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Unknown | 1991-04-08 | 1.2 MB |
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MacOS 8.1
|
Win98
|
DOS
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Confidence | Program | Detection | Match Type | Support
|
---|
100%
| file
| data
| default
| |
100%
| gt2
| Kopftext: 'ine that function alone by the command'
| default (weak)
|
|
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 69 6e 65 20 74 68 61 74 | 20 66 75 6e 63 74 69 6f |ine that| functio|
|00000010| 6e 20 61 6c 6f 6e 65 20 | 62 79 20 74 68 65 20 63 |n alone |by the c|
|00000020| 6f 6d 6d 61 6e 64 00 00 | 00 00 00 00 00 00 0a 00 |ommand..|........|
|00000030| 15 20 20 77 69 74 68 28 | 67 72 6f 62 6e 65 72 2c |. with(|grobner,|
|00000040| 20 3c 66 75 6e 63 74 69 | 6f 6e 3e 29 2c 20 6f 72 | <functi|on>), or|
|00000050| 20 64 65 66 69 6e 65 20 | 61 6c 6c 20 67 72 6f 62 | define |all grob|
|00000060| 6e 65 72 20 66 75 6e 63 | 74 69 6f 6e 73 20 62 79 |ner func|tions by|
|00000070| 20 74 68 65 20 63 6f 6d | 6d 61 6e 64 00 00 00 00 | the com|mand....|
|00000080| 00 00 0a 00 16 20 20 77 | 69 74 68 28 67 72 6f 62 |..... w|ith(grob|
|00000090| 6e 65 72 29 2e 20 20 54 | 6f 20 61 63 63 65 73 73 |ner). T|o access|
|000000a0| 20 61 20 67 72 6f 62 6e | 65 72 20 66 75 6e 63 74 | a grobn|er funct|
|000000b0| 69 6f 6e 20 77 69 74 68 | 6f 75 74 20 75 73 69 6e |ion with|out usin|
|000000c0| 67 20 74 68 65 20 77 69 | 74 68 20 63 6f 6d 6d 61 |g the wi|th comma|
|000000d0| 6e 64 2c 00 00 00 00 00 | 00 00 0a 00 0f 20 20 75 |nd,.....|..... u|
|000000e0| 73 65 20 74 68 65 20 66 | 75 6e 63 74 69 6f 6e 20 |se the f|unction |
|000000f0| 69 6e 20 74 68 65 20 66 | 6f 72 6d 20 67 72 6f 62 |in the f|orm grob|
|00000100| 6e 65 72 5b 3c 66 75 6e | 63 74 69 6f 6e 3e 5d 00 |ner[<fun|ction>].|
|00000110| 00 00 00 00 00 00 98 96 | 8d 00 0a 00 0e 2d 20 54 |........|.....- T|
|00000120| 68 65 20 66 75 6e 63 74 | 69 6f 6e 73 20 61 76 61 |he funct|ions ava|
|00000130| 69 6c 61 62 6c 65 20 61 | 72 65 20 74 68 65 20 66 |ilable a|re the f|
|00000140| 6f 6c 6c 6f 77 69 6e 67 | 3a 00 00 00 00 00 00 00 |ollowing|:.......|
|00000150| 00 00 98 96 8d 00 0a 00 | 12 20 20 20 20 20 20 20 |........|. |
|00000160| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 66 69 | | fi|
|00000170| 6e 64 75 6e 69 20 20 20 | 20 20 20 20 66 69 6e 69 |nduni | fini|
|00000180| 74 65 20 20 20 67 62 61 | 73 69 73 20 20 20 20 67 |te gba|sis g|
|00000190| 73 6f 6c 76 65 00 00 00 | 00 00 00 00 00 00 0a 00 |solve...|........|
|000001a0| 11 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|000001b0| 20 20 20 20 20 20 6c 65 | 61 64 6d 6f 6e 20 20 20 | le|admon |
|000001c0| 20 20 20 20 6e 6f 72 6d | 61 6c 66 20 20 73 6f 6c | norm|alf sol|
|000001d0| 76 61 62 6c 65 20 20 73 | 70 6f 6c 79 00 00 00 00 |vable s|poly....|
|000001e0| 00 00 0a 00 08 20 20 20 | 20 20 20 20 20 20 20 20 |..... | |
|000001f0| 20 20 20 20 20 20 20 20 | 20 20 00 00 00 00 00 00 | | ......|
|00000200| 00 00 0a 00 0e 2d 20 54 | 68 65 20 61 76 61 69 6c |.....- T|he avail|
|00000210| 61 62 6c 65 20 74 65 72 | 6d 20 6f 72 64 65 72 69 |able ter|m orderi|
|00000220| 6e 67 73 20 61 72 65 20 | 61 73 20 66 6f 6c 6c 6f |ngs are |as follo|
|00000230| 77 73 3a 00 00 00 00 00 | 00 00 98 96 8d 00 0a 00 |ws:.....|........|
|00000240| 14 20 20 20 20 20 20 20 | 20 20 20 70 6c 65 78 20 |. | plex |
|00000250| 20 20 20 20 20 20 20 20 | 20 70 75 72 65 20 6c 65 | | pure le|
|00000260| 78 69 63 6f 67 72 61 70 | 68 69 63 2c 20 77 68 65 |xicograp|hic, whe|
|00000270| 72 65 20 58 20 3d 20 5b | 78 31 2c 20 78 32 2c 20 |re X = [|x1, x2, |
|00000280| 2e 2e 2e 2c 20 78 6e 5d | 00 00 00 00 00 00 0a 00 |..., xn]|........|
|00000290| 0f 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|000002a0| 20 20 20 20 20 20 20 20 | 20 69 6e 64 75 63 65 73 | | induces|
|000002b0| 20 78 31 20 3e 20 78 32 | 20 3e 20 2e 2e 2e 20 3e | x1 > x2| > ... >|
|000002c0| 20 78 6e 00 00 00 00 00 | 00 00 0a 00 13 20 20 20 | xn.....|..... |
|000002d0| 20 20 20 20 20 20 20 74 | 64 65 67 20 20 20 20 20 | t|deg |
|000002e0| 20 20 20 20 20 74 6f 74 | 61 6c 20 64 65 67 72 65 | tot|al degre|
|000002f0| 65 20 28 67 72 61 64 75 | 61 74 65 64 29 2c 20 77 |e (gradu|ated), w|
|00000300| 69 74 68 20 74 69 65 73 | 20 62 72 6f 6b 65 6e 00 |ith ties| broken.|
|00000310| 00 00 00 00 00 00 0a 00 | 11 20 20 20 20 20 20 20 |........|. |
|00000320| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000330| 20 62 79 20 69 6e 76 65 | 72 73 65 20 6c 65 78 69 | by inve|rse lexi|
|00000340| 63 6f 67 72 61 70 68 69 | 63 61 6c 20 6f 72 64 65 |cographi|cal orde|
|00000350| 72 2e 00 00 00 00 00 00 | 00 00 0a 00 06 20 20 20 |r.......|..... |
|00000360| 20 20 20 20 20 20 20 20 | 20 20 00 00 00 00 00 00 | | ......|
|00000370| 00 00 0a 00 12 2d 20 46 | 6f 72 20 68 65 6c 70 20 |.....- F|or help |
|00000380| 77 69 74 68 20 61 20 70 | 61 72 74 69 63 75 6c 61 |with a p|articula|
|00000390| 72 20 66 75 6e 63 74 69 | 6f 6e 20 73 65 65 20 74 |r functi|on see t|
|000003a0| 68 65 20 69 6e 66 6f 72 | 6d 61 74 69 6f 6e 20 75 |he infor|mation u|
|000003b0| 6e 64 65 72 00 00 00 00 | 00 00 0a 00 13 20 20 67 |nder....|..... g|
|000003c0| 72 6f 62 6e 65 72 5b 3c | 66 75 6e 63 74 69 6f 6e |robner[<|function|
|000003d0| 3e 5d 2c 20 77 68 65 72 | 65 20 3c 66 75 6e 63 74 |>], wher|e <funct|
|000003e0| 69 6f 6e 3e 20 69 73 20 | 6f 6e 65 20 66 72 6f 6d |ion> is |one from|
|000003f0| 20 74 68 65 20 61 62 6f | 76 65 20 6c 69 73 74 2e | the abo|ve list.|
|00000400| 00 00 00 00 00 00 98 96 | 8d 00 0a 00 16 2d 20 48 |........|.....- H|
|00000410| 65 72 65 20 69 73 20 61 | 6e 20 65 78 61 6d 70 6c |ere is a|n exampl|
|00000420| 65 20 6f 66 20 75 73 69 | 6e 67 20 61 20 67 72 6f |e of usi|ng a gro|
|00000430| 62 6e 65 72 20 66 75 6e | 63 74 69 6f 6e 2e 20 20 |bner fun|ction. |
|00000440| 54 6f 20 66 69 6e 64 20 | 74 68 65 20 47 72 6f 62 |To find |the Grob|
|00000450| 6e 65 72 20 62 61 73 69 | 73 20 6f 66 00 00 00 00 |ner basi|s of....|
|00000460| 00 00 0a 00 15 20 20 61 | 20 73 65 74 20 6f 66 20 |..... a| set of |
|00000470| 70 6f 6c 79 6e 6f 6d 69 | 61 6c 73 20 46 20 6f 76 |polynomi|als F ov|
|00000480| 65 72 20 74 68 65 20 76 | 61 72 69 61 62 6c 65 73 |er the v|ariables|
|00000490| 20 58 20 3d 20 5b 78 5f | 31 2c 20 78 5f 32 2c 20 | X = [x_|1, x_2, |
|000004a0| 2e 2e 2e 2c 20 78 5f 6e | 5d 2c 20 77 69 74 68 00 |..., x_n|], with.|
|000004b0| 00 00 00 00 00 00 0a 00 | 16 20 20 72 65 73 70 65 |........|. respe|
|000004c0| 63 74 20 74 6f 20 74 6f | 74 61 6c 20 64 65 67 72 |ct to to|tal degr|
|000004d0| 65 65 20 6f 72 64 65 72 | 69 6e 67 2c 20 6f 6e 65 |ee order|ing, one|
|000004e0| 20 77 6f 75 6c 64 20 66 | 69 72 73 74 20 64 65 66 | would f|irst def|
|000004f0| 69 6e 65 20 46 20 61 6e | 64 20 58 2c 20 61 6e 64 |ine F an|d X, and|
|00000500| 20 74 68 65 6e 00 00 00 | 00 00 00 00 00 00 0a 00 | then...|........|
|00000510| 10 20 20 65 78 65 63 75 | 74 65 20 74 68 65 20 73 |. execu|te the s|
|00000520| 65 71 75 65 6e 63 65 20 | 6f 66 20 63 6f 6d 6d 61 |equence |of comma|
|00000530| 6e 64 73 20 74 68 61 74 | 20 61 70 70 65 61 72 73 |nds that| appears|
|00000540| 20 62 65 6c 6f 77 2e 00 | 00 00 00 00 00 00 98 96 | below..|........|
|00000550| 8d 00 0a 00 06 45 58 41 | 4d 50 4c 45 53 3a 20 20 |.....EXA|MPLES: |
|00000560| 20 00 00 00 00 00 00 00 | 00 00 0a 00 09 77 69 74 | .......|.....wit|
|00000570| 68 28 67 72 6f 62 6e 65 | 72 2c 20 67 62 61 73 69 |h(grobne|r, gbasi|
|00000580| 73 29 3b 20 20 00 00 00 | 00 00 00 00 00 00 0a 00 |s); ...|........|
|00000590| 07 67 62 61 73 69 73 28 | 46 2c 20 58 2c 20 74 64 |.gbasis(|F, X, td|
|000005a0| 65 67 29 3b 00 00 00 00 | 00 00 0a 00 0c 53 45 45 |eg);....|.....SEE|
|000005b0| 20 41 4c 53 4f 3a 20 20 | 77 69 74 68 2c 20 67 72 | ALSO: |with, gr|
|000005c0| 6f 62 6e 65 72 5b 3c 66 | 75 6e 63 74 69 6f 6e 3e |obner[<f|unction>|
|000005d0| 5d 00 00 00 00 00 00 00 | 00 04 32 96 41 00 0a 00 |].......|..2.A...|
|000005e0| 06 68 65 6c 70 2f 74 65 | 78 74 2f 67 72 6f 75 70 |.help/te|xt/group|
|000005f0| 00 00 18 00 03 00 0a 00 | 04 54 45 58 54 00 00 00 |........|.TEXT...|
|00000600| 00 00 00 00 00 00 2a 00 | 29 00 0a 00 03 20 20 20 |......*.|).... |
|00000610| 00 00 00 00 00 00 0a 00 | 14 48 45 4c 50 20 46 4f |........|.HELP FO|
|00000620| 52 3a 20 54 68 65 20 70 | 65 72 6d 75 74 61 74 69 |R: The p|ermutati|
|00000630| 6f 6e 20 67 72 6f 75 70 | 20 61 6e 64 20 66 69 6e |on group| and fin|
|00000640| 69 74 65 6c 79 2d 70 72 | 65 73 65 6e 74 65 64 20 |itely-pr|esented |
|00000650| 67 72 6f 75 70 20 70 61 | 63 6b 61 67 65 00 00 00 |group pa|ckage...|
|00000660| 00 00 00 00 00 00 98 96 | 8c 00 0a 00 07 43 41 4c |........|.....CAL|
|00000670| 4c 49 4e 47 20 53 45 51 | 55 45 4e 43 45 3a 00 00 |LING SEQ|UENCE:..|
|00000680| 00 00 00 00 00 00 0a 00 | 09 20 20 20 67 72 6f 75 |........|. grou|
|00000690| 70 5b 3c 66 75 6e 63 74 | 69 6f 6e 3e 5d 28 61 72 |p[<funct|ion>](ar|
|000006a0| 67 73 29 00 00 00 00 00 | 00 00 0a 00 07 20 20 20 |gs).....|..... |
|000006b0| 3c 66 75 6e 63 74 69 6f | 6e 3e 28 61 72 67 73 29 |<functio|n>(args)|
|000006c0| 00 00 00 00 00 00 98 96 | 8c 00 0a 00 06 53 59 4e |........|.....SYN|
|000006d0| 4f 50 53 49 53 3a 20 20 | 20 00 00 00 00 00 00 00 |OPSIS: | .......|
|000006e0| 00 00 0a 00 15 2d 20 54 | 6f 20 75 73 65 20 61 20 |.....- T|o use a |
|000006f0| 67 72 6f 75 70 20 66 75 | 6e 63 74 69 6f 6e 2c 20 |group fu|nction, |
|00000700| 65 69 74 68 65 72 20 64 | 65 66 69 6e 65 20 74 68 |either d|efine th|
|00000710| 61 74 20 66 75 6e 63 74 | 69 6f 6e 20 61 6c 6f 6e |at funct|ion alon|
|00000720| 65 20 62 79 20 74 68 65 | 20 63 6f 6d 6d 61 6e 64 |e by the| command|
|00000730| 00 00 00 00 00 00 0a 00 | 14 20 20 77 69 74 68 28 |........|. with(|
|00000740| 67 72 6f 75 70 2c 3c 66 | 75 6e 63 74 69 6f 6e 3e |group,<f|unction>|
|00000750| 29 2c 20 6f 72 20 64 65 | 66 69 6e 65 20 61 6c 6c |), or de|fine all|
|00000760| 20 67 72 6f 75 70 20 66 | 75 6e 63 74 69 6f 6e 73 | group f|unctions|
|00000770| 20 62 79 20 74 68 65 20 | 63 6f 6d 6d 61 6e 64 00 | by the |command.|
|00000780| 00 00 00 00 00 00 0a 00 | 06 20 20 77 69 74 68 28 |........|. with(|
|00000790| 67 72 6f 75 70 29 2e 00 | 00 00 00 00 00 00 98 96 |group)..|........|
|000007a0| 8c 00 0a 00 0f 2d 20 54 | 68 65 20 66 75 6e 63 74 |.....- T|he funct|
|000007b0| 69 6f 6e 73 20 69 6e 20 | 74 68 69 73 20 70 61 63 |ions in |this pac|
|000007c0| 6b 61 67 65 20 61 72 65 | 20 74 68 65 20 66 6f 6c |kage are| the fol|
|000007d0| 6c 6f 77 69 6e 67 3a 00 | 00 00 00 00 00 00 98 96 |lowing:.|........|
|000007e0| 8c 00 0a 00 12 20 20 20 | 20 20 20 20 20 20 20 20 |..... | |
|000007f0| 20 20 20 20 20 20 63 65 | 6e 74 72 61 6c 69 7a 65 | ce|ntralize|
|00000800| 72 20 20 20 63 6f 73 65 | 74 73 20 20 20 20 20 20 |r cose|ts |
|00000810| 63 6f 73 72 65 70 20 20 | 20 67 72 6f 75 70 6d 65 |cosrep | groupme|
|00000820| 6d 62 65 72 00 00 00 00 | 00 00 0a 00 12 20 20 20 |mber....|..... |
|00000830| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 67 72 | | gr|
|00000840| 6f 75 70 6f 72 64 65 72 | 20 20 20 20 69 6e 74 65 |ouporder| inte|
|00000850| 72 20 20 20 20 20 20 20 | 69 6e 76 70 65 72 6d 20 |r |invperm |
|00000860| 20 69 73 6e 6f 72 6d 61 | 6c 00 00 00 00 00 00 00 | isnorma|l.......|
|00000870| 00 00 0a 00 11 20 20 20 | 20 20 20 20 20 20 20 20 |..... | |
|00000880| 20 20 20 20 20 20 6d 75 | 6c 70 65 72 6d 73 20 20 | mu|lperms |
|00000890| 20 20 20 20 6e 6f 72 6d | 61 6c 69 7a 65 72 20 20 | norm|alizer |
|000008a0| 70 65 72 6d 72 65 70 20 | 20 70 72 65 73 00 00 00 |permrep | pres...|
|000008b0| 00 00 00 00 00 00 0a 00 | 07 20 20 20 20 20 20 20 |........|. |
|000008c0| 20 20 20 20 20 20 20 20 | 20 20 00 00 00 00 00 00 | | ......|
|000008d0| 00 00 0a 00 16 2d 20 49 | 6e 20 61 64 64 69 74 69 |.....- I|n additi|
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|000008f0| 63 6b 61 67 65 20 68 61 | 73 20 62 65 65 6e 20 6c |ckage ha|s been l|
|00000900| 6f 61 64 65 64 2c 20 74 | 68 65 20 74 79 70 65 20 |oaded, t|he type |
|00000910| 66 75 6e 63 74 69 6f 6e | 20 77 69 6c 6c 20 61 63 |function| will ac|
|00000920| 63 65 70 74 00 00 00 00 | 00 00 0a 00 16 20 20 64 |cept....|..... d|
|00000930| 69 73 6a 63 79 63 2c 20 | 61 6e 64 20 74 68 65 20 |isjcyc, |and the |
|00000940| 63 6f 6e 76 65 72 74 20 | 66 75 6e 63 74 69 6f 6e |convert |function|
|00000950| 20 77 69 6c 6c 20 61 63 | 63 65 70 74 20 64 69 73 | will ac|cept dis|
|00000960| 6a 63 79 63 20 61 6e 64 | 20 70 65 72 6d 6c 69 73 |jcyc and| permlis|
|00000970| 74 20 61 73 20 73 65 63 | 6f 6e 64 00 00 00 00 00 |t as sec|ond.....|
|00000980| 00 00 0a 00 16 20 20 61 | 72 67 75 6d 65 6e 74 73 |..... a|rguments|
|00000990| 2e 20 20 54 68 65 73 65 | 20 70 72 6f 76 69 64 65 |. These| provide|
|000009a0| 20 74 79 70 65 2d 63 68 | 65 63 6b 69 6e 67 20 61 | type-ch|ecking a|
|000009b0| 6e 64 20 63 6f 6e 76 65 | 72 73 69 6f 6e 20 72 6f |nd conve|rsion ro|
|000009c0| 75 74 69 6e 65 73 20 66 | 6f 72 20 74 68 65 20 64 |utines f|or the d|
|000009d0| 61 74 61 00 00 00 00 00 | 00 00 0a 00 15 20 20 74 |ata.....|..... t|
|000009e0| 79 70 65 73 20 75 73 65 | 64 20 77 69 74 68 69 6e |ypes use|d within|
|000009f0| 20 74 68 65 20 67 72 6f | 75 70 20 70 61 63 6b 61 | the gro|up packa|
|00000a00| 67 65 2e 20 20 53 65 65 | 20 74 68 65 20 69 6e 66 |ge. See| the inf|
|00000a10| 6f 72 6d 61 74 69 6f 6e | 20 6f 6e 20 74 68 65 20 |ormation| on the |
|00000a20| 74 79 70 65 20 61 6e 64 | 00 00 00 00 00 00 0a 00 |type and|........|
|00000a30| 0b 20 20 63 6f 6e 76 65 | 72 74 20 66 75 6e 63 74 |. conve|rt funct|
|00000a40| 69 6f 6e 73 20 66 6f 72 | 20 64 65 74 61 69 6c 73 |ions for| details|
|00000a50| 2e 00 00 00 00 00 00 00 | 00 00 98 96 8c 00 0a 00 |........|........|
|00000a60| 12 2d 20 46 6f 72 20 68 | 65 6c 70 20 77 69 74 68 |.- For h|elp with|
|00000a70| 20 61 20 70 61 72 74 69 | 63 75 6c 61 72 20 66 75 | a parti|cular fu|
|00000a80| 6e 63 74 69 6f 6e 20 73 | 65 65 20 74 68 65 20 69 |nction s|ee the i|
|00000a90| 6e 66 6f 72 6d 61 74 69 | 6f 6e 20 75 6e 64 65 72 |nformati|on under|
|00000aa0| 00 00 00 00 00 00 0a 00 | 13 20 20 67 72 6f 75 70 |........|. group|
|00000ab0| 5b 3c 66 75 6e 63 74 69 | 6f 6e 3e 5d 2c 20 77 68 |[<functi|on>], wh|
|00000ac0| 65 72 65 20 3c 66 75 6e | 63 74 69 6f 6e 3e 20 69 |ere <fun|ction> i|
|00000ad0| 73 20 6f 6e 65 20 66 72 | 6f 6d 20 74 68 65 20 61 |s one fr|om the a|
|00000ae0| 62 6f 76 65 20 6c 69 73 | 74 2e 00 00 00 00 00 00 |bove lis|t.......|
|00000af0| 00 00 98 96 8c 00 0a 00 | 16 2d 20 46 6f 72 20 68 |........|.- For h|
|00000b00| 65 6c 70 20 77 69 74 68 | 20 68 6f 77 20 74 6f 20 |elp with| how to |
|00000b10| 72 65 70 72 65 73 65 6e | 74 20 67 72 6f 75 70 73 |represen|t groups|
|00000b20| 2c 20 73 75 62 67 72 6f | 75 70 73 2c 20 61 6e 64 |, subgro|ups, and|
|00000b30| 20 67 72 6f 75 70 20 65 | 6c 65 6d 65 6e 74 73 20 | group e|lements |
|00000b40| 66 6f 72 20 74 68 69 73 | 00 00 00 00 00 00 0a 00 |for this|........|
|00000b50| 16 20 20 70 61 63 6b 61 | 67 65 2c 20 73 65 65 20 |. packa|ge, see |
|00000b60| 74 68 65 20 69 6e 66 6f | 72 6d 61 74 69 6f 6e 20 |the info|rmation |
|00000b70| 75 6e 64 65 72 20 67 72 | 6f 75 70 5b 67 72 65 6c |under gr|oup[grel|
|00000b80| 67 72 6f 75 70 5d 2c 20 | 67 72 6f 75 70 5b 70 65 |group], |group[pe|
|00000b90| 72 6d 67 72 6f 75 70 5d | 2c 20 61 6e 64 00 00 00 |rmgroup]|, and...|
|00000ba0| 00 00 00 00 00 00 0a 00 | 07 20 20 67 72 6f 75 70 |........|. group|
|00000bb0| 5b 73 75 62 67 72 65 6c | 5d 2e 00 00 00 00 00 00 |[subgrel|].......|
|00000bc0| 00 00 98 96 8c 00 0a 00 | 15 2d 20 41 6e 20 65 78 |........|.- An ex|
|00000bd0| 61 6d 70 6c 65 20 6f 66 | 20 75 73 69 6e 67 20 74 |ample of| using t|
|00000be0| 68 65 20 67 72 6f 75 70 | 20 70 61 63 6b 61 67 65 |he group| package|
|00000bf0| 20 74 6f 20 66 69 6e 64 | 20 74 68 65 20 6f 72 64 | to find| the ord|
|00000c00| 65 72 20 6f 66 20 61 20 | 70 65 72 6d 75 74 61 74 |er of a |permutat|
|00000c10| 69 6f 6e 00 00 00 00 00 | 00 00 0a 00 09 20 20 67 |ion.....|..... g|
|00000c20| 72 6f 75 70 20 69 73 20 | 74 68 65 20 66 6f 6c 6c |roup is |the foll|
|00000c30| 6f 77 69 6e 67 3a 00 00 | 00 00 00 00 00 00 98 96 |owing:..|........|
|00000c40| 8c 00 0a 00 06 45 58 41 | 4d 50 4c 45 53 3a 20 20 |.....EXA|MPLES: |
|00000c50| 20 00 00 00 00 00 00 00 | 00 00 0a 00 06 3e 20 77 | .......|.....> w|
|00000c60| 69 74 68 28 67 72 6f 75 | 70 29 3a 00 00 00 00 00 |ith(grou|p):.....|
|00000c70| 00 00 0a 00 12 3e 20 67 | 72 6f 75 70 6f 72 64 65 |.....> g|rouporde|
|00000c80| 72 28 70 65 72 6d 67 72 | 6f 75 70 28 38 2c 20 7b |r(permgr|oup(8, {|
|00000c90| 61 3d 5b 5b 31 2c 32 5d | 5d 2c 20 62 3d 5b 5b 31 |a=[[1,2]|], b=[[1|
|00000ca0| 2c 32 2c 33 2c 34 2c 35 | 2c 36 2c 37 2c 38 5d 5d |,2,3,4,5|,6,7,8]]|
|00000cb0| 7d 29 29 3b 00 00 00 00 | 00 00 0a 00 0d 20 20 20 |}));....|..... |
|00000cc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000cd0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ce0| 20 20 34 30 33 32 30 00 | 00 00 00 00 00 00 98 96 | 40320.|........|
|00000cf0| 8c 00 0a 00 14 53 45 45 | 20 41 4c 53 4f 3a 20 20 |.....SEE| ALSO: |
|00000d00| 77 69 74 68 2c 20 67 72 | 6f 75 70 5b 63 6f 6e 76 |with, gr|oup[conv|
|00000d10| 65 72 74 5d 2c 20 67 72 | 6f 75 70 5b 74 79 70 65 |ert], gr|oup[type|
|00000d20| 5d 2c 20 64 65 66 69 6e | 65 2c 20 63 6f 6d 62 69 |], defin|e, combi|
|00000d30| 6e 61 74 5b 70 65 72 6d | 75 74 65 5d 00 00 00 00 |nat[perm|ute]....|
|00000d40| 00 04 32 96 41 00 0a 00 | 07 68 65 6c 70 2f 74 65 |..2.A...|.help/te|
|00000d50| 78 74 2f 68 61 72 64 77 | 61 72 65 00 00 00 18 00 |xt/hardw|are.....|
|00000d60| 03 00 0a 00 04 54 45 58 | 54 00 00 00 00 00 00 00 |.....TEX|T.......|
|00000d70| 00 00 2a 00 32 00 0a 00 | 03 20 20 20 00 00 00 00 |..*.2...|. ....|
|00000d80| 00 00 0a 00 12 48 45 4c | 50 20 46 4f 52 3a 20 48 |.....HEL|P FOR: H|
|00000d90| 61 72 64 77 61 72 65 20 | 28 61 6e 64 20 6f 70 65 |ardware |(and ope|
|00000da0| 72 61 74 69 6e 67 20 73 | 79 73 74 65 6d 73 29 20 |rating s|ystems) |
|00000db0| 77 68 69 63 68 20 63 61 | 6e 20 72 75 6e 20 4d 61 |which ca|n run Ma|
|00000dc0| 70 6c 65 00 00 00 00 00 | 00 00 98 96 8d 00 0a 00 |ple.....|........|
|00000dd0| 06 53 59 4e 4f 50 53 49 | 53 3a 20 20 20 00 00 00 |.SYNOPSI|S: ...|
|00000de0| 00 00 00 00 00 00 0a 00 | 16 2d 20 41 74 20 74 68 |........|.- At th|
|00000df0| 65 20 74 69 6d 65 20 6f | 66 20 74 68 69 73 20 77 |e time o|f this w|
|00000e00| 72 69 74 69 6e 67 20 28 | 41 75 67 75 73 74 20 31 |riting (|August 1|
|00000e10| 39 39 30 29 20 4d 61 70 | 6c 65 20 72 75 6e 73 20 |990) Map|le runs |
|00000e20| 6f 6e 20 74 68 65 20 66 | 6f 6c 6c 6f 77 69 6e 67 |on the f|ollowing|
|00000e30| 20 73 79 73 2d 00 00 00 | 00 00 00 00 00 00 0a 00 | sys-...|........|
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|000053f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|00005440| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005450| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 2d | | -|
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|000054c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000054d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|00005560| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005570| 20 20 20 20 20 20 20 20 | 20 20 20 28 31 31 29 00 | | (11).|
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|00005630| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 28 | | (|
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|00005b20| 74 6f 72 2c 20 66 61 63 | 74 6f 72 2c 20 66 61 63 |tor, fac|tor, fac|
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|00005b70| 00 00 2a 00 22 00 0a 00 | 03 20 20 20 00 00 00 00 |..*."...|. ....|
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|00005b90| 67 63 64 20 2d 20 67 72 | 65 61 74 65 73 74 20 63 |gcd - gr|eatest c|
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|00005bb0| 20 69 6e 74 65 67 65 72 | 73 00 00 00 00 00 00 00 | integer|s.......|
|00005bc0| 00 00 0a 00 0f 46 55 4e | 43 54 49 4f 4e 3a 20 69 |.....FUN|CTION: i|
|00005bd0| 6c 63 6d 20 2d 20 6c 65 | 61 73 74 20 63 6f 6d 6d |lcm - le|ast comm|
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|00005c00| 8c 00 0a 00 07 43 41 4c | 4c 49 4e 47 20 53 45 51 |.....CAL|LING SEQ|
|00005c10| 55 45 4e 43 45 3a 00 00 | 00 00 00 00 00 00 0a 00 |UENCE:..|........|
|00005c20| 08 20 20 20 69 67 63 64 | 28 78 5f 31 2c 78 5f 32 |. igcd|(x_1,x_2|
|00005c30| 2c 2e 2e 2e 29 3b 00 00 | 00 00 00 00 00 00 0a 00 |,...);..|........|
|00005c40| 08 20 20 20 69 6c 63 6d | 28 78 5f 31 2c 78 5f 32 |. ilcm|(x_1,x_2|
|00005c50| 2c 2e 2e 2e 29 3b 00 00 | 00 00 00 00 00 00 98 96 |,...);..|........|
|00005c60| 8c 00 0a 00 05 50 41 52 | 41 4d 45 54 45 52 53 3a |.....PAR|AMETERS:|
|00005c70| 00 00 00 00 00 00 0a 00 | 0a 20 20 20 78 5f 31 2c |........|. x_1,|
|00005c80| 78 5f 32 2c 2e 2e 2e 20 | 2d 20 61 6e 79 20 69 6e |x_2,... |- any in|
|00005c90| 74 65 67 65 72 73 00 00 | 00 00 00 00 00 00 98 96 |tegers..|........|
|00005ca0| 8c 00 0a 00 06 53 59 4e | 4f 50 53 49 53 3a 20 20 |.....SYN|OPSIS: |
|00005cb0| 20 00 00 00 00 00 00 00 | 00 00 0a 00 16 2d 20 54 | .......|.....- T|
|00005cc0| 68 65 20 66 75 6e 63 74 | 69 6f 6e 20 69 67 63 64 |he funct|ion igcd|
|00005cd0| 20 63 6f 6d 70 75 74 65 | 73 20 74 68 65 20 67 72 | compute|s the gr|
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|00005cf0| 76 69 73 6f 72 20 6f 66 | 20 61 6e 20 61 72 62 69 |visor of| an arbi|
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|00005d20| 72 73 2e 20 20 54 68 65 | 20 66 75 6e 63 74 69 6f |rs. The| functio|
|00005d30| 6e 20 69 6c 63 6d 20 63 | 6f 6d 70 75 74 65 73 20 |n ilcm c|omputes |
|00005d40| 74 68 65 20 6c 65 61 73 | 74 20 63 6f 6d 6d 6f 6e |the leas|t common|
|00005d50| 20 6d 75 6c 74 69 70 6c | 65 20 6f 66 20 61 6e 00 | multipl|e of an.|
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|00005d90| 8c 00 0a 00 06 45 58 41 | 4d 50 4c 45 53 3a 20 20 |.....EXA|MPLES: |
|00005da0| 20 00 00 00 00 00 00 00 | 00 00 0a 00 06 3e 20 69 | .......|.....> i|
|00005db0| 67 63 64 28 29 3b 20 20 | 20 00 00 00 00 00 00 00 |gcd(); | .......|
|00005dc0| 00 00 0a 00 0d 20 20 20 | 20 20 20 20 20 20 20 20 |..... | |
|00005dd0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005de0| 20 20 20 20 20 20 20 20 | 20 20 20 20 30 00 00 00 | | 0...|
|00005df0| 00 00 00 00 00 00 98 96 | 8c 00 0a 00 06 3e 20 69 |........|.....> i|
|00005e00| 6c 63 6d 28 29 3b 20 20 | 20 00 00 00 00 00 00 00 |lcm(); | .......|
|00005e10| 00 00 0a 00 0d 20 20 20 | 20 20 20 20 20 20 20 20 |..... | |
|00005e20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005e30| 20 20 20 20 20 20 20 20 | 20 20 20 20 31 00 00 00 | | 1...|
|00005e40| 00 00 00 00 00 00 98 96 | 8c 00 0a 00 08 3e 20 69 |........|.....> i|
|00005e50| 67 63 64 28 20 2d 31 30 | 2c 20 36 2c 20 2d 38 20 |gcd( -10|, 6, -8 |
|00005e60| 29 3b 00 00 00 00 00 00 | 00 00 0a 00 0d 20 20 20 |);......|..... |
|00005e70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005e80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005e90| 20 20 20 20 32 00 00 00 | 00 00 00 00 00 00 98 96 | 2...|........|
|00005ea0| 8c 00 0a 00 08 3e 20 69 | 6c 63 6d 28 20 2d 31 30 |.....> i|lcm( -10|
|00005eb0| 2c 20 36 2c 20 2d 38 20 | 29 3b 00 00 00 00 00 00 |, 6, -8 |);......|
|00005ec0| 00 00 0a 00 0d 20 20 20 | 20 20 20 20 20 20 20 20 |..... | |
|00005ed0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005ee0| 20 20 20 20 20 20 20 20 | 20 20 20 31 32 30 00 00 | | 120..|
|00005ef0| 00 00 00 00 00 00 98 96 | 8c 00 0a 00 06 3e 20 69 |........|.....> i|
|00005f00| 67 63 64 28 20 61 2c 20 | 62 20 29 3b 00 00 00 00 |gcd( a, |b );....|
|00005f10| 00 00 0a 00 0e 20 20 20 | 20 20 20 20 20 20 20 20 |..... | |
|00005f20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005f30| 20 20 20 20 20 20 20 20 | 69 67 63 64 28 61 2c 20 | |igcd(a, |
|00005f40| 62 29 00 00 00 00 00 00 | 00 00 98 96 8c 00 0a 00 |b)......|........|
|00005f50| 07 53 45 45 20 41 4c 53 | 4f 3a 20 20 67 63 64 2c |.SEE ALS|O: gcd,|
|00005f60| 20 6c 63 6d 00 00 00 00 | 00 04 32 96 41 00 0a 00 | lcm....|..2.A...|
|00005f70| 07 68 65 6c 70 2f 74 65 | 78 74 2f 69 67 63 64 65 |.help/te|xt/igcde|
|00005f80| 78 00 00 00 00 00 18 00 | 03 00 0a 00 04 54 45 58 |x.......|.....TEX|
|00005f90| 54 00 00 00 00 00 00 00 | 00 00 2a 00 1a 00 0a 00 |T.......|..*.....|
|00005fa0| 03 20 20 20 00 00 00 00 | 00 00 0a 00 12 46 55 4e |. ....|.....FUN|
|00005fb0| 43 54 49 4f 4e 3a 20 69 | 67 63 64 65 78 20 2d 20 |CTION: i|gcdex - |
|00005fc0| 65 78 74 65 6e 64 65 64 | 20 45 75 63 6c 69 64 65 |extended| Euclide|
|00005fd0| 61 6e 20 61 6c 67 6f 72 | 69 74 68 6d 20 66 6f 72 |an algor|ithm for|
|00005fe0| 20 69 6e 74 65 67 65 72 | 73 00 00 00 00 00 00 00 | integer|s.......|
|00005ff0| 00 00 98 96 8d 00 0a 00 | 07 43 41 4c 4c 49 4e 47 |........|.CALLING|
|00006000| 20 53 45 51 55 45 4e 43 | 45 3a 00 00 00 00 00 00 | SEQUENC|E:......|
|00006010| 00 00 0a 00 0a 20 20 20 | 69 67 63 64 65 78 28 20 |..... |igcdex( |
|00006020| 61 2c 20 62 2c 20 27 73 | 27 2c 20 27 74 27 20 29 |a, b, 's|', 't' )|
|00006030| 3b 00 00 00 00 00 00 00 | 00 00 98 96 8d 00 0a 00 |;.......|........|
|00006040| 05 50 41 52 41 4d 45 54 | 45 52 53 3a 00 00 00 00 |.PARAMET|ERS:....|
|00006050| 00 00 0a 00 07 20 20 20 | 61 2c 62 20 2d 20 69 6e |..... |a,b - in|
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|00006070| 09 20 20 20 73 2c 74 20 | 2d 20 28 6f 70 74 69 6f |. s,t |- (optio|
|00006080| 6e 61 6c 29 20 6e 61 6d | 65 73 00 00 00 00 00 00 |nal) nam|es......|
|00006090| 00 00 98 96 8d 00 0a 00 | 06 53 59 4e 4f 50 53 49 |........|.SYNOPSI|
|000060a0| 53 3a 20 20 20 00 00 00 | 00 00 00 00 00 00 0a 00 |S: ...|........|
|000060b0| 13 2d 20 69 67 63 64 65 | 78 20 72 65 74 75 72 6e |.- igcde|x return|
|000060c0| 73 20 67 20 3d 20 69 67 | 63 64 28 61 2c 62 29 2c |s g = ig|cd(a,b),|
|000060d0| 20 61 6e 64 20 6f 70 74 | 69 6f 6e 61 6c 6c 79 20 | and opt|ionally |
|000060e0| 73 20 61 6e 64 2f 6f 72 | 20 74 20 73 75 63 68 20 |s and/or| t such |
|000060f0| 74 68 61 74 00 00 00 00 | 00 00 98 96 8d 00 0a 00 |that....|........|
|00006100| 08 20 20 20 20 20 20 20 | 20 20 67 20 3d 20 73 20 |. | g = s |
|00006110| 61 20 2b 20 74 20 62 00 | 00 00 00 00 00 00 98 96 |a + t b.|........|
|00006120| 8d 00 0a 00 06 45 58 41 | 4d 50 4c 45 53 3a 20 20 |.....EXA|MPLES: |
|00006130| 20 00 00 00 00 00 00 00 | 00 00 0a 00 08 3e 20 69 | .......|.....> i|
|00006140| 67 63 64 65 78 28 32 2c | 33 2c 27 73 27 2c 27 74 |gcdex(2,|3,'s','t|
|00006150| 27 29 3b 00 00 00 00 00 | 00 00 0a 00 0d 20 20 20 |');.....|..... |
|00006160| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00006170| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00006180| 20 20 20 20 31 00 00 00 | 00 00 00 00 00 00 98 96 | 1...|........|
|00006190| 8d 00 0a 00 05 3e 20 73 | 3b 20 74 3b 20 20 20 00 |.....> s|; t; .|
|000061a0| 00 00 00 00 00 00 0a 00 | 0d 20 20 20 20 20 20 20 |........|. |
|000061b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000061c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000061d0| 2d 31 00 00 00 00 00 00 | 00 00 98 96 8d 00 98 96 |-1......|........|
|000061e0| fc 00 98 96 8d 00 0a 00 | 0a 53 45 45 20 41 4c 53 |........|.SEE ALS|
|000061f0| 4f 3a 20 20 69 67 63 64 | 2c 20 69 6c 63 6d 2c 20 |O: igcd|, ilcm, |
|00006200| 67 63 64 65 78 00 00 00 | 00 00 00 00 00 04 32 96 |gcdex...|......2.|
|00006210| 41 00 0a 00 07 68 65 6c | 70 2f 74 65 78 74 2f 69 |A....hel|p/text/i|
|00006220| 6c 61 70 6c 61 63 65 00 | 00 00 18 00 03 00 0a 00 |laplace.|........|
|00006230| 04 54 45 58 54 00 00 00 | 00 00 00 00 00 00 2a 00 |.TEXT...|......*.|
|00006240| 38 00 0a 00 03 20 20 20 | 00 00 00 00 00 00 0a 00 |8.... |........|
|00006250| 0f 46 55 4e 43 54 49 4f | 4e 3a 20 69 6e 76 6c 61 |.FUNCTIO|N: invla|
|00006260| 70 6c 61 63 65 20 2d 20 | 69 6e 76 65 72 73 65 20 |place - |inverse |
|00006270| 4c 61 70 6c 61 63 65 20 | 74 72 61 6e 73 66 6f 72 |Laplace |transfor|
|00006280| 6d 00 00 00 00 00 00 00 | 00 00 98 96 8d 00 0a 00 |m.......|........|
|00006290| 07 43 41 4c 4c 49 4e 47 | 20 53 45 51 55 45 4e 43 |.CALLING| SEQUENC|
|000062a0| 45 3a 00 00 00 00 00 00 | 00 00 0a 00 09 20 20 20 |E:......|..... |
|000062b0| 69 6e 76 6c 61 70 6c 61 | 63 65 28 65 78 70 72 2c |invlapla|ce(expr,|
|000062c0| 20 73 2c 20 74 29 00 00 | 00 00 00 00 00 00 98 96 | s, t)..|........|
|000062d0| 8d 00 0a 00 05 50 41 52 | 41 4d 45 54 45 52 53 3a |.....PAR|AMETERS:|
|000062e0| 00 00 00 00 00 00 0a 00 | 0c 20 20 20 65 78 70 72 |........|. expr|
|000062f0| 20 2d 20 65 78 70 72 65 | 73 73 69 6f 6e 20 74 6f | - expre|ssion to|
|00006300| 20 62 65 20 74 72 61 6e | 73 66 6f 72 6d 65 64 00 | be tran|sformed.|
|00006310| 00 00 00 00 00 00 0a 00 | 10 20 20 20 73 20 20 20 |........|. s |
|00006320| 20 2d 20 76 61 72 69 61 | 62 6c 65 20 65 78 70 72 | - varia|ble expr|
|00006330| 20 69 73 20 74 72 61 6e | 73 66 6f 72 6d 65 64 20 | is tran|sformed |
|00006340| 77 69 74 68 20 72 65 73 | 70 65 63 74 20 74 6f 00 |with res|pect to.|
|00006350| 00 00 00 00 00 00 0a 00 | 11 20 20 20 74 20 20 20 |........|. t |
|00006360| 20 2d 20 76 61 72 69 61 | 62 6c 65 20 74 6f 20 72 | - varia|ble to r|
|00006370| 65 70 6c 61 63 65 20 73 | 20 69 6e 20 74 72 61 6e |eplace s| in tran|
|00006380| 73 66 6f 72 6d 65 64 20 | 65 78 70 72 65 73 73 69 |sformed |expressi|
|00006390| 6f 6e 00 00 00 00 00 00 | 00 00 98 96 8d 00 0a 00 |on......|........|
|000063a0| 06 53 59 4e 4f 50 53 49 | 53 3a 20 20 20 00 00 00 |.SYNOPSI|S: ...|
|000063b0| 00 00 00 00 00 00 0a 00 | 16 2d 20 54 68 65 20 66 |........|.- The f|
|000063c0| 75 6e 63 74 69 6f 6e 20 | 69 6e 76 6c 61 70 6c 61 |unction |invlapla|
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|000063e0| 6e 76 65 72 73 65 20 4c | 61 70 6c 61 63 65 20 74 |nverse L|aplace t|
|000063f0| 72 61 6e 73 66 6f 72 6d | 61 74 69 6f 6e 20 74 6f |ransform|ation to|
+--------+-------------------------+-------------------------+--------+--------+
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