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`100%`	file	MacBinary II, Tue Oct 5 19:56:21 1993, modified Tue Oct 5 19:56:21 1993, creator 'MPAD', type ASCII, 17811 bytes "MathPad.doc" , at 0x4613 402 bytes resource	default (weak)
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|000028d0| 20 61 74 20 31 2e 0d 20 | 42 3d 7b 41 2c 7b 34 30 | at 1.. |B={A,{40|
|000028e0| 2c 35 30 2c 36 30 7d 2c | 41 2b 31 7d 20 20 20 2d |,50,60},|A+1}   -|
|000028f0| 2d 20 4d 75 6c 74 69 64 | 69 6d 65 6e 73 69 6f 6e |- Multid|imension|
|00002900| 61 6c 20 61 72 72 61 79 | 2e 0d 20 42 3a 7b 7b 31 |al array|.. B:{{1|
|00002910| 30 2e 30 2c 32 30 2e 30 | 2c 33 30 2e 30 7d 2c 7b |0.0,20.0|,30.0},{|
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|00002930| 7b 31 31 2e 30 2c 32 31 | 2e 30 2c 33 31 2e 30 7d |{11.0,21|.0,31.0}|
|00002940| 7d 0d 20 42 5b 31 5d 3a | 7b 31 30 2e 30 2c 32 30 |}. B[1]:|{10.0,20|
|00002950| 2e 30 2c 33 30 2e 30 7d | 0d 20 42 5b 31 5d 5b 32 |.0,30.0}|. B[1][2|
|00002960| 5d 3a 32 30 2e 30 0d 20 | 42 5b 31 2c 32 5d 3a 32 |]:20.0. |B[1,2]:2|
|00002970| 30 2e 30 3b 20 20 20 20 | 20 20 20 20 20 2d 2d 20 |0.0;    |     -- |
|00002980| 42 6f 74 68 20 66 6f 72 | 6d 73 20 6f 66 20 69 6e |Both for|ms of in|
|00002990| 64 65 78 69 6e 67 20 61 | 72 65 20 61 6c 6c 6f 77 |dexing a|re allow|
|000029a0| 65 64 0d 0d 20 41 5b 32 | 3a 33 5d 3a 7b 32 30 2e |ed.. A[2|:3]:{20.|
|000029b0| 30 2c 33 30 2e 30 7d 3b | 20 20 20 20 2d 2d 20 5b |0,30.0};|    -- [|
|000029c0| 6c 6f 3a 68 69 5d 20 73 | 65 6c 65 63 74 73 20 61 |lo:hi] s|elects a|
|000029d0| 20 73 75 62 20 61 72 72 | 61 79 2e 0d 20 41 5b 32 | sub arr|ay.. A[2|
|000029e0| 3a 33 5d 5b 32 3a 32 5d | 3a 7b 33 30 2e 30 7d 3b |:3][2:2]|:{30.0};|
|000029f0| 20 20 20 20 2d 2d 20 63 | 6f 6e 73 65 63 75 74 69 |    -- c|onsecuti|
|00002a00| 76 65 20 73 65 6c 65 63 | 74 69 6f 6e 73 20 6f 70 |ve selec|tions op|
|00002a10| 65 72 61 74 65 20 6f 6e | 20 74 68 65 20 73 61 6d |erate on| the sam|
|00002a20| 65 20 64 69 6d 65 6e 73 | 69 6f 6e 0d 20 41 5b 3a |e dimens|ion. A[:|
|00002a30| 32 5d 3a 7b 31 30 2e 30 | 2c 32 30 2e 30 7d 3b 20 |2]:{10.0|,20.0}; |
|00002a40| 20 20 20 20 2d 2d 20 6c | 6f 20 61 6e 64 2f 6f 72 |    -- l|o and/or|
|00002a50| 20 68 69 20 6d 61 79 20 | 62 65 20 6f 6d 69 74 74 | hi may |be omitt|
|00002a60| 65 64 2e 0d 20 42 5b 32 | 3a 5d 3a 7b 7b 34 30 2e |ed.. B[2|:]:{{40.|
|00002a70| 30 2c 35 30 2e 30 2c 36 | 30 2e 30 7d 2c 7b 31 31 |0,50.0,6|0.0},{11|
|00002a80| 2e 30 2c 32 31 2e 30 2c | 33 31 2e 30 7d 7d 0d 0d |.0,21.0,|31.0}}..|
|00002a90| 20 51 5b 69 5d 3d 69 2a | 31 31 20 20 2d 2d 41 72 | Q[i]=i*|11  --Ar|
|00002aa0| 72 61 79 73 20 63 61 6e | 20 62 65 20 64 65 66 69 |rays can| be defi|
|00002ab0| 6e 65 64 20 69 6e 20 74 | 65 72 6d 73 20 6f 66 20 |ned in t|erms of |
|00002ac0| 74 68 65 69 72 20 69 6e | 64 65 78 20 76 61 6c 75 |their in|dex valu|
|00002ad0| 65 73 2e 0d 20 51 5b 32 | 5d 3a 32 32 2e 30 0d 0d |es.. Q[2|]:22.0..|
|00002ae0| 2d 2d 64 69 6d 5b 5d 20 | 69 73 20 75 73 65 64 20 |--dim[] |is used |
|00002af0| 74 6f 20 73 65 74 20 74 | 68 65 20 6e 75 6d 62 65 |to set t|he numbe|
|00002b00| 72 20 6f 66 20 65 6c 65 | 6d 65 6e 74 73 20 66 6f |r of ele|ments fo|
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|00002b20| 69 74 69 6f 6e 0d 20 49 | 5b 69 2c 6a 5d 20 3d 20 |ition. I|[i,j] = |
|00002b30| 31 20 77 68 65 6e 20 69 | 3d 6a 2c 30 20 6f 74 68 |1 when i|=j,0 oth|
|00002b40| 65 72 77 69 73 65 20 20 | 20 64 69 6d 5b 33 2c 33 |erwise  | dim[3,3|
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|00002b60| 2e 30 7d 2c 7b 30 2e 30 | 2c 31 2e 30 2c 30 2e 30 |.0},{0.0|,1.0,0.0|
|00002b70| 7d 2c 7b 30 2e 30 2c 30 | 2e 30 2c 31 2e 30 7d 7d |},{0.0,0|.0,1.0}}|
|00002b80| 0d 0d 2d 2d 41 72 72 61 | 79 73 20 6d 61 79 20 62 |..--Arra|ys may b|
|00002b90| 65 20 75 73 65 64 20 66 | 72 65 65 6c 79 20 69 6e |e used f|reely in|
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|00002bc0| 66 6f 72 6d 65 64 20 6f | 6e 20 65 61 63 68 20 65 |formed o|n each e|
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|00002bf0| 63 6f 6e 74 61 69 6e 20 | 61 73 20 6d 61 6e 79 20 |contain |as many |
|00002c00| 65 6c 65 6d 65 6e 74 73 | 20 61 73 20 6e 65 65 64 |elements| as need|
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|00002c20| 32 2e 30 2c 36 33 2e 30 | 7d 0d 20 32 2b 41 3a 7b |2.0,63.0|}. 2+A:{|
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|00002c40| 20 6c 6f 67 28 41 29 3a | 7b 31 2e 30 2c 31 2e 33 | log(A):|{1.0,1.3|
|00002c50| 2c 31 2e 35 7d 0d 20 41 | 2a 51 3a 7b 31 31 30 2e |,1.5}. A|*Q:{110.|
|00002c60| 30 2c 34 34 30 2e 30 2c | 39 39 30 2e 30 7d 3b 20 |0,440.0,|990.0}; |
|00002c70| 2d 2d 4e 6f 74 65 3a 20 | 74 68 69 73 20 69 73 20 |--Note: |this is |
|00002c80| 6e 6f 74 20 6d 61 74 72 | 69 78 20 6d 75 6c 74 69 |not matr|ix multi|
|00002c90| 70 6c 79 0d 20 51 5b 41 | 5d 3a 3f 20 41 5b 3f 5d |ply. Q[A|]:? A[?]|
|00002ca0| 3b 20 20 20 20 20 20 20 | 20 20 20 20 20 20 2d 2d |;       |      --|
|00002cb0| 41 72 72 61 79 73 20 6d | 61 79 20 6e 6f 74 20 62 |Arrays m|ay not b|
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|00002cd0| 76 61 6c 75 65 73 2e 0d | 0d 2d 2d 46 75 6e 63 74 |values..|.--Funct|
|00002ce0| 69 6f 6e 73 20 63 61 6e | 20 75 73 65 20 69 6e 64 |ions can| use ind|
|00002cf0| 65 78 20 76 61 6c 75 65 | 73 0d 20 73 6b 69 70 28 |ex value|s. skip(|
|00002d00| 7a 7a 2c 62 79 29 5b 69 | 5d 20 3d 20 7a 7a 5b 69 |zz,by)[i|] = zz[i|
|00002d10| 2a 62 79 5d 0d 20 73 6b | 69 70 28 51 2c 32 29 3a |*by]. sk|ip(Q,2):|
|00002d20| 7b 32 32 2e 30 2c 34 34 | 2e 30 2c 36 36 2e 30 2c |{22.0,44|.0,66.0,|
|00002d30| 2e 2e 2e 7d 0d 20 6d 75 | 6c 74 69 70 6c 79 28 41 |...}. mu|ltiply(A|
|00002d40| 2c 42 29 5b 69 2c 6a 5d | 20 3d 20 73 75 6d 28 41 |,B)[i,j]| = sum(A|
|00002d50| 5b 69 2c 6b 5d 2a 42 5b | 6b 2c 6a 5d 2c 6b 2c 31 |[i,k]*B[|k,j],k,1|
|00002d60| 2c 63 6f 75 6e 74 28 42 | 29 29 20 64 69 6d 0d 20 |,count(B|)) dim. |
|00002d70| 20 20 20 20 20 20 20 20 | 20 20 20 20 5b 63 6f 75 |        |    [cou|
|00002d80| 6e 74 28 41 29 2c 63 6f | 75 6e 74 28 42 5b 31 5d |nt(A),co|unt(B[1]|
|00002d90| 29 5d 0d 20 6d 75 6c 74 | 69 70 6c 79 28 7b 41 7d |)]. mult|iply({A}|
|00002da0| 2c 49 29 3a 7b 7b 31 30 | 2e 30 2c 32 30 2e 30 2c |,I):{{10|.0,20.0,|
|00002db0| 33 30 2e 30 7d 7d 0d 0d | 2d 2d 2d 2d 2d 2d 2d 2d |30.0}}..|--------|
|00002dc0| 2d 20 42 75 69 6c 74 2d | 69 6e 20 66 75 6e 63 74 |- Built-|in funct|
|00002dd0| 69 6f 6e 73 20 66 6f 72 | 20 61 72 72 61 79 73 0d |ions for| arrays.|
|00002de0| 20 63 6f 75 6e 74 28 41 | 29 3a 33 2e 30 3b 20 20 | count(A|):3.0;  |
|00002df0| 2d 2d 20 63 6f 75 6e 74 | 28 29 20 72 65 74 75 72 |-- count|() retur|
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|00002e20| 20 20 63 6f 75 6e 74 28 | 42 29 3a 33 2e 30 3b 20 |  count(|B):3.0; |
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|00002e40| 69 6e 20 31 73 74 20 64 | 69 6d 65 6e 73 69 6f 6e |in 1st d|imension|
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|00002e60| 3b 20 20 20 20 2d 2d 20 | 73 63 61 6c 61 72 0d 20 |;    -- |scalar. |
|00002e70| 20 63 6f 75 6e 74 28 51 | 29 3a 3f 3b 20 20 20 20 | count(Q|):?;    |
|00002e80| 20 20 20 2d 2d 20 69 6e | 66 69 6e 69 74 65 20 61 |   -- in|finite a|
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|00002ea0| 30 2e 30 3b 20 20 2d 2d | 20 63 61 6c 63 75 6c 61 |0.0;  --| calcula|
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|000030c0| 74 20 63 6f 6d 6d 61 6e | 64 20 63 61 6e 20 61 6c |t comman|d can al|
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|00003580| 6f 20 61 6e 64 2f 6f 72 | 20 5a 68 69 20 66 72 6f |o and/or| Zhi fro|
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