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Cream of the Crop 20 (Terry Blount) (1996).iso
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ALGEDENG.HLP
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1996-06-06
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Help text for the Algebra Editor
Copyright (c) 1994,1996 John Henckel
Permission to use, copy, modify, distribute and sell this software
and its documentation for any purpose is hereby granted without fee,
provided that the above copyright notice appear in all copies and
that both that copyright notice and this permission notice appear
in supporting documentation. All programs contained herein are provided
to you "as is". The implied warranties of merchantability and fitness
for a particular purpose are expressly disclaimed.
╔═════════════╗
║ QUICK START ║
╚═════════════╝
To load the sample data file:
1. Click "Load" in the upper right corner (or press 'l').
2. Type "alged" and press Enter.
Play with the sample data file and if you have any trouble, print the
short tutorial in the alged.doc file.
(Press Esc to return, or press any key for more help...)
----------------------------------------------------------------------------
My name is John Henckel (internet: henckel@vnet.ibm.com). I am a computer
hobbyist; I like to write computer programs to amuse myself, and this is one
of them. I also recommend my 2D collision simulator "Impact" found in
http://www.coast.net/SimTel/msdos/simulatn.html. Thanks to my family for
letting me work on this. Thanks to my manager at IBM in Rochester, Minnesota
for permitting me to offer this program for free to the public.
Alged is a program for solving algebra problems. There are other programs
that can do symbolic formula manipulations, such as MathCad and Mathematica.
The advantages of Alged are that it is
* Free! The source code is also free!
* Light weight (it runs on a PC/XT with 256K of memory)
* Easy to use, ideal for education
* Fast and flexible 2D and 3D graphics
* Can be customized and translated (Flemish and French included).
Of course, there are limitations. Alged is by no means a "commercial grade"
product (though I've seen worse!) Alged does not handle matrices, series,
integrals, derivatives, or transcendental transformations. Imaginary numbers
are supported only with the five basic operators (add, subt, mult, div, exp).
Alged is a tool for symbolic math, so I have purposely avoided the "number
crunching" algorithms.
----------------------------------------------------------------------------
Input Instructions:
The Alged screen has a menu at the top and a work area at the bottom. At the
lower left is the time of day and the percentage of heap memory used. (When
the heap reaches 100% Alged will exit.) You manipulate the formulas in the
work area by clicking on parts of them and then clicking on the menu. You
click the left mouse button in the work area to select the current expression
or the PICK. The pick is highlighted. You click the right mouse button in
the work area to select the KEY expression. The key is copied to the bottom
of the screen. Notice that it is legal to click on the key, so the pick may
be a subset of the key. To scroll the work area, you can click on the border.
If your computer does not have a mouse, (or you just don't like to use it)
you can use the [pageup], [pagedown] and [end] keys to select the pick.
These keys descend the binary tree stored in memory. You can copy the pick to
the key by pressing '.'. You can type the key by pressing 'k'. You can copy
the key to the work area by pressing [Insert]. You can delete the key by
pressing [Enter]. To scroll the work area, you can use the arrow keys.
Some of the operations on the menu only use the pick, and some use both the
pick and the key. Unless otherwise specified, the menu descriptions below
apply to the pick only.
(New for version 3.4) The polynomial operations (such as PolyFact and
PolyDiv) do not require you to specify the key. If no key is specified,
they will use the variable 'x' or the first variable found in the
expression. If the pick is an equation, the polynomial operations will
automatically select one side or the other.
----------------------------------------------------------------------------
Menu Description:
Simplify [space] simplify expression. It sorts it, combines common terms,
calculates numbers, and rewrites it in canonical form.
Note: Another similar function is SimpStep which is assigned to the 'x'.
The SimpStep function shows the intermediate steps of the simplification.
Distribute [d] distribute multiplication over add and subtract, and distribute
exponents over multiplication and division.
Note: Another similar function is DistChild which is assigned to the 'D'
(press shift and 'd'). The DistChild function is different in two ways.
1. DistChild does a top-down distribution. For example,
(x*(a + b))^2 ---> (x^2)*(a + b)^2 using DistChild
(x*(a + b))^2 ---> (x*a + x*b)^2 using Distribute
2. DistChild does not distribute the top level factors in an expression
or equation. You can use DistChild to simplify the result of a
factorization, like FactPoly or FactQuad.
Calculate [c] calculate all numbers. e.g. 3*2 => 6.
PrimeFact [v] find the prime factorization of integers. (This is limited by
the ?d user option).
Integer [i] convert real numbers to integers if possible. e.g. 1.5 => 3/2
This algorithm has two strategies. First, it looks for repeating patterns
in the fractional part of the number. At least two repeating digits must
be significant. If that fails, it searches for an integer, d, such that d*x
is an integer. The user parameters ?e and ?d are used here.
Associate [a] rotates the elements of an associative group.
Comm-Deno [m] This is a TOGGLE to create a common denominator or to distribute
division over add and subtract.
CharMode [8] toggle ascii 7-bit or 8-bit. This is useful if you use
print-screen.
Poly-Coef [p] collect the coefficients of a polynomial. The pick must be a
polynomial (not an equation) and the key must be the expression use as the
base of the polynomial.
e.g. pick is a*x + b*x + c, key is x ==> result is c + (a + b)*x
Center [home] horizontally center the formulas (this is default).
Poly-Div [\] polynomial division. The pick must be a division (not an
equation) and the numerator must be a polynomial with degree greater
than or equal to the denominator. The key must be the base variable.
e.g. pick is (x^2 - y^2)/(x - y) and key is x. ==> result is x + y.
FactQuad [q] factor a 2nd degree polynomial using the quadratic equation.
The pick must be a 2nd degree polynomial (not an equation) The key must
be the base variable.
e.g. pick is (x^2 - y^2) and key is x. ==> result is (x + y)(x - y).
FactCubic [3] factor a 3rd degree polynomial using the cubic equation.
The pick must be a 3rd degree polynomial (not an equation) The key must
be the base variable. e.g. pick is (x^3 - y^3) and key is x. ==> result
(after integer and several calculate and simplify) is
(x - y)*(x + (0.5 - 0.86i)*y)*(x + (0.5 + 0.86i)*y).
Note: This function isn't working very well. Sometimes it gives the
wrong answer, and sometimes it uses up all memory. The problem appears to
be with non-singular roots. Only use it as a last resort.
FactPoly [f] factor a polynomial using rational roots. The coefficients
of the polynomial should not contains any non-integer numbers. The pick
must be a polynomial. The key must be the base variable. e.g. pick
is (x^4 - y^4) and key is x. ==> result is (x - y)(x + y)(x - iy)(x + iy).
Note: If the polynomial has non-integer coefficients, sometimes
FactPoly will still work if you "fix" it using Calculate & Integer.
To force integer coefficients, put the terms of the polynomial over a
common denominator. e.g. with x^2 - 0.5*x - 3 press Integer, Simplify,
CommDeno, to get (x^2*2 - x - 3*2)/2. Now select the numerator (press
End) and then FactPoly.
Substitute [u] performs substitution using the key over the pick. The key
must be an equation. e.g. pick is a*x + b, key is x