HGG's Partial Fraction Program:
This program was written by Hans-Gregor Gehrke (hgg@unicum.de) (www.geocities.com/hggehrke) for TI83 and TI83-Plus calculators. This is Freeware, I am not reliable for any damages to grades hardware, software etc..) Give it to friends etc. as you wish. (Please read the documentation to ensure the most efficient usage of the program.) I use this program to split fractions before I integrate them. I would be happy about your feedback. This may result in more and better programs.
Content:
What are the limitations of the program?
Downsides:
Put onto you calculator:
HGGPFRAC.8xp
_HGGEX.8xp
_HGGSTFL.8xp
_HGGSTRC.8xp
_HGGSTRP.8xp
Run HGGPFRAC to access the program.
If you start the program, you should see a menu with four options. They are self-explanatory.
"1:ENTER NUM" will define the numerator of the fraction. Enter any expression (as you would enter a function it the Y= editor) for the numerator. x is the variable, other real variables are overwritten will the program is run, thus you should NOT use them as constants.
Ok this are the important rules for the numerator:
use only positive-integer-orders for x. Do not use x^-1, x^.5 or 3^x etc. Use x^2, x^3 etc.
If the numerator is a constant, it cannot be equal zero.
The numerator must be defined for x=-2 to x=30
Constants as "pi", "e", cos(25) may be used. (will however turn into decimals in the result)
"2:ENTER ENUM" will define the enumerator. The first input is the number of factors. This must be an integer between 1 and 6. A repeated factor as (x+1)^2 is counted as one factor. (Repeated factors) Consider that each additional factors adds exponentially to the calculation time. Especially repeated factors and quadratic factors are time consuming.
The next step will be the entering of the factors. Enter each factor and press enter. (It will take about 2-3 sec. after each factor to store it.).
Enter each factor as a linear or quadratic function. (like x+1 or x^2+2x+4)
Do not repeat factors. (Make sure that the quadratic factors cannot be factored to linear factors) ((ax)(bx) are not to separate factors, they need to be entered as abx (one factor)). Otherwise the program will not find results.
Do not enter non linear and non quadratic factors
Use the correct method to enter repeated factors.
close ALL parenthesis, because the program does not automatically do so.
(You do not need to put each factor into Parentheses, the program will do this automatically.)
you need at least 1 repeated factor or two unrepeated factors.
"3:SPLIT!" will start the calculation. In case the numerator and enumerator are not correctly defined, this option will have no effect. (Be patient it takes some time until the result appears. The number in the lower left on the screen shows the percentage.)
As the result is displayed, use the left and right arrows to scroll through the answer. Press [Clear] to quit. If you leave the Calculator alone for more than 3 minutes or you press the [2nd]-Button in the answer-displaying state, the calculator will pause. Press [Enter] to continue. (The answer will reappear and you can scroll or quit.) (This feature was added to prevent battery drainage, if the calculator is left at that stage.)
To sum up, I want to show an example, how to use the program: (x+5)/((x+1)(x-1))
Start HGGPFRAC
Chose "1:ENTER NUM" in the menu.
Enter: x+5 (Press [Enter])
Chose "2:ENTER ENUM" from the menu.
Enter 2 to define the number of factors. (Press [Enter])
Enter x+1 (Press [Enter])
Enter x-1 (Press [Enter])
Chose "3:SPLIT!" from the menu.
Wait for the calculations to be completed.
Scroll with the left and right arrow through the result. You should see:
3x+5 -2 3
________ = ___ + ___
(x+1)(x-1) x+1 x-1
The size of the program is already pretty big, thus I spared the strings required to describe the errors and gave every error a code. Here are the meanings:
Code 1: The numerator is zero. The numerator of the fraction cannot be zero, because the whole fraction would be zero.
Code 2: You did not define enough factors. It is required to have at least 1 repeated or two unrepeated factors.
Code 3: The last factor is neither linear nor quadratic. All factors must be linear or quadratic. Review the section on repeated factors.
Code 4: "Bad Factors". This happens if the program could not solve the system of equations. A factors was most probably entered more than once. Review repeated factors.
Code 5: The last factor is a constant. A factor cannot be a constant. Multiply one of the other factors with this constant and enter it as one factor.
Code 6: You tired to repeat a factor more than three times. The program does not support such factors.
If the program should stop and display a "SYNTAX" error. You may have entered a factor or the numerator with the wrong syntax. (Close parenthesis!)
If you get a "MEMORY" error, you ran out of RAM. This program needs a lot of temporary RAM.
Sorry, but you can not enter a repeated factor as (Factor)^n. You must enter it as
Factor,n
n can be 1, 2 or 3. (Thus each factor can be repeated up to three times.)
Lets say you want to split (3x+5)/(x+1)^3.
Start the program.
Chose option 1 in the menu and enter the numerator: 3x+5. (Press [Enter])
Chose option 2 from the menu to enter the enumerator.
Press 1, because one factor is needed. (Press [Enter])
Enter x+1,3 for "FACTOR 1/1:" (Press [Enter])
Chose option 3 from the menu after the factor is processed
Wait for the calculation to be completed.
Use the arrows to see all of the answer. You should see:
3x+5 0 3 2
________ = ___ + _______ + ______
((x+1)^3) x+1 (x+1)^2 (x+1)^3
What are the limitations of the program:
The problems are:
Improper fraction will be evaluated incorrectly. An answer is shown, but it is most probably incorrect. Thus make sure that the order of "X" is higher in the enumerator.
If a factor is repeated the calculations will say: "BAD FACTORS... ERROR! CODE: 4" this means, that the program could not split the fraction. Check, whether you factored all quadratic polynomials.
Long calculation times. The times range from 10 seconds for two linear factors to minutes for many factors. Normal text-book fractions should however be solved fairly quickly (faster than doing all the calculations by hand)
The precision with many factors is not perfect. Again text-book problems should be OK.
This program is intended to convert a fraction to a sum of multiply fraction as:
(x+5)/((x+1)(x-1)= -2/(x+1) + 3/(x-1)
This is important for calculus integration problems.
The theory is that a proper fraction which has multiply different linear factors (ex: 'x+1')in its enumerator can be split into a sum of fractions where each element has the enumerator of one factor:
(Function)* A B
________________ = ______ + ______ ....
(Factor1)(Factor2)... Factor1 Factor2
* (Function) may be a constant, linear, or higher order function. The fraction must be a proper fraction.
In case one or more quadratic factors (x^2+x+2) are in the enumerator, the numerator of the elements in the sum must be a linear factor:
(Function)* Ax+B Cx+D
________________ = ______ + ______ ....
(Factor1)(Factor2)... Factor1 Factor2
If factors are repeated, another setup is used:
(Function)* A B C
____________ = __________ + _________ + ______ ....
(Factor1)^3... (Factor1)^3 (Factor1)^2 Factor1
My program supports up to 6 linear and/or quadratic factors. Each of these factors can be repeated up to three times.