[275ecc] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[341696] | 4 | /* $Id$ */ |
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[275ecc] | 5 | /* |
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| 6 | * ABSTRACT: numbers modulo n |
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| 7 | */ |
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| 8 | |
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[691dba] | 9 | #include "config.h" |
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[18cb65] | 10 | #include <misc/auxiliary.h> |
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[275ecc] | 11 | |
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[c90b43] | 12 | #ifdef HAVE_RINGS |
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[f1c465f] | 13 | |
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[18cb65] | 14 | #include <misc/mylimits.h> |
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[2d805a] | 15 | #include <coeffs/coeffs.h> |
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[31213a4] | 16 | #include <reporter/reporter.h> |
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| 17 | #include <omalloc/omalloc.h> |
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[2d805a] | 18 | #include <coeffs/numbers.h> |
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| 19 | #include <coeffs/longrat.h> |
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| 20 | #include <coeffs/mpr_complex.h> |
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| 21 | #include <coeffs/rmodulon.h> |
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[e3b233] | 22 | #include "si_gmp.h" |
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[8d0331d] | 23 | |
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[f1c465f] | 24 | #include <string.h> |
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| 25 | |
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[73a9ffb] | 26 | /// Our Type! |
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| 27 | static const n_coeffType ID = n_Zn; |
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| 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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| 35 | if (nCoeff_is_Ring_ModN(r)) Print("// Z/%s\n", s); |
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| 36 | else if (nCoeff_is_Ring_PtoM(r)) Print("// Z/%s^%lu\n", s, r->modExponent); |
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| 37 | omFreeSize((ADDRESS)s, l); |
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| 38 | } |
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| 39 | |
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[b19ab84] | 40 | static BOOLEAN nrnCoeffsEqual(const coeffs r, n_coeffType n, void * parameter) |
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| 41 | { |
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| 42 | /* test, if r is an instance of nInitCoeffs(n,parameter) */ |
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| 43 | return (n==n_Zn) && (mpz_cmp(r->modNumber,(mpz_ptr)parameter)==0); |
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| 44 | } |
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| 45 | |
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| 46 | |
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[14b11bb] | 47 | /* for initializing function pointers */ |
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[1cce47] | 48 | BOOLEAN nrnInitChar (coeffs r, void* p) |
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[14b11bb] | 49 | { |
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[73a9ffb] | 50 | assume( getCoeffType(r) == ID ); |
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[1112b76] | 51 | nrnInitExp((int)(long)(p), r); |
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[f0797c] | 52 | r->ringtype = 2; |
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[9bb5457] | 53 | |
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[73a9ffb] | 54 | /* next computation may yield wrong characteristic as r->modNumber |
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| 55 | is a GMP number */ |
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| 56 | r->ch = mpz_get_ui(r->modNumber); |
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[e90dfd6] | 57 | |
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| 58 | r->cfInit = nrnInit; |
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| 59 | r->cfDelete = nrnDelete; |
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| 60 | r->cfCopy = nrnCopy; |
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| 61 | r->cfSize = nrnSize; |
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| 62 | r->cfInt = nrnInt; |
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| 63 | r->cfAdd = nrnAdd; |
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| 64 | r->cfSub = nrnSub; |
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| 65 | r->cfMult = nrnMult; |
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| 66 | r->cfDiv = nrnDiv; |
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| 67 | r->cfIntDiv = nrnIntDiv; |
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| 68 | r->cfIntMod = nrnMod; |
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| 69 | r->cfExactDiv = nrnDiv; |
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| 70 | r->cfNeg = nrnNeg; |
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| 71 | r->cfInvers = nrnInvers; |
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| 72 | r->cfDivBy = nrnDivBy; |
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| 73 | r->cfDivComp = nrnDivComp; |
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| 74 | r->cfGreater = nrnGreater; |
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| 75 | r->cfEqual = nrnEqual; |
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| 76 | r->cfIsZero = nrnIsZero; |
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| 77 | r->cfIsOne = nrnIsOne; |
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| 78 | r->cfIsMOne = nrnIsMOne; |
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| 79 | r->cfGreaterZero = nrnGreaterZero; |
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| 80 | r->cfWrite = nrnWrite; |
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| 81 | r->cfRead = nrnRead; |
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| 82 | r->cfPower = nrnPower; |
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| 83 | r->cfSetMap = nrnSetMap; |
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| 84 | r->cfNormalize = ndNormalize; |
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| 85 | r->cfLcm = nrnLcm; |
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| 86 | r->cfGcd = nrnGcd; |
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| 87 | r->cfIsUnit = nrnIsUnit; |
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| 88 | r->cfGetUnit = nrnGetUnit; |
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| 89 | r->cfExtGcd = nrnExtGcd; |
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| 90 | r->cfName = ndName; |
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[7a8011] | 91 | r->cfCoeffWrite = nrnCoeffWrite; |
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[b19ab84] | 92 | r->nCoeffIsEqual = nrnCoeffsEqual; |
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[14b11bb] | 93 | #ifdef LDEBUG |
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[e90dfd6] | 94 | r->cfDBTest = nrnDBTest; |
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[14b11bb] | 95 | #endif |
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[5d594a9] | 96 | return FALSE; |
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[14b11bb] | 97 | } |
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| 98 | |
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[8e1c4e] | 99 | /* |
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| 100 | * create a number from int |
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| 101 | */ |
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[2f3764] | 102 | number nrnInit(long i, const coeffs r) |
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[8e1c4e] | 103 | { |
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[3c3880b] | 104 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 105 | mpz_init_set_si(erg, i); |
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[e90dfd6] | 106 | mpz_mod(erg, erg, r->modNumber); |
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[8e1c4e] | 107 | return (number) erg; |
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| 108 | } |
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| 109 | |
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[9bb5457] | 110 | void nrnDelete(number *a, const coeffs) |
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[8e1c4e] | 111 | { |
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[befecbc] | 112 | if (*a == NULL) return; |
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[8e1c4e] | 113 | mpz_clear((int_number) *a); |
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[7d90aa] | 114 | omFreeBin((void *) *a, gmp_nrz_bin); |
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[bac8611] | 115 | *a = NULL; |
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| 116 | } |
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| 117 | |
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[9bb5457] | 118 | number nrnCopy(number a, const coeffs) |
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[bac8611] | 119 | { |
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[3c3880b] | 120 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[bac8611] | 121 | mpz_init_set(erg, (int_number) a); |
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| 122 | return (number) erg; |
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| 123 | } |
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| 124 | |
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[9bb5457] | 125 | int nrnSize(number a, const coeffs) |
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[bac8611] | 126 | { |
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| 127 | if (a == NULL) return 0; |
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[a604c3] | 128 | return sizeof(mpz_t); |
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[8e1c4e] | 129 | } |
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| 130 | |
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| 131 | /* |
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[25d15e] | 132 | * convert a number to int |
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[8e1c4e] | 133 | */ |
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[9bb5457] | 134 | int nrnInt(number &n, const coeffs) |
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[8e1c4e] | 135 | { |
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[e90dfd6] | 136 | return (int)mpz_get_si((int_number) n); |
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[8e1c4e] | 137 | } |
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| 138 | |
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[275ecc] | 139 | /* |
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| 140 | * Multiply two numbers |
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| 141 | */ |
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[e90dfd6] | 142 | number nrnMult(number a, number b, const coeffs r) |
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[275ecc] | 143 | { |
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[e90dfd6] | 144 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e56ad] | 145 | mpz_init(erg); |
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[e90dfd6] | 146 | mpz_mul(erg, (int_number)a, (int_number) b); |
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| 147 | mpz_mod(erg, erg, r->modNumber); |
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[8e56ad] | 148 | return (number) erg; |
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[275ecc] | 149 | } |
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| 150 | |
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[e90dfd6] | 151 | void nrnPower(number a, int i, number * result, const coeffs r) |
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[8e1c4e] | 152 | { |
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[e90dfd6] | 153 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 154 | mpz_init(erg); |
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[e90dfd6] | 155 | mpz_powm_ui(erg, (int_number)a, i, r->modNumber); |
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[8e1c4e] | 156 | *result = (number) erg; |
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| 157 | } |
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| 158 | |
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[e90dfd6] | 159 | number nrnAdd(number a, number b, const coeffs r) |
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[8e1c4e] | 160 | { |
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[e90dfd6] | 161 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 162 | mpz_init(erg); |
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[e90dfd6] | 163 | mpz_add(erg, (int_number)a, (int_number) b); |
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| 164 | mpz_mod(erg, erg, r->modNumber); |
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[8e1c4e] | 165 | return (number) erg; |
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| 166 | } |
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| 167 | |
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[e90dfd6] | 168 | number nrnSub(number a, number b, const coeffs r) |
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[8e1c4e] | 169 | { |
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[e90dfd6] | 170 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 171 | mpz_init(erg); |
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[e90dfd6] | 172 | mpz_sub(erg, (int_number)a, (int_number) b); |
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| 173 | mpz_mod(erg, erg, r->modNumber); |
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[8e1c4e] | 174 | return (number) erg; |
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| 175 | } |
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| 176 | |
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[e90dfd6] | 177 | number nrnNeg(number c, const coeffs r) |
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[8e1c4e] | 178 | { |
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[0b7bf7] | 179 | if( !nrnIsZero(c, r) ) |
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| 180 | // Attention: This method operates in-place. |
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[9bb5457] | 181 | mpz_sub((int_number)c, r->modNumber, (int_number)c); |
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[a539ad] | 182 | return c; |
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[8e1c4e] | 183 | } |
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| 184 | |
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[e90dfd6] | 185 | number nrnInvers(number c, const coeffs r) |
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[8e1c4e] | 186 | { |
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[e90dfd6] | 187 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 188 | mpz_init(erg); |
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[e90dfd6] | 189 | mpz_invert(erg, (int_number)c, r->modNumber); |
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[8e1c4e] | 190 | return (number) erg; |
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| 191 | } |
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| 192 | |
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[275ecc] | 193 | /* |
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[e90dfd6] | 194 | * Give the smallest k, such that a * x = k = b * y has a solution |
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| 195 | * TODO: lcm(gcd,gcd) better than gcd(lcm) ? |
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[275ecc] | 196 | */ |
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[e90dfd6] | 197 | number nrnLcm(number a, number b, const coeffs r) |
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[275ecc] | 198 | { |
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[196b4b] | 199 | number erg = nrnGcd(NULL, a, r); |
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| 200 | number tmp = nrnGcd(NULL, b, r); |
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[e90dfd6] | 201 | mpz_lcm((int_number)erg, (int_number)erg, (int_number)tmp); |
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[8e1c4e] | 202 | nrnDelete(&tmp, NULL); |
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[e90dfd6] | 203 | return (number)erg; |
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[275ecc] | 204 | } |
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| 205 | |
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| 206 | /* |
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[e90dfd6] | 207 | * Give the largest k, such that a = x * k, b = y * k has |
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[275ecc] | 208 | * a solution. |
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| 209 | */ |
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[e90dfd6] | 210 | number nrnGcd(number a, number b, const coeffs r) |
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[275ecc] | 211 | { |
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[8391d8] | 212 | if ((a == NULL) && (b == NULL)) return nrnInit(0,r); |
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[e90dfd6] | 213 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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| 214 | mpz_init_set(erg, r->modNumber); |
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| 215 | if (a != NULL) mpz_gcd(erg, erg, (int_number)a); |
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| 216 | if (b != NULL) mpz_gcd(erg, erg, (int_number)b); |
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| 217 | return (number)erg; |
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[8e56ad] | 218 | } |
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| 219 | |
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[8e1c4e] | 220 | /* Not needed any more, but may have room for improvement |
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[e90dfd6] | 221 | number nrnGcd3(number a,number b, number c,ring r) |
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[af378f7] | 222 | { |
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[3c3880b] | 223 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[af378f7] | 224 | mpz_init(erg); |
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[e90dfd6] | 225 | if (a == NULL) a = (number)r->modNumber; |
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| 226 | if (b == NULL) b = (number)r->modNumber; |
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| 227 | if (c == NULL) c = (number)r->modNumber; |
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| 228 | mpz_gcd(erg, (int_number)a, (int_number)b); |
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| 229 | mpz_gcd(erg, erg, (int_number)c); |
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| 230 | mpz_gcd(erg, erg, r->modNumber); |
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| 231 | return (number)erg; |
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[af378f7] | 232 | } |
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[8e1c4e] | 233 | */ |
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[af378f7] | 234 | |
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[8e56ad] | 235 | /* |
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[e90dfd6] | 236 | * Give the largest k, such that a = x * k, b = y * k has |
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[8e56ad] | 237 | * a solution and r, s, s.t. k = s*a + t*b |
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| 238 | */ |
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[e90dfd6] | 239 | number nrnExtGcd(number a, number b, number *s, number *t, const coeffs r) |
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[8e56ad] | 240 | { |
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[e90dfd6] | 241 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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| 242 | int_number bs = (int_number)omAllocBin(gmp_nrz_bin); |
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| 243 | int_number bt = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e56ad] | 244 | mpz_init(erg); |
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| 245 | mpz_init(bs); |
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| 246 | mpz_init(bt); |
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[e90dfd6] | 247 | mpz_gcdext(erg, bs, bt, (int_number)a, (int_number)b); |
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| 248 | mpz_mod(bs, bs, r->modNumber); |
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| 249 | mpz_mod(bt, bt, r->modNumber); |
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| 250 | *s = (number)bs; |
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| 251 | *t = (number)bt; |
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| 252 | return (number)erg; |
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[275ecc] | 253 | } |
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| 254 | |
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[9bb5457] | 255 | BOOLEAN nrnIsZero(number a, const coeffs) |
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[275ecc] | 256 | { |
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[01d4d3] | 257 | #ifdef LDEBUG |
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[191795] | 258 | if (a == NULL) return FALSE; |
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[01d4d3] | 259 | #endif |
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[e90dfd6] | 260 | return 0 == mpz_cmpabs_ui((int_number)a, 0); |
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[275ecc] | 261 | } |
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| 262 | |
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[9bb5457] | 263 | BOOLEAN nrnIsOne(number a, const coeffs) |
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[275ecc] | 264 | { |
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[191795] | 265 | #ifdef LDEBUG |
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| 266 | if (a == NULL) return FALSE; |
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| 267 | #endif |
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[e90dfd6] | 268 | return 0 == mpz_cmp_si((int_number)a, 1); |
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[8e56ad] | 269 | } |
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| 270 | |
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[e90dfd6] | 271 | BOOLEAN nrnIsMOne(number a, const coeffs r) |
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[8e56ad] | 272 | { |
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[191795] | 273 | #ifdef LDEBUG |
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| 274 | if (a == NULL) return FALSE; |
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| 275 | #endif |
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[e90dfd6] | 276 | mpz_t t; mpz_init_set(t, (int_number)a); |
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| 277 | mpz_add_ui(t, t, 1); |
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| 278 | bool erg = (0 == mpz_cmp(t, r->modNumber)); |
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| 279 | mpz_clear(t); |
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| 280 | return erg; |
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[275ecc] | 281 | } |
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| 282 | |
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[9bb5457] | 283 | BOOLEAN nrnEqual(number a, number b, const coeffs) |
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[275ecc] | 284 | { |
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[e90dfd6] | 285 | return 0 == mpz_cmp((int_number)a, (int_number)b); |
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[275ecc] | 286 | } |
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| 287 | |
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[9bb5457] | 288 | BOOLEAN nrnGreater(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 nrnGreaterZero(number k, const coeffs) |
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[275ecc] | 294 | { |
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[e90dfd6] | 295 | return 0 < mpz_cmp_si((int_number)k, 0); |
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[8e1c4e] | 296 | } |
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| 297 | |
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[e90dfd6] | 298 | BOOLEAN nrnIsUnit(number a, const coeffs r) |
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[8e1c4e] | 299 | { |
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[e90dfd6] | 300 | number tmp = nrnGcd(a, (number)r->modNumber, r); |
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| 301 | bool res = nrnIsOne(tmp, r); |
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[8e1c4e] | 302 | nrnDelete(&tmp, NULL); |
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| 303 | return res; |
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[275ecc] | 304 | } |
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| 305 | |
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[e90dfd6] | 306 | number nrnGetUnit(number k, const coeffs r) |
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[1e579c6] | 307 | { |
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[e90dfd6] | 308 | if (mpz_divisible_p(r->modNumber, (int_number)k)) return nrnInit(1,r); |
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[97c4ad] | 309 | |
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[e90dfd6] | 310 | int_number unit = (int_number)nrnGcd(k, 0, r); |
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| 311 | mpz_tdiv_q(unit, (int_number)k, unit); |
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| 312 | int_number gcd = (int_number)nrnGcd((number)unit, 0, r); |
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| 313 | if (!nrnIsOne((number)gcd,r)) |
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[af378f7] | 314 | { |
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[31e857] | 315 | int_number ctmp; |
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| 316 | // tmp := unit^2 |
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[4d1ae5] | 317 | int_number tmp = (int_number) nrnMult((number) unit,(number) unit,r); |
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[31e857] | 318 | // gcd_new := gcd(tmp, 0) |
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[14b11bb] | 319 | int_number gcd_new = (int_number) nrnGcd((number) tmp, 0, r); |
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[4d1ae5] | 320 | while (!nrnEqual((number) gcd_new,(number) gcd,r)) |
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[af378f7] | 321 | { |
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[31e857] | 322 | // gcd := gcd_new |
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| 323 | ctmp = gcd; |
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[af378f7] | 324 | gcd = gcd_new; |
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[31e857] | 325 | gcd_new = ctmp; |
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| 326 | // tmp := tmp * unit |
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| 327 | mpz_mul(tmp, tmp, unit); |
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[e90dfd6] | 328 | mpz_mod(tmp, tmp, r->modNumber); |
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[31e857] | 329 | // gcd_new := gcd(tmp, 0) |
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[e90dfd6] | 330 | mpz_gcd(gcd_new, tmp, r->modNumber); |
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[af378f7] | 331 | } |
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[e90dfd6] | 332 | // unit := unit + modNumber / gcd_new |
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| 333 | mpz_tdiv_q(tmp, r->modNumber, gcd_new); |
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[31e857] | 334 | mpz_add(unit, unit, tmp); |
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[e90dfd6] | 335 | mpz_mod(unit, unit, r->modNumber); |
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[31e857] | 336 | nrnDelete((number*) &gcd_new, NULL); |
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| 337 | nrnDelete((number*) &tmp, NULL); |
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[af378f7] | 338 | } |
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[31e857] | 339 | nrnDelete((number*) &gcd, NULL); |
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[e90dfd6] | 340 | return (number)unit; |
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[1e579c6] | 341 | } |
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| 342 | |
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[e90dfd6] | 343 | BOOLEAN nrnDivBy(number a, number b, const coeffs r) |
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[275ecc] | 344 | { |
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[97c4ad] | 345 | if (a == NULL) |
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[e90dfd6] | 346 | return mpz_divisible_p(r->modNumber, (int_number)b); |
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[97c4ad] | 347 | else |
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[a8b44d] | 348 | { /* b divides a iff b/gcd(a, b) is a unit in the given ring: */ |
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[14b11bb] | 349 | number n = nrnGcd(a, b, r); |
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[a8b44d] | 350 | mpz_tdiv_q((int_number)n, (int_number)b, (int_number)n); |
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[14b11bb] | 351 | bool result = nrnIsUnit(n, r); |
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[a8b44d] | 352 | nrnDelete(&n, NULL); |
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| 353 | return result; |
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| 354 | } |
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[275ecc] | 355 | } |
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| 356 | |
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[14b11bb] | 357 | int nrnDivComp(number a, number b, const coeffs r) |
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[275ecc] | 358 | { |
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[4d1ae5] | 359 | if (nrnEqual(a, b,r)) return 2; |
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[31e857] | 360 | if (mpz_divisible_p((int_number) a, (int_number) b)) return -1; |
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| 361 | if (mpz_divisible_p((int_number) b, (int_number) a)) return 1; |
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[e90dfd6] | 362 | return 0; |
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[275ecc] | 363 | } |
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| 364 | |
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[e90dfd6] | 365 | number nrnDiv(number a, number b, const coeffs r) |
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[275ecc] | 366 | { |
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[e90dfd6] | 367 | if (a == NULL) a = (number)r->modNumber; |
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| 368 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e56ad] | 369 | mpz_init(erg); |
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[e90dfd6] | 370 | if (mpz_divisible_p((int_number)a, (int_number)b)) |
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[275ecc] | 371 | { |
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[e90dfd6] | 372 | mpz_divexact(erg, (int_number)a, (int_number)b); |
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| 373 | return (number)erg; |
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[275ecc] | 374 | } |
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| 375 | else |
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| 376 | { |
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[e90dfd6] | 377 | int_number gcd = (int_number)nrnGcd(a, b, r); |
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| 378 | mpz_divexact(erg, (int_number)b, gcd); |
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| 379 | if (!nrnIsUnit((number)erg, r)) |
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[8e56ad] | 380 | { |
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[bca575c] | 381 | WerrorS("Division not possible, even by cancelling zero divisors."); |
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| 382 | WerrorS("Result is integer division without remainder."); |
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[67dbdb] | 383 | mpz_tdiv_q(erg, (int_number) a, (int_number) b); |
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[31e857] | 384 | nrnDelete((number*) &gcd, NULL); |
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[e90dfd6] | 385 | return (number)erg; |
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[8e56ad] | 386 | } |
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[31e857] | 387 | // a / gcd(a,b) * [b / gcd (a,b)]^(-1) |
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[e90dfd6] | 388 | int_number tmp = (int_number)nrnInvers((number) erg,r); |
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| 389 | mpz_divexact(erg, (int_number)a, gcd); |
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[12ea9d] | 390 | mpz_mul(erg, erg, tmp); |
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[31e857] | 391 | nrnDelete((number*) &gcd, NULL); |
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| 392 | nrnDelete((number*) &tmp, NULL); |
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[e90dfd6] | 393 | mpz_mod(erg, erg, r->modNumber); |
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| 394 | return (number)erg; |
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[275ecc] | 395 | } |
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| 396 | } |
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| 397 | |
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[e90dfd6] | 398 | number nrnMod(number a, number b, const coeffs r) |
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[6ea941] | 399 | { |
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| 400 | /* |
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[e90dfd6] | 401 | We need to return the number rr which is uniquely determined by the |
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[6ea941] | 402 | following two properties: |
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[e90dfd6] | 403 | (1) 0 <= rr < |b| (with respect to '<' and '<=' performed in Z x Z) |
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| 404 | (2) There exists some k in the integers Z such that a = k * b + rr. |
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[6ea941] | 405 | Consider g := gcd(n, |b|). Note that then |b|/g is a unit in Z/n. |
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| 406 | Now, there are three cases: |
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| 407 | (a) g = 1 |
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| 408 | Then |b| is a unit in Z/n, i.e. |b| (and also b) divides a. |
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[e90dfd6] | 409 | Thus rr = 0. |
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[6ea941] | 410 | (b) g <> 1 and g divides a |
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[e90dfd6] | 411 | Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again rr = 0. |
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[6ea941] | 412 | (c) g <> 1 and g does not divide a |
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| 413 | Then denote the division with remainder of a by g as this: |
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| 414 | a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b| |
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[e90dfd6] | 415 | fulfills (1) and (2), i.e. rr := t is the correct result. Hence |
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| 416 | in this third case, rr is the remainder of division of a by g in Z. |
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[e1634d] | 417 | Remark: according to mpz_mod: a,b are always non-negative |
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[6ea941] | 418 | */ |
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[e90dfd6] | 419 | int_number g = (int_number)omAllocBin(gmp_nrz_bin); |
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| 420 | int_number rr = (int_number)omAllocBin(gmp_nrz_bin); |
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[6ea941] | 421 | mpz_init(g); |
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[e90dfd6] | 422 | mpz_init_set_si(rr, 0); |
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| 423 | mpz_gcd(g, (int_number)r->modNumber, (int_number)b); // g is now as above |
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| 424 | if (mpz_cmp_si(g, (long)1) != 0) mpz_mod(rr, (int_number)a, g); // the case g <> 1 |
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[6ea941] | 425 | mpz_clear(g); |
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[3c3880b] | 426 | omFreeBin(g, gmp_nrz_bin); |
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[e90dfd6] | 427 | return (number)rr; |
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[6ea941] | 428 | } |
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| 429 | |
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[e90dfd6] | 430 | number nrnIntDiv(number a, number b, const coeffs r) |
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[275ecc] | 431 | { |
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[e90dfd6] | 432 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[8e56ad] | 433 | mpz_init(erg); |
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[e90dfd6] | 434 | if (a == NULL) a = (number)r->modNumber; |
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| 435 | mpz_tdiv_q(erg, (int_number)a, (int_number)b); |
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| 436 | return (number)erg; |
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[275ecc] | 437 | } |
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| 438 | |
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[d351d8] | 439 | /* |
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[d9301a] | 440 | * Helper function for computing the module |
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| 441 | */ |
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| 442 | |
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| 443 | int_number nrnMapCoef = NULL; |
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| 444 | |
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[9bb5457] | 445 | number nrnMapModN(number from, const coeffs /*src*/, const coeffs dst) |
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[d351d8] | 446 | { |
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[4d1ae5] | 447 | return nrnMult(from, (number) nrnMapCoef, dst); |
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[d351d8] | 448 | } |
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[d9301a] | 449 | |
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[9bb5457] | 450 | number nrnMap2toM(number from, const coeffs /*src*/, const coeffs dst) |
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[d9301a] | 451 | { |
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[e90dfd6] | 452 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[d9301a] | 453 | mpz_init(erg); |
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[e90dfd6] | 454 | mpz_mul_ui(erg, nrnMapCoef, (NATNUMBER)from); |
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| 455 | mpz_mod(erg, erg, dst->modNumber); |
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| 456 | return (number)erg; |
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[d9301a] | 457 | } |
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| 458 | |
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[9bb5457] | 459 | number nrnMapZp(number from, const coeffs /*src*/, const coeffs dst) |
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[894f5b1] | 460 | { |
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[e90dfd6] | 461 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[894f5b1] | 462 | mpz_init(erg); |
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[4d1ae5] | 463 | // TODO: use npInt(...) |
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[e90dfd6] | 464 | mpz_mul_si(erg, nrnMapCoef, (NATNUMBER)from); |
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| 465 | mpz_mod(erg, erg, dst->modNumber); |
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| 466 | return (number)erg; |
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[894f5b1] | 467 | } |
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| 468 | |
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[9bb5457] | 469 | number nrnMapGMP(number from, const coeffs /*src*/, const coeffs dst) |
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[d9301a] | 470 | { |
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[e90dfd6] | 471 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[d9301a] | 472 | mpz_init(erg); |
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[e90dfd6] | 473 | mpz_mod(erg, (int_number)from, dst->modNumber); |
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| 474 | return (number)erg; |
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[d9301a] | 475 | } |
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| 476 | |
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[9bb5457] | 477 | number nrnMapQ(number from, const coeffs src, const coeffs /*dst*/) |
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[894f5b1] | 478 | { |
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[e90dfd6] | 479 | int_number erg = (int_number)omAllocBin(gmp_nrz_bin); |
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[894f5b1] | 480 | mpz_init(erg); |
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[e90dfd6] | 481 | nlGMP(from, (number)erg, src); |
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| 482 | mpz_mod(erg, erg, src->modNumber); |
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| 483 | return (number)erg; |
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[894f5b1] | 484 | } |
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| 485 | |
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[4d1ae5] | 486 | nMapFunc nrnSetMap(const coeffs src, const coeffs dst) |
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[275ecc] | 487 | { |
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[14b11bb] | 488 | /* dst = currRing->cf */ |
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[1cce47] | 489 | if (nCoeff_is_Ring_Z(src)) |
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[d351d8] | 490 | { |
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[894f5b1] | 491 | return nrnMapGMP; |
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| 492 | } |
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[1cce47] | 493 | if (nCoeff_is_Q(src)) |
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[894f5b1] | 494 | { |
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| 495 | return nrnMapQ; |
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[d9301a] | 496 | } |
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[894f5b1] | 497 | // Some type of Z/n ring / field |
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[f0797c] | 498 | if (nCoeff_is_Ring_ModN(src) || nCoeff_is_Ring_PtoM(src) || |
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| 499 | nCoeff_is_Ring_2toM(src) || nCoeff_is_Zp(src)) |
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[d9301a] | 500 | { |
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[894f5b1] | 501 | if ( (src->ringtype > 0) |
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[e90dfd6] | 502 | && (mpz_cmp(src->modBase, dst->modBase) == 0) |
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| 503 | && (src->modExponent == dst->modExponent)) return nrnMapGMP; |
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[d351d8] | 504 | else |
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| 505 | { |
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[3c3880b] | 506 | int_number nrnMapModul = (int_number) omAllocBin(gmp_nrz_bin); |
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[894f5b1] | 507 | // Computing the n of Z/n |
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[1cce47] | 508 | if (nCoeff_is_Zp(src)) |
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[894f5b1] | 509 | { |
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| 510 | mpz_init_set_si(nrnMapModul, src->ch); |
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| 511 | } |
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| 512 | else |
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| 513 | { |
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| 514 | mpz_init(nrnMapModul); |
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[e90dfd6] | 515 | mpz_set(nrnMapModul, src->modNumber); |
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[894f5b1] | 516 | } |
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| 517 | // nrnMapCoef = 1 in dst if dst is a subring of src |
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| 518 | // nrnMapCoef = 0 in dst / src if src is a subring of dst |
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[d9301a] | 519 | if (nrnMapCoef == NULL) |
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[d351d8] | 520 | { |
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[3c3880b] | 521 | nrnMapCoef = (int_number) omAllocBin(gmp_nrz_bin); |
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[d9301a] | 522 | mpz_init(nrnMapCoef); |
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| 523 | } |
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[e90dfd6] | 524 | if (mpz_divisible_p(nrnMapModul, dst->modNumber)) |
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[894f5b1] | 525 | { |
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| 526 | mpz_set_si(nrnMapCoef, 1); |
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| 527 | } |
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| 528 | else |
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[4d1ae5] | 529 | if (nrnDivBy(NULL, (number) nrnMapModul,dst)) |
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[d9301a] | 530 | { |
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[e90dfd6] | 531 | mpz_divexact(nrnMapCoef, dst->modNumber, nrnMapModul); |
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| 532 | int_number tmp = dst->modNumber; |
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| 533 | dst->modNumber = nrnMapModul; |
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[4d1ae5] | 534 | if (!nrnIsUnit((number) nrnMapCoef,dst)) |
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[0959dc] | 535 | { |
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[e90dfd6] | 536 | dst->modNumber = tmp; |
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[4d1ae5] | 537 | nrnDelete((number*) &nrnMapModul, dst); |
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[0959dc] | 538 | return NULL; |
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| 539 | } |
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[4d1ae5] | 540 | int_number inv = (int_number) nrnInvers((number) nrnMapCoef,dst); |
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[e90dfd6] | 541 | dst->modNumber = tmp; |
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[d9301a] | 542 | mpz_mul(nrnMapCoef, nrnMapCoef, inv); |
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[e90dfd6] | 543 | mpz_mod(nrnMapCoef, nrnMapCoef, dst->modNumber); |
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[4d1ae5] | 544 | nrnDelete((number*) &inv, dst); |
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[d9301a] | 545 | } |
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| 546 | else |
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| 547 | { |
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[4d1ae5] | 548 | nrnDelete((number*) &nrnMapModul, dst); |
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[d9301a] | 549 | return NULL; |
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[d351d8] | 550 | } |
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[4d1ae5] | 551 | nrnDelete((number*) &nrnMapModul, dst); |
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[1cce47] | 552 | if (nCoeff_is_Ring_2toM(src)) |
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[d9301a] | 553 | return nrnMap2toM; |
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[1cce47] | 554 | else if (nCoeff_is_Zp(src)) |
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[894f5b1] | 555 | return nrnMapZp; |
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[d351d8] | 556 | else |
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[d9301a] | 557 | return nrnMapModN; |
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[d351d8] | 558 | } |
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| 559 | } |
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| 560 | return NULL; // default |
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[275ecc] | 561 | } |
---|
| 562 | |
---|
| 563 | /* |
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| 564 | * set the exponent (allocate and init tables) (TODO) |
---|
| 565 | */ |
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| 566 | |
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[1112b76] | 567 | void nrnSetExp(int m, coeffs r) |
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[275ecc] | 568 | { |
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[e90dfd6] | 569 | /* clean up former stuff */ |
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| 570 | if (r->modBase != NULL) mpz_clear(r->modBase); |
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| 571 | if (r->modNumber != NULL) mpz_clear(r->modNumber); |
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[20704f] | 572 | |
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[e90dfd6] | 573 | /* this is Z/m = Z/(m^1), hence set modBase = m, modExponent = 1: */ |
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| 574 | r->modBase = (int_number)omAllocBin(gmp_nrz_bin); |
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| 575 | mpz_init(r->modBase); |
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| 576 | mpz_set_ui(r->modBase, (unsigned long)m); |
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| 577 | r->modExponent = 1; |
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| 578 | r->modNumber = (int_number)omAllocBin(gmp_nrz_bin); |
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| 579 | mpz_init(r->modNumber); |
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| 580 | mpz_set(r->modNumber, r->modBase); |
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| 581 | /* mpz_pow_ui(r->modNumber, r->modNumber, r->modExponent); */ |
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[275ecc] | 582 | } |
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| 583 | |
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[e90dfd6] | 584 | /* We expect this ring to be Z/m for some m > 2 which is not a prime. */ |
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[1112b76] | 585 | void nrnInitExp(int m, coeffs r) |
---|
[275ecc] | 586 | { |
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[e90dfd6] | 587 | if (m <= 2) WarnS("nrnInitExp failed (m in Z/m too small)"); |
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[12ea9d] | 588 | nrnSetExp(m, r); |
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[275ecc] | 589 | } |
---|
| 590 | |
---|
| 591 | #ifdef LDEBUG |
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[9bb5457] | 592 | BOOLEAN nrnDBTest (number a, const char *, const int, const coeffs r) |
---|
[275ecc] | 593 | { |
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[01d4d3] | 594 | if (a==NULL) return TRUE; |
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[e90dfd6] | 595 | if ( (mpz_cmp_si((int_number) a, 0) < 0) || (mpz_cmp((int_number) a, r->modNumber) > 0) ) |
---|
[275ecc] | 596 | { |
---|
| 597 | return FALSE; |
---|
| 598 | } |
---|
| 599 | return TRUE; |
---|
| 600 | } |
---|
| 601 | #endif |
---|
| 602 | |
---|
[8e56ad] | 603 | /*2 |
---|
| 604 | * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc) |
---|
| 605 | */ |
---|
[a604c3] | 606 | static const char * nlCPEatLongC(char *s, mpz_ptr i) |
---|
[275ecc] | 607 | { |
---|
[85e68dd] | 608 | const char * start=s; |
---|
[af378f7] | 609 | if (!(*s >= '0' && *s <= '9')) |
---|
| 610 | { |
---|
| 611 | mpz_init_set_si(i, 1); |
---|
| 612 | return s; |
---|
| 613 | } |
---|
| 614 | mpz_init(i); |
---|
[8e56ad] | 615 | while (*s >= '0' && *s <= '9') s++; |
---|
| 616 | if (*s=='\0') |
---|
[275ecc] | 617 | { |
---|
[8e56ad] | 618 | mpz_set_str(i,start,10); |
---|
| 619 | } |
---|
| 620 | else |
---|
| 621 | { |
---|
| 622 | char c=*s; |
---|
| 623 | *s='\0'; |
---|
| 624 | mpz_set_str(i,start,10); |
---|
| 625 | *s=c; |
---|
[275ecc] | 626 | } |
---|
| 627 | return s; |
---|
| 628 | } |
---|
| 629 | |
---|
[14b11bb] | 630 | const char * nrnRead (const char *s, number *a, const coeffs r) |
---|
[275ecc] | 631 | { |
---|
[3c3880b] | 632 | int_number z = (int_number) omAllocBin(gmp_nrz_bin); |
---|
[275ecc] | 633 | { |
---|
[85e68dd] | 634 | s = nlCPEatLongC((char *)s, z); |
---|
[275ecc] | 635 | } |
---|
[e90dfd6] | 636 | mpz_mod(z, z, r->modNumber); |
---|
[8e56ad] | 637 | *a = (number) z; |
---|
[275ecc] | 638 | return s; |
---|
| 639 | } |
---|
| 640 | #endif |
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[8d0331d] | 641 | /* #ifdef HAVE_RINGS */ |
---|