":" prompt appears.  This is where you type in a line of symbolic math,
     and press ENDLINE.  After some time (up to a few minutes), the result will
     be displayed, followed by a new ":" prompt.  (If no printer or video is
     available, you can prevent the result from vanishing by setting DELAY 9).

(3)  To exit, press ENDLINE without any input.

(4)  After the ":" prompt, enter an expression using digits, decimal points,
     parentheses, and 1-letter variables together with operators +, -, /, *, and
     ^.  Since implied multiplication is allowed, you may omit all *'s.  Follow-
     ing each such input, an equivalent expression is displayed, derived by
     reordering, collecting like terms, and other mild transformations.  Note:
     X^2Y^2 means (X^2)(Y^2); X^YZ means (X^Y)*Z.  Spaces are ignored.  As
     examples, try these:

     3x^2y+5(xyx-7)     (note: y=Y; you may use lowercase if you wish)
     (a^2*b)^.5/a

(5)  Type < to turn on expansion of positive integer powers of sums and full
     distribution of numerator or denominator factors over numerator sums.  Type
     > to turn off these transformations.  For example, try these:

     < (x+y)(x-y)    note: "<" mode remains on until you turn it off with a ">".
     (x+y)/(x-y)+5
     >
     (x+y)/(x-y)+5     (just press up-arrow once; it's in the stack)

(6)  Expressions can include the six trig functions SIN, COS, TAN, COT, SEC, and
     CSC, and the inverses of the first three, ASN, ACS, and ATN.  Expressions
     can also contain the natural log and exponential functions, spelled LOG and
     EXP.  Parentheses can be omitted from around arguments that are constants,
     variables, functional forms, or the negatives of these.  Automatic trans-
     formations exploit symmetry, inversion, logs of powers, and numeric
     arguments.  As examples, try:

     > COS -x
     EXP LOG x     (same as EXPLOGx)
     LOG(x^2)
     4ATN1

(7)  When ALGEBRAIC expansion is turned on via <, logs of products or quotients
     are rephrased as sums or differences of logs, and other trig functions are
     replaced by sines and cosines.  Typing [ turns on HARMONIC expansion, which
     transforms positive integer powers and products of sines and cosines into
     'linear combinations' of sines and cosines of multiple angles and angle
     sums or differences.  Typing ] turns off harmonic expansion.  Try these:

     < LOG(xy/z)
     TANxCSCx
     [ SINxCOSy
     SINx^2+COSx^2 ]>

(8)  An entry of the form "variable = expression" causes the resulting value of
     the expression to be ASSIGNED to the variable for use in subsequent
     expressions.  For example, try:

     p=5(x+y+z)
     p+1/p+xLOGp

(9)  Follow an assignment with a ";" to suppress display of an assigned value.
     Try this:

     p=s+1;
     p^3

(10) Several assignments can precede an expression in a single entry, as long as
     they are separated by semicolons.  For example, try:

     p=r+1; q=l+p; q^2

(11) To prevent a variable from contributing its value to an expression, precede
     it by an apostrophe.  This provides a way of clearing a variable.  Try:

     p=L+5; p^2
     p='p; p^2

(12) If we enter the line "h='h; p=h+1; h=2; p^2" then H becomes 2 after P
     becomes H+1, so the displayed result is (H+1)^2 rather than 9.  However, we
     can follow the expression P^2 with the operator "@" to RE-EVALUATE it so
     that the H in it is updated to its new value 2.  "@" has the same order-of-
     operations precedence as addition.  Try it:

     h='h; p=h+1; h=2; p^2 @

(13) To determine the partial DERIVATIVE of an expression with respect to a
     variable, enter an expression of the form "expression % variable".  "%" is
     used to suggest a ratio of infinitesimals.  "%" has the same order-of-
     operations precedence as addition.  As examples, try these:

     x='x; a='a; ax^3+SINx % x
     a^2x^3%x%a

(14) To determine an antiderivative of an expression with respect to a variable,
     enter an expression of the form "expression $ variable".  "$" is used to
     suggest an INTEGRAL sign.  "$" has the same order-of-operations precedence
     as addition.  Avoid expansion of integrands, which may mask a known
     integrable pattern, because algebraic then harmonic expansion are tried
     automatically if the given form can't be integrated directly.  Try these:

     x='x; a='a; 3ax^2+COSx $ x
     COSLOGx/x$x

(15) If the expression contains a syntax error, an appropriate error message
     will point it out.  The ^ that points to the error will only be useful when
     a video or printer is in use via HP-IL.

*** Note: Due to an HP-71 bug discovered while running the "unlistable" version
of SYMBOLIX in RADIANS mode, the program is now available in totally unprotected
form (with proper line numbers, lines no longer than 96 characters each, etc.).
It is therefore easy to modify for custom input/output, or whatever.  Although
SYMBOLIX is now listable, it is NOT "public domain."  Give copies to all your
friends, but don't sell it, and be sure the first two lines (the copyright
notices) remain intact.                                                     -jkh