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|00000000| 00 3a 00 01 00 00 00 00 | f0 5a 63 6f 70 79 72 69 |.:......|.Zcopyri|
|00000010| 67 68 74 20 31 39 39 34 | 20 62 79 20 53 74 65 70 |ght 1994| by Step|
|00000020| 68 65 6e 20 42 6f 65 72 | 6e 65 72 2c 20 65 79 65 |hen Boer|ner, eye|
|00000030| 20 73 79 73 74 65 6d 73 | 2d 20 00 00 00 44 00 02 | systems|- ...D..|
|00000040| ff c4 00 00 f0 5a 43 49 | 53 2d 37 34 32 30 33 2c |.....ZCI|S-74203,|
|00000050| 32 32 31 37 20 20 20 41 | 4f 4c 2d 49 53 49 53 49 |2217   A|OL-ISISI|
|00000060| 4e 43 20 20 42 4d 55 47 | 2c 20 49 4e 54 45 52 4e |NC  BMUG|, INTERN|
|00000070| 45 54 20 45 59 45 53 59 | 53 40 43 52 4c 2e 43 4f |ET EYESY|S@CRL.CO|
|00000080| 4d 00 00 2c 00 03 ff ba | 00 00 f0 5a 4d 41 59 20 |M..,....|...ZMAY |
|00000090| 4e 4f 54 20 42 45 20 55 | 53 45 44 20 46 4f 52 20 |NOT BE U|SED FOR |
|000000a0| 43 4f 4d 4d 45 52 43 49 | 41 4c 20 47 41 49 4e 00 |COMMERCI|AL GAIN.|
|000000b0| 00 3c 00 04 ff d2 00 00 | f0 5a 54 52 4f 4e 20 62 |.<......|.ZTRON b|
|000000c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000000d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000000e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 00 00 00 4e |        |    ...N|
|000000f0| 00 05 ff c2 00 00 f0 13 | 20 20 20 20 20 20 20 20 |........|        |
|00000100| 20 20 20 20 20 20 20 73 | 6f 6c 76 65 20 66 6f 72 |       s|olve for|
|00000110| 20 72 6f 6f 74 73 20 6f | 66 20 70 6f 6c 79 6e 6f | roots o|f polyno|
|00000120| 6d 69 61 6c 20 65 71 75 | 61 74 69 6f 6e 20 69 6e |mial equ|ation in|
|00000130| 20 6f 6e 65 20 75 6e 6b | 6e 6f 77 6e 00 00 00 38 | one unk|nown...8|
|00000140| 00 06 ff b0 00 00 f0 13 | 20 20 20 20 20 20 20 20 |........|        |
|00000150| 20 20 20 20 20 20 20 66 | 72 6f 6d 20 6e 75 6d 65 |       f|rom nume|
|00000160| 72 69 63 61 6c 20 6d 65 | 74 68 6f 64 73 20 69 6e |rical me|thods in|
|00000170| 20 70 61 73 63 61 6c 00 | 00 36 00 07 ff c6 00 00 | pascal.|.6......|
|00000180| f0 08 20 34 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. 4    |        |
|00000190| 20 20 20 20 20 20 27 20 | 68 69 67 68 65 73 74 20 |      ' |highest |
|000001a0| 70 6f 77 65 72 20 6f 66 | 20 78 20 78 5e 34 00 00 |power of| x x^4..|
|000001b0| 00 5c 00 08 ff c8 00 00 | f0 13 20 20 3d 28 78 2d |.\......|..  =(x-|
|000001c0| 31 29 2a 28 78 2d 32 29 | 2a 28 78 2d 33 29 2a 28 |1)*(x-2)|*(x-3)*(|
|000001d0| 78 2d 34 29 20 3d 20 78 | 5e 34 20 2d 20 31 30 20 |x-4) = x|^4 - 10 |
|000001e0| 78 5e 33 20 2b 20 33 35 | 20 78 5e 32 20 2d 20 35 |x^3 + 35| x^2 - 5|
|000001f0| 30 20 78 20 2b 20 32 34 | 20 28 69 6d 61 67 69 6e |0 x + 24| (imagin|
|00000200| 61 72 79 20 61 6c 6c 20 | 7a 65 72 6f 29 00 00 2e |ary all |zero)...|
|00000210| 00 09 ff a2 00 00 f0 08 | 20 32 34 2c 30 2c 20 20 |........| 24,0,  |
|00000220| 2d 35 30 2c 30 2c 20 20 | 33 35 2c 30 2c 20 20 2d |-50,0,  |35,0,  -|
|00000230| 31 30 2c 30 2c 20 20 31 | 2c 30 20 20 20 00 00 08 |10,0,  1|,0   ...|
|00000240| 00 0a ff d0 00 00 00 00 | 00 40 00 00 ff f6 00 00 |........|.@......|
|00000250| f2 08 20 23 31 2c 20 22 | 7a 72 6f 6f 74 73 20 20 |.. #1, "|zroots  |
|00000260| 28 63 6c 69 63 6b 20 74 | 6f 20 65 78 69 74 29 22 |(click t|o exit)"|
|00000270| 2c 28 34 2c 33 38 29 2d | 28 36 35 30 2c 35 30 30 |,(4,38)-|(650,500|
|00000280| 29 3a f0 28 20 31 30 30 | 00 00 00 3a 00 0c ff be |):.( 100|...:....|
|00000290| 00 00 f0 64 20 30 2c 20 | 5f 63 61 73 65 49 6e 73 |...d 0, |_caseIns|
|000002a0| 65 6e 73 69 74 69 76 65 | 20 5f 73 74 72 52 65 73 |ensitive| _strRes|
|000002b0| 6f 75 72 63 65 20 5f 6d | 61 63 73 62 75 67 4c 61 |ource _m|acsbugLa|
|000002c0| 62 65 6c 73 00 00 00 0e | 00 0d ff c4 00 00 f0 1b |bels....|........|
|000002d0| 20 61 2d 7a 00 00 00 22 | 00 0e ff f0 00 00 5f 4d | a-z..."|......_M|
|000002e0| 31 20 3d 20 31 30 f0 5a | 6d 61 78 20 6f 72 64 65 |1 = 10.Z|max orde|
|000002f0| 72 20 6f 66 20 70 6f 6c | 79 00 00 36 00 0f ff dc |r of pol|y..6....|
|00000300| 00 00 f0 0a 20 61 28 32 | 2c 5f 4d 31 29 2c 72 6f |.... a(2|,_M1),ro|
|00000310| 6f 74 73 28 32 2c 5f 4d | 31 29 2c 43 31 2c 43 32 |ots(2,_M|1),C1,C2|
|00000320| 2c 61 64 28 32 2c 5f 4d | 31 29 2c 78 31 2c 78 32 |,ad(2,_M|1),x1,x2|
|00000330| 00 00 00 0c 00 10 ff c8 | 00 00 f0 1f 20 f0 66 00 |........|.... .f.|
|00000340| 00 2a 00 11 ff f2 00 02 | f0 61 20 f2 02 20 63 61 |.*......|.a .. ca|
|00000350| 62 73 28 61 31 2c 61 32 | 29 3a 78 3d f4 14 28 61 |bs(a1,a2|):x=..(a|
|00000360| 31 29 3a 79 3d f4 14 28 | 61 32 29 00 00 26 00 12 |1):y=..(|a2)..&..|
|00000370| ff d4 02 02 f0 0f 20 78 | 3d 30 20 f6 05 20 7a 3d |...... x|=0 .. z=|
|00000380| 79 20 3a f0 15 20 f0 0f | 20 79 3d 30 20 f6 05 20 |y :.. ..| y=0 .. |
|00000390| 7a 3d 78 00 00 1e 00 13 | ff d8 02 02 f0 0f 20 78 |z=x.....|...... x|
|000003a0| 3d 30 20 f6 08 20 79 3d | 30 20 f6 05 20 f0 6f 20 |=0 .. y=|0 .. .o |
|000003b0| f2 02 00 00 00 3e 00 14 | ff e0 02 02 f0 0f 20 78 |.....>..|...... x|
|000003c0| 3e 79 20 f6 05 20 7a 3d | 78 2a f4 16 28 31 23 2b |>y .. z=|x*..(1#+|
|000003d0| 79 2a 79 2f 28 78 2a 78 | 29 29 20 3a f0 15 20 7a |y*y/(x*x|)) :.. z|
|000003e0| 3d 79 2a f4 16 28 31 23 | 2b 78 2a 78 2f 28 79 2a |=y*..(1#|+x*x/(y*|
|000003f0| 79 29 29 00 00 1c 00 15 | ff c0 02 02 f0 5a 7a 3d |y)).....|.....Zz=|
|00000400| 53 51 52 28 61 31 2a 61 | 31 2b 61 32 2a 61 32 29 |SQR(a1*a|1+a2*a2)|
|00000410| 00 00 00 10 00 16 ff e2 | 00 00 f0 1f 20 f2 02 20 |........|.... .. |
|00000420| 3d 20 7a 00 00 1e 00 17 | ff ee 00 02 f0 61 20 f2 |= z.....|.....a .|
|00000430| 02 20 63 64 69 76 28 61 | 31 2c 61 32 2c 62 31 2c |. cdiv(a|1,a2,b1,|
|00000440| 62 32 29 00 00 1a 00 18 | ff e0 02 04 f0 00 20 f0 |b2).....|...... .|
|00000450| 0f 20 f4 14 28 62 31 29 | 3e f4 14 28 62 32 29 00 |. ..(b1)|>..(b2).|
|00000460| 00 3c 00 19 ff e4 04 04 | 72 3d 62 32 2f 62 31 3a |.<......|r=b2/b1:|
|00000470| 64 65 6e 3d 62 31 2b 72 | 2a 62 32 3a 63 31 3d 28 |den=b1+r|*b2:c1=(|
|00000480| 61 31 2b 61 32 2a 72 29 | 2f 64 65 6e 3a 63 32 3d |a1+a2*r)|/den:c2=|
|00000490| 28 61 32 2d 61 31 2a 72 | 29 2f 64 65 6e 00 00 0a |(a2-a1*r|)/den...|
|000004a0| 00 1a ff c2 02 04 f0 05 | 00 00 00 3c 00 1b ff f4 |........|...<....|
|000004b0| 04 04 72 3d 62 31 2f 62 | 32 3a 64 65 6e 3d 62 32 |..r=b1/b|2:den=b2|
|000004c0| 2b 72 2a 62 31 3a 63 31 | 3d 28 61 31 2a 72 2b 61 |+r*b1:c1|=(a1*r+a|
|000004d0| 32 29 2f 64 65 6e 3a 63 | 32 3d 28 61 32 2a 72 2d |2)/den:c|2=(a2*r-|
|000004e0| 61 31 29 2f 64 65 6e 00 | 00 12 00 1c ff c2 00 00 |a1)/den.|........|
|000004f0| f0 1f 20 f0 0f 3a f0 1f | 20 f2 02 00 00 28 00 1d |.. ..:..| ....(..|
|00000500| ff ec 00 02 f0 61 20 f2 | 02 20 6c 61 67 75 65 72 |.....a .|. laguer|
|00000510| 28 4d 2c 65 70 73 2c 70 | 6f 6c 69 73 68 25 2c 64 |(M,eps,p|olish%,d|
|00000520| 78 6f 6c 64 29 00 00 38 | 00 1e ff d6 02 02 65 70 |xold)..8|......ep|
|00000530| 73 73 3d 36 45 2d 30 38 | 3a 6d 61 78 69 74 3d 31 |ss=6E-08|:maxit=1|
|00000540| 30 30 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |00      |        |
|00000550| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 00 00 |        |      ..|
|00000560| 00 22 00 1f ff c6 02 04 | f0 01 20 69 74 65 72 3d |."......|.. iter=|
|00000570| 31 20 f6 04 20 6d 61 78 | 69 74 3a f0 31 20 69 74 |1 .. max|it:.1 it|
|00000580| 65 72 3b 00 00 34 00 20 | ff dc 04 04 62 31 3d 61 |er;..4. |....b1=a|
|00000590| 64 28 31 2c 4d 2b 31 29 | 3a 62 32 3d 61 64 28 32 |d(1,M+1)|:b2=ad(2|
|000005a0| 2c 4d 2b 31 29 3a 65 72 | 71 3d f2 02 20 63 61 62 |,M+1):er|q=.. cab|
|000005b0| 73 28 62 31 2c 62 32 29 | 00 00 00 32 00 21 ff ca |s(b1,b2)|...2.!..|
|000005c0| 04 04 64 31 3d 30 23 3a | 64 32 3d 30 23 3a 66 31 |..d1=0#:|d2=0#:f1|
|000005d0| 3d 30 23 3a 66 32 3d 30 | 23 3a 61 62 78 3d f2 02 |=0#:f2=0|#:abx=..|
|000005e0| 20 63 61 62 73 28 78 31 | 2c 78 32 29 00 00 00 18 | cabs(x1|,x2)....|
|000005f0| 00 22 ff cc 04 06 f0 01 | 20 6a 3d 4d 20 f6 04 20 |."......| j=M .. |
|00000600| 31 20 f6 06 20 2d 31 00 | 00 32 00 23 ff e6 06 06 |1 .. -1.|.2.#....|
|00000610| 64 75 6d 3d 78 31 2a 66 | 31 2d 78 32 2a 66 32 2b |dum=x1*f|1-x2*f2+|
|00000620| 64 31 3a 66 32 3d 78 32 | 2a 66 31 2b 78 31 2a 66 |d1:f2=x2|*f1+x1*f|
|00000630| 32 2b 64 32 3a 66 31 3d | 64 75 6d 00 00 32 00 24 |2+d2:f1=|dum..2.$|
|00000640| ff cc 06 06 64 75 6d 3d | 78 31 2a 64 31 2d 78 32 |....dum=|x1*d1-x2|
|00000650| 2a 64 32 2b 62 31 3a 64 | 32 3d 78 32 2a 64 31 2b |*d2+b1:d|2=x2*d1+|
|00000660| 78 31 2a 64 32 2b 62 32 | 3a 64 31 3d 64 75 6d 00 |x1*d2+b2|:d1=dum.|
|00000670| 00 3c 00 25 ff cc 06 06 | 64 75 6d 3d 78 31 2a 62 |.<.%....|dum=x1*b|
|00000680| 31 2d 78 32 2a 62 32 2b | 61 64 28 31 2c 6a 29 3a |1-x2*b2+|ad(1,j):|
|00000690| 62 32 3d 78 32 2a 62 31 | 2b 78 31 2a 62 32 2b 61 |b2=x2*b1|+x1*b2+a|
|000006a0| 64 28 32 2c 6a 29 3a 62 | 31 3d 64 75 6d 00 00 28 |d(2,j):b|1=dum..(|
|000006b0| 00 26 ff c2 06 06 7a 31 | 3d f2 02 20 63 61 62 73 |.&....z1|=.. cabs|
|000006c0| 28 62 31 2c 62 32 29 3a | 65 72 71 3d 7a 31 2b 61 |(b1,b2):|erq=z1+a|
|000006d0| 62 78 2a 65 72 71 00 00 | 00 0c 00 27 ff d6 04 04 |bx*erq..|...'....|
|000006e0| f0 07 20 6a 00 00 00 26 | 00 28 ff f2 04 04 65 72 |.. j...&|.(....er|
|000006f0| 71 3d 65 70 73 73 2a 65 | 72 71 3a 7a 31 3d f2 02 |q=epss*e|rq:z1=..|
|00000700| 20 63 61 62 73 28 62 31 | 2c 62 32 29 00 00 00 1c | cabs(b1|,b2)....|
|00000710| 00 29 ff d8 04 04 f0 0f | 20 7a 31 3c 3d 65 72 71 |.)......| z1<=erq|
|00000720| 20 f6 05 20 f0 6f 20 f2 | 02 20 00 00 00 28 00 2a | .. .o .|. ...(.*|
|00000730| ff e2 04 04 f2 02 20 63 | 64 69 76 28 64 31 2c 64 |...... c|div(d1,d|
|00000740| 32 2c 62 31 2c 62 32 29 | 3a 67 31 3d 63 31 3a 67 |2,b1,b2)|:g1=c1:g|
|00000750| 32 3d 63 32 00 00 00 24 | 00 2b ff d6 04 04 67 32 |2=c2...$|.+....g2|
|00000760| 31 3d 67 31 2a 67 31 2d | 67 32 2a 67 32 3a 67 32 |1=g1*g1-|g2*g2:g2|
|00000770| 32 3d 32 23 2a 67 31 2a | 67 32 00 00 00 28 00 2c |2=2#*g1*|g2...(.,|
|00000780| ff da 04 04 f2 02 20 63 | 64 69 76 28 66 31 2c 66 |...... c|div(f1,f|
|00000790| 32 2c 62 31 2c 62 32 29 | 3a 7a 31 3d 63 31 3a 7a |2,b1,b2)|:z1=c1:z|
|000007a0| 32 3d 63 32 00 00 00 20 | 00 2d ff d6 04 04 68 31 |2=c2... |.-....h1|
|000007b0| 3d 67 32 31 2d 32 23 2a | 7a 31 3a 68 32 3d 67 32 |=g21-2#*|z1:h2=g2|
|000007c0| 32 2d 32 23 2a 7a 32 00 | 00 32 00 2e ff de 04 04 |2-2#*z2.|.2......|
|000007d0| 64 75 6d 31 3d 28 4d 2d | 31 29 2a 28 4d 2a 68 31 |dum1=(M-|1)*(M*h1|
|000007e0| 2d 67 32 31 29 3a 64 75 | 6d 32 3d 28 4d 2d 31 29 |-g21):du|m2=(M-1)|
|000007f0| 2a 28 4d 2a 68 32 2d 67 | 32 32 29 00 00 28 00 2f |*(M*h2-g|22)..(./|
|00000800| ff cc 04 04 f0 11 20 22 | 63 73 71 72 74 22 3a 67 |...... "|csqrt":g|
|00000810| 70 31 3d 67 31 2b 73 71 | 31 3a 67 70 32 3d 67 32 |p1=g1+sq|1:gp2=g2|
|00000820| 2b 73 71 32 00 00 00 1c | 00 30 ff d6 04 04 67 6d |+sq2....|.0....gm|
|00000830| 31 3d 67 31 2d 73 71 31 | 3a 67 6d 32 3d 67 32 2d |1=g1-sq1|:gm2=g2-|
|00000840| 73 71 32 00 00 2e 00 31 | ff e2 04 04 7a 31 3d f2 |sq2....1|....z1=.|
|00000850| 02 20 63 61 62 73 28 67 | 70 31 2c 67 70 32 29 3a |. cabs(g|p1,gp2):|
|00000860| 7a 32 3d f2 02 20 63 61 | 62 73 28 67 6d 31 2c 67 |z2=.. ca|bs(gm1,g|
|00000870| 6d 32 29 00 00 2a 00 32 | ff d0 04 04 f0 0f 20 7a |m2)..*.2|...... z|
|00000880| 31 3c 7a 32 20 f6 05 20 | 67 70 31 3d 67 6d 31 3a |1<z2 .. |gp1=gm1:|
|00000890| 67 70 32 3d 67 6d 32 3a | 5a 45 23 3d 30 23 00 00 |gp2=gm2:|ZE#=0#..|
|000008a0| 00 2c 00 33 ff d4 04 04 | f2 02 20 63 64 69 76 28 |.,.3....|.. cdiv(|
|000008b0| 4d 2c 5a 45 23 2c 67 70 | 31 2c 67 70 32 29 3a 64 |M,ZE#,gp|1,gp2):d|
|000008c0| 78 31 3d 63 31 3a 64 78 | 32 3d 63 32 00 00 00 1c |x1=c1:dx|2=c2....|
|000008d0| 00 34 ff d2 04 04 78 31 | 31 3d 78 31 2d 64 78 31 |.4....x1|1=x1-dx1|
|000008e0| 3a 78 31 32 3d 78 32 2d | 64 78 32 00 00 3e 00 35 |:x12=x2-|dx2..>.5|
|000008f0| ff e2 04 04 f0 0f 20 78 | 31 3d 78 31 31 20 f6 07 |...... x|1=x11 ..|
|00000900| 20 78 32 3d 78 31 32 20 | f6 05 20 f0 31 20 22 63 | x2=x12 |.. .1 "c|
|00000910| 6f 6e 76 65 72 67 65 64 | 22 3a f0 6f 20 f2 02 f0 |onverged|":.o ...|
|00000920| 5a 63 6f 6e 76 65 72 67 | 65 64 00 00 00 46 00 36 |Zconverg|ed...F.6|
|00000930| ff c0 04 04 78 31 3d 78 | 31 31 3a 78 32 3d 78 31 |....x1=x|11:x2=x1|
|00000940| 32 3a 63 64 78 3d f2 02 | 20 63 61 62 73 28 64 78 |2:cdx=..| cabs(dx|
|00000950| 31 2c 64 78 32 29 3a 64 | 78 6f 6c 64 3d 63 64 78 |1,dx2):d|xold=cdx|
|00000960| 3a 7a 32 3d f2 02 20 63 | 61 62 73 28 78 31 2c 78 |:z2=.. c|abs(x1,x|
|00000970| 32 29 00 00 00 2e 00 37 | ff b8 04 04 f0 0f 20 70 |2).....7|...... p|
|00000980| 6f 6c 69 73 68 25 3d 30 | 20 f6 05 20 f0 0f 20 63 |olish%=0| .. .. c|
|00000990| 64 78 3c 3d 65 70 73 2a | 7a 32 20 f6 05 20 f0 6f |dx<=eps*|z2 .. .o|
|000009a0| 20 f2 02 00 00 2e 00 38 | ff d0 02 02 f0 07 20 69 | ......8|...... i|
|000009b0| 74 65 72 3a f0 31 20 22 | 74 6f 6f 20 6d 61 6e 79 |ter:.1 "|too many|
|000009c0| 20 69 74 65 72 61 74 69 | 6f 6e 73 22 3a f0 6f 20 | iterati|ons":.o |
|000009d0| f2 02 00 00 00 38 00 39 | ff d0 02 02 22 63 73 71 |.....8.9|...."csq|
|000009e0| 72 74 22 3a f0 0f 20 64 | 75 6d 31 3d 30 23 20 f6 |rt":.. d|um1=0# .|
|000009f0| 07 20 64 75 6d 32 3d 30 | 23 20 f6 05 20 73 71 31 |. dum2=0|# .. sq1|
|00000a00| 3d 30 23 3a 73 71 32 3d | 30 23 3a f0 12 00 00 1e |=0#:sq2=|0#:.....|
|00000a10| 00 3a ff c6 02 04 f0 00 | 20 f0 0f 20 f4 14 28 64 |.:......| .. ..(d|
|00000a20| 75 6d 31 29 3e f4 14 28 | 64 75 6d 32 29 00 00 40 |um1)>..(|dum2)..@|
|00000a30| 00 3b ff e0 04 04 57 3d | f4 16 28 f4 14 28 64 75 |.;....W=|..(..(du|
|00000a40| 6d 31 29 29 2a f4 16 28 | 2e 35 23 2a 28 31 23 2b |m1))*..(|.5#*(1#+|
|00000a50| f4 16 28 31 23 2b 64 75 | 6d 32 2a 64 75 6d 32 2f |..(1#+du|m2*dum2/|
|00000a60| 28 64 75 6d 31 2a 64 75 | 6d 31 29 29 29 29 00 00 |(dum1*du|m1))))..|
|00000a70| 00 0a 00 3c ff be 02 04 | f0 05 00 00 00 16 00 3d |...<....|.......=|
|00000a80| ff f4 04 04 72 3d f4 14 | 28 64 75 6d 31 2f 64 75 |....r=..|(dum1/du|
|00000a90| 6d 32 29 00 00 2c 00 3e | ff e8 04 04 57 3d f4 16 |m2)..,.>|....W=..|
|00000aa0| 28 f4 14 28 64 75 6d 32 | 29 29 2a f4 16 28 2e 35 |(..(dum2|))*..(.5|
|00000ab0| 23 2a 28 72 2b f4 16 28 | 31 23 2b 72 2a 72 29 29 |#*(r+..(|1#+r*r))|
|00000ac0| 29 00 00 0c 00 3f ff d2 | 02 02 f0 1f 20 f0 0f 00 |)....?..|.... ...|
|00000ad0| 00 16 00 40 ff f2 02 04 | f0 00 20 f0 0f 20 64 75 |...@....|.. .. du|
|00000ae0| 6d 31 3e 3d 30 23 20 00 | 00 1e 00 41 ff e8 04 04 |m1>=0# .|...A....|
|00000af0| 73 71 31 3d 57 3a 73 71 | 32 3d 64 75 6d 32 2f 28 |sq1=W:sq|2=dum2/(|
|00000b00| 32 23 2a 73 71 31 29 00 | 00 0a 00 42 ff e0 02 04 |2#*sq1).|...B....|
|00000b10| f0 05 00 00 00 26 00 43 | ff f4 04 04 f0 0f 20 64 |.....&.C|...... d|
|00000b20| 75 6d 32 3e 3d 30 23 20 | f6 05 20 73 71 32 3d 57 |um2>=0# |.. sq2=W|
|00000b30| 20 3a f0 15 20 73 71 32 | 3d 2d 57 00 00 18 00 44 | :.. sq2|=-W....D|
|00000b40| ff d8 04 04 73 71 31 3d | 64 75 6d 32 2f 28 32 23 |....sq1=|dum2/(2#|
|00000b50| 2a 73 71 32 29 00 00 10 | 00 45 ff e6 02 02 f0 1f |*sq2)...|.E......|
|00000b60| 20 f0 0f 3a f0 12 00 00 | 00 0c 00 46 ff ee 00 00 | ..:....|...F....|
|00000b70| f0 1f 20 f2 02 00 00 2c | 00 47 ff f2 00 02 f0 61 |.. ....,|.G.....a|
|00000b80| 20 f2 02 20 7a 72 6f 6f | 74 73 28 4d 2c 70 6f 6c | .. zroo|ts(M,pol|
|00000b90| 69 73 68 25 29 3a 65 70 | 73 3d 2e 30 30 30 30 30 |ish%):ep|s=.00000|
|00000ba0| 31 23 00 00 00 3c 00 48 | ff d2 00 02 f0 01 20 6a |1#...<.H|...... j|
|00000bb0| 3d 31 20 f6 04 20 4d 2b | 31 3a 61 64 28 31 2c 6a |=1 .. M+|1:ad(1,j|
|00000bc0| 29 3d 61 28 31 2c 6a 29 | 3a 61 64 28 32 2c 6a 29 |)=a(1,j)|:ad(2,j)|
|00000bd0| 3d 61 28 32 2c 6a 29 3a | f0 07 20 6a 3a 70 25 3d |=a(2,j):|.. j:p%=|
|00000be0| 30 00 00 50 00 49 ff c2 | 02 04 f0 01 20 6a 3d 4d |0..P.I..|.... j=M|
|00000bf0| 20 f6 04 20 31 20 f6 06 | 20 2d 31 3a 78 31 3d 30 | .. 1 ..| -1:x1=0|
|00000c00| 23 3a 78 32 3d 30 23 3a | 64 78 37 3d f2 02 20 63 |#:x2=0#:|dx7=.. c|
|00000c10| 61 62 73 28 78 31 2c 78 | 32 29 3a f2 02 20 6c 61 |abs(x1,x|2):.. la|
|00000c20| 67 75 65 72 28 6a 2c 65 | 70 73 2c 70 25 2c 64 78 |guer(j,e|ps,p%,dx|
|00000c30| 37 29 00 00 00 2c 00 4a | ff ae 04 04 f0 0f 20 f4 |7)...,.J|...... .|
|00000c40| 14 28 78 32 29 3c 3d 32 | 23 2a 65 70 73 2a 65 70 |.(x2)<=2|#*eps*ep|
|00000c50| 73 2a f4 14 28 78 31 29 | 20 f6 05 20 78 32 3d 30 |s*..(x1)| .. x2=0|
|00000c60| 23 00 00 3c 00 4b ff d2 | 04 04 72 6f 6f 74 73 28 |#..<.K..|..roots(|
|00000c70| 31 2c 6a 29 3d 78 31 3a | 72 6f 6f 74 73 28 32 2c |1,j)=x1:|roots(2,|
|00000c80| 6a 29 3d 78 32 3a 62 31 | 3d 61 64 28 31 2c 6a 2b |j)=x2:b1|=ad(1,j+|
|00000c90| 31 29 3a 62 32 3d 61 64 | 28 32 2c 6a 2b 31 29 00 |1):b2=ad|(2,j+1).|
|00000ca0| 00 4c 00 4c ff c2 04 06 | f0 01 20 6a 6a 3d 6a 20 |.L.L....|.. jj=j |
|00000cb0| f6 04 20 31 20 f6 06 20 | 2d 31 3a 63 63 31 3d 61 |.. 1 .. |-1:cc1=a|
|00000cc0| 64 28 31 2c 6a 6a 29 3a | 63 63 32 3d 61 64 28 32 |d(1,jj):|cc2=ad(2|
|00000cd0| 2c 6a 6a 29 3a 61 64 28 | 31 2c 6a 6a 29 3d 62 31 |,jj):ad(|1,jj)=b1|
|00000ce0| 3a 61 64 28 32 2c 6a 6a | 29 3d 62 32 00 00 00 3e |:ad(2,jj|)=b2...>|
|00000cf0| 00 4d ff b2 02 02 64 75 | 6d 3d 62 31 3a 62 31 3d |.M....du|m=b1:b1=|
|00000d00| 78 31 2a 64 75 6d 2d 78 | 32 2a 62 32 2b 63 63 31 |x1*dum-x|2*b2+cc1|
|00000d10| 3a 62 32 3d 78 32 2a 64 | 75 6d 2b 78 31 2a 62 32 |:b2=x2*d|um+x1*b2|
|00000d20| 2b 63 63 32 3a f0 07 20 | 6a 6a 2c 6a 00 00 00 16 |+cc2:.. |jj,j....|
|00000d30| 00 4e ff c0 02 04 f0 00 | 20 f0 0f 20 70 6f 6c 69 |.N......| .. poli|
|00000d40| 73 68 25 3c 30 00 00 38 | 00 4f ff e8 02 04 f0 01 |sh%<0..8|.O......|
|00000d50| 20 6a 3d 31 20 f6 04 20 | 4d 2b 31 3a 61 64 28 31 | j=1 .. |M+1:ad(1|
|00000d60| 2c 6a 29 3d 61 28 31 2c | 6a 29 3a 61 64 28 32 2c |,j)=a(1,|j):ad(2,|
|00000d70| 6a 29 3d 61 28 32 2c 6a | 29 3a f0 07 20 6a 00 00 |j)=a(2,j|):.. j..|
|00000d80| 00 38 00 50 ff c6 04 06 | 70 25 3d 2d 31 3a f0 01 |.8.P....|p%=-1:..|
|00000d90| 20 6a 3d 31 20 f6 04 20 | 4d 3a 64 75 6d 31 3d 72 | j=1 .. |M:dum1=r|
|00000da0| 6f 6f 74 73 28 31 2c 6a | 29 3a 64 75 6d 32 3d 72 |oots(1,j|):dum2=r|
|00000db0| 6f 6f 74 73 28 32 2c 6a | 29 00 00 1a 00 51 ff c6 |oots(2,j|)....Q..|
|00000dc0| 06 06 64 78 37 3d f2 02 | 20 63 61 62 73 28 78 31 |..dx7=..| cabs(x1|
|00000dd0| 2c 78 32 29 00 00 00 34 | 00 52 ff e4 04 04 f2 02 |,x2)...4|.R......|
|00000de0| 20 6c 61 67 75 65 72 28 | 4d 2c 65 70 73 2c 70 25 | laguer(|M,eps,p%|
|00000df0| 2c 64 78 37 29 3a 64 75 | 6d 31 3d 78 31 3a 64 75 |,dx7):du|m1=x1:du|
|00000e00| 6d 32 3d 78 32 3a f0 07 | 20 6a 00 00 00 0c 00 53 |m2=x2:..| j.....S|
|00000e10| ff ca 02 02 f0 1f 20 f0 | 0f 00 00 2e 00 54 ff f2 |...... .|.....T..|
|00000e20| 02 04 f0 01 20 6a 3d 32 | 20 f6 04 20 4d 3a 78 31 |.... j=2| .. M:x1|
|00000e30| 3d 72 6f 6f 74 73 28 31 | 2c 6a 29 3a 78 32 3d 72 |=roots(1|,j):x2=r|
|00000e40| 6f 6f 74 73 28 32 2c 6a | 29 00 00 3a 00 55 ff d0 |oots(2,j|)..:.U..|
|00000e50| 04 06 f0 01 20 69 3d 6a | 2d 31 20 f6 04 20 31 20 |.... i=j|-1 .. 1 |
|00000e60| f6 06 20 2d 31 3a f0 0f | 20 72 6f 6f 74 73 28 31 |.. -1:..| roots(1|
|00000e70| 2c 69 29 3c 3d 78 31 20 | f6 05 20 f0 0d 20 22 78 |,i)<=x1 |.. .. "x|
|00000e80| 66 6f 72 22 00 00 00 3c | 00 56 ff c4 04 04 72 6f |for"...<|.V....ro|
|00000e90| 6f 74 73 28 31 2c 69 2b | 31 29 3d 72 6f 6f 74 73 |ots(1,i+|1)=roots|
|00000ea0| 28 31 2c 69 29 3a 72 6f | 6f 74 73 28 32 2c 69 2b |(1,i):ro|ots(2,i+|
|00000eb0| 31 29 3d 72 6f 6f 74 73 | 28 32 2c 69 29 3a f0 07 |1)=roots|(2,i):..|
|00000ec0| 20 69 00 00 00 24 00 57 | ff c2 04 04 22 78 66 6f | i...$.W|...."xfo|
|00000ed0| 72 22 f0 0f 20 72 6f 6f | 74 73 28 31 2c 69 29 3e |r".. roo|ts(1,i)>|
|00000ee0| 78 31 20 f6 05 20 69 3d | 30 00 00 26 00 58 ff da |x1 .. i=|0..&.X..|
|00000ef0| 04 04 72 6f 6f 74 73 28 | 31 2c 69 2b 31 29 3d 78 |..roots(|1,i+1)=x|
|00000f00| 31 3a 72 6f 6f 74 73 28 | 32 2c 69 2b 31 29 3d 78 |1:roots(|2,i+1)=x|
|00000f10| 32 00 00 12 00 59 ff d8 | 00 00 f0 07 20 6a 3a f0 |2....Y..|.... j:.|
|00000f20| 1f 20 f2 02 00 00 00 12 | 00 5a ff ec 00 00 f0 0b |. ......|.Z......|
|00000f30| 20 4d 3a 4d 31 3d 4d 2b | 31 00 00 3a 00 5b ff ec | M:M1=M+|1..:.[..|
|00000f40| fc 00 f0 01 20 6a 3d 31 | 20 f6 04 20 4d 31 3a f0 |.... j=1| .. M1:.|
|00000f50| 01 20 69 3d 31 20 f6 04 | 20 32 3a f0 0b 20 61 28 |. i=1 ..| 2:.. a(|
|00000f60| 69 2c 6a 29 3a f0 07 20 | 69 2c 6a 3a 70 6f 6c 69 |i,j):.. |i,j:poli|
|00000f70| 73 68 25 3d 30 00 00 22 | 00 5c ff c4 00 00 f2 02 |sh%=0.."|.\......|
|00000f80| 20 7a 72 6f 6f 74 73 28 | 4d 2c 70 6f 6c 69 73 68 | zroots(|M,polish|
|00000f90| 25 29 3a f0 11 20 22 70 | 22 00 00 12 00 5d ff dc |%):.. "p|"....]..|
|00000fa0| 00 02 f0 01 20 69 3d 31 | 20 f6 04 20 4d 00 00 48 |.... i=1| .. M..H|
|00000fb0| 00 5e ff ec 02 02 72 6f | 6f 74 73 28 31 2c 69 29 |.^....ro|ots(1,i)|
|00000fc0| 3d 72 6f 6f 74 73 28 31 | 2c 69 29 2a 28 31 2b 2e |=roots(1|,i)*(1+.|
|00000fd0| 30 31 23 2a 69 29 3a 72 | 6f 6f 74 73 28 32 2c 69 |01#*i):r|oots(2,i|
|00000fe0| 29 3d 72 6f 6f 74 73 28 | 32 2c 69 29 2a 28 31 2b |)=roots(|2,i)*(1+|
|00000ff0| 2e 30 31 23 2a 69 29 00 | 00 0c 00 5f ff b6 00 00 |.01#*i).|..._....|
|00001000| f0 07 20 69 00 00 00 2e | 00 60 ff f2 00 00 70 6f |.. i....|.`....po|
|00001010| 6c 69 73 68 25 3d 2d 31 | 3a f2 02 20 7a 72 6f 6f |lish%=-1|:.. zroo|
|00001020| 74 73 28 4d 2c 70 6f 6c | 69 73 68 25 29 3a f0 11 |ts(M,pol|ish%):..|
|00001030| 20 22 70 22 00 00 00 1c | 00 61 ff d0 fe 00 f0 37 | "p"....|.a.....7|
|00001040| 20 f2 0b 28 5f 64 6f 77 | 6e 29 3d 30 3a f0 38 3a | ..(_dow|n)=0:.8:|
|00001050| f0 1f 00 00 00 3c 00 62 | ff e2 fe 00 22 70 22 f0 |.....<.b|...."p".|
|00001060| 31 3a f0 01 20 69 3d 31 | 20 f6 04 20 4d 3a f0 31 |1:.. i=1| .. M:.1|
|00001070| 20 69 3b 72 6f 6f 74 73 | 28 31 2c 69 29 3b 72 6f | i;roots|(1,i);ro|
|00001080| 6f 74 73 28 32 2c 69 29 | 3a f0 07 20 69 3a f0 12 |ots(2,i)|:.. i:..|
|00001090| 00 00 00 0a 00 63 ff c2 | 00 00 f0 1f 00 00 00 32 |.....c..|.......2|
|000010a0| 00 64 ff f4 00 00 f0 5a | 20 20 44 41 54 41 20 34 |.d.....Z|  DATA 4|
|000010b0| 20 20 27 20 6f 74 68 65 | 72 20 65 78 61 6d 70 6c |  ' othe|r exampl|
|000010c0| 65 73 20 28 61 6c 6c 20 | 6f 72 64 65 72 20 34 29 |es (all |order 4)|
|000010d0| 00 00 00 44 00 65 ff cc | 00 00 f0 08 20 32 34 2c |...D.e..|.... 24,|
|000010e0| 30 2c 2d 35 30 2c 30 2c | 33 35 2c 30 2c 2d 31 30 |0,-50,0,|35,0,-10|
|000010f0| 2c 30 2c 31 2c 30 20 20 | 20 20 20 20 20 20 20 20 |,0,1,0  |        |
|00001100| 20 20 27 32 34 2d 35 30 | 78 2b 33 35 58 32 2d 31 |  '24-50|x+35X2-1|
|00001110| 30 78 33 2b 78 34 00 00 | 00 34 00 66 ff ba 00 00 |0x3+x4..|.4.f....|
|00001120| f0 08 20 31 36 2e 30 2c | 30 2c 20 20 2d 34 2e 30 |.. 16.0,|0,  -4.0|
|00001130| 2c 30 2c 20 20 2d 33 2e | 30 2c 30 2c 20 20 2d 31 |,0,  -3.|0,0,  -1|
|00001140| 2e 30 2c 30 2c 20 20 2d | 38 2e 30 2c 30 00 00 24 |.0,0,  -|8.0,0..$|
|00001150| 00 67 ff ca 00 00 f0 08 | 20 2d 31 30 2c 30 2c 31 |.g......| -10,0,1|
|00001160| 31 2c 30 2c 2d 39 2c 30 | 2c 2d 31 33 2c 30 2c 38 |1,0,-9,0|,-13,0,8|
|00001170| 2c 30 00 00 00 26 00 68 | ff da 00 00 f0 08 20 39 |,0...&.h|...... 9|
|00001180| 30 2c 30 2c 2d 39 39 2c | 30 2c 38 31 2c 30 2c 31 |0,0,-99,|0,81,0,1|
|00001190| 31 37 2c 30 2c 2d 37 32 | 2c 30 00 00 00 20 00 69 |17,0,-72|,0... .i|
|000011a0| ff d8 00 00 f0 08 20 38 | 2c 30 2c 31 2c 30 2c 33 |...... 8|,0,1,0,3|
|000011b0| 2c 30 2c 34 2c 30 2c 2d | 31 36 2c 30 00 00 00 28 |,0,4,0,-|16,0...(|
|000011c0| 00 6a ff de 00 00 f0 08 | 20 30 2c 32 2e 30 2c 30 |.j......| 0,2.0,0|
|000011d0| 2c 30 2c 2d 31 2e 30 2c | 2d 32 2e 30 2c 30 2c 30 |,0,-1.0,|-2.0,0,0|
|000011e0| 2c 31 2e 30 2c 30 00 00 | 00 2c 00 6b ff d6 00 00 |,1.0,0..|.,.k....|
|000011f0| f0 08 20 31 36 2e 30 2c | 30 2c 2d 34 2e 30 2c 30 |.. 16.0,|0,-4.0,0|
|00001200| 2c 2d 33 2e 30 2c 30 2c | 2d 31 2e 30 2c 30 2c 2d |,-3.0,0,|-1.0,0,-|
|00001210| 38 2e 30 2c 30 00 00 08 | 00 6c ff d2 00 00 00 00 |8.0,0...|.l......|
|00001220| 00 08 00 6d ff f6 00 00 | 00 00 00 08 00 6e ff f6 |...m....|.....n..|
|00001230| 00 00 00 00 00 08 00 6f | ff f6 00 00 00 00 00 0a |.......o|........|
|00001240| ff ff ff f6 ff 76 f0 12 | 00 00                   |.....v..|..      |
+--------+-------------------------+-------------------------+--------+--------+