[275ecc] | 1 | /**************************************** |
---|
| 2 | * Computer Algebra System SINGULAR * |
---|
| 3 | ****************************************/ |
---|
[341696] | 4 | /* $Id$ */ |
---|
[275ecc] | 5 | /* |
---|
| 6 | * ABSTRACT: numbers modulo n |
---|
| 7 | */ |
---|
| 8 | |
---|
| 9 | #include <string.h> |
---|
[599326] | 10 | #include <kernel/mod2.h> |
---|
[275ecc] | 11 | #include <mylimits.h> |
---|
[599326] | 12 | #include <kernel/structs.h> |
---|
| 13 | #include <kernel/febase.h> |
---|
| 14 | #include <omalloc.h> |
---|
| 15 | #include <kernel/numbers.h> |
---|
| 16 | #include <kernel/longrat.h> |
---|
| 17 | #include <kernel/mpr_complex.h> |
---|
| 18 | #include <kernel/ring.h> |
---|
| 19 | #include <kernel/rmodulon.h> |
---|
| 20 | #include <kernel/si_gmp.h> |
---|
[275ecc] | 21 | |
---|
[c90b43] | 22 | #ifdef HAVE_RINGS |
---|
| 23 | extern omBin gmp_nrz_bin; |
---|
[275ecc] | 24 | |
---|
[12ea9d] | 25 | int_number nrnMinusOne = NULL; |
---|
| 26 | unsigned long nrnExponent = 0; |
---|
[275ecc] | 27 | |
---|
[8e1c4e] | 28 | /* |
---|
| 29 | * create a number from int |
---|
| 30 | */ |
---|
[8391d8] | 31 | number nrnInit (int i, const ring r) |
---|
[8e1c4e] | 32 | { |
---|
[3c3880b] | 33 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[8e1c4e] | 34 | mpz_init_set_si(erg, i); |
---|
[196b4b] | 35 | mpz_mod(erg, erg, r->nrnModul); |
---|
[8e1c4e] | 36 | return (number) erg; |
---|
| 37 | } |
---|
| 38 | |
---|
| 39 | void nrnDelete(number *a, const ring r) |
---|
| 40 | { |
---|
[befecbc] | 41 | if (*a == NULL) return; |
---|
[8e1c4e] | 42 | mpz_clear((int_number) *a); |
---|
[3c3880b] | 43 | omFreeBin((ADDRESS) *a, gmp_nrz_bin); |
---|
[bac8611] | 44 | *a = NULL; |
---|
| 45 | } |
---|
| 46 | |
---|
| 47 | number nrnCopy(number a) |
---|
| 48 | { |
---|
[3c3880b] | 49 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[bac8611] | 50 | mpz_init_set(erg, (int_number) a); |
---|
| 51 | return (number) erg; |
---|
| 52 | } |
---|
| 53 | |
---|
| 54 | number cfrnCopy(number a, const ring r) |
---|
| 55 | { |
---|
| 56 | return nrnCopy(a); |
---|
| 57 | } |
---|
| 58 | |
---|
| 59 | int nrnSize(number a) |
---|
| 60 | { |
---|
| 61 | if (a == NULL) return 0; |
---|
[a604c3] | 62 | return sizeof(mpz_t); |
---|
[8e1c4e] | 63 | } |
---|
| 64 | |
---|
| 65 | /* |
---|
[25d15e] | 66 | * convert a number to int |
---|
[8e1c4e] | 67 | */ |
---|
[cf74cd6] | 68 | int nrnInt(number &n, const ring r) |
---|
[8e1c4e] | 69 | { |
---|
[5dd581] | 70 | return (int) mpz_get_si( (int_number) n); |
---|
[8e1c4e] | 71 | } |
---|
| 72 | |
---|
[275ecc] | 73 | /* |
---|
| 74 | * Multiply two numbers |
---|
| 75 | */ |
---|
[8e56ad] | 76 | number nrnMult (number a, number b) |
---|
[275ecc] | 77 | { |
---|
[3c3880b] | 78 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[8e56ad] | 79 | mpz_init(erg); |
---|
| 80 | mpz_mul(erg, (int_number) a, (int_number) b); |
---|
[196b4b] | 81 | mpz_mod(erg, erg, currRing->nrnModul); |
---|
[8e56ad] | 82 | return (number) erg; |
---|
[275ecc] | 83 | } |
---|
| 84 | |
---|
[8e1c4e] | 85 | void nrnPower (number a, int i, number * result) |
---|
| 86 | { |
---|
[3c3880b] | 87 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[8e1c4e] | 88 | mpz_init(erg); |
---|
[196b4b] | 89 | mpz_powm_ui(erg, (int_number) a, i, currRing->nrnModul); |
---|
[8e1c4e] | 90 | *result = (number) erg; |
---|
| 91 | } |
---|
| 92 | |
---|
| 93 | number nrnAdd (number a, number b) |
---|
| 94 | { |
---|
[3c3880b] | 95 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[8e1c4e] | 96 | mpz_init(erg); |
---|
| 97 | mpz_add(erg, (int_number) a, (int_number) b); |
---|
[196b4b] | 98 | mpz_mod(erg, erg, currRing->nrnModul); |
---|
[8e1c4e] | 99 | return (number) erg; |
---|
| 100 | } |
---|
| 101 | |
---|
| 102 | number nrnSub (number a, number b) |
---|
| 103 | { |
---|
[3c3880b] | 104 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[8e1c4e] | 105 | mpz_init(erg); |
---|
| 106 | mpz_sub(erg, (int_number) a, (int_number) b); |
---|
[196b4b] | 107 | mpz_mod(erg, erg, currRing->nrnModul); |
---|
[8e1c4e] | 108 | return (number) erg; |
---|
| 109 | } |
---|
| 110 | |
---|
| 111 | number nrnNeg (number c) |
---|
| 112 | { |
---|
[1eef69] | 113 | // nNeg inplace !!! |
---|
[196b4b] | 114 | mpz_sub((int_number) c, currRing->nrnModul, (int_number) c); |
---|
[a539ad] | 115 | return c; |
---|
[8e1c4e] | 116 | } |
---|
| 117 | |
---|
| 118 | number nrnInvers (number c) |
---|
| 119 | { |
---|
[3c3880b] | 120 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[8e1c4e] | 121 | mpz_init(erg); |
---|
[196b4b] | 122 | mpz_invert(erg, (int_number) c, currRing->nrnModul); |
---|
[8e1c4e] | 123 | return (number) erg; |
---|
| 124 | } |
---|
| 125 | |
---|
[275ecc] | 126 | /* |
---|
| 127 | * Give the smallest non unit k, such that a * x = k = b * y has a solution |
---|
[8e1c4e] | 128 | * TODO: lcm(gcd,gcd) besser als gcd(lcm) ? |
---|
[275ecc] | 129 | */ |
---|
| 130 | number nrnLcm (number a,number b,ring r) |
---|
| 131 | { |
---|
[196b4b] | 132 | number erg = nrnGcd(NULL, a, r); |
---|
| 133 | number tmp = nrnGcd(NULL, b, r); |
---|
[8e1c4e] | 134 | mpz_lcm((int_number) erg, (int_number) erg, (int_number) tmp); |
---|
| 135 | nrnDelete(&tmp, NULL); |
---|
[d681e8] | 136 | return (number) erg; |
---|
[275ecc] | 137 | } |
---|
| 138 | |
---|
| 139 | /* |
---|
| 140 | * Give the largest non unit k, such that a = x * k, b = y * k has |
---|
| 141 | * a solution. |
---|
| 142 | */ |
---|
| 143 | number nrnGcd (number a,number b,ring r) |
---|
| 144 | { |
---|
[8391d8] | 145 | if ((a == NULL) && (b == NULL)) return nrnInit(0,r); |
---|
[3c3880b] | 146 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[196b4b] | 147 | mpz_init_set(erg, r->nrnModul); |
---|
[31e857] | 148 | if (a != NULL) mpz_gcd(erg, erg, (int_number) a); |
---|
| 149 | if (b != NULL) mpz_gcd(erg, erg, (int_number) b); |
---|
[8e56ad] | 150 | return (number) erg; |
---|
| 151 | } |
---|
| 152 | |
---|
[8e1c4e] | 153 | /* Not needed any more, but may have room for improvement |
---|
[af378f7] | 154 | number nrnGcd3 (number a,number b, number c,ring r) |
---|
| 155 | { |
---|
[3c3880b] | 156 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[af378f7] | 157 | mpz_init(erg); |
---|
[196b4b] | 158 | if (a == NULL) a = (number) r->nrnModul; |
---|
| 159 | if (b == NULL) b = (number) r->nrnModul; |
---|
| 160 | if (c == NULL) c = (number) r->nrnModul; |
---|
[af378f7] | 161 | mpz_gcd(erg, (int_number) a, (int_number) b); |
---|
| 162 | mpz_gcd(erg, erg, (int_number) c); |
---|
[196b4b] | 163 | mpz_gcd(erg, erg, r->nrnModul); |
---|
[af378f7] | 164 | return (number) erg; |
---|
| 165 | } |
---|
[8e1c4e] | 166 | */ |
---|
[af378f7] | 167 | |
---|
[8e56ad] | 168 | /* |
---|
| 169 | * Give the largest non unit k, such that a = x * k, b = y * k has |
---|
| 170 | * a solution and r, s, s.t. k = s*a + t*b |
---|
| 171 | */ |
---|
| 172 | number nrnExtGcd (number a, number b, number *s, number *t) |
---|
| 173 | { |
---|
[3c3880b] | 174 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
| 175 | int_number bs = (int_number) omAllocBin(gmp_nrz_bin); |
---|
| 176 | int_number bt = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[8e56ad] | 177 | mpz_init(erg); |
---|
| 178 | mpz_init(bs); |
---|
| 179 | mpz_init(bt); |
---|
| 180 | mpz_gcdext(erg, bs, bt, (int_number) a, (int_number) b); |
---|
[196b4b] | 181 | mpz_mod(bs, bs, currRing->nrnModul); |
---|
| 182 | mpz_mod(bt, bt, currRing->nrnModul); |
---|
[8e56ad] | 183 | *s = (number) bs; |
---|
| 184 | *t = (number) bt; |
---|
| 185 | return (number) erg; |
---|
[275ecc] | 186 | } |
---|
| 187 | |
---|
[8e1c4e] | 188 | BOOLEAN nrnIsZero (number a) |
---|
[275ecc] | 189 | { |
---|
[01d4d3] | 190 | #ifdef LDEBUG |
---|
[191795] | 191 | if (a == NULL) return FALSE; |
---|
[01d4d3] | 192 | #endif |
---|
[8e1c4e] | 193 | return 0 == mpz_cmpabs_ui((int_number) a, 0); |
---|
[275ecc] | 194 | } |
---|
| 195 | |
---|
[8e1c4e] | 196 | BOOLEAN nrnIsOne (number a) |
---|
[275ecc] | 197 | { |
---|
[191795] | 198 | #ifdef LDEBUG |
---|
| 199 | if (a == NULL) return FALSE; |
---|
| 200 | #endif |
---|
[8e1c4e] | 201 | return 0 == mpz_cmp_si((int_number) a, 1); |
---|
[8e56ad] | 202 | } |
---|
| 203 | |
---|
[8e1c4e] | 204 | BOOLEAN nrnIsMOne (number a) |
---|
[8e56ad] | 205 | { |
---|
[191795] | 206 | #ifdef LDEBUG |
---|
| 207 | if (a == NULL) return FALSE; |
---|
| 208 | #endif |
---|
[8e1c4e] | 209 | return 0 == mpz_cmp((int_number) a, nrnMinusOne); |
---|
[275ecc] | 210 | } |
---|
| 211 | |
---|
[8e1c4e] | 212 | BOOLEAN nrnEqual (number a,number b) |
---|
[275ecc] | 213 | { |
---|
[8e1c4e] | 214 | return 0 == mpz_cmp((int_number) a, (int_number) b); |
---|
[275ecc] | 215 | } |
---|
| 216 | |
---|
[8e1c4e] | 217 | BOOLEAN nrnGreater (number a,number b) |
---|
[275ecc] | 218 | { |
---|
[8e1c4e] | 219 | return 0 < mpz_cmp((int_number) a, (int_number) b); |
---|
[275ecc] | 220 | } |
---|
| 221 | |
---|
[8e1c4e] | 222 | BOOLEAN nrnGreaterZero (number k) |
---|
[275ecc] | 223 | { |
---|
[675ce47] | 224 | return 0 < mpz_cmp_si((int_number) k, 0); |
---|
[8e1c4e] | 225 | } |
---|
| 226 | |
---|
| 227 | BOOLEAN nrnIsUnit (number a) |
---|
| 228 | { |
---|
[196b4b] | 229 | number tmp = nrnGcd(a, (number) currRing->nrnModul, currRing); |
---|
[8e1c4e] | 230 | bool res = nrnIsOne(tmp); |
---|
| 231 | nrnDelete(&tmp, NULL); |
---|
| 232 | return res; |
---|
[275ecc] | 233 | } |
---|
| 234 | |
---|
[af378f7] | 235 | number nrnGetUnit (number k) |
---|
[1e579c6] | 236 | { |
---|
[196b4b] | 237 | if (mpz_divisible_p(currRing->nrnModul, (int_number) k)) return nrnInit(1,currRing); |
---|
[97c4ad] | 238 | |
---|
[31e857] | 239 | int_number unit = (int_number) nrnGcd(k, 0, currRing); |
---|
| 240 | mpz_tdiv_q(unit, (int_number) k, unit); |
---|
| 241 | int_number gcd = (int_number) nrnGcd((number) unit, 0, currRing); |
---|
| 242 | if (!nrnIsOne((number) gcd)) |
---|
[af378f7] | 243 | { |
---|
[31e857] | 244 | int_number ctmp; |
---|
| 245 | // tmp := unit^2 |
---|
| 246 | int_number tmp = (int_number) nrnMult((number) unit,(number) unit); |
---|
| 247 | // gcd_new := gcd(tmp, 0) |
---|
| 248 | int_number gcd_new = (int_number) nrnGcd((number) tmp, 0, currRing); |
---|
| 249 | while (!nrnEqual((number) gcd_new,(number) gcd)) |
---|
[af378f7] | 250 | { |
---|
[31e857] | 251 | // gcd := gcd_new |
---|
| 252 | ctmp = gcd; |
---|
[af378f7] | 253 | gcd = gcd_new; |
---|
[31e857] | 254 | gcd_new = ctmp; |
---|
| 255 | // tmp := tmp * unit |
---|
| 256 | mpz_mul(tmp, tmp, unit); |
---|
[196b4b] | 257 | mpz_mod(tmp, tmp, currRing->nrnModul); |
---|
[31e857] | 258 | // gcd_new := gcd(tmp, 0) |
---|
[196b4b] | 259 | mpz_gcd(gcd_new, tmp, currRing->nrnModul); |
---|
[af378f7] | 260 | } |
---|
[31e857] | 261 | // unit := unit + nrnModul / gcd_new |
---|
[196b4b] | 262 | mpz_tdiv_q(tmp, currRing->nrnModul, gcd_new); |
---|
[31e857] | 263 | mpz_add(unit, unit, tmp); |
---|
[196b4b] | 264 | mpz_mod(unit, unit, currRing->nrnModul); |
---|
[31e857] | 265 | nrnDelete((number*) &gcd_new, NULL); |
---|
| 266 | nrnDelete((number*) &tmp, NULL); |
---|
[af378f7] | 267 | } |
---|
[31e857] | 268 | nrnDelete((number*) &gcd, NULL); |
---|
| 269 | return (number) unit; |
---|
[1e579c6] | 270 | } |
---|
| 271 | |
---|
[8e1c4e] | 272 | BOOLEAN nrnDivBy (number a,number b) |
---|
[275ecc] | 273 | { |
---|
[97c4ad] | 274 | if (a == NULL) |
---|
[196b4b] | 275 | return mpz_divisible_p(currRing->nrnModul, (int_number) b); |
---|
[97c4ad] | 276 | else |
---|
| 277 | return mpz_divisible_p((int_number) a, (int_number) b); |
---|
[821a22] | 278 | /* |
---|
[196b4b] | 279 | number bs = nrnGcd(a, b, currRing); |
---|
[31e857] | 280 | mpz_tdiv_q((int_number) bs, (int_number) b, (int_number) bs); |
---|
[8e1c4e] | 281 | bool res = nrnIsUnit(bs); |
---|
| 282 | nrnDelete(&bs, NULL); |
---|
[af378f7] | 283 | return res; |
---|
[821a22] | 284 | */ |
---|
[275ecc] | 285 | } |
---|
| 286 | |
---|
[d351d8] | 287 | int nrnDivComp(number a, number b) |
---|
[275ecc] | 288 | { |
---|
[8e56ad] | 289 | if (nrnEqual(a, b)) return 0; |
---|
[31e857] | 290 | if (mpz_divisible_p((int_number) a, (int_number) b)) return -1; |
---|
| 291 | if (mpz_divisible_p((int_number) b, (int_number) a)) return 1; |
---|
[8e56ad] | 292 | return 2; |
---|
[275ecc] | 293 | } |
---|
| 294 | |
---|
| 295 | number nrnDiv (number a,number b) |
---|
| 296 | { |
---|
[196b4b] | 297 | if (a == NULL) a = (number) currRing->nrnModul; |
---|
[3c3880b] | 298 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[8e56ad] | 299 | mpz_init(erg); |
---|
[af378f7] | 300 | if (mpz_divisible_p((int_number) a, (int_number) b)) |
---|
[275ecc] | 301 | { |
---|
[8e56ad] | 302 | mpz_divexact(erg, (int_number) a, (int_number) b); |
---|
| 303 | return (number) erg; |
---|
[275ecc] | 304 | } |
---|
| 305 | else |
---|
| 306 | { |
---|
[196b4b] | 307 | int_number gcd = (int_number) nrnGcd(a, b, currRing); |
---|
[8e56ad] | 308 | mpz_divexact(erg, (int_number) b, gcd); |
---|
| 309 | if (!nrnIsUnit((number) erg)) |
---|
| 310 | { |
---|
[bca575c] | 311 | WerrorS("Division not possible, even by cancelling zero divisors."); |
---|
| 312 | WerrorS("Result is integer division without remainder."); |
---|
[67dbdb] | 313 | mpz_tdiv_q(erg, (int_number) a, (int_number) b); |
---|
[31e857] | 314 | nrnDelete((number*) &gcd, NULL); |
---|
[12ea9d] | 315 | return (number) erg; |
---|
[8e56ad] | 316 | } |
---|
[31e857] | 317 | // a / gcd(a,b) * [b / gcd (a,b)]^(-1) |
---|
| 318 | int_number tmp = (int_number) nrnInvers((number) erg); |
---|
[8e56ad] | 319 | mpz_divexact(erg, (int_number) a, gcd); |
---|
[12ea9d] | 320 | mpz_mul(erg, erg, tmp); |
---|
[31e857] | 321 | nrnDelete((number*) &gcd, NULL); |
---|
| 322 | nrnDelete((number*) &tmp, NULL); |
---|
[196b4b] | 323 | mpz_mod(erg, erg, currRing->nrnModul); |
---|
[8e56ad] | 324 | return (number) erg; |
---|
[275ecc] | 325 | } |
---|
| 326 | } |
---|
| 327 | |
---|
[6ea941] | 328 | number nrnMod (number a, number b) |
---|
| 329 | { |
---|
| 330 | /* |
---|
| 331 | We need to return the number r which is uniquely determined by the |
---|
| 332 | following two properties: |
---|
| 333 | (1) 0 <= r < |b| (with respect to '<' and '<=' performed in Z x Z) |
---|
| 334 | (2) There exists some k in the integers Z such that a = k * b + r. |
---|
| 335 | Consider g := gcd(n, |b|). Note that then |b|/g is a unit in Z/n. |
---|
| 336 | Now, there are three cases: |
---|
| 337 | (a) g = 1 |
---|
| 338 | Then |b| is a unit in Z/n, i.e. |b| (and also b) divides a. |
---|
| 339 | Thus r = 0. |
---|
| 340 | (b) g <> 1 and g divides a |
---|
| 341 | Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again r = 0. |
---|
| 342 | (c) g <> 1 and g does not divide a |
---|
| 343 | Then denote the division with remainder of a by g as this: |
---|
| 344 | a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b| |
---|
| 345 | fulfills (1) and (2), i.e. r := t is the correct result. Hence |
---|
| 346 | in this third case, r is the remainder of division of a by g in Z. |
---|
[e1634d] | 347 | Remark: according to mpz_mod: a,b are always non-negative |
---|
[6ea941] | 348 | */ |
---|
[3c3880b] | 349 | int_number g = (int_number) omAllocBin(gmp_nrz_bin); |
---|
| 350 | int_number r = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[6ea941] | 351 | mpz_init(g); |
---|
| 352 | mpz_init_set_si(r,(long)0); |
---|
[196b4b] | 353 | mpz_gcd(g, (int_number) currRing->nrnModul, (int_number)b); // g is now as above |
---|
[6ea941] | 354 | if (mpz_cmp_si(g, (long)1) != 0) mpz_mod(r, (int_number)a, g); // the case g <> 1 |
---|
| 355 | mpz_clear(g); |
---|
[3c3880b] | 356 | omFreeBin(g, gmp_nrz_bin); |
---|
[6ea941] | 357 | return (number)r; |
---|
| 358 | } |
---|
| 359 | |
---|
[275ecc] | 360 | number nrnIntDiv (number a,number b) |
---|
| 361 | { |
---|
[3c3880b] | 362 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[8e56ad] | 363 | mpz_init(erg); |
---|
[196b4b] | 364 | if (a == NULL) a = (number) currRing->nrnModul; |
---|
[8e56ad] | 365 | mpz_tdiv_q(erg, (int_number) a, (int_number) b); |
---|
| 366 | return (number) erg; |
---|
[275ecc] | 367 | } |
---|
| 368 | |
---|
[d351d8] | 369 | /* |
---|
[d9301a] | 370 | * Helper function for computing the module |
---|
| 371 | */ |
---|
| 372 | |
---|
| 373 | int_number nrnMapCoef = NULL; |
---|
| 374 | |
---|
[d351d8] | 375 | number nrnMapModN(number from) |
---|
| 376 | { |
---|
[d9301a] | 377 | return nrnMult(from, (number) nrnMapCoef); |
---|
[d351d8] | 378 | } |
---|
[d9301a] | 379 | |
---|
| 380 | number nrnMap2toM(number from) |
---|
| 381 | { |
---|
[3c3880b] | 382 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[d9301a] | 383 | mpz_init(erg); |
---|
| 384 | mpz_mul_ui(erg, nrnMapCoef, (NATNUMBER) from); |
---|
[196b4b] | 385 | mpz_mod(erg, erg, currRing->nrnModul); |
---|
[d9301a] | 386 | return (number) erg; |
---|
| 387 | } |
---|
| 388 | |
---|
[894f5b1] | 389 | number nrnMapZp(number from) |
---|
| 390 | { |
---|
[3c3880b] | 391 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[894f5b1] | 392 | mpz_init(erg); |
---|
| 393 | mpz_mul_si(erg, nrnMapCoef, (NATNUMBER) from); |
---|
[196b4b] | 394 | mpz_mod(erg, erg, currRing->nrnModul); |
---|
[894f5b1] | 395 | return (number) erg; |
---|
| 396 | } |
---|
| 397 | |
---|
| 398 | number nrnMapGMP(number from) |
---|
[d9301a] | 399 | { |
---|
[3c3880b] | 400 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[d9301a] | 401 | mpz_init(erg); |
---|
[196b4b] | 402 | mpz_mod(erg, (int_number) from, currRing->nrnModul); |
---|
[d9301a] | 403 | return (number) erg; |
---|
| 404 | } |
---|
| 405 | |
---|
[894f5b1] | 406 | number nrnMapQ(number from) |
---|
| 407 | { |
---|
[3c3880b] | 408 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[894f5b1] | 409 | mpz_init(erg); |
---|
| 410 | nlGMP(from, (number) erg); |
---|
[196b4b] | 411 | mpz_mod(erg, erg, currRing->nrnModul); |
---|
[894f5b1] | 412 | return (number) erg; |
---|
| 413 | } |
---|
| 414 | |
---|
[208e0c] | 415 | nMapFunc nrnSetMap(const ring src, const ring dst) |
---|
[275ecc] | 416 | { |
---|
[d9301a] | 417 | /* dst = currRing */ |
---|
| 418 | if (rField_is_Ring_Z(src)) |
---|
[d351d8] | 419 | { |
---|
[894f5b1] | 420 | return nrnMapGMP; |
---|
| 421 | } |
---|
| 422 | if (rField_is_Q(src)) |
---|
| 423 | { |
---|
| 424 | return nrnMapQ; |
---|
[d9301a] | 425 | } |
---|
[894f5b1] | 426 | // Some type of Z/n ring / field |
---|
| 427 | if (rField_is_Ring_ModN(src) || rField_is_Ring_PtoM(src) || rField_is_Ring_2toM(src) || rField_is_Zp(src)) |
---|
[d9301a] | 428 | { |
---|
[894f5b1] | 429 | if ( (src->ringtype > 0) |
---|
[c81a40] | 430 | && (mpz_cmp(src->ringflaga, dst->ringflaga) == 0) |
---|
[894f5b1] | 431 | && (src->ringflagb == dst->ringflagb)) return nrnMapGMP; |
---|
[d351d8] | 432 | else |
---|
| 433 | { |
---|
[3c3880b] | 434 | int_number nrnMapModul = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[894f5b1] | 435 | // Computing the n of Z/n |
---|
| 436 | if (rField_is_Zp(src)) |
---|
| 437 | { |
---|
| 438 | mpz_init_set_si(nrnMapModul, src->ch); |
---|
| 439 | } |
---|
| 440 | else |
---|
| 441 | { |
---|
| 442 | mpz_init(nrnMapModul); |
---|
[c81a40] | 443 | mpz_set(nrnMapModul, src->ringflaga); |
---|
[894f5b1] | 444 | mpz_pow_ui(nrnMapModul, nrnMapModul, src->ringflagb); |
---|
| 445 | } |
---|
| 446 | // nrnMapCoef = 1 in dst if dst is a subring of src |
---|
| 447 | // nrnMapCoef = 0 in dst / src if src is a subring of dst |
---|
[d9301a] | 448 | if (nrnMapCoef == NULL) |
---|
[d351d8] | 449 | { |
---|
[3c3880b] | 450 | nrnMapCoef = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[d9301a] | 451 | mpz_init(nrnMapCoef); |
---|
| 452 | } |
---|
[196b4b] | 453 | if (mpz_divisible_p(nrnMapModul, currRing->nrnModul)) |
---|
[894f5b1] | 454 | { |
---|
| 455 | mpz_set_si(nrnMapCoef, 1); |
---|
| 456 | } |
---|
| 457 | else |
---|
[d9301a] | 458 | if (nrnDivBy(NULL, (number) nrnMapModul)) |
---|
| 459 | { |
---|
[196b4b] | 460 | mpz_divexact(nrnMapCoef, currRing->nrnModul, nrnMapModul); |
---|
| 461 | int_number tmp = currRing->nrnModul; |
---|
| 462 | currRing->nrnModul = nrnMapModul; |
---|
[0959dc] | 463 | if (!nrnIsUnit((number) nrnMapCoef)) |
---|
| 464 | { |
---|
[196b4b] | 465 | currRing->nrnModul = tmp; |
---|
[0959dc] | 466 | nrnDelete((number*) &nrnMapModul, currRing); |
---|
| 467 | return NULL; |
---|
| 468 | } |
---|
[d9301a] | 469 | int_number inv = (int_number) nrnInvers((number) nrnMapCoef); |
---|
[196b4b] | 470 | currRing->nrnModul = tmp; |
---|
[d9301a] | 471 | mpz_mul(nrnMapCoef, nrnMapCoef, inv); |
---|
[196b4b] | 472 | mpz_mod(nrnMapCoef, nrnMapCoef, currRing->nrnModul); |
---|
[d9301a] | 473 | nrnDelete((number*) &inv, currRing); |
---|
| 474 | } |
---|
| 475 | else |
---|
| 476 | { |
---|
| 477 | nrnDelete((number*) &nrnMapModul, currRing); |
---|
| 478 | return NULL; |
---|
[d351d8] | 479 | } |
---|
[d9301a] | 480 | nrnDelete((number*) &nrnMapModul, currRing); |
---|
| 481 | if (rField_is_Ring_2toM(src)) |
---|
| 482 | return nrnMap2toM; |
---|
[894f5b1] | 483 | else if (rField_is_Zp(src)) |
---|
| 484 | return nrnMapZp; |
---|
[d351d8] | 485 | else |
---|
[d9301a] | 486 | return nrnMapModN; |
---|
[d351d8] | 487 | } |
---|
| 488 | } |
---|
| 489 | return NULL; // default |
---|
[275ecc] | 490 | } |
---|
| 491 | |
---|
| 492 | /* |
---|
| 493 | * set the exponent (allocate and init tables) (TODO) |
---|
| 494 | */ |
---|
| 495 | |
---|
| 496 | void nrnSetExp(int m, ring r) |
---|
| 497 | { |
---|
[196b4b] | 498 | if ((r->nrnModul != NULL) && (mpz_cmp(r->nrnModul, r->ringflaga) == 0) && (nrnExponent == r->ringflagb)) return; |
---|
[20704f] | 499 | |
---|
[12ea9d] | 500 | nrnExponent = r->ringflagb; |
---|
[196b4b] | 501 | if (r->nrnModul == NULL) |
---|
[12ea9d] | 502 | { |
---|
[3c3880b] | 503 | r->nrnModul = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[196b4b] | 504 | mpz_init(r->nrnModul); |
---|
[3c3880b] | 505 | nrnMinusOne = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[07b6ac] | 506 | mpz_init(nrnMinusOne); |
---|
[12ea9d] | 507 | } |
---|
[196b4b] | 508 | mpz_set(r->nrnModul, r->ringflaga); |
---|
| 509 | mpz_pow_ui(r->nrnModul, r->nrnModul, nrnExponent); |
---|
| 510 | mpz_sub_ui(nrnMinusOne, r->nrnModul, 1); |
---|
[275ecc] | 511 | } |
---|
| 512 | |
---|
| 513 | void nrnInitExp(int m, ring r) |
---|
| 514 | { |
---|
[12ea9d] | 515 | nrnSetExp(m, r); |
---|
[093f30e] | 516 | |
---|
[196b4b] | 517 | if (mpz_cmp_ui(r->nrnModul,2) <= 0) |
---|
[275ecc] | 518 | { |
---|
[093f30e] | 519 | WarnS("nrnInitExp failed"); |
---|
[275ecc] | 520 | } |
---|
| 521 | } |
---|
| 522 | |
---|
| 523 | #ifdef LDEBUG |
---|
[85e68dd] | 524 | BOOLEAN nrnDBTest (number a, const char *f, const int l) |
---|
[275ecc] | 525 | { |
---|
[01d4d3] | 526 | if (a==NULL) return TRUE; |
---|
[196b4b] | 527 | if ( (mpz_cmp_si((int_number) a, 0) < 0) || (mpz_cmp((int_number) a, currRing->nrnModul) > 0) ) |
---|
[275ecc] | 528 | { |
---|
| 529 | return FALSE; |
---|
| 530 | } |
---|
| 531 | return TRUE; |
---|
| 532 | } |
---|
| 533 | #endif |
---|
| 534 | |
---|
[8e56ad] | 535 | /*2 |
---|
| 536 | * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc) |
---|
| 537 | */ |
---|
[a604c3] | 538 | static const char * nlCPEatLongC(char *s, mpz_ptr i) |
---|
[275ecc] | 539 | { |
---|
[85e68dd] | 540 | const char * start=s; |
---|
[af378f7] | 541 | if (!(*s >= '0' && *s <= '9')) |
---|
| 542 | { |
---|
| 543 | mpz_init_set_si(i, 1); |
---|
| 544 | return s; |
---|
| 545 | } |
---|
| 546 | mpz_init(i); |
---|
[8e56ad] | 547 | while (*s >= '0' && *s <= '9') s++; |
---|
| 548 | if (*s=='\0') |
---|
[275ecc] | 549 | { |
---|
[8e56ad] | 550 | mpz_set_str(i,start,10); |
---|
| 551 | } |
---|
| 552 | else |
---|
| 553 | { |
---|
| 554 | char c=*s; |
---|
| 555 | *s='\0'; |
---|
| 556 | mpz_set_str(i,start,10); |
---|
| 557 | *s=c; |
---|
[275ecc] | 558 | } |
---|
| 559 | return s; |
---|
| 560 | } |
---|
| 561 | |
---|
[85e68dd] | 562 | const char * nrnRead (const char *s, number *a) |
---|
[275ecc] | 563 | { |
---|
[3c3880b] | 564 | int_number z = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[275ecc] | 565 | { |
---|
[85e68dd] | 566 | s = nlCPEatLongC((char *)s, z); |
---|
[275ecc] | 567 | } |
---|
[196b4b] | 568 | mpz_mod(z, z, currRing->nrnModul); |
---|
[8e56ad] | 569 | *a = (number) z; |
---|
[275ecc] | 570 | return s; |
---|
| 571 | } |
---|
| 572 | #endif |
---|