Changeset 6ea941 in git for kernel/rmodulon.cc
 Timestamp:
 Jul 3, 2009, 3:14:10 PM (14 years ago)
 Branches:
 (u'spielwiese', '8e0ad00ce244dfd0756200662572aef8402f13d5')
 Children:
 e1634d68136a437eacace709df6dc52c3227ad7f
 Parents:
 a209ec5a023aa3cf7d9f9167a249678feca0047b
 File:

 1 edited
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kernel/rmodulon.cc
ra209ec5 r6ea941 2 2 * Computer Algebra System SINGULAR * 3 3 ****************************************/ 4 /* $Id: rmodulon.cc,v 1.3 4 20090522 13:18:12 SingularExp $ */4 /* $Id: rmodulon.cc,v 1.35 20090703 13:14:10 seelisch Exp $ */ 5 5 /* 6 6 * ABSTRACT: numbers modulo n … … 317 317 return (number) erg; 318 318 } 319 } 320 321 number nrnMod (number a, number b) 322 { 323 /* 324 We need to return the number r which is uniquely determined by the 325 following two properties: 326 (1) 0 <= r < b (with respect to '<' and '<=' performed in Z x Z) 327 (2) There exists some k in the integers Z such that a = k * b + r. 328 Consider g := gcd(n, b). Note that then b/g is a unit in Z/n. 329 Now, there are three cases: 330 (a) g = 1 331 Then b is a unit in Z/n, i.e. b (and also b) divides a. 332 Thus r = 0. 333 (b) g <> 1 and g divides a 334 Then a = (a/g) * (b/g)^(1) * b (up to sign), i.e. again r = 0. 335 (c) g <> 1 and g does not divide a 336 Then denote the division with remainder of a by g as this: 337 a = s * g + t. Then t = a  s * g = a  s * (b/g)^(1) * b 338 fulfills (1) and (2), i.e. r := t is the correct result. Hence 339 in this third case, r is the remainder of division of a by g in Z. 340 */ 341 int_number g = (int_number) omAllocBin(gmp_nrn_bin); 342 int_number b_abs = (int_number) omAllocBin(gmp_nrn_bin); 343 int_number r = (int_number) omAllocBin(gmp_nrn_bin); 344 mpz_init(g); 345 mpz_init_set(b_abs,(int_number)b); 346 mpz_init_set_si(r,(long)0); 347 if (mpz_isNeg(b_abs)) mpz_neg(b_abs, b_abs); // b_abs now represents b 348 mpz_gcd(g, (int_number) nrnModul, b_abs); // g is now as above 349 if (mpz_cmp_si(g, (long)1) != 0) mpz_mod(r, (int_number)a, g); // the case g <> 1 350 mpz_clear(g); 351 mpz_clear(b_abs); 352 omFreeBin(g, gmp_nrn_bin); 353 omFreeBin(b_abs, gmp_nrn_bin); 354 return (number)r; 319 355 } 320 356
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