  --AlgebraZ--  version 3.6 for the TI-83

 Author: Devin Gardner  -  2000.02.04
 Email:  Cepaughfe@aol.com

	--^<<* Best viewed full-screen in ti83pc font *>>^--


AlgebraZ requires six seperate programs which are in one .83g group file. 
-prgmALGEBRAZ	2427  bytes on calculator
-prgmZGCD	 197
-prgmZFNC	 446
-prgmZDFG	 206
-prgmZRAD	 179
-prgmZDSP	  46
	Total:	3501  bytes
Also included:
-prgmZRAD1 (42 bytes), was the original BASIC
	   version of ZRAD. It's slower but much more
	   convenient to use. It does exactly the same
	   thing.
-This documantation.
-Z80 assembly source code file for ZRAD.

  As far as I know, AlgebraZ and the other included BASIC programs work just fine with the TI-83plus as well as the original 83, _HOWEVER_ the Assembly version of ZRAD will _NOT_ work on the 83plus.
  I'm going to release a TI-83plus version of it shortly from now.

*To anyone who wants to make their own program using my subroutines; I have slightly bigger, but MUCH more powerful versions that I'm using for new programs. I only left some stuff off the programs included here because AlgebraZ doesn't need it.*


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			-<*_Instructions_*>-
=============================================================================

  There are almost no instructions within the program (to save memory, sice it's already a hefty program), so you'll have to look at this to learn how to use it.

  First off, the program will return information about 2 basic types of functions: Linear equations and Quadratic equations, based on what type of info you give it.
  If you give this program to another person, make sure you give them ALL the additional programs that go with it.  Most of all however, make sure you explain to them how to use it and what everything is, since it can be pretty hard to understand.
    *Note that if you enter something invalid, the program will display the
     five kinds of stuff you can put in, then quit.

  The entire program works from the single first text Input in ALGEBRAZ, which you put everything on: there are no menus or anything, making it very quick, easy, and simple to use.

-----------------------------------------------------------------------------
			 * Linear Equations *
-----------------------------------------------------------------------------
*There are 3 types of information you can enter for a Linear Equation:

  -The coordinates of 2 Points: When you enter the coordinates, simply type them in one after the other, each seperated by a comma. As long as there are 4 commas in what you entered, the program thinks it's 2 points.
	*NO parentheses or brackets.
 Example:
   X  Y  X   Y
   |   |  |     |
?=2.34,6,2/3,9.7617

  -Slope + Point; the Slope of a line and the coordinates of 1 Point it passes through: When you enter this, make sure the Slope is FIRST, then the X- and Y-coordinates of the point, each seperated by a comma as with 2 Points.
 Example:
    M   X  Y
    |   |   |
?=15/7,2.34,6

  -A Standard Equation: When you enter this make sure there is an 'X', a 'Y', and a '=' in what you typed in. Make sure the coefficients come BEFORE the X and Y, and, naturally, that they aren't 0 (you can't do that in a Standard Equation, anyway).
 Example:
   A     B     C
   |     |     |
?=3/2X-1.125Y=23

  After entering any of those 3 types of information, the program will first display what you typed in at the top of the screen. It does that for Quadratic Equations as well. Next it displays all of these:

  -If you typed in 2 points, it displays the Distance in both simplified
 	radical form and regular decimal form, i.e."DIST=310 , 9.486833", or
 	if it can't do that, just in decimal form. After that it displays
	everything entering Slope+Point or a Standard Equ. would:

  -It displays the Standard Equation of the line, with X and Y coefficients
 	always made as integers; but the constant can be fractional. If you
 	entered a Standard Equ. with fractional X or Y coefficients the new
 	equation it displays is the "correct" one (and yes, it is equal to
 	the one you put in).
  -Then the Slope-Intercept form of the equation (which gives you both the
 	Slope and the coordinates of the Y-Intercept).
  -Then the coordinates of the X-Intercept as a fraction, since they're
 	always so tedious to figure out on paper.
  -Finally the new Slope-Intercept Equation is stored to Y, but left
 	"turned-off" (much more on this near the end of the document). If you
 	have anything important in Y, copy it to another function before
 	using this program.

-----------------------------------------------------------------------------
			* Quadratic Equations *
-----------------------------------------------------------------------------
*There are 2 types of information you can enter for a Quadratic Equation:

  -A Quadratic Equatoin: simply enter the Quadratic equation exactly as is (but always in Standard AX+BX+C form, and make sure the coefficients come BEFORE the variables).  As long as you type in an "X", it will think you're giving it a Quadratic Equation for a vertical-axis Parabola.  (Maybe also Hyperbolas next time...)
 Examples:
   A    B  C
   |    |  |
?=21X-59X+8			 -All of these are valid-
      A         B	C=0
      |         |
?=2.35/7X+1234/.13X
   A   C		B=0
   |   |
?=4X+16
    A			B=0, C=0
    |
?=.0379X

  -Vertex + Focus: the coordinates of the parabola's Vertex and Focus. Enter these just like you would enter two points. In fact, the only way the program can tell you're giving it Vertex+Focus and not the coordinates of a line is that the two X-Coordinates are always the same.
 Examples:
   X      Y     X  Y  
   |      |     |  |
?=.23,3.5/6.3,.23,0
  \          / \   /
     Vertex    Focus

  -After you enter something the program will first re-display your
	equation into simplified fractions and re-store the new version
	to Y. If your input was an equation with only integer coefficients,
	it will simply leave what you typed in at the top to speed things up.

  -Next it will factor the polynomial out completely into integer
 	binomials if it can, otherwise it will display "PRIME". Since
 	the first example can be factored, the program would display
 	"(3X-8)(7X-1)" for it.  The third example could also be
 	factored, and would return "(2X+4)(2X-4)".

  -Next it will display the "Standard Translated Conic Equation Of Parabola"
	in the form (X-H)=4(p)(Y-K). This little equation gives you a ton of
 	information you may or may not need, so pay attention:  The
 	coordinates of the Vertex of the parabola are (H,K).
	  "H", the X-coordinate, is with the "X-". "K", the Y-coordinate, is
 	with the "Y-". If nothing is with the X or Y (i.e. "(X)=..."), the
 	X- or Y-coordinate is 0. In "(X+3/4)=4(1/3)(Y-5)", the Vertex is
 	(3/4,5), get it? Be careful with those "+" and "-" signs or you
 	might copy a vertex onto your math paper with the wrong signs.
	  "P" is the distance between the Y-coordinates of the Vertex
 	and the Focus (they both lie on the 'Axis of Symmetry,' line which is
 	"X=the X-coordinate of the Vertex", so they both have the same
 	X-coordinate). If you don't know what a Focus is, ignore the next
 	numbers the program displays.
  -The fractions that are displayed next have the title, "Y=K+-P=", which is:
 	"Y (coordinates) equals K plus-or-minus P". The first number is the
 	actual Y-coordinate of the Focus, which IS P+K from the above
 	equation. The second number after the comma is the Y-value of the
 	Directix, a horizontal line with the equation "Y=K-P", which IS the
 	number it just gave you. Every point on the parabola is the same
 	distance from the Focus as it is from a vertical line to the Directix
 	line if you didn't know that.
  -Finally (and most importantly) it displays X-value of the Roots
 	(X-Intercepts) algebraicly in the form "X=(B+-(B-4AC))/(2A)" with a
 	fraction bar, plus-or-minus sign, or a "" sign if necessary. It will
 	also use an imaginary "" if it needs to, i.e. "491". Please note
 	that any Discriminants over 16 (1,000,000) are left as radicals and
 	not simplified UNLESS they are perfect-square-roots.
 -The original Discriminant is stored to the variable 'C' and the actual
 	Roots to 'A' and 'B', so you can call them up easily in [TRACE] mode
 	(if the Roots are imaginary or complex, though, it won't let you
 	input them on the Graph Screen). The Quadratic Equation you entered
 	is also stored to Y.

   The Quadratic section of the program might give you a slight problem with extremely large or small numbers, or really anything with a lot of digits in it, so be careful or the calculator will round things up for you with an "" exponent, or even clip numbers off the screen.
   This is especially true for the Roots and the "Conic Parabola" Equation, which has to fit 3 numbers which can be up to 9 digits long, AND all the equation-text all on one line.

-----------------------------------------------------------------------------
	     * To get the Axes back after the program runs *
-----------------------------------------------------------------------------

  When you use this program, the final equation of whatever you entered is stored to Y, and all other 'Y='functions are turned off (but not erased). Also, the Axes are turned off, and all the information displayed on the Graph Screen is stored to Pic9 (Picture 9). The Window settings are not changed.
  To graph the line after everything has been displayed, go to the [Y=] screen, "turn on" Y (press enter with the cursor on Y's "=" sign to highlight it), then press [GRAPH] or [TRACE].
  To get the Axes back, go to [FORMAT], select "AxesOn", and press [GRAPH].  Doing this will also clear everything AlgebraZ displayed; to get it all back while the graph and Axes still drawn, go to the [DRAW] menu, select "RecallPic ", press [9], then hit enter.

=============================================================================
*Note:

  AlgebraZ can't take any numbers greater than or equal to 111 in almost any part of the program, and because of the heavy multiplication it does, the calculator may give you "ERR:DOMAIN" for much smaller numbers, since certain commands just won't take numbers with really big (or really small) exponents.
  If you're doing a very large equation, or one where you only require a big decimal number for an answer, check the answers it gives you on the home screen to be sure, or just use another, simpler program.  But for general homework or tests in Algebra 1 or 2, or Geometry, this is by far the best program you could possibly find (as of the time I wrote this, at least).

***  One other thing; do NOT edit this program to be compatible with AShell, SOS, or ION.  If you run the program from a shell, your calculator will crash and freeze.
