HCoop / hcoop / debian / mlton.git / blame
| Commit | Line | Data |
|---|---|---|
| 7f918cf1 CE |
1 | signature MATRIX = |
| 2 | sig | |
| 3 | type 'entry matrix | |
| 4 | val make: int * int * (int * int -> 'entry) -> 'entry matrix | |
| 5 | val height: 'entry matrix -> int | |
| 6 | val width: 'entry matrix -> int | |
| 7 | val fetch: 'entry matrix * int * int -> 'entry | |
| 8 | val fetchRow: 'entry matrix * int -> int -> 'entry | |
| 9 | val fetchCol: 'entry matrix * int -> int -> 'entry | |
| 10 | val store: 'entry matrix * int * int * 'entry -> unit | |
| 11 | val storeRow: 'entry matrix * int -> int * 'entry -> unit | |
| 12 | val storeCol: 'entry matrix * int -> int * 'entry -> unit | |
| 13 | val rowSwap: 'entry matrix * int * int -> unit | |
| 14 | val colSwap: 'entry matrix * int * int -> unit | |
| 15 | val rowOp: 'entry matrix * int * int * ('entry * 'entry -> 'entry) -> unit | |
| 16 | val colOp: 'entry matrix * int * int * ('entry * 'entry -> 'entry) -> unit | |
| 17 | val copy: 'entry matrix -> 'entry matrix | |
| 18 | val map: 'entry1 matrix * ('entry1 -> 'entry2) -> 'entry2 matrix | |
| 19 | val toString: 'entry matrix * ('entry -> string) -> string | |
| 20 | end | |
| 21 | ||
| 22 | structure Matrix:> MATRIX = | |
| 23 | struct | |
| 24 | type 'entry matrix = int * int * 'entry array | |
| 25 | ||
| 26 | exception sizeError | |
| 27 | ||
| 28 | exception index | |
| 29 | ||
| 30 | exception foldError | |
| 31 | ||
| 32 | fun make (height: int, width: int, generator: int * int -> 'entry) | |
| 33 | : 'entry matrix = | |
| 34 | if height < 0 orelse width < 0 | |
| 35 | then raise sizeError | |
| 36 | else (height, | |
| 37 | width, | |
| 38 | Array.tabulate (height*width, | |
| 39 | fn z => generator (z div width, | |
| 40 | z mod width))) | |
| 41 | ||
| 42 | fun height (height, _, _) = height | |
| 43 | ||
| 44 | fun width (width, _, _) = width | |
| 45 | ||
| 46 | fun fetch ((height, width, mat), row, col) = | |
| 47 | if 0 <= row | |
| 48 | andalso row < height | |
| 49 | andalso 0 <= col | |
| 50 | andalso col < width | |
| 51 | then Array.sub (mat, col + width*row) | |
| 52 | else raise index | |
| 53 | ||
| 54 | fun fetchRow ((height, width, mat), row) = | |
| 55 | if 0 <= row andalso row < height | |
| 56 | then let val offset = width * row | |
| 57 | in fn col => | |
| 58 | if 0 <= col andalso col < width | |
| 59 | then Array.sub (mat, col + offset) | |
| 60 | else raise index | |
| 61 | end | |
| 62 | else raise index | |
| 63 | ||
| 64 | fun fetchCol ((height, width, mat), col) = | |
| 65 | if 0 <= col andalso col < width | |
| 66 | then fn row => | |
| 67 | if 0 <= row andalso row < height | |
| 68 | then Array.sub (mat, col + width*row) | |
| 69 | else raise index | |
| 70 | else raise index | |
| 71 | ||
| 72 | fun store ((height, width, mat), row, col, entry) = | |
| 73 | if 0 <= row | |
| 74 | andalso row < height | |
| 75 | andalso 0 <= col | |
| 76 | andalso col < width | |
| 77 | then Array.update (mat, col + width*row, entry) | |
| 78 | else raise index | |
| 79 | ||
| 80 | fun storeRow ((height, width, mat), row) = | |
| 81 | if 0 <= row andalso row < height | |
| 82 | then let val offset = width * row | |
| 83 | in fn (col, entry) => | |
| 84 | if 0 <= col andalso col < width | |
| 85 | then Array.update (mat, col + offset, entry) | |
| 86 | else raise index | |
| 87 | end | |
| 88 | else raise index | |
| 89 | ||
| 90 | fun storeCol ((height, width, mat), col) = | |
| 91 | if 0 <= col andalso col < width | |
| 92 | then fn (row, entry) => | |
| 93 | if 0 <= row andalso row < height | |
| 94 | then Array.update (mat, col + width*row, entry) | |
| 95 | else raise index | |
| 96 | else raise index | |
| 97 | ||
| 98 | fun swapLoop (from1: int -> 'entry, | |
| 99 | to1: int * 'entry -> unit, | |
| 100 | from2: int -> 'entry, | |
| 101 | to2: int * 'entry -> unit, | |
| 102 | limit: int): unit = | |
| 103 | let fun loop (i: int): unit = | |
| 104 | if i = limit | |
| 105 | then () | |
| 106 | else let val tmp = from1 i | |
| 107 | in to1 (i, from2 i); | |
| 108 | to2 (i, tmp); | |
| 109 | loop (i + 1) | |
| 110 | end | |
| 111 | in loop 0 | |
| 112 | end | |
| 113 | ||
| 114 | fun rowSwap (mat as (height, width, _), row1, row2): unit = | |
| 115 | if 0 <= row1 andalso row1 < height | |
| 116 | andalso 0 <= row2 andalso row2 < height | |
| 117 | then if row1 = row2 | |
| 118 | then () | |
| 119 | else swapLoop (fetchRow (mat, row1), | |
| 120 | storeRow (mat, row1), | |
| 121 | fetchRow (mat, row2), | |
| 122 | storeRow (mat, row2), | |
| 123 | width) | |
| 124 | else raise index | |
| 125 | ||
| 126 | fun colSwap (mat as (height, width, _), col1, col2): unit = | |
| 127 | if 0 <= col1 andalso col1 < width | |
| 128 | andalso 0 <= col2 andalso col2 < width | |
| 129 | then if col1 = col2 | |
| 130 | then () | |
| 131 | else swapLoop (fetchCol (mat, col1), | |
| 132 | storeCol (mat, col1), | |
| 133 | fetchCol (mat, col2), | |
| 134 | storeCol (mat, col2), | |
| 135 | height) | |
| 136 | else raise index | |
| 137 | ||
| 138 | fun opLoop (from1: int -> 'entry, | |
| 139 | from2: int -> 'entry, | |
| 140 | to2: int * 'entry -> unit, | |
| 141 | limit: int, | |
| 142 | f: 'entry * 'entry -> 'entry): unit = | |
| 143 | let fun loop (i: int): unit = | |
| 144 | if i = limit | |
| 145 | then () | |
| 146 | else ( | |
| 147 | to2 (i, | |
| 148 | f (from1 i, from2 i)); | |
| 149 | loop (i + 1)) | |
| 150 | in loop 0 | |
| 151 | end | |
| 152 | ||
| 153 | fun rowOp (mat as (height, width, _), | |
| 154 | row1, | |
| 155 | row2, | |
| 156 | f: 'entry * 'entry -> 'entry): unit = | |
| 157 | if 0 <= row1 andalso row1 < height | |
| 158 | andalso 0 <= row2 andalso row2 < height | |
| 159 | andalso row1 <> row2 | |
| 160 | then opLoop (fetchRow (mat, row1), | |
| 161 | fetchRow (mat, row2), | |
| 162 | storeRow (mat, row2), | |
| 163 | width, | |
| 164 | f) | |
| 165 | else raise index | |
| 166 | ||
| 167 | fun colOp (mat as (height, width, _), | |
| 168 | col1, | |
| 169 | col2, | |
| 170 | f: 'entry * 'entry -> 'entry): unit = | |
| 171 | if 0 <= col1 andalso col1 < width | |
| 172 | andalso 0 <= col2 andalso col2 < width | |
| 173 | andalso col1 <> col2 | |
| 174 | then opLoop (fetchCol (mat, col1), | |
| 175 | fetchCol (mat, col2), | |
| 176 | storeCol (mat, col2), | |
| 177 | height, | |
| 178 | f) | |
| 179 | else raise index | |
| 180 | ||
| 181 | fun copy ((height, width, mat)) = | |
| 182 | (height, | |
| 183 | width, | |
| 184 | Array.tabulate (Array.length mat, | |
| 185 | fn i => Array.sub (mat, i))) | |
| 186 | ||
| 187 | fun map ((height, width, mat: 'entry1 Array.array), | |
| 188 | f: 'entry1 -> 'entry2) | |
| 189 | : 'entry2 matrix = | |
| 190 | (height, | |
| 191 | width, | |
| 192 | Array.tabulate (Array.length mat, | |
| 193 | fn i => f (Array.sub (mat, i)))) | |
| 194 | ||
| 195 | (* Natural fold a range of integers in reverse. *) | |
| 196 | fun naturalFold (limit: int, | |
| 197 | state: 'state, | |
| 198 | folder: int * 'state -> 'state): 'state = | |
| 199 | let fun loop (i: int, state: 'state) = | |
| 200 | if i = 0 | |
| 201 | then state | |
| 202 | else loop (i - 1, folder (i - 1, state)) | |
| 203 | in if limit < 0 | |
| 204 | then raise foldError | |
| 205 | else loop (limit, state) | |
| 206 | end | |
| 207 | ||
| 208 | ||
| 209 | local val blank8 = Byte.charToByte #" " | |
| 210 | ||
| 211 | fun makeBlanks size = | |
| 212 | let val blanks = Word8Vector.tabulate (size, | |
| 213 | fn _ => blank8) | |
| 214 | in Byte.bytesToString blanks | |
| 215 | end | |
| 216 | ||
| 217 | in fun toString (mat: 'entry matrix, f: 'entry -> string): string = | |
| 218 | let val mat as (height, width, _) = map (mat, f) | |
| 219 | fun maxSize from (i, width) = Int.max (String.size (from i), | |
| 220 | width) | |
| 221 | fun colWidth col = naturalFold (height, | |
| 222 | 0, | |
| 223 | maxSize (fetchCol (mat, | |
| 224 | col))) | |
| 225 | val widths = Vector.tabulate (width, colWidth) | |
| 226 | fun doRow (row: int, ac: string list): string list = | |
| 227 | let val from = fetchRow (mat, row) | |
| 228 | fun loop (col: int, ac: string list) = | |
| 229 | let val next = from col | |
| 230 | val ac = next::ac | |
| 231 | val s = String.size next | |
| 232 | val pad = Vector.sub (widths, col) - s | |
| 233 | val ac = if pad <= 0 | |
| 234 | then ac | |
| 235 | else (makeBlanks pad)::ac | |
| 236 | in if col = 0 | |
| 237 | then ac | |
| 238 | else loop (col - 1, | |
| 239 | " "::ac) | |
| 240 | end | |
| 241 | val ac = "\n"::ac | |
| 242 | in if width = 0 | |
| 243 | then ac | |
| 244 | else loop (width - 1, ac) | |
| 245 | end | |
| 246 | val pieces = naturalFold (height, | |
| 247 | [], | |
| 248 | doRow) | |
| 249 | in String.concat pieces | |
| 250 | end | |
| 251 | end | |
| 252 | end | |
| 253 | ||
| 254 | val zero = IntInf.fromInt 0 | |
| 255 | ||
| 256 | fun smaller (a: IntInf.int, b: IntInf.int): bool = | |
| 257 | (not (a = zero)) | |
| 258 | andalso (b = zero orelse IntInf.< (IntInf.abs a , IntInf.abs b)) | |
| 259 | ||
| 260 | fun smithNormalForm (mat: IntInf.int Matrix.matrix): IntInf.int Matrix.matrix = | |
| 261 | let val height = Matrix.height mat | |
| 262 | val width = Matrix.width mat | |
| 263 | val mat = Matrix.copy mat | |
| 264 | val range = Int.min (width, height) | |
| 265 | fun dd pos = | |
| 266 | let val matCol = Matrix.fetchCol (mat, pos) | |
| 267 | val matRow = Matrix.fetchRow (mat, pos) | |
| 268 | val _ = print ("dd: pos = " ^ (Int.toString pos) ^ "\n") | |
| 269 | fun swapRowLoop (best, bestRow, bestCol, row) = | |
| 270 | if row >= height | |
| 271 | then (Matrix.rowSwap (mat, pos, bestRow); | |
| 272 | Matrix.colSwap (mat, pos, bestCol)) | |
| 273 | else let val matRow = Matrix.fetchRow (mat, row) | |
| 274 | fun swapColLoop (best, bestRow, bestCol, col) = | |
| 275 | if col >= width | |
| 276 | then swapRowLoop (best, bestRow, bestCol, row + 1) | |
| 277 | else let val next = matRow col | |
| 278 | in if smaller (next, best) | |
| 279 | then swapColLoop (next, row, col, col + 1) | |
| 280 | else swapColLoop (best, bestRow, bestCol, col + 1) | |
| 281 | end | |
| 282 | in swapColLoop (best, bestRow, bestCol, pos) | |
| 283 | end | |
| 284 | fun rowLoop row = | |
| 285 | if row < height | |
| 286 | then if (matCol row) = zero | |
| 287 | then rowLoop (row + 1) | |
| 288 | else (Matrix.rowOp (mat, | |
| 289 | pos, | |
| 290 | row, | |
| 291 | let val x = IntInf.~ (IntInf.quot(matCol row, matCol pos)) | |
| 292 | in fn (lhs, rhs) => IntInf.+ (IntInf.* (lhs, x), rhs) | |
| 293 | end); | |
| 294 | if (matCol row) = zero | |
| 295 | then rowLoop (row + 1) | |
| 296 | else hitPosAgain ()) | |
| 297 | else let fun colLoop col = | |
| 298 | if col < width | |
| 299 | then if (matRow col) = zero | |
| 300 | then colLoop (col + 1) | |
| 301 | else (Matrix.colOp (mat, | |
| 302 | pos, | |
| 303 | col, | |
| 304 | let val x = IntInf.~ (IntInf.quot (matRow col, matRow pos)) | |
| 305 | in fn (lhs, rhs) => IntInf.+ (IntInf.* (lhs, x), rhs) | |
| 306 | end); | |
| 307 | if (matRow col) = zero | |
| 308 | then colLoop (col + 1) | |
| 309 | else hitPosAgain ()) | |
| 310 | else () | |
| 311 | in colLoop (pos + 1) | |
| 312 | end | |
| 313 | and hitPosAgain () = (swapRowLoop (zero, pos, pos, pos); | |
| 314 | rowLoop (pos + 1)) | |
| 315 | in hitPosAgain () | |
| 316 | end | |
| 317 | fun loop pos = | |
| 318 | if pos = range | |
| 319 | then mat | |
| 320 | else (dd pos; | |
| 321 | loop (pos + 1)) | |
| 322 | in loop 0 | |
| 323 | end | |
| 324 | ||
| 325 | val table = [[ 8, ~3, 1, 3, 6, 9, ~2, 4, ~9, ~9, 2, 3, 8, ~1, 3, ~5, 4, ~3, ~5, ~6, 8, 1, 4, ~5, 7, ~4, ~4, ~7, 7, 1, 4, ~3, 8, 4, ~4, ~8, 5, ~9, 3, ~4, 1, 9, ~8, ~6, ~2, 8, ~9, ~5, ~3, ~3], | |
| 326 | [ 0, 8, ~6, ~2, ~3, 4, 5, ~2, 7, ~7, ~6, ~7, ~3, ~4, 9, 7, ~3, 3, 0, 3, 3, ~8, ~8, 2, 3, 8, 3, ~2, ~4, 3, ~6, ~6, ~2, 6, 5, ~1, ~3, 1, 8, ~8, 2, 1, ~7, ~7, ~7, ~3, ~6, 6, ~4, ~9], | |
| 327 | [ 0, ~5, 8, ~9, 2, 4, 2, 7, ~4, 9, ~3, 6, ~2, 3, ~3, 0, ~9, 5, 8, ~1, 2, ~8, 3, 4, ~6, 5, ~6, ~5, ~8, 0, ~5, 3, ~2, ~5, 8, 7, ~1, 1, ~1, 7, 6, 3, 6, 5, 6, 8, 7, 9, 7, ~3], | |
| 328 | [ 5, 4, 7, 2, 3, ~9, 7, ~7, 3, ~8, 7, 5, 5, ~2, ~6, ~3, 6, 5, 3, ~1, ~1, 4, 5, ~5, 5, 9, 9, 3, 8, ~3, ~1, 9, ~9, 6, ~7, 7, 4, 6, ~8, ~9, 0, ~3, ~2, ~7, 1, ~2, ~6, 7, 7, 7], | |
| 329 | [ 2, 9, 9, 3, ~4, 0, 9, 2, 5, 3, ~5, ~3, ~1, 1, 8, ~6, 2, ~4, ~8, ~7, ~8, 4, 5, 8, ~1, ~1, 7, 2, 5, 5, ~4, ~7, ~3, ~7, 6, ~4, ~5, ~8, ~5, ~9, ~8, 5, ~5, ~5, 0, 8, 8, 6, 4, ~1], | |
| 330 | [ 5, 5, 1, ~7, 3, ~5, 4, 9, 3, 4, 4, ~5, 7, ~1, 7, 4, ~7, 7, ~7, ~2, 9, ~9, 0, ~4, ~4, 0, 2, 6, 3, ~1, 6, 6, 8, ~6, ~4, ~9, 3, ~2, ~5, 5, ~3, 2, ~1, ~6, 9, 3, ~3, ~8, ~9, 7], | |
| 331 | [ 7, 1, 2, 7, 6, 5, ~6, ~3, ~4, ~8, 0, 9, 6, 1, 2, ~5, 4, 4, 4, ~6, ~7, ~9, ~6, 2, ~4, 5, ~2, 1, 0, 1, ~8, 7, ~7, ~5, 4, 1, ~5, 4, ~4, ~2, ~3, 1, 1, 3, 4, ~4, ~5, 9, 8, ~2], | |
| 332 | [ 6, 2, ~1, ~8, 4, ~7, 7, ~3, ~2, ~5, 3, 0, 3, ~9, 3, 3, 9, ~1, 4, 8, ~9, 6, ~5, 9, 5, ~1, ~1, ~9, 7, ~2, 3, 9, 8, 9, 2, 7, 7, 6, ~1, ~1, ~2, ~2, ~7, 3, ~6, 0, ~9, 4, 3, 7], | |
| 333 | [ 0, ~6, ~3, ~7, ~1, 5, ~2, 8, ~5, ~3, ~8, 7, ~2, ~2, 0, ~8, 4, 8, 9, ~5, ~4, ~8, ~1, 7, 1, 1, 6, ~9, ~4, 0, 8, 4, 3, ~7, 6, 0, 1, 8, 6, ~1, ~1, ~7, 9, ~9, ~5, ~2, ~2, ~1, 1, 0], | |
| 334 | [~4, 9, 6, ~3, ~2, ~6, ~3, 4, 8, ~8, 1, ~5, 9, 7, 9, 7, ~9, ~6, 6, 1, ~3, 3, ~3, ~7, 1, 7, ~7, 0, ~2, 7, ~4, ~6, 0, 1, ~3, ~5, ~9, ~7, 8, 4, 9, ~8, ~8, ~7, ~6, 7, 6, ~3, ~8, 5], | |
| 335 | [ 6, 7, ~5, ~9, 6, 1, 8, 4, ~2, 7, ~7, ~1, ~9, 1, ~6, ~5, 4, 9, 6, 0, ~8, ~3, 1, ~3, 8, ~3, 2, 9, ~3, ~9, ~1, ~3, 4, 3, 2, ~9, ~5, ~3, 8, ~4, 8, 5, ~4, 7, 6, ~8, 7, 6, ~5, 5], | |
| 336 | [ 1, 7, ~8, ~9, ~7, ~3, 8, 9, ~7, ~1, ~7, 4, 0, 0, 1, ~5, 9, ~8, ~1, ~2, 3, 5, 9, ~9, 5, 4, ~9, 1, ~4, ~2, 3, ~4, 8, ~6, ~4, ~8, ~5, ~5, 4, ~2, ~4, ~1, ~9, ~5, 2, ~9, 2, ~9, ~2, ~3], | |
| 337 | [~5, ~4, ~4, 9, 2, 7, ~2, 6, 7, 2, ~9, 4, 2, 7, 8, ~9, 2, 5, 3, 9, 6, 3, 0, ~7, ~6, ~7, 6, ~2, 9, ~3, ~6, 9, ~9, 2, 2, ~6, ~1, 4, ~3, 3, 0, 6, ~3, 4, 9, 9, ~6, 5, 5, ~5], | |
| 338 | [ 5, ~7, 8, ~4, 8, 8, ~4, ~9, 6, 0, ~3, 6, 0, 8, 8, ~6, ~2, 5, 4, ~1, ~8, 1, ~3, ~1, 2, 3, ~9, ~9, ~5, 1, 8, ~5, ~3, 0, ~4, ~9, 0, ~6, 3, ~1, ~7, 0, 8, 9, ~6, ~1, ~9, 1, ~6, 2], | |
| 339 | [ 7, ~5, ~1, 5, ~2, 7, 0, ~7, ~1, 8, 8, ~3, 9, ~5, 7, ~8, ~8, ~4, 3, 2, ~1, 8, ~2, 1, 2, 5, 0, ~6, 7, 3, 3, 7, ~5, 5, ~1, 1, 0, ~8, 1, 0, 0, ~4, 6, 9, ~5, ~6, 3, ~5, 8, 5], | |
| 340 | [~4, ~2, 3, ~3, ~1, 2, ~2, ~1, ~9, ~5, 1, 0, 0, 2, 9, ~3, ~9, 2, 9, 3, 8, ~3, 4, 8, 8, 3, ~3, ~1, ~4, 4, ~6, ~9, 5, ~2, 1, 3, ~7, ~5, ~6, ~5, ~8, 4, ~8, ~3, 5, 0, 7, ~9, 6, 2], | |
| 341 | [ 5, 1, 4, ~3, ~1, ~9, 5, ~8, ~8, 6, 1, 1, ~2, 7, 5, 6, ~4, 2, ~7, 0, ~7, ~3, ~5, 9, 3, 4, ~6, 8, ~4, 3, 6, 0, 2, 3, ~6, 3, 9, 4, 1, ~4, 6, ~5, ~7, 0, ~1, ~8, ~3, ~9, 9, 7], | |
| 342 | [ 2, ~6, ~1, 8, 4, ~3, ~1, ~6, ~2, ~8, ~2, ~1, ~1, ~5, ~9, ~8, 9, ~9, 5, 1, 9, ~1, ~6, 9, ~7, 2, 8, ~7, 4, ~9, 7, 6, ~2, 1, ~2, ~7, 8, 0, 5, 0, ~5, ~7, ~6, 0, 4, 0, 3, ~8, 5, 4], | |
| 343 | [~2, 9, ~9, ~6, 1, ~8, 8, 4, ~6, 8, 1, ~3, ~7, 8, ~5, 2, ~8, 1, 3, ~2, 6, 6, 6, 1, 0, 0, ~7, 7, ~3, ~3, 0, ~4, 3, ~7, ~6, 7, 5, 9, ~5, 7, ~8, 2, 3, ~8, ~7, 6, ~5, ~5, ~8, ~9], | |
| 344 | [~7, ~4, 4, 1, ~1, ~3, ~8, 3, 7, 9, 8, 3, 0, 4, 4, ~1, ~5, 4, 2, 2, 0, 6, ~6, 2, ~9, 8, ~9, 3, ~2, 2, 6, 6, 1, 7, 1, 0, ~8, 2, 3, ~3, 8, 9, 5, 5, ~6, 4, ~7, ~4, ~2, ~3], | |
| 345 | [~5, 8, 6, 1, ~6, ~6, 6, 1, 1, ~3, ~9, ~6, 2, ~7, 2, ~1, 6, ~6, 0, 2, ~7, 8, ~8, 4, 9, ~3, 9, ~7, ~9, ~6, ~4, ~4, ~5, 8, 2, ~5, ~4, ~3, 5, 2, 1, ~3, ~3, ~7, ~9, 3, 7, ~7, 3, ~8], | |
| 346 | [~4, ~7, ~2, 2, ~4, ~2, 6, ~3, ~1, ~4, 0, ~5, 9, 7, ~6, ~9, 7, ~9, ~6, 2, ~3, 1, 5, ~9, 4, ~5, 4, ~9, 1, ~2, ~2, 4, 0, 4, ~8, ~8, 3, ~1, ~5, ~4, ~9, ~7, 7, 6, 3, ~9, 6, 4, ~4, ~7], | |
| 347 | [~9, 6, 6, ~5, ~1, ~7, 4, ~9, 4, ~1, 6, ~4, 7, 2, 8, 7, 3, 1, ~7, 7, 7, 9, 8, ~9, 7, 2, 1, 2, ~8, 4, 5, 6, 7, 2, ~7, 6, 8, 4, ~9, 7, ~5, 6, 9, ~1, 9, 2, 0, 9, 3, 6], | |
| 348 | [ 4, ~3, 8, 0, ~2, ~2, 2, ~3, 8, 3, 1, ~8, ~5, ~2, 5, 6, 8, 0, ~3, 4, ~2, 4, ~9, ~5, 7, 6, ~4, ~7, 2, 4, ~3, ~8, ~9, 9, 8, ~9, 3, ~7, 4, ~7, ~5, 4, 9, 3, ~6, ~3, ~7, 4, 2, ~2], | |
| 349 | [~8, ~8, 6, ~2, ~6, 8, ~3, 3, ~1, ~7, 1, 9, 1, 7, ~6, 8, ~2, ~9, ~1, 3, ~4, 7, 8, ~1, 9, ~9, 6, ~3, 5, 0, 2, 5, ~1, ~6, ~6, 1, 8, 6, ~3, ~9, ~1, 9, ~2, 9, ~8, ~7, ~3, 6, ~3, ~3], | |
| 350 | [ 5, ~2, 3, 0, ~9, ~8, ~6, 1, 8, 0, 1, 2, ~8, ~2, 0, ~9, ~8, 0, 5, ~3, ~4, 5, 6, ~2, ~5, 0, ~9, 9, ~9, ~5, 9, 9, ~5, ~2, 4, 3, 8, ~8, ~7, 5, ~3, ~2, 2, 3, 9, 7, ~1, 0, 4, ~1], | |
| 351 | [~4, 5, ~5, 7, 8, 9, 7, ~3, 1, 9, ~7, ~1, 8, ~5, ~1, 2, ~8, 1, 0, 9, ~8, ~1, 6, ~1, 9, ~8, 7, 4, ~8, 7, 0, ~6, 2, 3, 7, 4, ~3, ~5, 9, ~3, 0, 6, ~9, 2, 4, ~8, 6, ~7, 9, 1], | |
| 352 | [ 7, 0, ~9, 6, 8, 2, 2, 5, ~6, ~6, 9, ~5, 9, 2, 2, ~8, 0, ~6, ~9, ~6, ~4, ~9, 8, ~2, 9, 7, ~5, ~1, 7, 2, ~7, 7, ~1, ~3, 6, 6, 1, ~4, 0, ~1, ~6, ~5, 6, ~7, ~3, ~2, 8, 2, ~9, 8], | |
| 353 | [ 8, ~7, ~9, ~6, 9, ~7, ~7, 6, ~8, 9, 5, ~4, 1, ~7, ~8, ~6, ~3, 8, ~8, 1, ~8, 6, 9, ~3, ~7, 7, 1, 6, 1, 0, 8, ~5, ~8, 8, ~9, 0, 4, 4, 3, ~4, 6, ~3, ~9, 0, 4, ~4, ~5, ~9, ~5, ~8], | |
| 354 | [~3, ~2, 8, 1, ~1, ~1, ~4, 3, 7, ~2, ~9, 9, ~8, ~9, 6, ~4, 7, ~1, ~5, ~3, ~9, 0, ~3, 0, 7, 9, 1, ~2, 7, ~9, ~6, 3, 3, ~4, ~7, ~3, ~4, ~8, ~2, ~3, ~9, ~2, ~6, 3, ~6, ~4, 7, ~5, ~8, ~1], | |
| 355 | [~9, ~9, ~2, ~9, ~9, 9, 6, 6, 7, 5, ~1, ~2, 1, 5, 2, ~3, ~4, 1, ~6, 0, ~3, ~9, ~1, 7, 0, ~9, 5, ~2, ~2, 5, 3, 4, ~1, 6, ~6, 3, ~6, 7, ~1, 5, ~8, ~4, ~2, ~2, ~6, ~5, ~6, 3, ~1, 4], | |
| 356 | [ 7, 7, 8, 7, 6, 1, ~2, 5, ~6, 9, 4, 8, 5, 0, ~4, ~2, ~2, ~5, ~2, ~6, 9, ~8, ~2, ~5, ~9, 3, ~6, ~3, ~4, ~5, ~2, 6, 1, 6, ~5, 0, ~3, ~2, 4, ~6, 1, 6, ~1, 3, ~9, 2, ~3, 1, 5, ~6], | |
| 357 | [ 6, 4, ~7, 3, ~7, 9, 1, ~7, ~8, 0, ~6, 8, 4, 1, 9, 6, 8, 3, 0, 9, 0, 4, 9, ~7, ~7, 1, 5, 1, ~5, 6, 9, 2, 4, 1, ~9, 8, 4, 5, 8, 3, 2, ~9, ~6, ~9, 9, ~9, 7, ~6, ~4, 3], | |
| 358 | [~3, ~9, ~4, 2, 3, 9, ~9, 8, ~9, 9, ~4, ~9, ~5, 5, 0, 7, 3, ~5, ~8, 2, ~3, 0, ~9, ~3, 1, 9, 4, 5, ~1, 8, 0, ~4, ~2, 9, ~4, ~1, 3, 5, 9, ~1, 1, 4, ~8, ~2, ~3, 5, 1, 5, ~6, 7], | |
| 359 | [ 9, ~3, 2, ~9, 3, 4, 0, 7, ~5, 9, 0, ~6, 7, ~2, 3, ~7, 2, ~5, ~2, 6, 3, ~9, ~5, ~9, 5, 2, ~5, ~3, 8, ~5, 6, 2, 9, ~7, ~7, ~7, ~6, 9, ~3, 6, 0, 6, ~6, ~9, 4, ~3, ~9, 0, ~4, ~9], | |
| 360 | [~4, ~8, 8, ~7, 7, 0, ~6, ~6, 8, ~9, ~4, 5, ~3, ~1, 7, ~5, ~6, ~1, 8, 6, ~2, 1, ~1, 5, ~9, 1, ~1, ~7, ~6, ~6, ~6, ~4, 6, 3, ~5, ~5, ~6, 2, 3, ~6, ~8, ~3, 8, ~2, ~5, ~4, ~3, 1, 4, ~4], | |
| 361 | [ 4, ~6, 2, 6, 2, ~8, 8, 5, 8, ~2, 0, ~6, ~1, ~6, ~2, 2, 6, ~9, ~7, ~6, ~4, ~4, ~7, ~2, 8, 6, 3, ~7, ~6, 8, 2, 3, 4, 5, 3, 4, ~6, 8, 8, ~1, 4, ~5, 6, 2, 8, ~3, ~9, ~2, 6, 7], | |
| 362 | [ 3, ~4, 0, ~3, ~5, 0, ~2, ~6, ~2, 8, 5, ~9, ~4, ~8, ~6, 0, 8, 9, 1, ~2, 8, 2, ~2, 8, 9, 3, 3, 5, ~9, ~3, ~2, 7, 2, 9, 0, 4, 8, ~9, 0, ~6, 9, ~9, 9, ~4, 8, ~8, ~8, 2, ~3, 2], | |
| 363 | [~1, 3, ~9, ~8, ~7, 6, ~6, 3, 0, 5, ~5, 1, 2, ~2, ~3, 7, 7, 3, ~4, ~2, ~9, ~5, ~1, 9, 6, 8, 2, 8, 7, ~3, 4, 6, 6, 0, ~2, 2, ~7, ~7, 6, ~3, 8, 2, 1, 0, 8, ~1, 3, 9, 8, 6], | |
| 364 | [ 1, ~2, ~3, 6, 5, 5, ~6, ~4, ~5, 1, 1, 6, ~7, ~4, ~3, 4, 4, ~8, ~9, 7, ~2, ~3, ~7, ~2, 1, 2, 0, 8, ~6, ~5, ~5, 7, 8, 5, ~2, 3, 9, 0, 5, 1, 3, ~4, ~6, 1, 4, ~9, ~2, 5, 4, 3], | |
| 365 | [ 3, 3, 9, ~2, 6, 9, 4, 9, 4, ~8, 5, ~1, 3, ~2, 1, ~7, ~3, 2, 2, 0, ~3, 3, 8, 2, 0, ~5, 7, 1, 4, ~8, 8, ~9, ~1, 1, ~9, ~4, 5, 2, 2, 8, 6, 1, 6, ~2, 2, 7, 1, ~6, ~1, ~1], | |
| 366 | [ 4, ~2, 4, ~1, ~5, ~1, 5, ~2, 3, ~4, ~5, 0, 2, ~4, 6, 4, ~3, 2, 2, 5, ~6, ~7, ~9, ~1, ~9, ~9, 6, 0, 6, 5, 9, ~1, 3, ~3, ~8, 8, ~8, 8, 4, 5, ~1, ~5, 1, 0, 3, ~2, 5, 6, 6, 5], | |
| 367 | [~4, 9, 6, 8, ~9, 5, 5, ~3, ~7, 7, 6, 8, ~8, 0, 4, ~1, 9, 5, ~7, 0, ~1, ~2, 3, 6, 0, 4, ~3, 1, 4, 6, 4, 0, 5, ~1, 7, ~7, ~6, ~8, ~3, ~6, 7, ~1, ~3, ~2, ~3, ~5, 3, 1, ~8, ~9], | |
| 368 | [~6, 4, ~5, 9, 9, ~7, ~1, ~8, ~4, 2, ~6, 0, ~6, ~6, 7, 6, 0, 1, 7, ~7, 0, ~4, ~6, ~8, ~9, 5, ~6, ~9, 2, ~7, ~2, ~6, 9, 4, ~5, 0, 4, ~4, ~5, 6, 9, 1, ~6, ~5, 3, ~1, 7, ~7, ~6, 7], | |
| 369 | [~8, 7, 7, ~6, 7, ~4, 8, 0, ~9, ~8, ~3, 7, ~3, 3, 8, ~7, ~2, ~7, 5, 5, ~5, 4, 6, 2, 4, 1, 4, ~9, ~3, 8, 8, ~9, ~4, ~2, 1, ~3, 1, 3, 9, ~5, ~8, ~2, 7, 8, 9, 2, 0, 1, ~9, 6], | |
| 370 | [~7, 1, ~9, 5, ~5, ~5, 7, 6, ~5, ~9, ~6, ~8, ~6, 9, 7, 9, 0, ~5, 7, 7, ~6, 4, 5, ~9, ~1, ~2, ~7, 3, ~5, ~2, ~5, 5, ~3, ~4, ~2, ~8, 2, ~8, 0, ~8, 0, ~8, 9, 8, ~5, ~5, 1, 3, 5, ~4], | |
| 371 | [~8, ~8, 0, ~5, ~8, ~6, 3, ~6, ~4, 6, 1, ~5, ~6, ~8, ~4, ~6, ~2, ~6, 6, ~4, 8, 8, 4, ~5, ~1, 0, 9, ~8, ~3, ~1, ~8, 7, ~3, 0, ~7, 1, ~7, ~1, ~7, 3, ~7, 3, ~4, ~8, 8, ~7, ~9, ~8, 3, 2], | |
| 372 | [ 3, 6, 8, ~9, 7, 1, ~9, 9, 3, 8, 6, 4, ~2, 1, ~8, 4, ~7, ~4, ~3, 3, ~5, ~6, ~7, ~2, 0, ~4, 5, 2, 5, 6, 3, ~8, 2, ~5, ~7, 6, 8, ~2, ~5, ~4, 9, 9, 2, ~2, ~2, 7, 4, 4, ~2, 3], | |
| 373 | [ 6, 6, ~5, ~2, ~8, ~2, ~9, 0, 2, 4, ~6, ~9, 9, 0, ~8, ~3, ~1, ~2, ~1, 6, 8, 2, ~9, 5, ~2, 1, 7, ~6, 5, 1, ~1, 4, ~4, ~7, ~6, ~3, ~8, 2, 2, 5, 5, ~6, 5, 3, 3, 7, 4, 7, ~3, ~9], | |
| 374 | [~9, 6, ~4, 1, 3, ~8, ~8, ~8, ~1, 5, 1, 1, ~1, 6, 5, 1, ~1, 5, ~8, 8, ~7, ~5, ~1, ~1, 6, ~8, ~3, ~1, ~2, ~6, ~5, ~5, ~6, 0, 2, 2, 7, ~1, ~5, ~7, ~1, ~3, 7, 6, 0, 2, 4, ~5, 0, ~4]] | |
| 375 | ||
| 376 | fun f (x, y) = List.nth (List.nth (table, x), y) | |
| 377 | fun show m = print (Matrix.toString (m, IntInf.toString)) | |
| 378 | val _ = | |
| 379 | let val dim = 32 | |
| 380 | val big = Matrix.map (Matrix.make (dim, dim, f), IntInf.fromInt) | |
| 381 | in show big; | |
| 382 | print "\n"; | |
| 383 | show (smithNormalForm big) | |
| 384 | end | |
| 385 |