__Exponential Algebraic
Calculator__

__Created
By____
David@TechForText.com,
©2010__

__To contact the author use the
above email address, or__

__Left click on these words for a website
communication form.__

__This website
provides a free calculation device (____Exponential Algebraic
Calculator____) in the online
JavaScript and spreadsheet formats, for solving e____quations similar
to:__
**AX ^{V}+BX^{V}+KX^{V}+DX^{V}+EX^{V}=W**.

__If you want the
spreadsheet version of the____ Exponential Algebraic Calculator,
(available in Microsoft Excel, and OpenOffice Calc)
or additional information, scroll all the way down, beneath the online
Calculator.__
Alternatively, you can use the hyperlink table of contents of this website,
which is located just below the online calculator. **To
go directly to the table of contents left click on these
words.**

__Exponential Algebraic
Calculator____ __

**The Exponential Algebraic
Calculator**
solves equations similar to

If the equations you want to solve
has less terms than the above, and looks like this: **AX ^{V}+BX^{V}+KX^{V}=W**

When there are no (apparent)
coefficients multiplying variables, such as **X ^{V}=W** (

Below, is the online version of
the ** Exponential Algebraic Calculator**, embedded in this
webpage. Note, if you print your calculated results from this Calculator
all of the text on this website will be printed.

__The Online Version of the
Exponential Algebraic Calculator__

__THE HYPERLINK TABLE OF CONTENTS OF
THIS WEBSITE__

__Left
click with the mouse, on the UPPER PORTION of the blue words that relate to the
topic or subtopic you are interested in.__

**If you want a diverse assortment of
calculation devices for algebra and trigonometry, go to the main website at
www.TechForText.com/Algebra****,
****This can be done by left clicking on
these words. **

**Exponential Algebraic Calculator** 2

**The Online
Version of the Exponential Algebraic Calculator** 3

**System
Requirements for the**. 9

**Exponential Algebraic Calculator,** 9

**And Links
to Obtain the Free Downloads**
9

**The
Software You Need for the Downloads**
9

**Exponential Algebraic Calculator In the**
10

**Microsoft
Excel, OpenOffice Calc, And Javascript Formats**. 10

**Number
Handling Capacity and Error Messages of** 12

**The
Exponential Algebraic Calculator**
12

**The
Exponential Algebraic Calculator Can Handle**. 12

**Very Large
and Very Small Numbers,** 12

**General
Error Messages Displayed by**. 13

**The
Exponential Algebraic Calculator** 13

**Creating
Exponential Algebraic Calculator** 14

**Creating
the JavaScript Version of** 14

**The
Exponential Algebraic Calculator** 14

**Creating
the Calculation Mechanism**.. 14

**For the
Exponential Algebraic Calculator** 14

**Two Values
for X, and the ****Error-Checking Mechanism**.. 17

**Of the
Exponential Algebraic Calculator**
17

**A User
Controllable Rounding Mechanism**
22

**Services
Offered by the Author** 26

**Services
Offered by the Author David@TechForText.com**.. 27

__Exponential Algebraic
Calculator____,__

__And
Links____ to Obtain the Free
Downloads__

__The Software You Need for the
Downloads__

The spreadsheet versions of the
__Exponential Algebraic Calculator__ require either Microsoft Excel, or the
OpenOffice.org software package. In addition, Microsoft Windows is
required for the spreadsheet versions.

The JavaScript version of the Exponential Algebraic Calculator can run on any operating system that has JavaScript support, but I only tested it with Microsoft Windows. In addition, the JavaScript version requires a browser that supports JavaScript. Almost all modern operating systems and browsers support JavaScript.

__Exponential Algebraic
Calculator____ In the____ __

__Microsoft Excel, OpenOffice Calc,
And Javascript Formats__

** **

** **

__Note: If you do not have Microsoft Excel,
download the OpenOffice.org software package, because it is free and it is
almost as good as the Microsoft Office suite. To download go to www.OpenOffice.org or left
click on these words.__** **

** **

** **

__Number Handling
Capacity and Error Messages of__

__The
____Exponential Algebraic
Calculator__

__The
Exponential Algebraic Calculator Can Handle__

__Very Large and Very Small
Numbers,__

**The Exponential Algebraic
Calculator**
can handle very large and very small numbers with well OVER 250 digits.
This applies to all
the versions of the Calculator, except for
the

When many digits are
involved the ** Exponential Algebraic Calculator** in the Excel and
online JavaScript format display numbers in scientific notation. An
uppercase

An example, of a large number is
10000000000000000000, and it is displayed by the __Exponential Algebraic
Calculator (__ JavaScript and Excel) in scientific notation, in this format:
1.00E+19. An example of a very small number is 0.0000000000000000001, and
it is displayed by the Calculator in scientific notation in this format:
1.00E-19. (Note: sometimes numbers that are extremely small are rounded to
zero, by the Calculator.)

__General Error Messages Displayed
by__

__The Exponential Algebraic
Calculator__

This Calculator shows an error message when there are no solutions for the numbers that were entered. The Calculator also shows an error message if a sub-calculation or the values of X exceed 307 digits.

__Creating Exponential
Algebraic Calculator__

__Creating the JavaScript Version
of____
__

__The Exponential Algebraic
Calculator__

The JavaScript version of the Exponential Algebraic Calculator was created from the spreadsheet version. This involves specialized software to convert Microsoft Excel to the JavaScript format. Thus, almost all of the material on this website applies to both spreadsheet and JavaScript versions.

__Creating the Calculation
Mechanism__

__For
the Exponential Algebraic Calculator__

The Exponential
Algebraic Calculator was created by solving **AX ^{V}+BX^{V}+KX^{V}+DX^{V}+EX^{V}=W
**for

**X=((W/(A+B+K+D+E)) ^{(1/V)}**

This formula had to
be converted into a format that Microsoft Excel would understand. To do
this the Microsoft Excel name mechanism was used to define the letters in the
formula **in terms
of input boxes for ****V,
****A, B, K, D, E,
and W.**

For additional information on using the name mechanism in Microsoft Excel see the following websites, which can be done by left clicking on the web addresses.

Words on website:”**Define and
use names in formulas” ****http://office.microsoft.com/en-us/excel/HA101471201033.aspx#backtotop**

Words on website: “Introduction To Defined Names”

**http://www.cpearson.com/excel/DefinedNames.aspx**

After the above step
was completed, (define the letters in the formula **in terms of input boxes) it
was**
necessary to convert the implied instructions in the formula, into a format that
spreadsheet software can understand. That is, for Microsoft Excel,
OpenOffice Calc, and many other brands of spreadsheet software, the following
notation is used:

For division, a slash: /

For multiplication, an asterisk: *

For **X=((W/(A+B+K+D+E)) ^{(1/V)} For the Exponent
^{(1/V)}
** ^ was used,
^(1/V). For example 100^(1/V), and when V=2: 100^(1/2)=10

** **

As a result of the
modifications described above the formula: **X=((W/(A+B+K+D+E)) ^{(1/V)}** was converted
to:

** **

**=((W/(A+B+K+D+E))^(1/V)**** **

The cell that this formula is placed in becomes the display box for the calculated value of X.

__Two Values for X, and
the ____Error-Checking____
Mechanism__

__Of the Exponential
Algebraic Calculator__

When solving an
algebraic equation of the type **AX ^{V}+BX^{V}+KX^{V}+DX^{V}+EX^{V}=W**

10X^{2}+30X^{2}+20X^{2}+15X^{2}+25X^{2}=10000

100X^{2 }=10000

X^{2} =100

**X=10** and **X=-10 **

** **

There are many other sets of
numbers that will produce only one correct value for X, or even no value for X,
in terms of real numbers, for the equation:
**AX ^{V}+BX^{V}+KX^{V}+DX^{V}+EX^{V}=W.
**

Thus, the ** Exponential Algebraic
Calculator**
required some method of evaluating the numbers that were entered, and the
calculated results, to determine if there are one or two values for X, in terms
of real numbers.

However, the simplest way for a
computer to determine if there are two values, one value, or no values, for
**X**, is to substitute calculated results into the equation:
**AX ^{V}+BX^{V}+KX^{V}+DX^{V}+EX^{V}=W.**
This is the method that I used, because it also serves a general error-checking
purpose. For example, if the computer malfunctioned, the software became
corrupt, or if I made an error while creating the calculation device, the
error-checking mechanism would indicate errors, with most, if not all,
calculated results.

The calculated result for
X_{1} is determined with the following formula =((W/(A+B+K+D+E))^(1/v)) Then, the calculated result
for X_{1} is **NOT** rounded down in this formula, and this is sent
to the following equation:

(Note, numbers that are used for the error-checking are rounded down to a predetermined number of decimal places to prevent rounding errors. This can be seen in the following formulas, with the word ROUND.)

=ROUND((A*X^v+B*X^v+K*X^v+D*X^v+E*X^v),H28) The result from this
equation should equal the value the user entered for W, if there are NO errors,
and if the calculated results satisfies the equation: AX^{V}+BX^{V}+KX^{V}+DX^{V}+EX^{V}=W
Since the above is NOT certain, it is necessary to represent this result with
**Wc**.

**Wr** is equal to the value entered by
the user for W, but it is rounded down to a predetermined number of decimal
places, to prevent rounding errors, with the following formula: =ROUND(W, H28)

In the following formula the
absolute value of (Wr-Wc) is used to check the calculation, X_{1} and to
determine the degree of error, if any.

=IF((ABS(Wr-Wc)<(5/100) ), (Wr-Wc), "")

With the above formula, if there is an error less than 5/100, the calculated results are displayed for Wr-Wc. If there is no error the result is zero, which is usually the case for most numbers. If the error is greater than 5/100, no calculated result is displayed for Wr-Wc.

In the yellow display box for
**X _{1}** there will be NO result displayed if the error is greater than 5/100, based
on the absolute value of (Wr-Wc). This is achieved with the following
formula.

=IF( (ABS(Wr-Wc)<(5/100)), ROUND(X, H16), "" )

Then the calculated result for
X_{2} is calculated with the following formula.

=-((W/(A+B+K+D+E))^(1/v))

Note the negative sign on the left
side of the above formula. The calculated result from this formula is
represented by negX, which is checked in the ** Exponential Algebraic
Calculator**
with the following equation:

=ROUND((A*negX^v+B*negX^v+K*negX^v+D*negX^v+E*negX^v),H28)

**The calculated result from this
equation is represented by Wnc. **

In the following equation the
relative degree of error for **X _{2}** is calculated, with the
absolute value of

=IF((ABS(Wr-Wnc)<(5/100) ), (Wr-Wnc), "")

Finally, in the yellow display box
for **X _{2}** NO results will be displayed if the error is greater
than 5/100, based on the absolute value of (

=IF( (ABS(Wr- Wnc)<(5/100)), ROUND(X, H16), "")

__A User Controllable Rounding
Mechanism__

In general, it is often necessary to round down numbers to a specific number of decimal places, especially when the numbers are calculated results. Very often, the last few decimal places of a calculation are not needed, or not mathematically significant. This can happen when the calculations are based on measurements that are less precise than the calculated results.

Rounding down the number of decimal places can also prevent confusing rounding errors. That is computers often make slight calculation errors when converting to binary and back to the decimal system. This often involves a whole number, followed by a decimal point, and a series of nines. For example, when the correct calculation should result in 2, the computer calculates 1.999999999999.

Calculation devices often have
built-in mechanisms to round down calculated results to a predetermined number
of decimal places, such as six decimal places. The ** Exponential
Algebraic Calculator** has such a mechanism,

Interestingly, the number in the
input boxes, to control the number of decimal places, can be equal to or
**less** than zero. That is the number
of decimal places can be rounded down to a negative number. To explain
this I will use the number **1234.123** as an example. When this number
is rounded to one decimal place it is **1234.1**. When it is rounded to
**zero** decimal places it is **1234**, **-1** decimal places it is
**1230**, **-2** decimal places it is **1200**, and **-3** decimal
places it is **1000**.

I created the rounding mechanism
described above, __with the input boxes, for the user to control the number of
decimal places. __ I did this by modifying the conventional Microsoft
Excel formula, for rounding numbers. The conventional formula is as
follows: =ROUND(number, number of decimal places). My
modification involved entering a cell designation instead of the number of
decimal places in the formula. For example, if X is the number, and 28E is
a cell designation, then the modified formula is =ROUND(X, 28E). With this example, cell
E28 is an input box. That is the number of decimal places of the
calculation is determined by the number entered in cell 28E, with this
example.

A generalized version of the above formula is:

=ROUND(number, cell designation). This formula will also function in OpenOffice Calc, and probably in a number of other brands of spreadsheet software. The formula and the related concept have potential utility with many types of calculation devices. The general concept, (input boxes to allow users to control the number of decimal places of calculated results) can be incorporated into the design of any type of calculation device. However, the configuration of the formula as presented above only applies to spreadsheets, or any format that was created by converting a spreadsheet, such as JavaScript.

The ** Exponential Algebraic
Calculator** has two input boxes to control the number of decimal places,
one is for the calculated results of X

__Services Offered by
the Author__

** **

This website was designed to
maximize efficiency and ease-of-use (usability, user-friendliness). The
text is presented with relatively large fonts. The paragraphs are short,
and the sentence structure and wording were written to maximize comprehension*.
The website has a very simple layout, on a single page, with a hyperlinked
table of contents. This makes it easy to __navigate intuitively__, by
scrolling or by left clicking on a topic or subtopic in the table of
contents. All the links for downloads and other websites are also written
with large fonts, and clearly marked as links, such as with the following words:
* left click on these words*.

Note: The material on this website is technical, and to understand every detail requires slow and careful reading. In addition, knowledge of mathematics and some familiarity with spreadsheets and computer technology is also needed for maximum comprehension. However, portions of the material, excluding the precise details, can be understood by almost anyone.

__Services Offered by
the Author David@TechForText.com__

I design and build user-friendly
software based calculation devices for __arithmetic__, __accounting__,
__currency exchange rates__,
__algebra__, __trigonometry__,
__correlations__, __calculus__, and databases with built-in calculation
devices. I also create attractive online calculation devices for
websites. I generally make these devices in the Microsoft Excel,
OpenOffice.org, and the JavaScript formats, but I can work with other
spreadsheet formats besides the above.

**For a list of websites with calculation
devices that I created, left click on these words, or go to the following
website: www.TechForText.com/Math**

I can create web communication forms for your website. This includes forms with built-in calculation devices.

I write instructions for the devices I build. I can also write instructions for software and computer devices created by others. In addition, I can write advertising for your websites, products and services.

For a list of all the services I
offer see **www.TechForText.com**

For a list of all my websites see
**www.David100.com**

My resume is online at: **www.David100.com/R**

I can provide the services
mentioned above on a fee-for-service basis, or possibly based on temporary or
permanent employment. If you are interested in my services, and want
additional contact information or more data on the services I offer, you can
email me at **David@TechForText.com
**or **use a website communication
form, by left clicking on these words.**

I am located in the USA. If you are a great distance from my locality or are in another country, this is not important. I can provide these services worldwide, because the software and websites I make can be delivered through the Internet to any locality, providing there are no governmental restrictions.

**To return to the top of this website left click on these
words**

** **