wscott@ecn.purdue.edu (Wayne H Scott) (10/19/90)
Several people have requested it so... Here is a version of my polynomial routines that will work on a HP-28. My thanks to craig cantello who made the necessary changes to the programs. Also, my mail server has had a bug and was not answering mail for a day. If a request has not come back, send it again. Here it is, my polynomial routines version 3. for the HP28. This package include the following programs. TRIM Strip leading zeros from polynomial object. IRT Invert root program. Given n roots it return a nth degree polynomial. PDER Derivative of a polynomial. RDER Derivative of a rational function. PF Partial Fractions. (Handles multiple roots!) FCTP Factor polynomial RT Find roots of any polynomial L2A Convert a list to an array and back. PADD Add two polynomials PMUL Multiply two polynomials. PDIV Divide two polynomials. EVPLY Evalulate a polynomial at a point. COEF Given an equation return a polynomial list. These programs should work on a 28s, but I might have use the HP-48 only These programs all work on polynomials in the follows form: 3*X^3-7*X^2+5 is entered as { 3 -7 0 5 } so going down the list... The first program is FCTP. (factor polynomial) When it is passed the cooeficients of a polynomial in a list it returns the factor of that polynomal. ex: 1: { 1 -17.8 99.41 -261.218 352.611 -134.106 } FCTP 3: { 1 -4.2 2.1 } 2: { 1 -3.3 6.2 } 1: { 1 -10.3 } This tells us that X^5-17.8*X^4+99.41*X^3-261.218*X^2+352.611*X-134.106 factors to (X^2-4.2*X+2.1)*(X^2-3.3*X+6.2)*(X-10.3) The next program is RT. (Roots) If given a polynmoial it return its roots. ex: 1: { 1 -17.8 99.41 -261.218 352.611 -134.106 } RT 5: 3.61986841536 4: .58013158464 3: (1.65, 1.8648056199) 2: (1.65, -1.8648056199) 1: 10.3 Very Useful! These programs use the BAIRS program which performs Bairstow's method of quadratic factors and QUD with does the quadratic equation. TRIM is used to strip the leading zeros from a polynomial list. {0 0 3 0 7 } TRIM => { 3 0 7 } RDER will give the derivative of a rational function. ie. d x + 4 -X^2 - 8*x + 31 -- ------------- = -------------------------------- dx x^2 - 7*x + 3 x^4 - 14*x^3 + 55*x^2 - 42*x + 9 2: { 1 4 } 1: { 1 -7 3 } RDER 2: { -1 -8 31 } 1: { 1 -14 55 -42 9 } I don't know about you but I think it's useful. IRT will return a polynomial whose roots you specify. ie. If a transfer function has zeros at -1, 1 and 5 the function is x^3 - 5*x^2 - x + 5 1: { -1 1 5 } IRT 1: { 1 -5 -1 5 } PDER will return the derivtive of a polynomial. .ie The d/dx (x^3 - 5*x^2 - x + 5) = 3*x^2 - 10*x - 1 1: { 1 -5 -1 5 } PDER 1: { 3 -10 -1 } PF will do a partial fraction expansion on a transfer function. .ie s + 5 1/18 5/270 2/3 1/9 2/27 ----------------- = ----- + ----- - ------- - ------- - ----- (s-4)(s+2)(s-1)^3 (s-4) (s+2) (s-1)^3 (s-1)^2 (s-1) 2: { 1 5 } 1: { 4 -2 1 1 1 } PF 1: { 5.5555e-2 1.85185e-2 -.6666 -.11111 -.074074 } This program expects the polynomial of the numerator to be on level 2 and a list with the poles to be on level 1. Repeated poles are suported but they must be listed in order. The output is a list of the values of the fraction in the same order as the poles were entered. PADD, PMUL, and PDIV are all obvious, they take two polynomial lists off the stack and perform the operation on them. PDIV returns the polynomial and the remainder polynomial. L2A converts a list to and array. (and back) 1: { 1 2 3 } L2A 1: [ 1 2 3 ] L2A 1: { 1 2 3 } EVPLY evalutates and polynomial at a point. x^3 - 3*x^2 +10*x - 5 | x=2.5 = 16.875 2: { 1 -3 10 -5 } 1: 2.5 EVPLY 1: 16.875 TRIM \<< LIST-> \-> n \<< n WHILE ROLL DUP 0 == REPEAT DROP n 1 - DUP `n` STO END n ROLLD IF n 0 == THEN { 0 } ELSE n \->LIST END \>> \>> RDER \<< \-> F G \<< G F PDER PMUL G PDER { -1 } PMUL F PMUL PADD G G PMUL \>> \>> IRT \<< LIST-> \-> n \<< IF n 0 > THEN 1 n START n ROLL { 1 } SWAP NEG + NEXT ELSE { 1 } END IF n 1 > THEN 2 n START PMUL NEXT END \>> \>> PDER \<< LIST-> \-> n \<< 1 n FOR i n ROLL n i - * NEXT DROP IF n 1 == THEN { 0 } ELSE n 1 - \->LIST END \>> \>> PF \<< MAXR ->NUM { } \-> Z P OLD LAST \<< 1 P SIZE FOR I P I GET \-> p1 \<< IF p1 OLD \=/ THEN Z p1 EVPLY 1 P SIZE FOR J IF P J GET P I GET \=/ THEN p1 P J GET - / END NEXT p1 'OLD' STO { } 'LAST' STO ELSE IF { } LAST SAME THEN 1 { } 1 P SIZE FOR K P K GET IF DUP p1 == THEN DROP ELSE + END NEXT IRT Z SWAP ELSE LAST LIST-> DROP END RDER DUP2 5 PICK 1 + 3 ROLLD 3 \->LIST 'LAST' STO p1 EVPLY SWAP p1 EVPLY SWAP / SWAP FACT / END \>> NEXT P SIZE \->LIST \>> \>> FCTP \<< IF DUP SIZE 3 > THEN DUP BAIRS SWAP OVER PDIV DROP FCTP END \>> RT \<< TRIM DUP SIZE \-> n \<< IF n 3 > THEN DUP BAIRS SWAP OVER PDIV DROP \-> A B \<< A RT B RT \>> ELSE IF n 2 > THEN QUD ELSE LIST\-> DROP NEG SWAP / END END \>> \>> L2A \<< IF DUP TYPE 5 == THEN LIST-> \->ARRY ELSE ARRY-> 1 GET \->LIST END \>> PADD \<< DUP2 SIZE SWAP SIZE \-> A B nB nA \<< A L2A B L2A IF nA nB < THEN SWAP END IF nA nB \=/ THEN 1 nA nB - ABS START 0 NEXT END nA nB - ABS 1 + ROLL ARRY-> 1 GET nA nB - ABS + \->ARRY + L2A \>> \>> PMUL \<< DUP2 SIZE SWAP SIZE \-> A B nB nA \<< { } IF nB 1 > THEN 2 nB START 0 + NEXT END DUP A + SWAP + 'A' STO A LIST-> \->ARRY B LIST-> DROP IF nB 1 > THEN 2 nB FOR J J ROLL NEXT END IF 3 nA nB + \<= THEN 3 nA nB + START 0 NEXT END nA nB 1 - 2 * + \->ARRY 2 nA nB + START DUP2 DOT 3 ROLLD ARRY-> SWAP nA nB 1 - 2 * + 1 + ROLLD \->ARRY NEXT DROP2 nA nB + 1 - \->LIST \>> \>> PDIV \<< DUP SIZE 3 ROLLD LIST-> \->ARRY SWAP LIST-> \->ARRY \-> c b a \<< a b WHILE OVER SIZE 1 GET c \>= REPEAT DIVV END DROP \-> d \<< a SIZE 1 GET c 1 - - \->LIST d ARRY-> LIST-> DROP \->LIST \>> \>> \>> EVPLY \<< OVER IF DUP TYPE 5 == THEN SIZE ELSE SIZE 1 GET END \-> a r n \<< a 1 GET IF n 1 > THEN 2 n FOR i r * a i GET + NEXT END \>> \>> COEF \<< \-> E n \<< 0 n FOR I 0 'X' STO E EVAL 'X' PURGE E 'X' \.d 'E' STO I FACT / NEXT 2 n 1 + FOR I I ROLL NEXT n 1 + \->LIST \>> \>> DIVV \<< DUP 1 GET \-> a b c \<< a 1 GET c / DUP b * a SIZE RDM a SWAP - ARRY-> 1 GETI 1 - PUT \->ARRY SWAP DROP b \>> \>> QUD \<< LIST\-> \->ARRY DUP 1 GET / ARRY\-> DROP ROT DROP SWAP 2 / NEG DUP SQ ROT - \v/ DUP2 + 3 ROLLD - \>> BAIRS \<< LIST-> 1 1 \-> n R S \<< DO 0 n 1 + PICK 0 0 0 4 PICK 5 n + 7 FOR J J PICK R 7 PICK * + S 8 PICK * + 7 ROLL DROP DUP 6 ROLLD R 3 PICK * + S 4 PICK * + 5 ROLL DROP -1 STEP 3 PICK SQ 3 PICK 6 PICK * - IF DUP 0 == THEN DROP 1 1 ELSE 6 PICK 6 PICK * 5 PICK 9 PICK * - OVER / 4 PICK 9 PICK * 8 PICK 7 PICK * - ROT / END DUP S + 'S' STO SWAP DUP R + 'R' STO UNTIL R\->C ABS .000000001 < 7 ROLLD 6 DROPN END n DROPN 1 R NEG S NEG 3 \->LIST \>> \>> Wayne Scott | INTERNET: wscott@en.ecn.purdue.edu Electrical Engineering | BITNET: wscott%ea.ecn.purdue.edu@purccvm Purdue University | UUCP: {purdue, pur-ee}!en.ecn.purdue.edu!wscott -- _______________________________________________________________________________ Wayne Scott | INTERNET: wscott@ecn.purdue.edu Electrical Engineering | BITNET: wscott%ecn.purdue.edu@purccvm Purdue University | UUCP: {purdue, pur-ee}!ecn.purdue.edu!wscott
akcs.jimcox@hpcvbbs.UUCP (james e. cox) (10/30/90)
In an attempt to use the polynomial programs, I have been unable to get them to work. I am new at programing and could use some advice on these programs. The first question is if these programs can be used on a 48SX. I was led to believe that the 48SX could use programs from the 28S. If I am wrong about this, please let me know. The only programs in the bunch that would work were, Trim, Irt, L2A, and Evply. Thank You.