[275ecc] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /* |
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| 5 | * ABSTRACT: numbers modulo n |
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| 6 | */ |
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| 7 | |
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[691dba] | 8 | #include "config.h" |
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[18cb65] | 9 | #include <misc/auxiliary.h> |
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[275ecc] | 10 | |
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[c90b43] | 11 | #ifdef HAVE_RINGS |
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[f1c465f] | 12 | |
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[18cb65] | 13 | #include <misc/mylimits.h> |
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[2d805a] | 14 | #include <coeffs/coeffs.h> |
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[31213a4] | 15 | #include <reporter/reporter.h> |
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| 16 | #include <omalloc/omalloc.h> |
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[2d805a] | 17 | #include <coeffs/numbers.h> |
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| 18 | #include <coeffs/longrat.h> |
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| 19 | #include <coeffs/mpr_complex.h> |
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| 20 | #include <coeffs/rmodulon.h> |
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[e3b233] | 21 | #include "si_gmp.h" |
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[8d0331d] | 22 | |
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[f1c465f] | 23 | #include <string.h> |
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| 24 | |
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[73a9ffb] | 25 | /// Our Type! |
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| 26 | static const n_coeffType ID = n_Zn; |
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[0486a3] | 27 | static const n_coeffType ID2 = n_Znm; |
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[73a9ffb] | 28 | |
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[8d0331d] | 29 | extern omBin gmp_nrz_bin; |
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[275ecc] | 30 | |
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[03f7b5] | 31 | void nrnCoeffWrite (const coeffs r, BOOLEAN /*details*/) |
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[7a8011] | 32 | { |
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| 33 | long l = (long)mpz_sizeinbase(r->modBase, 10) + 2; |
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| 34 | char* s = (char*) omAlloc(l); |
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[0486a3] | 35 | s= mpz_get_str (s, 10, r->modBase); |
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| 36 | if (nCoeff_is_Ring_ModN(r)) Print("// coeff. ring is : Z/%s\n", s); |
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| 37 | else if (nCoeff_is_Ring_PtoM(r)) Print("// coeff. ring is : Z/%s^%lu\n", s, r->modExponent); |
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[7a8011] | 38 | omFreeSize((ADDRESS)s, l); |
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| 39 | } |
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| 40 | |
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[b19ab84] | 41 | static BOOLEAN nrnCoeffsEqual(const coeffs r, n_coeffType n, void * parameter) |
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| 42 | { |
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| 43 | /* test, if r is an instance of nInitCoeffs(n,parameter) */ |
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[a2da9e] | 44 | return (n==n_Zn) && (mpz_cmp_ui(r->modNumber,(long)parameter)==0); |
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[b19ab84] | 45 | } |
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| 46 | |
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| 47 | |
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[14b11bb] | 48 | /* for initializing function pointers */ |
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[1cce47] | 49 | BOOLEAN nrnInitChar (coeffs r, void* p) |
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[14b11bb] | 50 | { |
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[0486a3] | 51 | assume( (getCoeffType(r) == ID) || (getCoeffType (r) == ID2) ); |
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| 52 | ZnmInfo * info= (ZnmInfo *) p; |
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[dc07cbe] | 53 | r->modBase= info->base; |
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[9bb5457] | 54 | |
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[0486a3] | 55 | nrnInitExp (info->exp, r); |
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| 56 | |
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[73a9ffb] | 57 | /* next computation may yield wrong characteristic as r->modNumber |
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| 58 | is a GMP number */ |
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| 59 | r->ch = mpz_get_ui(r->modNumber); |
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[e90dfd6] | 60 | |
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| 61 | r->cfInit = nrnInit; |
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| 62 | r->cfDelete = nrnDelete; |
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| 63 | r->cfCopy = nrnCopy; |
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| 64 | r->cfSize = nrnSize; |
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| 65 | r->cfInt = nrnInt; |
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| 66 | r->cfAdd = nrnAdd; |
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| 67 | r->cfSub = nrnSub; |
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| 68 | r->cfMult = nrnMult; |
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| 69 | r->cfDiv = nrnDiv; |
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| 70 | r->cfIntDiv = nrnIntDiv; |
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| 71 | r->cfIntMod = nrnMod; |
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| 72 | r->cfExactDiv = nrnDiv; |
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| 73 | r->cfNeg = nrnNeg; |
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| 74 | r->cfInvers = nrnInvers; |
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| 75 | r->cfDivBy = nrnDivBy; |
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| 76 | r->cfDivComp = nrnDivComp; |
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| 77 | r->cfGreater = nrnGreater; |
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| 78 | r->cfEqual = nrnEqual; |
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| 79 | r->cfIsZero = nrnIsZero; |
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| 80 | r->cfIsOne = nrnIsOne; |
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| 81 | r->cfIsMOne = nrnIsMOne; |
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| 82 | r->cfGreaterZero = nrnGreaterZero; |
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[ce1f78] | 83 | r->cfWriteLong = nrnWrite; |
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[e90dfd6] | 84 | r->cfRead = nrnRead; |
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| 85 | r->cfPower = nrnPower; |
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| 86 | r->cfSetMap = nrnSetMap; |
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| 87 | r->cfNormalize = ndNormalize; |
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| 88 | r->cfLcm = nrnLcm; |
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| 89 | r->cfGcd = nrnGcd; |
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| 90 | r->cfIsUnit = nrnIsUnit; |
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| 91 | r->cfGetUnit = nrnGetUnit; |
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| 92 | r->cfExtGcd = nrnExtGcd; |
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| 93 | r->cfName = ndName; |
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[7a8011] | 94 | r->cfCoeffWrite = nrnCoeffWrite; |
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[b19ab84] | 95 | r->nCoeffIsEqual = nrnCoeffsEqual; |
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[8c6bd4d] | 96 | r->cfInit_bigint = nrnMapQ; |
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| 97 | |
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[14b11bb] | 98 | #ifdef LDEBUG |
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[e90dfd6] | 99 | r->cfDBTest = nrnDBTest; |
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[14b11bb] | 100 | #endif |
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[5d594a9] | 101 | return FALSE; |
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[14b11bb] | 102 | } |
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| 103 | |
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[8e1c4e] | 104 | /* |
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| 105 | * create a number from int |
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| 106 | */ |
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[2f3764] | 107 | number nrnInit(long i, const coeffs r) |
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[8e1c4e] | 108 | { |
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[3c3880b] | 109 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 110 | mpz_init_set_si(erg, i); |
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[e90dfd6] | 111 | mpz_mod(erg, erg, r->modNumber); |
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[8e1c4e] | 112 | return (number) erg; |
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| 113 | } |
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| 114 | |
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[9bb5457] | 115 | void nrnDelete(number *a, const coeffs) |
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[8e1c4e] | 116 | { |
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[befecbc] | 117 | if (*a == NULL) return; |
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[8e1c4e] | 118 | mpz_clear((int_number) *a); |
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[7d90aa] | 119 | omFreeBin((void *) *a, gmp_nrz_bin); |
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[bac8611] | 120 | *a = NULL; |
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| 121 | } |
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| 122 | |
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[9bb5457] | 123 | number nrnCopy(number a, const coeffs) |
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[bac8611] | 124 | { |
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[3c3880b] | 125 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[bac8611] | 126 | mpz_init_set(erg, (int_number) a); |
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| 127 | return (number) erg; |
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| 128 | } |
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| 129 | |
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[9bb5457] | 130 | int nrnSize(number a, const coeffs) |
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[bac8611] | 131 | { |
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| 132 | if (a == NULL) return 0; |
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[a604c3] | 133 | return sizeof(mpz_t); |
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[8e1c4e] | 134 | } |
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| 135 | |
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| 136 | /* |
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[25d15e] | 137 | * convert a number to int |
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[8e1c4e] | 138 | */ |
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[9bb5457] | 139 | int nrnInt(number &n, const coeffs) |
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[8e1c4e] | 140 | { |
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[e90dfd6] | 141 | return (int)mpz_get_si((int_number) n); |
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[8e1c4e] | 142 | } |
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| 143 | |
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[275ecc] | 144 | /* |
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| 145 | * Multiply two numbers |
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| 146 | */ |
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[e90dfd6] | 147 | number nrnMult(number a, number b, const coeffs r) |
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[275ecc] | 148 | { |
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[e90dfd6] | 149 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e56ad] | 150 | mpz_init(erg); |
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[e90dfd6] | 151 | mpz_mul(erg, (int_number)a, (int_number) b); |
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| 152 | mpz_mod(erg, erg, r->modNumber); |
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[8e56ad] | 153 | return (number) erg; |
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[275ecc] | 154 | } |
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| 155 | |
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[e90dfd6] | 156 | void nrnPower(number a, int i, number * result, const coeffs r) |
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[8e1c4e] | 157 | { |
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[e90dfd6] | 158 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 159 | mpz_init(erg); |
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[e90dfd6] | 160 | mpz_powm_ui(erg, (int_number)a, i, r->modNumber); |
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[8e1c4e] | 161 | *result = (number) erg; |
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| 162 | } |
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| 163 | |
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[e90dfd6] | 164 | number nrnAdd(number a, number b, const coeffs r) |
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[8e1c4e] | 165 | { |
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[e90dfd6] | 166 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 167 | mpz_init(erg); |
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[e90dfd6] | 168 | mpz_add(erg, (int_number)a, (int_number) b); |
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| 169 | mpz_mod(erg, erg, r->modNumber); |
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[8e1c4e] | 170 | return (number) erg; |
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| 171 | } |
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| 172 | |
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[e90dfd6] | 173 | number nrnSub(number a, number b, const coeffs r) |
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[8e1c4e] | 174 | { |
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[e90dfd6] | 175 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 176 | mpz_init(erg); |
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[e90dfd6] | 177 | mpz_sub(erg, (int_number)a, (int_number) b); |
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| 178 | mpz_mod(erg, erg, r->modNumber); |
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[8e1c4e] | 179 | return (number) erg; |
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| 180 | } |
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| 181 | |
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[e90dfd6] | 182 | number nrnNeg(number c, const coeffs r) |
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[8e1c4e] | 183 | { |
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[0b7bf7] | 184 | if( !nrnIsZero(c, r) ) |
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| 185 | // Attention: This method operates in-place. |
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[9bb5457] | 186 | mpz_sub((int_number)c, r->modNumber, (int_number)c); |
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[a539ad] | 187 | return c; |
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[8e1c4e] | 188 | } |
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| 189 | |
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[e90dfd6] | 190 | number nrnInvers(number c, const coeffs r) |
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[8e1c4e] | 191 | { |
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[e90dfd6] | 192 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 193 | mpz_init(erg); |
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[e90dfd6] | 194 | mpz_invert(erg, (int_number)c, r->modNumber); |
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[8e1c4e] | 195 | return (number) erg; |
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| 196 | } |
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| 197 | |
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[275ecc] | 198 | /* |
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[e90dfd6] | 199 | * Give the smallest k, such that a * x = k = b * y has a solution |
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| 200 | * TODO: lcm(gcd,gcd) better than gcd(lcm) ? |
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[275ecc] | 201 | */ |
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[e90dfd6] | 202 | number nrnLcm(number a, number b, const coeffs r) |
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[275ecc] | 203 | { |
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[196b4b] | 204 | number erg = nrnGcd(NULL, a, r); |
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| 205 | number tmp = nrnGcd(NULL, b, r); |
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[e90dfd6] | 206 | mpz_lcm((int_number)erg, (int_number)erg, (int_number)tmp); |
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[8e1c4e] | 207 | nrnDelete(&tmp, NULL); |
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[e90dfd6] | 208 | return (number)erg; |
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[275ecc] | 209 | } |
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| 210 | |
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| 211 | /* |
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[e90dfd6] | 212 | * Give the largest k, such that a = x * k, b = y * k has |
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[275ecc] | 213 | * a solution. |
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| 214 | */ |
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[e90dfd6] | 215 | number nrnGcd(number a, number b, const coeffs r) |
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[275ecc] | 216 | { |
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[8391d8] | 217 | if ((a == NULL) && (b == NULL)) return nrnInit(0,r); |
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[e90dfd6] | 218 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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| 219 | mpz_init_set(erg, r->modNumber); |
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| 220 | if (a != NULL) mpz_gcd(erg, erg, (int_number)a); |
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| 221 | if (b != NULL) mpz_gcd(erg, erg, (int_number)b); |
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| 222 | return (number)erg; |
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[8e56ad] | 223 | } |
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| 224 | |
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[8e1c4e] | 225 | /* Not needed any more, but may have room for improvement |
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[e90dfd6] | 226 | number nrnGcd3(number a,number b, number c,ring r) |
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[af378f7] | 227 | { |
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[3c3880b] | 228 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[af378f7] | 229 | mpz_init(erg); |
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[e90dfd6] | 230 | if (a == NULL) a = (number)r->modNumber; |
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| 231 | if (b == NULL) b = (number)r->modNumber; |
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| 232 | if (c == NULL) c = (number)r->modNumber; |
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| 233 | mpz_gcd(erg, (int_number)a, (int_number)b); |
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| 234 | mpz_gcd(erg, erg, (int_number)c); |
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| 235 | mpz_gcd(erg, erg, r->modNumber); |
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| 236 | return (number)erg; |
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[af378f7] | 237 | } |
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[8e1c4e] | 238 | */ |
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[af378f7] | 239 | |
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[8e56ad] | 240 | /* |
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[e90dfd6] | 241 | * Give the largest k, such that a = x * k, b = y * k has |
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[8e56ad] | 242 | * a solution and r, s, s.t. k = s*a + t*b |
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| 243 | */ |
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[e90dfd6] | 244 | number nrnExtGcd(number a, number b, number *s, number *t, const coeffs r) |
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[8e56ad] | 245 | { |
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[e90dfd6] | 246 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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| 247 | int_number bs = (int_number)omAllocBin(gmp_nrz_bin); |
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| 248 | int_number bt = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e56ad] | 249 | mpz_init(erg); |
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| 250 | mpz_init(bs); |
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| 251 | mpz_init(bt); |
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[e90dfd6] | 252 | mpz_gcdext(erg, bs, bt, (int_number)a, (int_number)b); |
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| 253 | mpz_mod(bs, bs, r->modNumber); |
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| 254 | mpz_mod(bt, bt, r->modNumber); |
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| 255 | *s = (number)bs; |
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| 256 | *t = (number)bt; |
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| 257 | return (number)erg; |
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[275ecc] | 258 | } |
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| 259 | |
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[9bb5457] | 260 | BOOLEAN nrnIsZero(number a, const coeffs) |
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[275ecc] | 261 | { |
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[01d4d3] | 262 | #ifdef LDEBUG |
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[191795] | 263 | if (a == NULL) return FALSE; |
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[01d4d3] | 264 | #endif |
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[e90dfd6] | 265 | return 0 == mpz_cmpabs_ui((int_number)a, 0); |
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[275ecc] | 266 | } |
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| 267 | |
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[9bb5457] | 268 | BOOLEAN nrnIsOne(number a, const coeffs) |
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[275ecc] | 269 | { |
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[191795] | 270 | #ifdef LDEBUG |
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| 271 | if (a == NULL) return FALSE; |
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| 272 | #endif |
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[e90dfd6] | 273 | return 0 == mpz_cmp_si((int_number)a, 1); |
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[8e56ad] | 274 | } |
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| 275 | |
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[e90dfd6] | 276 | BOOLEAN nrnIsMOne(number a, const coeffs r) |
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[8e56ad] | 277 | { |
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[191795] | 278 | #ifdef LDEBUG |
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| 279 | if (a == NULL) return FALSE; |
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| 280 | #endif |
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[e90dfd6] | 281 | mpz_t t; mpz_init_set(t, (int_number)a); |
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| 282 | mpz_add_ui(t, t, 1); |
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| 283 | bool erg = (0 == mpz_cmp(t, r->modNumber)); |
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| 284 | mpz_clear(t); |
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| 285 | return erg; |
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[275ecc] | 286 | } |
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| 287 | |
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[9bb5457] | 288 | BOOLEAN nrnEqual(number a, number b, const coeffs) |
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[275ecc] | 289 | { |
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[e90dfd6] | 290 | return 0 == mpz_cmp((int_number)a, (int_number)b); |
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[275ecc] | 291 | } |
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| 292 | |
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[9bb5457] | 293 | BOOLEAN nrnGreater(number a, number b, const coeffs) |
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[275ecc] | 294 | { |
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[e90dfd6] | 295 | return 0 < mpz_cmp((int_number)a, (int_number)b); |
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[275ecc] | 296 | } |
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| 297 | |
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[9bb5457] | 298 | BOOLEAN nrnGreaterZero(number k, const coeffs) |
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[275ecc] | 299 | { |
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[e90dfd6] | 300 | return 0 < mpz_cmp_si((int_number)k, 0); |
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[8e1c4e] | 301 | } |
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| 302 | |
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[e90dfd6] | 303 | BOOLEAN nrnIsUnit(number a, const coeffs r) |
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[8e1c4e] | 304 | { |
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[e90dfd6] | 305 | number tmp = nrnGcd(a, (number)r->modNumber, r); |
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| 306 | bool res = nrnIsOne(tmp, r); |
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[8e1c4e] | 307 | nrnDelete(&tmp, NULL); |
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| 308 | return res; |
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[275ecc] | 309 | } |
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| 310 | |
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[e90dfd6] | 311 | number nrnGetUnit(number k, const coeffs r) |
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[1e579c6] | 312 | { |
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[e90dfd6] | 313 | if (mpz_divisible_p(r->modNumber, (int_number)k)) return nrnInit(1,r); |
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[97c4ad] | 314 | |
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[e90dfd6] | 315 | int_number unit = (int_number)nrnGcd(k, 0, r); |
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| 316 | mpz_tdiv_q(unit, (int_number)k, unit); |
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| 317 | int_number gcd = (int_number)nrnGcd((number)unit, 0, r); |
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| 318 | if (!nrnIsOne((number)gcd,r)) |
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[af378f7] | 319 | { |
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[31e857] | 320 | int_number ctmp; |
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| 321 | // tmp := unit^2 |
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[4d1ae5] | 322 | int_number tmp = (int_number) nrnMult((number) unit,(number) unit,r); |
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[31e857] | 323 | // gcd_new := gcd(tmp, 0) |
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[14b11bb] | 324 | int_number gcd_new = (int_number) nrnGcd((number) tmp, 0, r); |
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[4d1ae5] | 325 | while (!nrnEqual((number) gcd_new,(number) gcd,r)) |
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[af378f7] | 326 | { |
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[31e857] | 327 | // gcd := gcd_new |
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| 328 | ctmp = gcd; |
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[af378f7] | 329 | gcd = gcd_new; |
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[31e857] | 330 | gcd_new = ctmp; |
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| 331 | // tmp := tmp * unit |
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| 332 | mpz_mul(tmp, tmp, unit); |
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[e90dfd6] | 333 | mpz_mod(tmp, tmp, r->modNumber); |
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[31e857] | 334 | // gcd_new := gcd(tmp, 0) |
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[e90dfd6] | 335 | mpz_gcd(gcd_new, tmp, r->modNumber); |
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[af378f7] | 336 | } |
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[e90dfd6] | 337 | // unit := unit + modNumber / gcd_new |
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| 338 | mpz_tdiv_q(tmp, r->modNumber, gcd_new); |
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[31e857] | 339 | mpz_add(unit, unit, tmp); |
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[e90dfd6] | 340 | mpz_mod(unit, unit, r->modNumber); |
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[31e857] | 341 | nrnDelete((number*) &gcd_new, NULL); |
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| 342 | nrnDelete((number*) &tmp, NULL); |
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[af378f7] | 343 | } |
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[31e857] | 344 | nrnDelete((number*) &gcd, NULL); |
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[e90dfd6] | 345 | return (number)unit; |
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[1e579c6] | 346 | } |
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| 347 | |
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[e90dfd6] | 348 | BOOLEAN nrnDivBy(number a, number b, const coeffs r) |
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[275ecc] | 349 | { |
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[97c4ad] | 350 | if (a == NULL) |
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[e90dfd6] | 351 | return mpz_divisible_p(r->modNumber, (int_number)b); |
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[97c4ad] | 352 | else |
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[a8b44d] | 353 | { /* b divides a iff b/gcd(a, b) is a unit in the given ring: */ |
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[14b11bb] | 354 | number n = nrnGcd(a, b, r); |
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[a8b44d] | 355 | mpz_tdiv_q((int_number)n, (int_number)b, (int_number)n); |
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[14b11bb] | 356 | bool result = nrnIsUnit(n, r); |
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[a8b44d] | 357 | nrnDelete(&n, NULL); |
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| 358 | return result; |
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| 359 | } |
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[275ecc] | 360 | } |
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| 361 | |
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[14b11bb] | 362 | int nrnDivComp(number a, number b, const coeffs r) |
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[275ecc] | 363 | { |
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[4d1ae5] | 364 | if (nrnEqual(a, b,r)) return 2; |
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[31e857] | 365 | if (mpz_divisible_p((int_number) a, (int_number) b)) return -1; |
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| 366 | if (mpz_divisible_p((int_number) b, (int_number) a)) return 1; |
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[e90dfd6] | 367 | return 0; |
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[275ecc] | 368 | } |
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| 369 | |
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[e90dfd6] | 370 | number nrnDiv(number a, number b, const coeffs r) |
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[275ecc] | 371 | { |
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[e90dfd6] | 372 | if (a == NULL) a = (number)r->modNumber; |
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| 373 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e56ad] | 374 | mpz_init(erg); |
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[e90dfd6] | 375 | if (mpz_divisible_p((int_number)a, (int_number)b)) |
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[275ecc] | 376 | { |
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[e90dfd6] | 377 | mpz_divexact(erg, (int_number)a, (int_number)b); |
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| 378 | return (number)erg; |
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[275ecc] | 379 | } |
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| 380 | else |
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| 381 | { |
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[e90dfd6] | 382 | int_number gcd = (int_number)nrnGcd(a, b, r); |
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| 383 | mpz_divexact(erg, (int_number)b, gcd); |
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| 384 | if (!nrnIsUnit((number)erg, r)) |
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[8e56ad] | 385 | { |
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[bca575c] | 386 | WerrorS("Division not possible, even by cancelling zero divisors."); |
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| 387 | WerrorS("Result is integer division without remainder."); |
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[67dbdb] | 388 | mpz_tdiv_q(erg, (int_number) a, (int_number) b); |
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[31e857] | 389 | nrnDelete((number*) &gcd, NULL); |
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[e90dfd6] | 390 | return (number)erg; |
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[8e56ad] | 391 | } |
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[31e857] | 392 | // a / gcd(a,b) * [b / gcd (a,b)]^(-1) |
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[e90dfd6] | 393 | int_number tmp = (int_number)nrnInvers((number) erg,r); |
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| 394 | mpz_divexact(erg, (int_number)a, gcd); |
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[12ea9d] | 395 | mpz_mul(erg, erg, tmp); |
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[31e857] | 396 | nrnDelete((number*) &gcd, NULL); |
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| 397 | nrnDelete((number*) &tmp, NULL); |
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[e90dfd6] | 398 | mpz_mod(erg, erg, r->modNumber); |
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| 399 | return (number)erg; |
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[275ecc] | 400 | } |
---|
| 401 | } |
---|
| 402 | |
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[e90dfd6] | 403 | number nrnMod(number a, number b, const coeffs r) |
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[6ea941] | 404 | { |
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| 405 | /* |
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[e90dfd6] | 406 | We need to return the number rr which is uniquely determined by the |
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[6ea941] | 407 | following two properties: |
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[e90dfd6] | 408 | (1) 0 <= rr < |b| (with respect to '<' and '<=' performed in Z x Z) |
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| 409 | (2) There exists some k in the integers Z such that a = k * b + rr. |
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[6ea941] | 410 | Consider g := gcd(n, |b|). Note that then |b|/g is a unit in Z/n. |
---|
| 411 | Now, there are three cases: |
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| 412 | (a) g = 1 |
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| 413 | Then |b| is a unit in Z/n, i.e. |b| (and also b) divides a. |
---|
[e90dfd6] | 414 | Thus rr = 0. |
---|
[6ea941] | 415 | (b) g <> 1 and g divides a |
---|
[e90dfd6] | 416 | Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again rr = 0. |
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[6ea941] | 417 | (c) g <> 1 and g does not divide a |
---|
| 418 | Then denote the division with remainder of a by g as this: |
---|
| 419 | a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b| |
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[e90dfd6] | 420 | fulfills (1) and (2), i.e. rr := t is the correct result. Hence |
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| 421 | in this third case, rr is the remainder of division of a by g in Z. |
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[e1634d] | 422 | Remark: according to mpz_mod: a,b are always non-negative |
---|
[6ea941] | 423 | */ |
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[e90dfd6] | 424 | int_number g = (int_number)omAllocBin(gmp_nrz_bin); |
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| 425 | int_number rr = (int_number)omAllocBin(gmp_nrz_bin); |
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[6ea941] | 426 | mpz_init(g); |
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[e90dfd6] | 427 | mpz_init_set_si(rr, 0); |
---|
| 428 | mpz_gcd(g, (int_number)r->modNumber, (int_number)b); // g is now as above |
---|
| 429 | if (mpz_cmp_si(g, (long)1) != 0) mpz_mod(rr, (int_number)a, g); // the case g <> 1 |
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[6ea941] | 430 | mpz_clear(g); |
---|
[3c3880b] | 431 | omFreeBin(g, gmp_nrz_bin); |
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[e90dfd6] | 432 | return (number)rr; |
---|
[6ea941] | 433 | } |
---|
| 434 | |
---|
[e90dfd6] | 435 | number nrnIntDiv(number a, number b, const coeffs r) |
---|
[275ecc] | 436 | { |
---|
[e90dfd6] | 437 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e56ad] | 438 | mpz_init(erg); |
---|
[e90dfd6] | 439 | if (a == NULL) a = (number)r->modNumber; |
---|
| 440 | mpz_tdiv_q(erg, (int_number)a, (int_number)b); |
---|
| 441 | return (number)erg; |
---|
[275ecc] | 442 | } |
---|
| 443 | |
---|
[d351d8] | 444 | /* |
---|
[d9301a] | 445 | * Helper function for computing the module |
---|
| 446 | */ |
---|
| 447 | |
---|
| 448 | int_number nrnMapCoef = NULL; |
---|
| 449 | |
---|
[9bb5457] | 450 | number nrnMapModN(number from, const coeffs /*src*/, const coeffs dst) |
---|
[d351d8] | 451 | { |
---|
[4d1ae5] | 452 | return nrnMult(from, (number) nrnMapCoef, dst); |
---|
[d351d8] | 453 | } |
---|
[d9301a] | 454 | |
---|
[9bb5457] | 455 | number nrnMap2toM(number from, const coeffs /*src*/, const coeffs dst) |
---|
[d9301a] | 456 | { |
---|
[e90dfd6] | 457 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
---|
[d9301a] | 458 | mpz_init(erg); |
---|
[e90dfd6] | 459 | mpz_mul_ui(erg, nrnMapCoef, (NATNUMBER)from); |
---|
| 460 | mpz_mod(erg, erg, dst->modNumber); |
---|
| 461 | return (number)erg; |
---|
[d9301a] | 462 | } |
---|
| 463 | |
---|
[9bb5457] | 464 | number nrnMapZp(number from, const coeffs /*src*/, const coeffs dst) |
---|
[894f5b1] | 465 | { |
---|
[e90dfd6] | 466 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
---|
[894f5b1] | 467 | mpz_init(erg); |
---|
[4d1ae5] | 468 | // TODO: use npInt(...) |
---|
[e90dfd6] | 469 | mpz_mul_si(erg, nrnMapCoef, (NATNUMBER)from); |
---|
| 470 | mpz_mod(erg, erg, dst->modNumber); |
---|
| 471 | return (number)erg; |
---|
[894f5b1] | 472 | } |
---|
| 473 | |
---|
[9bb5457] | 474 | number nrnMapGMP(number from, const coeffs /*src*/, const coeffs dst) |
---|
[d9301a] | 475 | { |
---|
[e90dfd6] | 476 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
---|
[d9301a] | 477 | mpz_init(erg); |
---|
[e90dfd6] | 478 | mpz_mod(erg, (int_number)from, dst->modNumber); |
---|
| 479 | return (number)erg; |
---|
[d9301a] | 480 | } |
---|
| 481 | |
---|
[8c6bd4d] | 482 | number nrnMapQ(number from, const coeffs src, const coeffs dst) |
---|
[894f5b1] | 483 | { |
---|
[e90dfd6] | 484 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
---|
[894f5b1] | 485 | mpz_init(erg); |
---|
[e90dfd6] | 486 | nlGMP(from, (number)erg, src); |
---|
[8c6bd4d] | 487 | mpz_mod(erg, erg, dst->modNumber); |
---|
[e90dfd6] | 488 | return (number)erg; |
---|
[894f5b1] | 489 | } |
---|
| 490 | |
---|
[4d1ae5] | 491 | nMapFunc nrnSetMap(const coeffs src, const coeffs dst) |
---|
[275ecc] | 492 | { |
---|
[14b11bb] | 493 | /* dst = currRing->cf */ |
---|
[1cce47] | 494 | if (nCoeff_is_Ring_Z(src)) |
---|
[d351d8] | 495 | { |
---|
[894f5b1] | 496 | return nrnMapGMP; |
---|
| 497 | } |
---|
[1cce47] | 498 | if (nCoeff_is_Q(src)) |
---|
[894f5b1] | 499 | { |
---|
| 500 | return nrnMapQ; |
---|
[d9301a] | 501 | } |
---|
[894f5b1] | 502 | // Some type of Z/n ring / field |
---|
[f0797c] | 503 | if (nCoeff_is_Ring_ModN(src) || nCoeff_is_Ring_PtoM(src) || |
---|
| 504 | nCoeff_is_Ring_2toM(src) || nCoeff_is_Zp(src)) |
---|
[d9301a] | 505 | { |
---|
[66ce6d] | 506 | if ( (!nCoeff_is_Zp(src)) |
---|
[e90dfd6] | 507 | && (mpz_cmp(src->modBase, dst->modBase) == 0) |
---|
| 508 | && (src->modExponent == dst->modExponent)) return nrnMapGMP; |
---|
[d351d8] | 509 | else |
---|
| 510 | { |
---|
[3c3880b] | 511 | int_number nrnMapModul = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[894f5b1] | 512 | // Computing the n of Z/n |
---|
[1cce47] | 513 | if (nCoeff_is_Zp(src)) |
---|
[894f5b1] | 514 | { |
---|
| 515 | mpz_init_set_si(nrnMapModul, src->ch); |
---|
| 516 | } |
---|
| 517 | else |
---|
| 518 | { |
---|
| 519 | mpz_init(nrnMapModul); |
---|
[e90dfd6] | 520 | mpz_set(nrnMapModul, src->modNumber); |
---|
[894f5b1] | 521 | } |
---|
| 522 | // nrnMapCoef = 1 in dst if dst is a subring of src |
---|
| 523 | // nrnMapCoef = 0 in dst / src if src is a subring of dst |
---|
[d9301a] | 524 | if (nrnMapCoef == NULL) |
---|
[d351d8] | 525 | { |
---|
[3c3880b] | 526 | nrnMapCoef = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[d9301a] | 527 | mpz_init(nrnMapCoef); |
---|
| 528 | } |
---|
[e90dfd6] | 529 | if (mpz_divisible_p(nrnMapModul, dst->modNumber)) |
---|
[894f5b1] | 530 | { |
---|
| 531 | mpz_set_si(nrnMapCoef, 1); |
---|
| 532 | } |
---|
| 533 | else |
---|
[4d1ae5] | 534 | if (nrnDivBy(NULL, (number) nrnMapModul,dst)) |
---|
[d9301a] | 535 | { |
---|
[e90dfd6] | 536 | mpz_divexact(nrnMapCoef, dst->modNumber, nrnMapModul); |
---|
| 537 | int_number tmp = dst->modNumber; |
---|
| 538 | dst->modNumber = nrnMapModul; |
---|
[4d1ae5] | 539 | if (!nrnIsUnit((number) nrnMapCoef,dst)) |
---|
[0959dc] | 540 | { |
---|
[e90dfd6] | 541 | dst->modNumber = tmp; |
---|
[4d1ae5] | 542 | nrnDelete((number*) &nrnMapModul, dst); |
---|
[0959dc] | 543 | return NULL; |
---|
| 544 | } |
---|
[4d1ae5] | 545 | int_number inv = (int_number) nrnInvers((number) nrnMapCoef,dst); |
---|
[e90dfd6] | 546 | dst->modNumber = tmp; |
---|
[d9301a] | 547 | mpz_mul(nrnMapCoef, nrnMapCoef, inv); |
---|
[e90dfd6] | 548 | mpz_mod(nrnMapCoef, nrnMapCoef, dst->modNumber); |
---|
[4d1ae5] | 549 | nrnDelete((number*) &inv, dst); |
---|
[d9301a] | 550 | } |
---|
| 551 | else |
---|
| 552 | { |
---|
[4d1ae5] | 553 | nrnDelete((number*) &nrnMapModul, dst); |
---|
[d9301a] | 554 | return NULL; |
---|
[d351d8] | 555 | } |
---|
[4d1ae5] | 556 | nrnDelete((number*) &nrnMapModul, dst); |
---|
[1cce47] | 557 | if (nCoeff_is_Ring_2toM(src)) |
---|
[d9301a] | 558 | return nrnMap2toM; |
---|
[1cce47] | 559 | else if (nCoeff_is_Zp(src)) |
---|
[894f5b1] | 560 | return nrnMapZp; |
---|
[d351d8] | 561 | else |
---|
[d9301a] | 562 | return nrnMapModN; |
---|
[d351d8] | 563 | } |
---|
| 564 | } |
---|
| 565 | return NULL; // default |
---|
[275ecc] | 566 | } |
---|
| 567 | |
---|
| 568 | /* |
---|
| 569 | * set the exponent (allocate and init tables) (TODO) |
---|
| 570 | */ |
---|
| 571 | |
---|
[0486a3] | 572 | void nrnSetExp(unsigned long m, coeffs r) |
---|
[275ecc] | 573 | { |
---|
[e90dfd6] | 574 | /* clean up former stuff */ |
---|
| 575 | if (r->modNumber != NULL) mpz_clear(r->modNumber); |
---|
[20704f] | 576 | |
---|
[0486a3] | 577 | r->modExponent= m; |
---|
[e90dfd6] | 578 | r->modNumber = (int_number)omAllocBin(gmp_nrz_bin); |
---|
[0486a3] | 579 | mpz_init_set (r->modNumber, r->modBase); |
---|
| 580 | mpz_pow_ui (r->modNumber, r->modNumber, m); |
---|
[275ecc] | 581 | } |
---|
| 582 | |
---|
[0486a3] | 583 | /* We expect this ring to be Z/n^m for some m > 0 and for some n > 2 which is not a prime. */ |
---|
| 584 | void nrnInitExp(unsigned long m, coeffs r) |
---|
[275ecc] | 585 | { |
---|
[12ea9d] | 586 | nrnSetExp(m, r); |
---|
[0486a3] | 587 | assume (r->modNumber != NULL); |
---|
| 588 | if (mpz_cmp_ui(r->modNumber,2) <= 0) |
---|
| 589 | WarnS("nrnInitExp failed (m in Z/m too small)"); |
---|
[275ecc] | 590 | } |
---|
| 591 | |
---|
| 592 | #ifdef LDEBUG |
---|
[9bb5457] | 593 | BOOLEAN nrnDBTest (number a, const char *, const int, const coeffs r) |
---|
[275ecc] | 594 | { |
---|
[01d4d3] | 595 | if (a==NULL) return TRUE; |
---|
[e90dfd6] | 596 | if ( (mpz_cmp_si((int_number) a, 0) < 0) || (mpz_cmp((int_number) a, r->modNumber) > 0) ) |
---|
[275ecc] | 597 | { |
---|
| 598 | return FALSE; |
---|
| 599 | } |
---|
| 600 | return TRUE; |
---|
| 601 | } |
---|
| 602 | #endif |
---|
| 603 | |
---|
[8e56ad] | 604 | /*2 |
---|
| 605 | * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc) |
---|
| 606 | */ |
---|
[a604c3] | 607 | static const char * nlCPEatLongC(char *s, mpz_ptr i) |
---|
[275ecc] | 608 | { |
---|
[85e68dd] | 609 | const char * start=s; |
---|
[af378f7] | 610 | if (!(*s >= '0' && *s <= '9')) |
---|
| 611 | { |
---|
| 612 | mpz_init_set_si(i, 1); |
---|
| 613 | return s; |
---|
| 614 | } |
---|
| 615 | mpz_init(i); |
---|
[8e56ad] | 616 | while (*s >= '0' && *s <= '9') s++; |
---|
| 617 | if (*s=='\0') |
---|
[275ecc] | 618 | { |
---|
[8e56ad] | 619 | mpz_set_str(i,start,10); |
---|
| 620 | } |
---|
| 621 | else |
---|
| 622 | { |
---|
| 623 | char c=*s; |
---|
| 624 | *s='\0'; |
---|
| 625 | mpz_set_str(i,start,10); |
---|
| 626 | *s=c; |
---|
[275ecc] | 627 | } |
---|
| 628 | return s; |
---|
| 629 | } |
---|
| 630 | |
---|
[14b11bb] | 631 | const char * nrnRead (const char *s, number *a, const coeffs r) |
---|
[275ecc] | 632 | { |
---|
[3c3880b] | 633 | int_number z = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[275ecc] | 634 | { |
---|
[85e68dd] | 635 | s = nlCPEatLongC((char *)s, z); |
---|
[275ecc] | 636 | } |
---|
[e90dfd6] | 637 | mpz_mod(z, z, r->modNumber); |
---|
[8e56ad] | 638 | *a = (number) z; |
---|
[275ecc] | 639 | return s; |
---|
| 640 | } |
---|
| 641 | #endif |
---|
[8d0331d] | 642 | /* #ifdef HAVE_RINGS */ |
---|