Partial Fraction Decomposition for TI-85 by Ravi Prasad (4/17/92) ----begin documentation---- You must first run the uudecode "UUD20" program which will create the "PRTLFRAC.85P" file and then you must run the "LINK85" program to load the file to your TI85. While writing the partial fraction program, I was forced to write an n'th order derivative program. A small routine in the "PRTLFRAC" program determines the derivative of a function F(x) = U(x) / V(x). The "DERIV" routine lets you get the n'th derivative of a polynomial. Since I needed to get a derivative of a function f(x) = u(x) / g(x), I used a combination of divide and multiply and deriv in a loop to get the required result. The multiply and divide routines are basically the same ones currently on the archive listed as "Pmul" and "Pdiv" with only slight modifications as needed. To properly add or subtract polynomials, I was also had to write a routine that would fix the list size of different degree polynomials. This routine can be used seperately as can the DERIV routine to do further handle polynomials. Running the program. Simply execute the "PRTLFRAC" program by selecting it from the PROG menu You will be prompted to enter N(x) and the roots to D(x). N(x) is the numerator of the function to be worked on. Accordingly, D(x) is the denominator of the same function. Due to accuracy problems, I was forced to write a routine where you must enter the roots of the denominator versus entering the denominator polynomial itselt. Anyway, I latter emply the multiply routine and build the needed denominator. It is a good idea to enter duplicated roots of D(x) at the same time, although not necessary. After a while, the partial fraction decomposition is done and the necessary information presented in matrix form. The matrix is also saved under the variable "x" for your future review. Again, due to accuracy problems on the TI, I have employed a routine which randomly selects a number and checks the value of this number in the original function, and then in the newly decomposed fraction form. If a difference between the two exist by more than the "tol" value setup in you TI-85, the matrix presented is displayed with question marks. I have found that in most cases, the difference is trivial and can be ignored. The difference between the two versions are held in the greek character "omega" for your further review. 2 example: give the x F(x) = ------------------- 2 (x+1) (x+2) 2 enter in LIST form N(x): {1,0,0} which represents 1x + 0x + 0 enter in LIST form Roots of D(x): {-1,-1,-2} which shows -1 as a double root the solution presented in matrix form says that the fuction F(x) can also be represented as: -3 1 4 -------- + ----------- + ---------- 1 2 1 (x+1) (x+1) (x+2) The numerator values (-3,1,4) are presented in row 1 of the matrix The values (x+n) where n is 1,1,2 are presented in row 2 of the matrix The powers on the denominator (1,2,1) appear in row 3. The matrix has been organixed such that each column corresponds to each term. Again, as previously mentioned, if the computational difference greater than the internal "tol" value exist between the original function and the decomposed form, the screen has question marks displed next to the sample matrix. In most cases this is not anything significant. One last note, as always, I have made common practice to start all program variables with the greek letter omega. This makes deletion of the variables much easier since they appear all together in the memory management screen. ----end documentation---- ----begin ascii---- \START\ \COMMENT=Program file dated 04/30/93, 08:52 \NAME=PRTLFRAC \FILE=prtlfrac.85P Lbl START ClLCD Disp "DECOMPOSE F=N(x)/D(x)" Disp "NOTE:\deg\N(x) < \deg\D(x) !!" Disp " Ans=\UC-Sigma\\hexA\i/(x+\hexB\i)^\hexC\i" Disp "---------------------" Input "N(x)=",\UC-Omega\NUM Input "ROOTS OF D(x)=",\UC-Omega\ROOT sortA \UC-Omega\ROOT\->\\UC-Omega\ROOT dimL \UC-Omega\ROOT\->\\UC-Omega\\LC-beta\:{3,\UC-Omega\\LC-beta\}\->\d\#\ im \UC-Omega\SOL {1}\->\\UC-Omega\L2 For(\UC-Omega\B,1,\UC-Omega\\LC-beta\) {1,\(-)\\UC-Omega\ROOT(\UC-Omega\B)}\->\\UC-Omega\L1 10\->\\UC-Omega\RTS:Goto MULTIPLY Lbl RTS10 \UC-Omega\ML\->\\UC-Omega\L2 End \UC-Omega\ML\->\\UC-Omega\DEN Lbl TEST1 int (100*rand)+1\->\\UC-Omega\TSTPT For(\UC-Omega\B,1,\UC-Omega\\LC-beta\) If angle \UC-Omega\ROOT(\UC-Omega\B)\<>\0 Then (\UC-Omega\TSTPT,0)\->\\UC-Omega\TSTPT Goto TEST2 End End Lbl TEST2 For(\UC-Omega\B,1,\UC-Omega\\LC-beta\) If \UC-Omega\TSTPT==\UC-Omega\ROOT(\UC-Omega\B) Goto TEST1 End Fill(0,\UC-Omega\SOL):\li>vc\ \(-)\\UC-Omega\ROOT\->\\UC-Omega\SOL(2,1)\#\ 1\->\\UC-Omega\A:1\->\\UC-Omega\DerN Lbl MAIN 0\->\\UC-Omega\K:0\->\\UC-Omega\n If \UC-Omega\A\<=\\UC-Omega\\LC-beta\ Then \UC-Omega\ROOT(\UC-Omega\A)\->\\UC-Omega\\LC-alpha\ For(\UC-Omega\B,1,\UC-Omega\\LC-beta\) If \UC-Omega\ROOT(\UC-Omega\B)==\UC-Omega\\LC-alpha\ \UC-Omega\K+1\->\\UC-Omega\K End {1,\(-)\\UC-Omega\\LC-alpha\}\->\\UC-Omega\L1:{1}\->\\UC-Omega\L2 For(\UC-Omega\B,1,\UC-Omega\K) 20\->\\UC-Omega\RTS:Goto MULTIPLY Lbl RTS20 \UC-Omega\ML\->\\UC-Omega\L2 End \UC-Omega\DEN\->\\UC-Omega\N:\UC-Omega\ML\->\\UC-Omega\D 30\->\\UC-Omega\RTS:Goto DIVIDE Lbl RTS30 \UC-Omega\Q\->\\UC-Omega\TMPDEN:\UC-Omega\NUM\->\\UC-Omega\TMPNUM (pEval(\UC-Omega\TMPNUM,\UC-Omega\\LC-alpha\)/pEval(\UC-Omega\TMPDEN,\UC-Omega\\#\ \LC-alpha\))\->\\UC-Omega\SOL(1,\UC-Omega\A+\UC-Omega\K-1) \UC-Omega\K\->\\UC-Omega\SOL(3,\UC-Omega\A+\UC-Omega\K-1) If \UC-Omega\K>1 Then For(\UC-Omega\n,1,\UC-Omega\K-1) \UC-Omega\TMPNUM\->\\UC-Omega\F 40\->\\UC-Omega\RTS:Goto DERIV Lbl RTS40 \UC-Omega\DER\->\\UC-Omega\Uder \UC-Omega\TMPDEN\->\\UC-Omega\F 50\->\\UC-Omega\RTS:Goto DERIV Lbl RTS50 \UC-Omega\DER\->\\UC-Omega\Vder \UC-Omega\TMPDEN\->\\UC-Omega\L1:\UC-Omega\Uder\->\\UC-Omega\L2 60\->\\UC-Omega\RTS:Goto MULTIPLY Lbl RTS60 \UC-Omega\ML\->\\UC-Omega\N1 \UC-Omega\TMPNUM\->\\UC-Omega\L1:\UC-Omega\Vder\->\\UC-Omega\L2 70\->\\UC-Omega\RTS:Goto MULTIPLY Lbl RTS70 \UC-Omega\ML\->\\UC-Omega\N2 If dimL \UC-Omega\N1\\UC-Omega\WANTSIZ \UC-Omega\N1\->\\UC-Omega\LST 80\->\\UC-Omega\RTS:Goto SIZFIX Lbl RTS80 \UC-Omega\LST\->\\UC-Omega\N1 End If dimL \UC-Omega\N1>dimL \UC-Omega\N2 Then dimL \UC-Omega\N1\->\\UC-Omega\WANTSIZ \UC-Omega\N2\->\\UC-Omega\LST 90\->\\UC-Omega\RTS:Goto SIZFIX Lbl RTS90 \UC-Omega\LST\->\\UC-Omega\N2 End (\UC-Omega\N1-\UC-Omega\N2)\->\\UC-Omega\TMPNUM \UC-Omega\TMPDEN\->\\UC-Omega\L1:\UC-Omega\L1\->\\UC-Omega\L2 100\->\\UC-Omega\RTS:Goto MULTIPLY Lbl RTS100 \UC-Omega\ML\->\\UC-Omega\TMPDEN (1/\UC-Omega\n!)*(pEval(\UC-Omega\TMPNUM,\UC-Omega\\LC-alpha\)/pEval(\UC-Omega\\#\ TMPDEN,\UC-Omega\\LC-alpha\))\->\\UC-Omega\SOL(1,\UC-Omega\A+\UC-Omega\\#\ K-\UC-Omega\n-1) \UC-Omega\K-\UC-Omega\n\->\\UC-Omega\SOL(3,\UC-Omega\A+\UC-Omega\K-\UC-Omega\\#\ n-1) End \UC-Omega\A+\UC-Omega\K\->\\UC-Omega\A:0\->\\UC-Omega\K End \UC-Omega\A+\UC-Omega\K\->\\UC-Omega\A Goto MAIN End Goto FINISHED Lbl MULTIPLY dimL \UC-Omega\L1\->\\UC-Omega\S1 dimL \UC-Omega\L2\->\\UC-Omega\S2 \UC-Omega\S1+\UC-Omega\S2-1\->\dimL \UC-Omega\DL Fill(0,\UC-Omega\DL) \UC-Omega\DL\->\\UC-Omega\ML For(\UC-Omega\I,1,\UC-Omega\S2,1) Fill(0,\UC-Omega\DL) For(\UC-Omega\J,1,\UC-Omega\S1,1) \UC-Omega\L1(\UC-Omega\J)\->\\UC-Omega\DL(\UC-Omega\J+\UC-Omega\I-1) End \UC-Omega\L2(\UC-Omega\I)*\UC-Omega\DL+\UC-Omega\ML\->\\UC-Omega\ML End Goto RTSCHK Lbl DIVIDE 0\->\\UC-Omega\Q dimL \UC-Omega\N\->\\UC-Omega\S1 dimL \UC-Omega\D\->\\UC-Omega\S2 \UC-Omega\S1-\UC-Omega\S2+1\->\\UC-Omega\ND \UC-Omega\ND\->\dimL \UC-Omega\Q \UC-Omega\D\->\\UC-Omega\D2 \UC-Omega\S1\->\dimL \UC-Omega\D2 \UC-Omega\N\->\\UC-Omega\Rem For(\UC-Omega\I,1,\UC-Omega\ND,1) \UC-Omega\Rem(\UC-Omega\I)/\UC-Omega\D(1)\->\\UC-Omega\M \UC-Omega\M\->\\UC-Omega\Q(\UC-Omega\I) \UC-Omega\Rem-(\UC-Omega\M*\UC-Omega\D2)\->\\UC-Omega\Rem Fill(0,\UC-Omega\D2) For(\UC-Omega\J,1,\UC-Omega\S2,1) \UC-Omega\D(\UC-Omega\J)\->\\UC-Omega\D2(\UC-Omega\I+\UC-Omega\J) End End Goto RTSCHK Lbl DERIV \UC-Omega\F\->\\UC-Omega\DER dimL \UC-Omega\F\->\\UC-Omega\Fsize If \UC-Omega\DerN\>=\\UC-Omega\Fsize Then 1\->\dimL \UC-Omega\DER:0\->\\UC-Omega\DER(1) Goto DONE End \UC-Omega\Fsize-\UC-Omega\DerN\->\dimL \UC-Omega\DER For(\UC-Omega\B,1,\UC-Omega\Fsize-\UC-Omega\DerN) \UC-Omega\F(\UC-Omega\B)*(\UC-Omega\Fsize-\UC-Omega\B)!/(\UC-Omega\Fsiz\#\ e-\UC-Omega\B-\UC-Omega\DerN)!\->\\UC-Omega\DER(\UC-Omega\B) Lbl DONE End Goto RTSCHK Lbl SIZFIX dimL \UC-Omega\LST\->\\UC-Omega\ORGSZ \UC-Omega\WANTSIZ\->\dimL \UC-Omega\LST 0\->\\UC-Omega\\LC-gamma\ For(\UC-Omega\B,\UC-Omega\ORGSZ,1,\(-)\1) \UC-Omega\LST(\UC-Omega\B)\->\\UC-Omega\LST(\UC-Omega\WANTSIZ-\UC-Omega\\#\ \LC-gamma\) 0\->\\UC-Omega\LST(\UC-Omega\B):\UC-Omega\\LC-gamma\+1\->\\UC-Omega\\LC-gamma\\#\ End Goto RTSCHK Lbl RTSCHK If \UC-Omega\RTS==10 Goto RTS10 If \UC-Omega\RTS==20 Goto RTS20 If \UC-Omega\RTS==30 Goto RTS30 If \UC-Omega\RTS==40 Goto RTS40 If \UC-Omega\RTS==50 Goto RTS50 If \UC-Omega\RTS==60 Goto RTS60 If \UC-Omega\RTS==70 Goto RTS70 If \UC-Omega\RTS==80 Goto RTS80 If \UC-Omega\RTS==90 Goto RTS90 If \UC-Omega\RTS==100 Goto RTS100 Lbl FINISHED 0\->\\UC-Omega\A:\UC-Omega\SOL\->\x For(\UC-Omega\B,1,\UC-Omega\\LC-beta\) x(1,\UC-Omega\B)/((\UC-Omega\TSTPT+x(2,\UC-Omega\B))^x(3,\UC-Omega\B))+\#\ \UC-Omega\A\->\\UC-Omega\A End (pEval(\UC-Omega\NUM,\UC-Omega\TSTPT)/pEval(\UC-Omega\DEN,\UC-Omega\TST\#\ PT))\->\\UC-Omega\B ClLCD Disp "Ans=\UC-Sigma\\hexA\i/(x+\hexB\i)^\hexC\i" Disp " [\hexA\1,\hexA\2,\hexA\3.....]" Disp " [\hexB\1,\hexB\2,\hexB\3.....]" Disp " [\hexC\1,\hexC\2,\hexC\3.....]" abs (\UC-Omega\A-\UC-Omega\B)\->\\UC-Omega\ If \UC-Omega\>tol Then Outpt(2,1,"????") Outpt(3,1," ?") Outpt(4,1," ?" End x\>Frac\ \STOP\ ----end ascii---- ----begin uue---- begin 644 prtlfrac.85p M*BI423@U*BH:#`!0"D@(2$BUD1IF4MRD(MRD1E"@R+,I"*2E> M>"@S+,I"*2DKRD$); Mon, 7 Jun 1993 19:28:00 -0400 Received: from umdesun7.umd.umich.edu by umdsun2.umd.umich.edu (4.1/SMI-4.1) id AA02983; Mon, 7 Jun 93 19:26:37 EDT Received: by umdesun7.umd.umich.edu (4.1/SMI-4.1) id AA00682; Mon, 7 Jun 93 19:25:29 EDT Date: Mon, 7 Jun 1993 19:25:09 -0400 (EDT) From: ravi prasad Subject: To: Graph TI bulletin board Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII PUT SERPL.RAV This program is used by me quite frequently as it quickly computes the Equivelent Resistor, Cap, and Inductor values etc. ----begin documentation---- You must first run the uudecode "UUD20" program which will create the "SerPl.85P" file and then you must run the "LINK85" program to load the file to your TI85. Running the program. Simply execute the "SerPl" program by selecting it from the PROG menu. Since Cappacitors in series along with Conductance in series have the same simplification routine as Resistors, Inductors, and Impedences in parallel, you can use this program to simplify some of the computations for their equivelent values. Example: If you have 5 resistors in Parallel, simply type the value of each resistor one at a time. When done, type "0" as the last resistor (zero) value. The equivelent resistor value is given. Since parallel inductors and Impedence values are calculated in the same manner as resistors in prallel, the above technique may again be used except replacing resistor value by the inductor value. Since Cappacitors in series and Conductance in series are computed in the same manner as resistors in parallel, simply type the cappacitor values in place of the resistor values. The same is true for conductance. Req -----> Resistor equivelent Leq -----> Inductor equivelent Zeq -----> Impedence equivelent Ceq -----> Cappacitor equivelent Geq -----> Conductance equivelent NOTE: THE PROGRAM WILL ALSO HANDLE COMPLEX VALUES, AS IT WAS NECESSARY FOR ME TO BE ABLE TO WORK WITH IMPEDENCE EXPRESSED AS "jwc" or "1/jwl" etc. FOR CAPS AND INDUCTORS RESPECTIVELY. To enter complex numbers such as "1/(jwc)" I usually type "1/(0,w*c)" where omega "w" is the angular fequency of the input signal and "c" is the cappacitor value. I hope this program save someone a little time. I know it saves me a LOT of time. If any problems exist, feel free to talk to me at my email address: rpd@umdsun2.umd.umich.edu I have been using this program for over a year without any problems. ----end documentation---- ----begin ASCII---- \START\ \COMMENT=Program file dated 04/17/93, 17:55 \NAME=SerPl \FILE=SERPL.85P ClLCD Disp "This program finds" Disp "parallel Req,Leq,Zeq" Disp "or series Ceq,Geq" Disp "~~~~~~~~~~~~~~~~~~~~":0\->\\UC-Omega\ Lbl \UC-Omega\ Input "LRC:",\UC-Omega\\UC-Omega\ If norm \UC-Omega\\UC-Omega\\<>\0 Then \UC-Omega\+\UC-Omega\\UC-Omega\\^-1\\->\\UC-Omega\ Goto \UC-Omega\ Else End ClLCD:Disp "Circuit Equiv. Value":\UC-Omega\\^-1\ \STOP\ ----end ASCII---- ----begin UUE---- begin 644 serpl.85p M*BI423@U*BH:#`!0