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1994-03-11
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Misty Expression Evaluator Version 2.1 p 1.
copyright 1994 by Peter Neuendorffer
_______________________________________________________________________
I. INTRODUCTION 1
What it does
Shareware
Installation
II. CALCULATION 2
Expressions
Operators and Variables
III. FEATURES 3
Evaluate
Store
Retrieve
History
Log
Minus Root
Info
IV. FRACTIONAL EXPONENTS 5
(see important NOTE on pg 5)
V. GRAPHING A FUNCTION 6
VI. ITERATION 8
_______________________________________________________________________
I. INTRODUCTION
This software functions much like a pocket calculator. You
can do arithmetic and store formulas as numerical expressions.
Numerical expressions can be arithmetic or a combination of
variables. The expression could be 2+2, or a+b, or it could
be the formula for the hypotenuse of a triangle (sqrt(b^2+h^2)).
You can store these expressions on disk with the Store feature.
You can save your answers on disk with the Log feature. You
can call up previous answers and variables from the current
session with the History feature. You can recall stored
expressions and edit them again with the Retrieve feature.
A crib sheet of information is provided in the Info feature.
Say your expression is "a+b" (without the quotations). You
could evaluate this by entering in "a+b" (without the quotations)
in the Evaluate option. Then fill in the variable values for
a, and b. Then press enter. The answer is given. More on what
you can do in the section below entitled CALCUALATION.
This software handles addition, subtraction, multiplication,
division, exponents (including fractional exponents), sine,
cosine and tangent. You can use decimal or "real" numbers.
Scientific notation is supported, such as "2E+5".
Shareware: This program is Shareware. It is not free.
You may distribute it freely, and use it yourself for a period
of up to three weeks. Then, on the honor system, pay for it
by sending $15.00 to:
Peter Neuendorffer
1399 Commonwealth Ave #11, Allston MA 02134
Telephone Suppport for Misty: 617-254-2213 voice (7-11PM EST)
NO further media will be sent, as this program is complete.
Installation: Copy all the files to an empty sub directory on
your hard drive. A hard drive is recommended but not mandatory.
Run the software from the drive and directory that it is located.
From DOS run MISTY. This is NOT a Windows program.
For the graphing function only, a VGA or higher resolution color
graphics card is required.
II. CALCULATION p 2.
-Expressions.
In the English, or other word language, an expression is a
collection of symbols that takes on one agreed upon meaning.
Much as in word languages, an arithmetic expression is a collection
of numbers or variables (operands) combined with arithmetic symbols
-such as "-" or "+"- (operators). These symbols are combined according
to certain rules, or the "math". If this sounds like gobbledygook,
here are some examples of expressions that this software excepts,
and evaluates:
expression ....operator..... means
5 constant the number five.
5+2 + addition five plus two.
5-2 - subtration five minus two.
5*2 * multiplication five times two.
5/2 / division five divided by
two giving a decimal answer.
sin(2) sin sine the sine of two.
cos(2) cos cosine the cosine of two.
tan(2) tan tangent the tangent of two.
a+b + addition The value of a plus
the value of b
4^2 ^ exponent 4 squared (4*4)
4^(1/2) ^ exponent the square root of 4
sqrt(8) sqrt square root square root of 8
2E+1 E scientific 2 times 10 (once)
2E-1 E " 2 times .1 (once)
-----------------------------------------------------
Actual expressions can be quite long: (a*b/c)+0.5^(3.1)-2/4
In addition the trigometric constant "pi" is supported as pi.
-----------------------------------------------------
You may enclose parts of the expression in parentheses ()
For example, (4+b)*6 is allowed, and is different
from 4+b*6 in the order that the numbers are combined.
The first example adds 4 to b first, while the second
multiplies b times 6.
------------------------------------------------------
You may use the single letter variables a through z in
your expressions, excepting the letter e which is reserved
for scientific notation.
------------------------------------------------------
- Operators and Variables.
In the order that they are evaluated by the software:
+ - "unary" a negative number such as -10
E scientific
^ exponent
sin cos tan trigometric functions taken on angles
that are given in radians.
multiply divide
add subtract
--------------------------------------------------------
Variables always have a given value at the time you evaluate your
expression. The variable letters you use "stand in" for the
value, which you fill in. Thus is your expression is a+b-c, then
you need to fill in the values of the variables, such as a=1, b=2, c=3.
This software does not use formulas with the equals sign. If you
enter in a formula for an expression, such as a=b+c, then everything
to the left of the equals sign, including the equals sign, is ignored.
----------------------------------------------------------
Positive and negative numbers from -10^36 to 10^36 are supported.
The accuracy of fractional exponents less than one varies. 2^(1/3)
is quite accurate to four places. 2^(1/3.1) is not so accurate.
Numbers are generally significant to 10 places. Such as 1234567890
III. FEATURES p 3.
-Evaluate.
This is where you get your answers and evaluate expressions.
From the main menu, select Evaluate with the up and down arrow
keys, and press Enter.
Now enter in an expression. When you press Enter any time you
enter an expression, the expression is "remembered" for the
next time you enter in an expression.
You are taken to a black screen where you see your expression.
If there were no letter variables in the expression, your answer
is given. Press Escape to exit back to the main menu.
If there are letter variables in your expression, such as in the
expression s*b^3/4, you may fill in the values for the variables.
Use the up, down, left and right arrow keys to select the variable,
and type in the value. Don't press Enter till you are done.
After you press enter, your answer is given.
Repeat the process, or press Escape to exit. The F10 key will allow
you to take the last answer anytime, and use it for a variable value.
When entering in variables, you may use an expresssion, even one
involving other variable letters. If you use a letter that is
not in the expression, the value of the letter is zero.
Some errors may occur. They could be "divide by zero" because
the calculation involved dividing by zero. Error in expression
ususally indicates that the expression is written incorrectly.
A circular reference means you have variables that depend on each
other. Too many terms means the expression is too complicated.
If the expression involves a fracional root of any kind of a
negative number than the error "attempt to take root of negative
number" is displayd.
-----------------------------------------------------------
You will find this process repeated in the Features "Retrieve"
and "History Display" with variations.
-Store.
You may wish to store an expression (not the answer) for a rainy
day. To do this, choose Store from the main menu. Then enter
in an expression. Then give it a title in words such as
"Area of a circle". Then you can add any notes you wish to include.
The expression is now stored on disk.
-Retrieve
You retrieve an expression that is stored on disk. Choose Retrieve
from the main menu. Then you have two choices:
Use stored expression:
You will see a menu of your stored expressions. If it is
longer than a page, use the page up and page down keys.
Use the up and down arrow keys to select an expression,
and press Enter. You are now brought to the same screen
as in Evaluate, and you can Evaluate the expression, or
press Escape to exit.
Edit stored expression:
You can edit the expression, title, and notes, but you
will not be using the expresssion directly to get an answer.
(III. FEATURES continued) p 4.
-History Display.
Whenever you evaluate an expression, a revolving "snapshot" is
taken of the screen. The last 20 answers are saved in this
history list. From the main menu, select History Display.
Use the page up key to go back in the list. Forward with page down.
If you want to re-avaluate a previous answer, press F3 on the
screen you wish to evaluate. You are brought once again to
the same screen as in Evaluate.
Otherwise press Escape to exit.
-Minus Roots:
This is a toggle switch that Enables/Disables the ability
of the software to recognize alternative root solutions
(see Fractional Exponents section below). If "Enabled",
the software will report solutions that depend on negative
roots. If "Disabled" this feature will not be reported.
Toggle the switch by selecting "Minus Roots" from the
main menu, and pressing Enter.
-Log.
You can store your current session on disk with a "Log" file. Note
this is different from the stored expressions, which do not contain
answers; and it is different from the History list, which only
exists while you run the program.
Turn on the log file by choosing Log from the main menu. Enter a
file name such as save.doc. Press Escape. Now any time you
get an answer, the screen will be saved in the file save.doc on
disk. Turn off the log file by selecting Log again from the
main menu. If you use a log file name that already exists, the
log is added on to the previous file on disk.
-Info: A screen of notes on this software. Select Info from the main
menu. Press Escape to exit.
IV. FRACTIONAL EXPONENTS p 5.
Fractional Exponents of Positive Numbers
----------------------------------------
When a positive number is taken to a fractional exponent,
sometimes it has two solutions. For example, 4^.5, or
sqrt(4) has two solutions, 2 and -2 . You can see that
both 2 squared, and minus 2 sqaured yield 4.
The fractional exponents that work in this way are 1/2,
1/4, 1/6, 1/8 and so on.
This software gives you all the answers for your function
involving these even fracional exponents. After you obtain
an answer to your expression in the Evaluate option, if there
are multiple solutions, the prompt "F1=other roots" will
appear. Press F1, and the various answers will pop up.
Press Escape to return to the last screen.
In the pop-up window of alternative solutions, the signs
of each exponental solution for each answer are shown.
Thus if the answer has [-] before it, the answer reflects
the negative solution. If the answer has [+] before it,
the answer reflects the positive solution. Additional
"[ ]"'s show each possible solution if there is more than
one possible negatative solution in your expression.
The word "dos not apply" refers to a negative solution for
an exponent that depends on a variable.
Up to three possible fractional exponents in a given function
are calculed in this way. If there are more than three, say
in the expression a^.5+b^.5+c^.5+d^.5, then only the positive
solutions are calculated. An expression such as
a^.5+b^.5+c^.5
could generate up to eight solutions at a time.
------------------------------------------------------------
Fractional Exponents of Negative Numbers
----------------------------------------
When a negative number is taken to a fractional exponent,
only certain odd fractions generate a real solution.
Thus the square root of -2 is not a real number, and will generate
the error message "bad or unknown root of a negative number".
The odd exponents that are supported are 1/3, 1/5, 1/7....1/9..
and so on. Also an internal table of exponents supports
the exponents x/3, x/5, x/7, x/9, x/11, x/13, x/15, x/17, x/19,
where x is an integer between 1 and the denominator.
This guarentees that if you specify an exponent in your expression
as a fraction, with the denominator between 2 and 19, the
software can process the function. Example b^(6/11).
The software attempts to convert decimal exponents to a fraction.
If you use a decimal for the exponent, or a variable, the software
may not be able to get an answer from the exponent.
NOTE: Small fractional exponents taken of numbers equal or larger than
10E7 will not be calculated. Example: (10^8)^(1/10) will generate
an overflow error. If the base number is bigger than 10E7 and
the axponent involves a fraction smaller than 1/9 than an
"overflow" message will appear. If the base number is smaller,
or the exponent is a larger fraction, the answer will appear.
V. GRAPHING A FUNCTION p. 6
1. Drawing the Graph:
Version 2.0 of Misty provides the ability to see your function
as a graph. Choose Evaluate, and Enter in a function ,such
as a/2.
Now choose a variable (if there is more than one variable)
that you wish to see your function graphed "against". That is
if you graph "a/2", then the graph would be generated using
a RANGE of values for a, rather than just one value. This
is the Independent Variable, in our example, "a".
Fill in the values you want for the other variables. These values
will be constant for the graph.
Instead of filling in a value for your Independent Variable,
("a"), move the cursor to the line on the screen that says
"a=" (or "b=" if you chose "b"). Now press the F5 function key.
You will be asked for a range for the Independent Variable
("a"). The lower range might be -10, and the upper range might
be 10. Thus the graph would be plotted against values of "a"
from -10 to 10.
You will be asked three questions, which you answer "Y" for
yes, and "N" for no:
"10's Scale?":
Do you want the ranges of the horizontal and vertical axes
expanded to the next power of 10? Thus if the horizontal
varied from -78 to 54, the range would be converted to
-10^2 to 10^2 (-100 to 100).
"Same scale?":
Do you want both the answer (the vertical)
axis) and the Independent Variable (horizontal axis) to
be in the same scale? If you choose yes, even if the
values of the answer are considerably larger than the
values of "a", the vertical axis is still topped at the
same value (10) as the horizontal.
If you choose "N" for not same scale,
then all values of the answer are included, but the
relative distances in the horizontal and vertical axes
could be different- Say the answer varied from -100 to 100,
but the independent variable only varied from -10 to 10.
"Connect Dots?":
Do you wish the graph do draw lines between the points
on the graph?
----------------------------------------------------------------
(V. GRAPHING A FUNCTION continued) p. 7
2. Viewing the Graph
If your graph had no valid solutions, an error box will
pop up displaying the problem. Otherwise, if all is well,
you should see your graph.
---------------------------------------------------------------
Axes:
The coordinates of the horizontal axis are on the far left
and right of the screen, half-way from top to bottom. This is
the range of the independent variable ("a") you plotted. Eighty
slices of this range were taken to yield 80 points to plot.
The coordinates of the vertical axis are half-way from left
to right, at the top and bottom of the screen. This is the
range of the answers.
----------------------------------------------------------------
Crosshatch:
You can add a crosshatch to your axis by pressing F2.
This is to better judge the values of your plotted line or curve.
---------------------------------------------------------------
F3: Answers
You can obtain particular answers for this plotted line or
curve. Press F3. Then use the right and left arrows to
move the dotted line from left to right. The answer for that
value is at the top right of the screen. This is the point where
the dotted line crosses the plotted point or curve.
You can fine tune this dotted bar with the up and down arrow
keys.
F1: Alternative Answers
Some graphs show more than one line. This is because the function
involved a fractional exponent. (see section above). Whike using
the F3 option, you may see these alternative answers by pressing
F1. Escape to get back to the graph.
---------------------------------------------------------------
Page Up:Last Graph
If you have plotted a graph just previously in this session, this
last graph may be overlayed on the current one. Press Page Up
to see the last graph, and then Page Down to remove it. You may
also get incremental answers with the F3 key. The values
and answers are displayed for the second graph at the bottom
of the screen.
VI. ITERATION p 8.
By iteration I mean displaying a range of answers for the
expression. For example, if the expression is a^2, meaning
a squared, you could get answers for a range of a, say
1^2, 2^2, 3^2. This is much like what the software does
to create a graph, except all the answers are displayed for
you.
To do the Iteration, enter in an exression under Evaluate,
or using the History List or Retrieve-Use options. Once
you press enter, as ususal you see a black screen with the
expression displayed along with your variables. You have
to have at least one variable letter in the expression for
the iteration to work.
Now, if there is more than one variable, fill in the values
for the variable you wish to stay the same. Then move the
cursor to the variable letter you wish to have the range of.
Press F6. Now enter in the starting value for this variable.
For example if you wanted to calculate a^2 starting at a
value of 10 for a, enter in 10.
Now enter the amount to add to the variable for each answer.
For example, enter in 1 to get answers with values of a increased
by one for each answer.
You are now asked if you want the numbers displayed rounded
off to 4 decimal places. Otherwise the numbers will appear
in "e" scientific notation.
You should get the values of your variable on the left of the
screen now, and the answers on the right. Press Page-Down to
continue with more values, or after a couple of pages have
gone bye, press Page-Up to see any previous page, Press
Escoape to exit.
