BBS in a Box 5

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MacBinary | 1989-05-31 | 70.6 KB | [TEXT/OMEG]
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This file was processed as: MacBinary (archive/macBinary).

You can browse this item here: Moment Methods
Confidence	Program	Detection	Match Type	Support
`10%`	dexvert	MacBinary `(archive/macBinary)`	fallback	Supported
`1%`	dexvert	Text File `(text/txt)`	fallback	Supported
`100%`	file	MacBinary II, inited, Wed May 31 02:28:20 1989, modified Wed May 31 02:28:20 1989, creator 'OMEG', type ASCII, 36727 bytes "Moment Methods" Mathematica notebook version 2.x, at 0x8ff7 35451 bytes resource Mathematica notebook version 2.x	default (weak)
`99%`	file	data	default
`74%`	TrID	Macintosh plain text (MacBinary)	default
`25%`	TrID	MacBinary 2	default (weak)
`100%`	siegfried	fmt/1762 MacBinary (II)	default
`100%`	lsar	MacBinary	default
id metadata
key	value
macFileType	`[TEXT]`
macFileCreator	`[OMEG]`
hex view
+--------+-------------------------+-------------------------+--------+--------+
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|00001800| 31 30 31 38 2c 32 3b 31 | 30 31 39 2c 34 3b 31 30 |1018,2;1|019,4;10|
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|00001860| 32 3b 31 31 34 35 2c 34 | 3b 31 31 34 37 2c 32 3b |2;1145,4|;1147,2;|
|00001870| 31 31 35 32 2c 34 3b 31 | 31 35 33 2c 31 3b 31 31 |1152,4;1|153,1;11|
|00001880| 36 30 2c 32 3b 31 31 36 | 31 2c 34 3b 31 31 36 32 |60,2;116|1,4;1162|
|00001890| 2c 32 3b 31 31 36 36 2c | 34 3b 31 31 36 37 2c 31 |,2;1166,|4;1167,1|
|000018a0| 3b 31 32 30 31 2c 32 3b | 31 32 30 32 2c 34 3b 31 |;1201,2;|1202,4;1|
|000018b0| 32 30 33 2c 31 3b 31 32 | 30 38 2c 32 3b 31 32 30 |203,1;12|08,2;120|
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|000018f0| 31 32 2c 30 2c 30 2c 30 | 3b 33 30 2c 31 34 2c 31 |12,0,0,0|;30,14,1|
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|00002590| 0d 7b 7b 31 2f 33 7d 7d | 0d 3b 5b 6f 5d 0d 20 20 |.{{1/3}}|.;[o].  |
|000025a0| 31 0d 7b 7b 2d 7d 7d 0d | 20 20 33 0d 3a 5b 73 74 |1.{{-}}.|  3.:[st|
|000025b0| 61 72 74 47 72 6f 75 70 | 3b 20 66 6f 6e 74 20 3d |artGroup|; font =|
|000025c0| 20 69 6e 70 75 74 3b 20 | 5d 0d 67 56 65 63 20 3d | input; |].gVec =|
|000025d0| 20 49 6e 74 65 67 72 61 | 74 65 5b 20 20 77 20 67 | Integra|te[  w g|
|000025e0| 2c 20 7b 78 2c 30 2c 31 | 7d 5d 0d 3a 5b 69 6e 61 |, {x,0,1|}].:[ina|
|000025f0| 63 74 69 76 65 3b 20 6f | 75 74 70 75 74 3b 20 65 |ctive; o|utput; e|
|00002600| 6e 64 47 72 6f 75 70 3b | 20 66 6f 6e 74 20 3d 20 |ndGroup;| font = |
|00002610| 6f 75 74 70 75 74 3b 20 | 5d 0d 7b 31 31 2f 33 30 |output; |].{11/30|
|00002620| 7d 0d 3b 5b 6f 5d 0d 20 | 31 31 0d 7b 2d 2d 7d 0d |}.;[o]. |11.{--}.|
|00002630| 20 33 30 0d 3a 5b 69 6e | 61 63 74 69 76 65 3b 20 | 30.:[in|active; |
|00002640| 66 6f 6e 74 20 3d 20 74 | 65 78 74 3b 20 5d 0d 53 |font = t|ext; ].S|
|00002650| 69 6e 63 65 20 61 20 3d | 20 49 6e 76 65 72 73 65 |ince a =| Inverse|
|00002660| 5b 6c 5d 2e 67 56 65 63 | 20 77 65 20 67 65 74 3a |[l].gVec| we get:|
|00002670| 0d 3b 5b 73 5d 0d 33 3a | 30 2c 30 3b 36 2c 31 3b |.;[s].3:|0,0;6,1;|
|00002680| 32 35 2c 30 3b 33 34 2c | 2d 31 3b 0d 32 3a 32 2c |25,0;34,|-1;.2:2,|
|00002690| 31 36 2c 31 30 2c 50 61 | 6c 61 74 69 6e 6f 2c 30 |16,10,Pa|latino,0|
|000026a0| 2c 31 32 2c 30 2c 30 2c | 30 3b 31 2c 31 32 2c 31 |,12,0,0,|0;1,12,1|
|000026b0| 30 2c 43 6f 75 72 69 65 | 72 2c 30 2c 31 32 2c 30 |0,Courie|r,0,12,0|
|000026c0| 2c 30 2c 30 3b 0d 3a 5b | 73 74 61 72 74 47 72 6f |,0,0;.:[|startGro|
|000026d0| 75 70 3b 20 66 6f 6e 74 | 20 3d 20 69 6e 70 75 74 |up; font| = input|
|000026e0| 3b 20 5d 0d 61 20 3d 20 | 49 6e 76 65 72 73 65 5b |; ].a = |Inverse[|
|000026f0| 6c 5d 2e 67 56 65 63 0d | 3a 5b 69 6e 61 63 74 69 |l].gVec.|:[inacti|
|00002700| 76 65 3b 20 6f 75 74 70 | 75 74 3b 20 65 6e 64 47 |ve; outp|ut; endG|
|00002710| 72 6f 75 70 3b 20 66 6f | 6e 74 20 3d 20 6f 75 74 |roup; fo|nt = out|
|00002720| 70 75 74 3b 20 5d 0d 7b | 31 31 2f 31 30 7d 0d 3b |put; ].{|11/10}.;|
|00002730| 5b 6f 5d 0d 20 31 31 0d | 7b 2d 2d 7d 0d 20 31 30 |[o]. 11.|{--}. 10|
|00002740| 0d 3a 5b 69 6e 61 63 74 | 69 76 65 3b 20 65 6e 64 |.:[inact|ive; end|
|00002750| 47 72 6f 75 70 3b 20 66 | 6f 6e 74 20 3d 20 74 65 |Group; f|ont = te|
|00002760| 78 74 3b 20 5d 0d 54 68 | 65 20 73 61 6d 65 20 72 |xt; ].Th|e same r|
|00002770| 65 73 75 6c 74 20 61 73 | 20 48 61 72 72 69 6e 67 |esult as| Harring|
|00002780| 74 6f 6e 2e 0d 3a 5b 69 | 6e 61 63 74 69 76 65 3b |ton..:[i|nactive;|
|00002790| 20 73 74 61 72 74 47 72 | 6f 75 70 3b 20 43 63 6c | startGr|oup; Ccl|
|000027a0| 6f 73 65 64 3b 20 66 6f | 6e 74 20 3d 20 73 75 62 |osed; fo|nt = sub|
|000027b0| 73 65 63 74 69 6f 6e 3b | 20 5d 0d 46 6f 72 20 68 |section;| ].For h|
|000027c0| 69 67 68 65 72 20 6f 72 | 64 65 72 20 73 6f 6c 75 |igher or|der solu|
|000027d0| 74 69 6f 6e 73 20 77 65 | 20 68 61 76 65 3a 0d 3a |tions we| have:.:|
|000027e0| 5b 73 74 61 72 74 47 72 | 6f 75 70 3b 20 66 6f 6e |[startGr|oup; fon|
|000027f0| 74 20 3d 20 69 6e 70 75 | 74 3b 20 5d 0d 6e 4d 61 |t = inpu|t; ].nMa|
|00002800| 78 20 3d 20 33 3b 0d 66 | 20 3d 20 54 61 62 6c 65 |x = 3;.f| = Table|
|00002810| 5b 20 78 20 2d 20 78 5e | 28 6e 2b 31 29 2c 20 7b |[ x - x^|(n+1), {|
|00002820| 6e 2c 6e 4d 61 78 7d 5d | 3b 0d 77 20 3d 20 66 3b |n,nMax}]|;.w = f;|
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|00002840| 6d 65 74 68 6f 64 20 61 | 67 61 69 6e 20 2a 29 0d |method a|gain *).|
|00002850| 6c 20 3d 20 49 6e 74 65 | 67 72 61 74 65 5b 20 4f |l = Inte|grate[ O|
|00002860| 75 74 65 72 5b 54 69 6d | 65 73 2c 20 77 2c 20 4c |uter[Tim|es, w, L|
|00002870| 5b 66 5d 5d 2c 20 7b 78 | 2c 30 2c 31 7d 5d 3b 0d |[f]], {x|,0,1}];.|
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|00002890| 5b 20 20 77 20 67 2c 20 | 7b 78 2c 30 2c 31 7d 5d |[  w g, |{x,0,1}]|
|000028a0| 3b 0d 61 20 3d 20 49 6e | 76 65 72 73 65 5b 6c 5d |;.a = In|verse[l]|
|000028b0| 20 2e 20 67 56 65 63 3b | 0d 3a 5b 73 74 61 72 74 | . gVec;|.:[start|
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|000028d0| 70 75 74 3b 20 5d 0d 28 | 2a 20 77 68 65 6e 20 6e |put; ].(|* when n|
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|000028f0| 29 20 77 65 20 66 69 6e | 64 20 74 68 65 20 65 78 |) we fin|d the ex|
|00002900| 61 63 74 20 73 6f 6c 75 | 74 69 6f 6e 3a 20 2a 29 |act solu|tion: *)|
|00002910| 0d 4c 5b 61 2e 66 5d 0d | 3a 5b 69 6e 61 63 74 69 |.L[a.f].|:[inacti|
|00002920| 76 65 3b 20 6f 75 74 70 | 75 74 3b 20 65 6e 64 47 |ve; outp|ut; endG|
|00002930| 72 6f 75 70 3b 20 66 6f | 6e 74 20 3d 20 6f 75 74 |roup; fo|nt = out|
|00002940| 70 75 74 3b 20 5d 0d 2d | 28 2d 31 20 2d 20 34 2a |put; ].-|(-1 - 4*|
|00002950| 78 5e 32 29 0d 3b 5b 6f | 5d 0d 20 20 20 20 20 20 |x^2).;[o|].      |
|00002960| 20 20 20 20 32 0d 2d 28 | 2d 31 20 2d 20 34 20 78 |    2.-(|-1 - 4 x|
|00002970| 20 29 0d 3a 5b 73 74 61 | 72 74 47 72 6f 75 70 3b | ).:[sta|rtGroup;|
|00002980| 20 43 63 6c 6f 73 65 64 | 3b 20 66 6f 6e 74 20 3d | Cclosed|; font =|
|00002990| 20 69 6e 70 75 74 3b 20 | 5d 0d 4d 61 74 72 69 78 | input; |].Matrix|
|000029a0| 46 6f 72 6d 5b 6c 5d 0d | 3a 5b 69 6e 61 63 74 69 |Form[l].|:[inacti|
|000029b0| 76 65 3b 20 6f 75 74 70 | 75 74 3b 20 65 6e 64 47 |ve; outp|ut; endG|
|000029c0| 72 6f 75 70 3b 20 66 6f | 6e 74 20 3d 20 6f 75 74 |roup; fo|nt = out|
|000029d0| 70 75 74 3b 20 5d 0d 4d | 61 74 72 69 78 46 6f 72 |put; ].M|atrixFor|
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|000029f0| 35 7d 2c 20 7b 31 2f 32 | 2c 20 34 2f 35 2c 20 31 |5}, {1/2|, 4/5, 1|
|00002a00| 7d 2c 20 0d 20 20 20 20 | 20 20 7b 33 2f 35 2c 20 |}, .    |  {3/5, |
|00002a10| 31 2c 20 39 2f 37 7d 7d | 5d 0d 3b 5b 6f 5d 0d 31 |1, 9/7}}|].;[o].1|
|00002a20| 20 20 31 20 20 33 0d 2d | 20 20 2d 20 20 2d 0d 33 |  1  3.-|  -  -.3|
|00002a30| 20 20 32 20 20 35 0d 20 | 20 0d 31 20 20 34 0d 2d |  2  5. | .1  4.-|
|00002a40| 20 20 2d 20 20 31 0d 32 | 20 20 35 0d 20 20 0d 33 |  -  1.2|  5.  .3|
|00002a50| 20 20 20 20 20 39 0d 2d | 20 20 31 20 20 2d 0d 35 |     9.-|  1  -.5|
|00002a60| 20 20 20 20 20 37 0d 3a | 5b 73 74 61 72 74 47 72 |     7.:|[startGr|
|00002a70| 6f 75 70 3b 20 43 63 6c | 6f 73 65 64 3b 20 66 6f |oup; Ccl|osed; fo|
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|00002a90| 74 72 69 78 46 6f 72 6d | 5b 54 72 61 6e 73 70 6f |trixForm|[Transpo|
|00002aa0| 73 65 5b 7b 67 56 65 63 | 2c 61 7d 5d 5d 0d 3a 5b |se[{gVec|,a}]].:[|
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|00002ae0| 72 69 78 46 6f 72 6d 5b | 7b 7b 31 31 2f 33 30 2c |rixForm[|{{11/30,|
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|00002b10| 0d 3b 5b 6f 5d 0d 31 31 | 20 20 20 31 0d 2d 2d 20 |.;[o].11|   1.-- |
|00002b20| 20 20 2d 0d 33 30 20 20 | 20 32 0d 20 20 20 0d 37 |  -.30  | 2.   .7|
|00002b30| 0d 2d 2d 20 20 20 30 0d | 31 32 0d 20 20 20 0d 35 |.--   0.|12.   .5|
|00002b40| 31 20 20 20 31 0d 2d 2d | 20 20 20 2d 0d 37 30 20 |1   1.--|   -.70 |
|00002b50| 20 20 33 0d 3a 5b 69 6e | 61 63 74 69 76 65 3b 20 |  3.:[in|active; |
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|00002b70| 20 3d 20 73 75 62 73 75 | 62 73 65 63 74 69 6f 6e | = subsu|bsection|
|00002b80| 3b 20 5d 0d 54 68 65 20 | 61 62 6f 76 65 20 73 6f |; ].The |above so|
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|00002bb0| 20 70 6c 6f 74 20 62 65 | 6c 6f 77 20 67 65 6e 65 | plot be|low gene|
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|00002c00| 6d 65 20 63 6f 65 66 66 | 69 63 69 65 6e 74 73 20 |me coeff|icients |
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|00004650| 20 31 20 2b 20 34 20 78 | 20 5e 32 0d 09 09 09 09 | 1 + 4 x| ^2.....|
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|00004780| 20 76 61 6c 75 65 73 20 | 66 6f 72 20 6e 4d 61 78 | values |for nMax|
|00004790| 20 2a 29 0d 78 6d 20 3d | 20 6d 2f 28 6e 4d 61 78 | *).xm =| m/(nMax|
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|000047b0| 28 6e 2b 31 29 3b 0d 67 | 20 3d 20 31 20 2b 20 34 |(n+1);.g| = 1 + 4|
|000047c0| 20 78 5e 32 3b 0d 4c 5b | 66 5f 5d 20 3a 3d 20 2d | x^2;.L[|f_] := -|
|000047d0| 44 5b 20 66 2c 20 7b 78 | 2c 32 7d 5d 0d 3a 5b 73 |D[ f, {x|,2}].:[s|
|000047e0| 74 61 72 74 47 72 6f 75 | 70 3b 20 66 6f 6e 74 20 |tartGrou|p; font |
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|00004800| 20 4c 5b 66 6e 5d 20 2f | 2e 20 78 2d 3e 78 6d 09 | L[fn] /|. x->xm.|
|00004810| 28 2a 20 6a 75 73 74 20 | 73 75 62 73 74 69 74 75 |(* just |substitu|
|00004820| 74 65 20 78 6d 20 66 6f | 72 20 78 20 2a 29 0d 3a |te xm fo|r x *).:|
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|00004870| 20 6e 29 29 2f 28 31 20 | 2b 20 6e 4d 61 78 29 5e | n))/(1 |+ nMax)^|
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|00004890| 31 20 2b 20 6e 0d 6d 20 | 20 20 20 20 20 20 6e 20 |1 + n.m |      n |
|000048a0| 28 31 20 2b 20 6e 29 0d | 2d 2d 2d 2d 2d 2d 2d 2d |(1 + n).|--------|
|000048b0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 0d 20 20 20 20 20 20 |--------|-.      |
|000048c0| 20 20 20 20 2d 31 20 2b | 20 6e 0d 28 31 20 2b 20 |    -1 +| n.(1 + |
|000048d0| 6e 4d 61 78 29 0d 3a 5b | 73 74 61 72 74 47 72 6f |nMax).:[|startGro|
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|00004910| 74 69 74 75 74 65 20 78 | 6d 20 66 6f 72 20 78 20 |titute x|m for x |
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|00004930| 75 74 70 75 74 3b 20 65 | 6e 64 47 72 6f 75 70 3b |utput; e|ndGroup;|
|00004940| 20 66 6f 6e 74 20 3d 20 | 6f 75 74 70 75 74 3b 20 | font = |output; |
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|00004960| 20 2b 20 6e 4d 61 78 29 | 5e 32 0d 3b 5b 6f 5d 0d | + nMax)|^2.;[o].|
|00004970| 20 20 20 20 20 20 20 20 | 20 20 32 0d 20 20 20 20 |        |  2.    |
|00004980| 20 20 20 34 20 6d 0d 31 | 20 2b 20 2d 2d 2d 2d 2d |   4 m.1| + -----|
|00004990| 2d 2d 2d 2d 2d 2d 0d 20 | 20 20 20 20 20 20 20 20 |------. |        |
|000049a0| 20 20 20 20 20 32 0d 20 | 20 20 20 28 31 20 2b 20 |     2. |   (1 + |
|000049b0| 6e 4d 61 78 29 0d 3a 5b | 69 6e 61 63 74 69 76 65 |nMax).:[|inactive|
|000049c0| 3b 20 65 6e 64 47 72 6f | 75 70 3b 20 66 6f 6e 74 |; endGro|up; font|
|000049d0| 20 3d 20 74 65 78 74 3b | 20 5d 0d 54 68 65 20 61 | = text;| ].The a|
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|000049f0| 20 66 6f 72 20 6c 6d 6e | 20 61 6e 64 20 67 6d 20 | for lmn| and gm |
|00004a00| 61 72 65 20 74 68 65 20 | 73 61 6d 65 20 61 73 20 |are the |same as |
|00004a10| 48 61 72 72 69 6e 67 74 | 6f 6e 2e 20 54 68 65 73 |Harringt|on. Thes|
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|00004a30| 61 20 77 65 69 67 68 74 | 69 6e 67 20 66 75 6e 63 |a weight|ing func|
|00004a40| 74 69 6f 6e 20 6f 66 3a | 0d 20 20 20 20 20 20 20 |tion of:|.       |
|00004a50| 20 20 20 20 20 77 6d 20 | 3d 20 64 28 78 2d 78 6d |     wm |= d(x-xm|
|00004a60| 29 0d 3b 5b 73 5d 0d 31 | 33 3a 30 2c 30 3b 32 37 |).;[s].1|3:0,0;27|
|00004a70| 2c 31 3b 32 39 2c 30 3b | 33 35 2c 31 3b 33 36 2c |,1;29,0;|35,1;36,|
|00004a80| 30 3b 31 32 32 2c 32 3b | 31 32 33 2c 33 3b 31 32 |0;122,2;|123,3;12|
|00004a90| 34 2c 32 3b 31 32 37 2c | 34 3b 31 32 38 2c 32 3b |4,2;127,|4;128,2;|
|00004aa0| 31 33 32 2c 33 3b 31 33 | 33 2c 32 3b 31 33 34 2c |132,3;13|3,2;134,|
|00004ab0| 30 3b 31 33 35 2c 2d 31 | 3b 0d 35 3a 34 2c 31 36 |0;135,-1|;.5:4,16|
|00004ac0| 2c 31 30 2c 50 61 6c 61 | 74 69 6e 6f 2c 30 2c 31 |,10,Pala|tino,0,1|
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|00004ae0| 61 6c 61 74 69 6e 6f 2c | 30 2c 31 30 2c 30 2c 30 |alatino,|0,10,0,0|
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|00004b30| 53 79 6d 62 6f 6c 2c 30 | 2c 31 32 2c 30 2c 30 2c |Symbol,0|,12,0,0,|
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|00004c30| 20 77 20 4c 5b 66 5d 20 | 77 65 20 6e 65 65 64 20 | w L[f] |we need |
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|00004db0| 0d 67 20 3d 20 31 20 2b | 20 34 20 78 5e 32 3b 0d |.g = 1 +| 4 x^2;.|
|00004dc0| 4c 5b 66 5f 5d 20 3a 3d | 20 2d 44 5b 20 66 2c 20 |L[f_] :=| -D[ f, |
|00004dd0| 7b 78 2c 32 7d 5d 0d 3a | 5b 69 6e 61 63 74 69 76 |{x,2}].:|[inactiv|
|00004de0| 65 3b 20 73 74 61 72 74 | 47 72 6f 75 70 3b 20 43 |e; start|Group; C|
|00004df0| 63 6c 6f 73 65 64 3b 20 | 66 6f 6e 74 20 3d 20 73 |closed; |font = s|
|00004e00| 75 62 73 65 63 74 69 6f | 6e 3b 20 5d 0d 46 6f 72 |ubsectio|n; ].For|
|00004e10| 20 61 6c 6c 20 73 6f 6c | 75 74 69 6f 6e 73 20 77 | all sol|utions w|
|00004e20| 65 20 68 61 76 65 20 28 | 6a 75 73 74 20 63 68 61 |e have (|just cha|
|00004e30| 6e 67 65 20 6e 4d 61 78 | 29 3a 0d 3a 5b 73 74 61 |nge nMax|):.:[sta|
|00004e40| 72 74 47 72 6f 75 70 3b | 20 66 6f 6e 74 20 3d 20 |rtGroup;| font = |
|00004e50| 69 6e 70 75 74 3b 20 5d | 0d 6e 4d 61 78 20 3d 20 |input; ]|.nMax = |
|00004e60| 32 3b 0d 66 20 3d 20 54 | 61 62 6c 65 5b 20 78 20 |2;.f = T|able[ x |
|00004e70| 2d 20 78 5e 28 6e 2b 31 | 29 2c 20 7b 6e 2c 6e 4d |- x^(n+1|), {n,nM|
|00004e80| 61 78 7d 5d 3b 0d 6c 20 | 3d 20 54 61 62 6c 65 5b |ax}];.l |= Table[|
|00004e90| 20 4c 5b 66 5d 20 2f 2e | 20 78 2d 3e 6d 2f 28 6e | L[f] /.| x->m/(n|
|00004ea0| 4d 61 78 2b 31 29 2c 20 | 7b 6d 2c 6e 4d 61 78 7d |Max+1), |{m,nMax}|
|00004eb0| 5d 3b 20 28 2a 20 6d 61 | 74 72 69 78 20 2a 29 0d |]; (* ma|trix *).|
|00004ec0| 67 56 65 63 20 3d 20 54 | 61 62 6c 65 5b 20 67 20 |gVec = T|able[ g |
|00004ed0| 2f 2e 20 78 2d 3e 6d 2f | 28 6e 4d 61 78 2b 31 29 |/. x->m/|(nMax+1)|
|00004ee0| 2c 20 7b 6d 2c 6e 4d 61 | 78 7d 5d 3b 0d 61 20 3d |, {m,nMa|x}];.a =|
|00004ef0| 20 49 6e 76 65 72 73 65 | 5b 6c 5d 20 2e 20 67 56 | Inverse|[l] . gV|
|00004f00| 65 63 3b 0d 3a 5b 73 74 | 61 72 74 47 72 6f 75 70 |ec;.:[st|artGroup|
|00004f10| 3b 20 66 6f 6e 74 20 3d | 20 69 6e 70 75 74 3b 20 |; font =| input; |
|00004f20| 5d 0d 7b 6c 2c 61 2c 67 | 56 65 63 7d 0d 3a 5b 69 |].{l,a,g|Vec}.:[i|
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|00004f50| 3d 20 6f 75 74 70 75 74 | 3b 20 5d 0d 7b 7b 7b 32 |= output|; ].{{{2|
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|00004f80| 39 2c 20 32 35 2f 39 7d | 7d 0d 3b 5b 6f 5d 0d 20 |9, 25/9}|}.;[o]. |
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|00004fa0| 20 20 20 31 20 20 20 32 | 20 20 20 20 31 33 20 20 |   1   2|    13  |
|00004fb0| 32 35 0d 7b 7b 7b 32 2c | 20 32 7d 2c 20 7b 32 2c |25.{{{2,| 2}, {2,|
|00004fc0| 20 34 7d 7d 2c 20 7b 2d | 2d 2c 20 2d 7d 2c 20 7b | 4}}, {-|-, -}, {|
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|00004fe0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 31 38 20 |        |     18 |
|00004ff0| 20 33 20 20 20 20 39 20 | 20 20 39 0d 3a 5b 73 74 | 3    9 |  9.:[st|
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|00005040| 20 2a 29 0d 4c 5b 61 2e | 66 5d 0d 3a 5b 69 6e 61 | *).L[a.|f].:[ina|
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|00005090| 20 31 0d 2d 28 2d 28 2d | 29 20 2d 20 34 20 78 29 | 1.-(-(-|) - 4 x)|
|000050a0| 0d 20 20 20 20 39 0d 3a | 5b 73 74 61 72 74 47 72 |.    9.:|[startGr|
|000050b0| 6f 75 70 3b 20 66 6f 6e | 74 20 3d 20 69 6e 70 75 |oup; fon|t = inpu|
|000050c0| 74 3b 20 5d 0d 28 2a 20 | 77 68 65 6e 20 6e 4d 61 |t; ].(* |when nMa|
|000050d0| 78 20 3d 20 33 20 77 65 | 20 66 69 6e 64 20 74 68 |x = 3 we| find th|
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