			      GraphIt! OPERATORS
	Operator/Function   Meaning
	═════════════════   ═════════════════════════════════════════════
	+, -, *, /	    add, subtract, multiply, divide
	^		    exponentiation
	{[( )]}		    parentheses: may be nested to any extent,
			    braces and brackets are provided for ease of
			    reading but the parser will NOT differentiate
			    between "{" and "(" and "[".

	abs		    absolute value
	acos, asin, atan    arc cosine, arc sine, and arc tangent
	cos, cosh	    cosine and hyperbolic cosine
	exp		    Euler's number to the specified power
	int		    greatest integer ([x] is not supported)
	ln, log		    natural logarithm, logarithm base 10  ┌─────────┐
	sin, sinh	    sine, hyperbolic sine		  │PgDn for │
	sqr		    square root				  │more help│
	tan, tanh	    tangent, hyperbolic tangent		  └─────────┘
     ---> NOTE that all trig functions work in RADIANS, not degrees. <---

      Besides the variables x and y, 2 other "variables" (pi [3.14159...] and
    e [Euler's number: 2.718...]) are legal identifiers for your convenience.
			       CALLING FUNCTIONS
    The  parser's  ability  to determine exactly what you want to pass  as  an
argument  to a function is somewhat limited,  so I suggest you make it a habit
to enclose the desired expression in parentheses.  "cos x"  may work fine  but
"cos 2x"  is interpreted as "(cos 2)*x"  and "cos x^2"  turns out "(cos x)^2".
Typing "cos (2x)" or "cos (x^2)" instead works perfectly.
      The order of operations is the standard algebraic left to right of:
				   Functions
				  Parentheses
				   Exponents
			  Multiplication and division
			   Addition and subtraction

    GraphIt! supports implied multiplication of  variables and constants as in
"3x" or "5(2x+3)", but not of variables  and other alphabetic identifiers such
as functions  and built-in  transcendental  numbers like "xx",  "xcos(x)",  or
"xpi",  so  you must  include the times  sign in those cases.  (Implied multi-
plication of the  two variables x and  y [i.e. "xy=1"] IS supported, however.)
The  parser may reject some  complex expressions for no apparent  reason. Keep
trying!  I suggest  liberal use  of parentheses:  if you are  not sure whether
something will  be interpreted correctly,  go back and put  parentheses around
it. (One exception: do NOT enclose the entire expression on either side of the
equals sign in parentheses.)                         Press PgDn for more help.
			     GRAPHING THE EQUATION

    To interrupt a graph  when the computer is  in the process  of drawing it,
hit any  key and the  program  will display on the  bottom  line the  message:
"PAUSE at x=#, y=#. Press ESC to quit, any other key to restart...",  where  #
indicates  the x and y  coordinates  you  stopped it at.  If you  mistyped the
equation and want to fix it, just press ESC.
    Be patient!  GraphIt! may  need  a while to produce  a quality  graph on a
slower machine.  To speed up the  graphing,  you may  want to  select a  lower
Fineness value.


			       THE GRAPHING LOOP

    When the graph for your equation is complete,  you will again be given the
"Graph?" prompt  at the bottom of the screen.  If you'd like to start all over
with a  completely  different  equation,  press ESC  and the input  field will
clear.  If you'd rather modify the last equation, go right ahead; it's already
stored safe  and sound in the redraw queue  (for more  information see Section
III: Using AutoRedraw  and the Redraw Queue).  To exit the  otherwise infinite
graphing loop, press enter or escape on a blank line (escape twice will always
work).
					Press PgDn for help on error messages.
				ERROR MESSAGES

    Eleven error  messages may be  encountered when  graphing  (apart from the
messages ingrained in  the library functions which I cannot control).  Five of
them are fatal; the equation cannot be graphed and you must edit it. They will
cause the computer to beep so you know there is a problem. The other six apply
only to specific  point(s) for which a y-value cannot be generated.  They will
not appear  unless you  ask for  them using the  Warnings option and then they
appear silently. 

"Found bad operation or mismatched parentheses. Press any key to retype..."
    You  either  left  out a paren somewhere,  left out one  or  both  of  the
    operands for a binary operation or the argument for a function,  or  typed
    some other weird thing the  parser and evaluator couldn't digest.  Examine
    your equation carefully and fix whatever seems to be the problem.

"Found unknown identifier. Press any key to retype equation."
    Unfortunately, the evaluator isn't set up to return what caused the error,
    so you'll have to look for it yourself.  Check that your equation contains
    only valid identifiers  (x, y, pi, e, and the functions listed above)  and
    that you separated  each  of them with an operator, space,  or  some other
    punctuation.
					   Press PgDn for more error messages.
			   ERROR MESSAGES continued

"No equals sign or more than one found. Press any key to edit equation."
    To be a valid and graphable, your equation must include exactly one equals
    sign ['=']. If you get this error, you either left out the '=' or
    accidentally typed two or more of them.

"No 'y' variable or more than one found. Press any key to edit equation."
    Although GraphIt! has been enhanced to isolate ONE 'y' variable and graph
    some relations, it cannot graph an equation without a 'y', like "x=4". It
    also cannot perform the factoring needed to isolate the variable 'y' when
    it occurs more than once (i.e. "x=y^2+3y"). If you can adjust the equation
    so it uses only one 'y', do so; otherwise it can't be graphed.

"Can't find the inverse of this function of y. Press a key to edit equation."
    You tried to graph an equation like "int(y)=x" or "abs(y)=x" for which y
    cannot be isolated by taking the inverse of the function. The functions
    which cannot be isolated are "abs", "cosh", "sinh", "tanh", and "int". If
    you can't adjust the equation so this error does not occur, it is not
    graphable.


					   Press PgDn for more error messages.
			    WARNING ERROR MESSAGES
"Overflow at x=#.##." 
    Some  function or operation generated a number too large to fit into a  8-
    byte floating point variable. The point at x=#.##  was not graphed.

"Division by zero at x=#.##."
    At #.## your equation attempted division by zero so the point was skipped.

"Can't raise a negative number to a fractional power. [x=#.##]"
    Due to the possibility of getting an even root of a negative number, the C
    Library pow()  function  refuses to process any arguments like these.  The
    portion of your graph (if any) where the base is not negative or the power
    is not fractional should be graphed perfectly. This error also occurs when
    you take the square root of a negative number with the "sqr" function.

"Can't find the logarithm of a negative number. [x=#.##]"
    The natural logarithm (ln) and base 10 logarithm (log) functions are
    defined only on x greater than zero.

"Domain error: asin/acos functions defined only on -1≤x≤1. [x=#.##]"
    The arcsine (asin) and arc cosine (acos) functions are only defined
    between -1 and 1 (the range of the sin and cos functions).
──────────────End of Graphing help. Press ESC to return to menu.──────────────
