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Unknown  |  1990-03-24  |  1.3 KB
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+--------+-------------------------+-------------------------+--------+--------+
|00000000| 0d 00 05 13 20 f4 20 20 | 3e 50 6f 6c 79 52 6f 6f |.... .  |>PolyRoo|
|00000010| 74 73 32 0d 00 0a 36 20 | f4 20 42 41 49 52 53 54 |ts2...6 |. BAIRST|
|00000020| 4f 57 27 53 20 4d 45 54 | 48 4f 44 20 46 4f 52 20 |OW'S MET|HOD FOR |
|00000030| 54 48 45 20 52 4f 4f 54 | 53 20 4f 46 20 41 20 50 |THE ROOT|S OF A P|
|00000040| 4f 4c 59 4e 4f 4d 49 41 | 4c 0d 00 14 31 20 f4 20 |OLYNOMIA|L...1 . |
|00000050| 4f 46 20 54 48 45 20 46 | 4f 52 4d 20 41 28 30 29 |OF THE F|ORM A(0)|
|00000060| 2a 58 5e 4e 2b 41 28 31 | 29 2a 58 5e 28 4e 2d 31 |*X^N+A(1|)*X^(N-1|
|00000070| 29 2e 2e 2e 2e 2b 41 28 | 4e 29 0d 00 1e 28 20 f4 |)....+A(|N)...( .|
|00000080| 20 47 49 56 45 53 20 41 | 4c 4c 20 52 4f 4f 54 53 | GIVES A|LL ROOTS|
|00000090| 2c 20 52 45 41 4c 20 41 | 4e 44 20 43 4f 4d 50 4c |, REAL A|ND COMPL|
|000000a0| 45 58 0d 00 28 14 20 f4 | 20 42 59 20 4c 2e 45 2e |EX..(. .| BY L.E.|
|000000b0| 57 45 41 56 45 52 0d 00 | 2d 1e 20 f4 20 6d 6f 64 |WEAVER..|-. . mod|
|000000c0| 69 66 69 65 64 20 62 79 | 20 42 52 49 41 4e 20 43 |ified by| BRIAN C|
|000000d0| 4f 57 41 4e 0d 00 32 27 | 20 e8 20 22 50 52 49 4e |OWAN..2'| . "PRIN|
|000000e0| 54 20 4f 55 54 20 52 45 | 53 55 4c 54 53 3f 20 3a |T OUT RE|SULTS? :|
|000000f0| 20 59 2f 4e 20 20 22 2c | 20 41 24 0d 00 3c 1b 20 | Y/N  ",| A$..<. |
|00000100| e7 20 41 24 3d 22 59 22 | 20 84 20 41 24 3d 22 79 |. A$="Y"| . A$="y|
|00000110| 22 20 8c 20 ef 32 0d 00 | 46 09 20 2a 46 58 36 0d |" . .2..|F. *FX6.|
|00000120| 00 50 23 20 e8 20 22 20 | 4f 52 44 45 52 20 4f 46 |.P# . " |ORDER OF|
|00000130| 20 50 4f 4c 59 4e 4f 4d | 49 41 4c 3f 20 20 22 20 | POLYNOM|IAL?  " |
|00000140| 4e 25 0d 00 5a 18 20 de | 20 41 28 4e 25 29 2c 42 |N%..Z. .| A(N%),B|
|00000150| 28 4e 25 29 2c 43 28 4e | 25 29 0d 00 64 3d 20 e3 |(N%),C(N|%)..d= .|
|00000160| 20 49 25 20 3d 20 30 20 | b8 20 4e 25 3a 20 f1 20 | I% = 0 |. N%: . |
|00000170| 22 43 4f 45 46 46 49 43 | 49 45 4e 54 20 4f 46 20 |"COEFFIC|IENT OF |
|00000180| 50 4f 57 45 52 20 20 22 | 3b 4e 25 2d 49 25 3b 20 |POWER  "|;N%-I%; |
|00000190| 20 22 20 3d 20 22 3b 0d | 00 6e 17 20 e8 20 22 20 | " = ";.|.n. . " |
|000001a0| 20 22 20 41 28 49 25 29 | 3a 20 ed 20 49 25 0d 00 | " A(I%)|: . I%..|
|000001b0| 78 12 20 56 25 3d 31 3a | 20 41 5a 3d 41 28 30 29 |x. V%=1:| AZ=A(0)|
|000001c0| 0d 00 82 25 20 e3 20 49 | 25 3d 30 20 b8 20 4e 25 |...% . I|%=0 . N%|
|000001d0| 3a 20 41 28 49 25 29 3d | 41 28 49 25 29 2f 41 5a |: A(I%)=|A(I%)/AZ|
|000001e0| 3a ed 20 49 25 0d 00 8c | 12 20 f2 66 69 6e 64 28 |:. I%...|. .find(|
|000001f0| 41 28 29 2c 4e 25 29 0d | 00 a0 14 20 4e 25 3d 4e |A(),N%).|... N%=N|
|00000200| 25 2d 32 3a 56 25 3d 56 | 25 2b 32 0d 00 aa 0c 20 |%-2:V%=V|%+2.... |
|00000210| c8 8e 20 4e 25 20 ca 0d | 00 b4 2f 20 c9 20 31 20 |.. N% ..|../ . 1 |
|00000220| 3a 20 50 3d 42 28 31 29 | 3a 20 f1 20 22 52 4f 4f |: P=B(1)|: . "ROO|
|00000230| 54 20 20 22 3b 56 25 3b | 22 20 20 49 53 20 20 22 |T  ";V%;|"  IS  "|
|00000240| 3b 2d 42 28 31 29 0d 00 | be 24 20 c9 20 32 20 3a |;-B(1)..|.$ . 2 :|
|00000250| 20 50 3d 42 28 31 29 3a | 51 3d 42 28 32 29 3a f2 | P=B(1):|Q=B(2):.|
|00000260| 70 72 69 6e 74 28 50 2c | 51 29 0d 00 c8 27 20 7f |print(P,|Q)...' .|
|00000270| 20 e3 20 49 25 3d 30 20 | b8 20 4e 25 3a 41 28 49 | . I%=0 |. N%:A(I|
|00000280| 25 29 3d 42 28 49 25 29 | 3a ed 3a e5 20 8d 74 4c |%)=B(I%)|:.:. .tL|
|00000290| 40 0d 00 d2 06 20 cb 0d | 00 dc 07 20 ef 33 0d 00 |@.... ..|... .3..|
|000002a0| e6 06 20 e0 0d 00 f0 12 | 20 dd 20 f2 70 72 69 6e |.. .....| . .prin|
|000002b0| 74 28 50 2c 51 29 0d 00 | fa 1f 20 48 31 3d 2d 50 |t(P,Q)..|.. H1=-P|
|000002c0| 2f 32 3a 48 32 3d b6 28 | 94 28 50 2a 50 2d 34 2a |/2:H2=.(|.(P*P-4*|
|000002d0| 51 29 29 2f 32 0d 01 04 | 4b 20 e7 20 50 2a 50 3e |Q))/2...|K . P*P>|
|000002e0| 34 2a 51 20 8c 20 f1 22 | 52 4f 4f 54 20 20 22 3b |4*Q . ."|ROOT  ";|
|000002f0| 56 25 3b 22 20 20 49 53 | 20 20 22 3b 48 31 2d 48 |V%;"  IS|  ";H1-H|
|00000300| 32 3a 20 f1 22 52 4f 4f | 54 20 20 22 3b 56 25 2b |2: ."ROO|T  ";V%+|
|00000310| 31 3b 22 20 20 49 53 20 | 20 22 3b 48 31 2b 48 32 |1;"  IS | ";H1+H2|
|00000320| 0d 01 0e 3e 20 e7 20 50 | 2a 50 3c 34 2a 51 20 8c |...> . P|*P<4*Q .|
|00000330| 20 f1 22 52 4f 4f 54 53 | 20 20 22 3b 56 25 3b 22 | ."ROOTS|  ";V%;"|
|00000340| 2c 22 3b 56 25 2b 31 3b | 22 20 41 52 45 20 20 22 |,";V%+1;|" ARE  "|
|00000350| 3b 48 31 3b 22 2b 2d 20 | 6a 2a 22 3b 48 32 0d 01 |;H1;"+- |j*";H2..|
|00000360| 18 06 20 e1 0d 01 40 14 | 20 dd 20 f2 66 69 6e 64 |.. ...@.| . .find|
|00000370| 28 41 28 29 2c 4e 25 29 | 0d 01 54 15 20 ea 20 42 |(A(),N%)|..T. . B|
|00000380| 28 4e 25 29 2c 43 28 4e | 25 29 2c 49 25 0d 01 5e |(N%),C(N|%),I%..^|
|00000390| 0c 20 50 3d 30 3a 51 3d | 30 0d 01 68 06 20 f5 0d |. P=0:Q=|0..h. ..|
|000003a0| 01 72 4d 20 42 28 30 29 | 3d 41 28 30 29 3a 42 28 |.rM B(0)|=A(0):B(|
|000003b0| 31 29 3d 41 28 31 29 2d | 50 2a 42 28 30 29 3a e3 |1)=A(1)-|P*B(0):.|
|000003c0| 20 49 25 3d 32 20 b8 20 | 4e 25 3a 42 28 49 25 29 | I%=2 . |N%:B(I%)|
|000003d0| 3d 41 28 49 25 29 2d 50 | 2a 42 28 49 25 2d 31 29 |=A(I%)-P|*B(I%-1)|
|000003e0| 2d 51 2a 42 28 49 25 2d | 32 29 3a ed 0d 01 7c 1f |-Q*B(I%-|2):...|.|
|000003f0| 20 43 28 30 29 3d 42 28 | 30 29 3a 43 28 31 29 3d | C(0)=B(|0):C(1)=|
|00000400| 42 28 31 29 2d 50 2a 43 | 28 30 29 0d 01 86 51 20 |B(1)-P*C|(0)...Q |
|00000410| e3 20 49 25 3d 32 20 b8 | 20 4e 25 2d 32 3a 43 28 |. I%=2 .| N%-2:C(|
|00000420| 49 25 29 3d 42 28 49 25 | 29 2d 50 2a 43 28 49 25 |I%)=B(I%|)-P*C(I%|
|00000430| 2d 31 29 2d 51 2a 43 28 | 49 25 2d 32 29 3a ed 3a |-1)-Q*C(|I%-2):.:|
|00000440| 43 28 4e 25 2d 31 29 3d | 2d 50 2a 43 28 4e 25 2d |C(N%-1)=|-P*C(N%-|
|00000450| 32 29 2d 51 2a 43 28 4e | 25 2d 33 29 0d 01 90 26 |2)-Q*C(N|%-3)...&|
|00000460| 20 44 3d 43 28 4e 25 2d | 32 29 2a 43 28 4e 25 2d | D=C(N%-|2)*C(N%-|
|00000470| 32 29 2d 43 28 4e 25 2d | 31 29 2a 43 28 4e 25 2d |2)-C(N%-|1)*C(N%-|
|00000480| 33 29 0d 01 9a 16 20 e7 | 20 44 3c 31 45 2d 35 20 |3).... .| D<1E-5 |
|00000490| 8c 20 44 3d 2e 30 30 35 | 0d 01 a4 32 20 44 50 3d |. D=.005|...2 DP=|
|000004a0| 20 28 42 28 4e 25 2d 31 | 29 2a 43 28 4e 25 2d 32 | (B(N%-1|)*C(N%-2|
|000004b0| 29 2d 42 28 4e 25 29 2a | 43 28 4e 25 2d 33 29 29 |)-B(N%)*|C(N%-3))|
|000004c0| 2f 44 3a 20 50 3d 50 2b | 44 50 0d 01 ae 32 20 44 |/D: P=P+|DP...2 D|
|000004d0| 51 3d 2d 28 42 28 4e 25 | 2d 31 29 2a 43 28 4e 25 |Q=-(B(N%|-1)*C(N%|
|000004e0| 2d 31 29 2d 42 28 4e 25 | 29 2a 43 28 4e 25 2d 32 |-1)-B(N%|)*C(N%-2|
|000004f0| 29 29 2f 44 3a 20 51 3d | 51 2b 44 51 0d 01 b8 19 |))/D: Q=|Q+DQ....|
|00000500| 20 fd 20 94 28 28 44 50 | 29 2b 94 28 44 51 29 29 | . .((DP|)+.(DQ))|
|00000510| 3c 31 45 2d 38 0d 01 bd | 10 20 f2 70 72 69 6e 74 |<1E-8...|. .print|
|00000520| 28 50 2c 51 29 0d 01 c2 | 06 20 e1 0d ff          |(P,Q)...|. ...   |
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