Inequality Solver v. 4.2.1

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Program: isolve.89z (.9xz) (.v2z)
Author : Michael Pierce
E-mail : mikee385@yahoo.com


While the solve function on the TI-89, TI-89 Titanium, TI-92+, and Voyage 200 can only solve 
relatively simple inequality equations and partially simplify more complex ones, this 
function can solve most single variable equations, including polynomials and multiple 
equations.  It is not limited to linear inequalities, and answers can be returned in either 
symbolic or approximate form. The answer will be output in a way similar to the answers 
returned by the solve function.

Requires:
-TI-89, TI-89 Titanium, TI-92+, or Voyage 200
-AMS 2.04 or above
In order to use this function as part of an expression (such as isolve(x>3,x)->varname or
isolve(sin(x)>0,x)|x<10 and x>-2) or use it in a TI-Basic program or function, you must 
install either IPR by Cyril Pascal (http://sirryl.multimania.com) or a shell such as
DoorsOS, Universal OS, PreOS, or KerNO since AMS 2.xx and AMS 3.xx forbid the use of ASM 
programs in expressions.  If you are using IPR, you'll first need to install Kevin
Kofler's HW3Patch (http://www.tigen.org/kevin.kofler/ti89prog/) before installing IPR, 
and if you're using a TI-89 Titanium, you'll also need to run IPR through GhostBuster by
Olivier Armand and Kevin Kofler (http://www.tigen.org/kevin.kofler/ti89prog/) before
installing it in order to ensure that the calculator doesn't crash when you try to use 
isolve as part of an expression.

For certain trig functions, some operating system versions will not return all of the 
correct answers (particularly equations that use a combination of trignometric and 
algebraic expressions, such as 2*(1-cos(2x))>3*sin(2x)).  Since this is a bug in the 
operating system, there is nothing I can do to fix it.  Also, AMS 2.08 and 2.09 cannot 
correctly simplify expressions with the combination of inequalities and fractional
exponents (or square roots).  In these instances, the result will be returned unsimplified
to ensure accuracy.

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ZIP Contents:

isolve.89z - function for TI-89 or TI-89 Titanium
isolve.9xz - function for TI-92+
isolve.v2z - function for Voyage 200

isolve README.txt - this file
Version History.txt - history of the changes and improvements made to this program

src/isolve.c - Source code for this program
	Included for informational purposes, check license at the bottom of this README

ti-basic/isolve.89f (.9xf) (.v2f) - Original version of this program written in TI-Basic
	Included for informational and historic purposes 

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Syntax:

isolve([equation],[variable])
or
isolve([equation],[variable],[lower bound],[upper bound])
or
isolve([equation],[variable])|[constraint expression]

	-[equation] can be most single variable equations and any form of the equation can 
		be solved.  It must contain the variable specified, and can only contain one 
		undefined variable (specified by [variable]).

		Ex: isolve(3x-2>0,x) will return x>2/3
		    isolve(y^2+2<3y,y) will return y<2 and y>1

		Multiple equations can also be solved.  Simply enter the equations joined by
 		an "and or an "or", depending on what you want to solve for. Every equation
		must contain the variable specified.

		Ex: isolve(0<z-3 and z-3<5,z) will return z<8 and z>3
		    isolve(x^2>4 and x^2<9 or x+3<-3,x) will return 
			x<3 and x>2 or x<-2 and x>-3 or x<-6

		CAUTION: 
		AMS 2.08 and 2.09 have some problems with simplifying certain expressions 
		(specifically those with square roots or fractional exponents) and may 
		return incorrect values.  To avoid this, this function displays the solution
		unsimplified if the calculator cannot simplify it correctly.  If you attempt
		to use this expression elsewhere, it will most likely not transfer correctly.
		Alternatively, you can approximate the results by pressing [diamond]+[Enter]
		or by having the calculator in approximate mode.

		NOTE ABOUT TRIG FUNCTIONS: 
		To eliminate answers with @n (which are awkwardly handled in inequalities on 
		AMS 2.xx), all solving with trig functions will be limited so that the 
		variable is within the range of [0,2*pi] if the calculator is in radians or 
		[0,360] if it's in degrees. This can be overridden by passing an upper and 
		lower bound to the function or by specifying an appropriate constraint 
		expression.

	
	-[variable] can be any single variable as long as it fits the TI restrictions
		for variable names and is found in every expression in [equation].

	-[lower bound] and [upper bound] are optional arguments used to specify a range for
		the answers.  This is primarily used if the variable being solved lies 
		inside of a trig function, such as isolve(sin(x)>0,x,0,720°) which finds the
		ranges between 0 and 720 degrees where the sin is greater than zero.  The
		bounds are considered to be inclusive, e.g. isolve(sin(x)>0,x,0,720°)
		translates into isolve(sin(x)>0,x)|x<=720° and x>=0.

	-[constraint expression] is an optional argument used to specify a range for the 
		answers, but allows more freedom than [upper bound] and [lower bound] can
		provide.  For example, you could use a one-sided bound such as:
		isolve(abs(x)>2,x)|x>0, which returns x>2.  However, expressions containing
		trig functions must be specified with a closed range.  Something like 
		isolve(sin(x)>0,x)|x>0 is not a valid constraint expression, but
		isolve(sin(x)>0,x)|x>0 and x<20 is valid.  Aside from this limitation, any 
		expression allowed by the operating system is valid. This functionality
		requires the installation of either IPR by Cyril Pascal, available at
		http://sirryl.multimania.com, or a shell like DoorsOS, Universal OS, PreOS, 
		or KerNO since AMS 2.xx and 3.xx forbids the use of ASM programs in 
		expressions.  Additionally, you'll need to first install HW3Patch by Kevin 
		Kofler.  If you're using a TI-89 Titanium, you'll also need to run IPR 
		through GhostBuster by Olivier Armand and Kevin Kofler.

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Bugs/Limitations

-can only solve for a single variable (but to my knowledge, it isn't mathematically
	possible to solve simultaneous inequalities for multiple variables so it 
	doesn't really matter).
-solutions with roots or fractional exponents can return false ranges if
	those values are not approximated in AMS 2.08 and 2.09, and these solutions 
	are therefore displayed unsimplified; not a problem on earlier and later 
	operating systems.
-the variable is limited to the range of [0,2*pi] or [0,360°] if it lies inside
	a trig function due to the inability of the calc to correctly display the 
	@n symbol with inequality signs in AMS 2.xx; specifiying an upper and lower 
	bound or a constraint expression will override this.
-certain operating systems will not always return every answer to certain trig 
	functions.  This is a problem that I cannot solve with programming.
-complex numbers are not supported because the calculator can return some
 	confusing and even scary looking results (try cSolve(abs(x)=5,x) and
	see what I mean, then try it in different complex modes).
-complicated equations can take a considerable amount of time to calculate,
	especially complex trig functions and other larger equations: when 
	expanded, (x+1)(x+2)(x+3)(x+4)(x+5)(x+6)(x+7)(x+8)(x+9)(x+10)>0 takes 
	between 14 and 15 seconds to complete on a TI-89 with AMS 2.09 
	(calculated using Ticktest v1.01 by Francesco Orabona).

If you find any bugs or have any suggestions, please e-mail me at
mikee385@yahoo.com

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License

This is freeware.  You may not charge for it.

The code is open source.  It is there to help in with your own projects and to
give you ideas.  You may not explicitly take anything from the code to use in 
any of your own projects.

There is no limit on calculator-to-calculator distribution.  Distribution on the
internet of this program is limited to ticalc.org.  If you wish to distribute
this program as a subroutine for another program, then my permission is needed.

I do not guarantee that this program works and cannot be held responsible for
anything that may happen to your calculator. I have tried hard to remove all
memory leaks and control any error conditions that may occur, but I am not
perfect.  If you believe there is a problem with the program, please contact
me at mikee385@yahoo.com and I will do my best to fix it.  This program comes
with no warranty, so use it at you own risk.