[255eaa] | 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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[691dba] | 7 | #include "config.h" |
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[18cb65] | 8 | #include <misc/auxiliary.h> |
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[f1c465f] | 9 | |
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| 10 | #ifdef HAVE_RINGS |
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[255eaa] | 11 | |
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| 12 | #include <string.h> |
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[18cb65] | 13 | #include <misc/mylimits.h> |
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[2d805a] | 14 | #include <coeffs/coeffs.h> |
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[18cb65] | 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/rintegers.h> |
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[e3b233] | 21 | #include "si_gmp.h" |
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[255eaa] | 22 | |
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[73a9ffb] | 23 | /// Our Type! |
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| 24 | static const n_coeffType ID = n_Z; |
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[255eaa] | 25 | |
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[a604c3] | 26 | omBin gmp_nrz_bin = omGetSpecBin(sizeof(mpz_t)); |
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[1e579c6] | 27 | |
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[255eaa] | 28 | /* |
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| 29 | * Multiply two numbers |
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| 30 | */ |
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[9bb5457] | 31 | number nrzMult (number a, number b, const coeffs) |
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[255eaa] | 32 | { |
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[1d03c4e] | 33 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[255eaa] | 34 | mpz_init(erg); |
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[1e579c6] | 35 | mpz_mul(erg, (int_number) a, (int_number) b); |
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[255eaa] | 36 | return (number) erg; |
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| 37 | } |
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| 38 | |
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| 39 | /* |
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| 40 | * Give the smallest non unit k, such that a * x = k = b * y has a solution |
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| 41 | */ |
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[9bb5457] | 42 | number nrzLcm (number a,number b,const coeffs) |
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[255eaa] | 43 | { |
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[1d03c4e] | 44 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[255eaa] | 45 | mpz_init(erg); |
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[1e579c6] | 46 | mpz_lcm(erg, (int_number) a, (int_number) b); |
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| 47 | return (number) erg; |
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[255eaa] | 48 | } |
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| 49 | |
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| 50 | /* |
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| 51 | * Give the largest non unit k, such that a = x * k, b = y * k has |
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| 52 | * a solution. |
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| 53 | */ |
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[9bb5457] | 54 | number nrzGcd (number a,number b,const coeffs) |
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[255eaa] | 55 | { |
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[1d03c4e] | 56 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[1e579c6] | 57 | mpz_init(erg); |
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| 58 | mpz_gcd(erg, (int_number) a, (int_number) b); |
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| 59 | return (number) erg; |
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| 60 | } |
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| 61 | |
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| 62 | /* |
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| 63 | * Give the largest non unit k, such that a = x * k, b = y * k has |
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| 64 | * a solution and r, s, s.t. k = s*a + t*b |
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| 65 | */ |
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[9bb5457] | 66 | number nrzExtGcd (number a, number b, number *s, number *t, const coeffs) |
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[1e579c6] | 67 | { |
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[1d03c4e] | 68 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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| 69 | int_number bs = (int_number) omAllocBin(gmp_nrz_bin); |
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| 70 | int_number bt = (int_number) omAllocBin(gmp_nrz_bin); |
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[255eaa] | 71 | mpz_init(erg); |
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[1e579c6] | 72 | mpz_init(bs); |
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| 73 | mpz_init(bt); |
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| 74 | mpz_gcdext(erg, bs, bt, (int_number) a, (int_number) b); |
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| 75 | *s = (number) bs; |
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| 76 | *t = (number) bt; |
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| 77 | return (number) erg; |
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[255eaa] | 78 | } |
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| 79 | |
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[9bb5457] | 80 | void nrzPower (number a, int i, number * result, const coeffs) |
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[255eaa] | 81 | { |
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[1d03c4e] | 82 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[255eaa] | 83 | mpz_init(erg); |
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[1e579c6] | 84 | mpz_pow_ui(erg, (int_number) a, i); |
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| 85 | *result = (number) erg; |
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[255eaa] | 86 | } |
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| 87 | |
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| 88 | /* |
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| 89 | * create a number from int |
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| 90 | */ |
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[2f3764] | 91 | number nrzInit (long i, const coeffs) |
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[255eaa] | 92 | { |
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[1d03c4e] | 93 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[255eaa] | 94 | mpz_init_set_si(erg, i); |
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| 95 | return (number) erg; |
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| 96 | } |
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| 97 | |
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[9bb5457] | 98 | void nrzDelete(number *a, const coeffs) |
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[1e579c6] | 99 | { |
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[befecbc] | 100 | if (*a == NULL) return; |
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[1e579c6] | 101 | mpz_clear((int_number) *a); |
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[bac8611] | 102 | omFreeBin((ADDRESS) *a, gmp_nrz_bin); |
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[befecbc] | 103 | *a = NULL; |
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[bac8611] | 104 | } |
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| 105 | |
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[9bb5457] | 106 | number nrzCopy(number a, const coeffs) |
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[bac8611] | 107 | { |
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[1d03c4e] | 108 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[bac8611] | 109 | mpz_init_set(erg, (int_number) a); |
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| 110 | return (number) erg; |
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| 111 | } |
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| 112 | |
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[c14846c] | 113 | #if 0 |
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[9bb5457] | 114 | number nrzCopyMap(number a, const coeffs /*src*/, const coeffs dst) |
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[bac8611] | 115 | { |
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[85d8bee] | 116 | return nrzCopy(a,dst); |
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[bac8611] | 117 | } |
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[c14846c] | 118 | #endif |
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[bac8611] | 119 | |
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[9bb5457] | 120 | int nrzSize(number a, const coeffs) |
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[bac8611] | 121 | { |
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| 122 | if (a == NULL) return 0; |
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[a604c3] | 123 | return sizeof(mpz_t); |
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[1e579c6] | 124 | } |
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| 125 | |
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[255eaa] | 126 | /* |
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[9600b0] | 127 | * convert a number to int |
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[255eaa] | 128 | */ |
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[9bb5457] | 129 | int nrzInt(number &n, const coeffs) |
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[255eaa] | 130 | { |
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[25d15e] | 131 | return (int) mpz_get_si( (int_number)n); |
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[255eaa] | 132 | } |
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| 133 | |
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[9bb5457] | 134 | number nrzAdd (number a, number b, const coeffs) |
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[255eaa] | 135 | { |
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[1d03c4e] | 136 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[255eaa] | 137 | mpz_init(erg); |
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[1e579c6] | 138 | mpz_add(erg, (int_number) a, (int_number) b); |
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[255eaa] | 139 | return (number) erg; |
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| 140 | } |
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| 141 | |
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[9bb5457] | 142 | number nrzSub (number a, number b, const coeffs) |
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[255eaa] | 143 | { |
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[1d03c4e] | 144 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[255eaa] | 145 | mpz_init(erg); |
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[1e579c6] | 146 | mpz_sub(erg, (int_number) a, (int_number) b); |
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| 147 | return (number) erg; |
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| 148 | } |
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| 149 | |
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[9bb5457] | 150 | number nrzGetUnit (number, const coeffs r) |
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[1e579c6] | 151 | { |
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[85d8bee] | 152 | return nrzInit(1, r); |
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[255eaa] | 153 | } |
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| 154 | |
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[9bb5457] | 155 | BOOLEAN nrzIsUnit (number a, const coeffs) |
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[1e579c6] | 156 | { |
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| 157 | return 0 == mpz_cmpabs_ui((int_number) a, 1); |
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| 158 | } |
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| 159 | |
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[9bb5457] | 160 | BOOLEAN nrzIsZero (number a, const coeffs) |
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[255eaa] | 161 | { |
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[1e579c6] | 162 | return 0 == mpz_cmpabs_ui((int_number) a, 0); |
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[255eaa] | 163 | } |
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| 164 | |
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[9bb5457] | 165 | BOOLEAN nrzIsOne (number a, const coeffs) |
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[255eaa] | 166 | { |
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[a0d9be] | 167 | return (a!=NULL) && (0 == mpz_cmp_si((int_number) a, 1)); |
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[b18621] | 168 | } |
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| 169 | |
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[9bb5457] | 170 | BOOLEAN nrzIsMOne (number a, const coeffs) |
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[b18621] | 171 | { |
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[a0d9be] | 172 | return (a!=NULL) && (0 == mpz_cmp_si((int_number) a, -1)); |
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[255eaa] | 173 | } |
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| 174 | |
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[9bb5457] | 175 | BOOLEAN nrzEqual (number a,number b, const coeffs) |
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[255eaa] | 176 | { |
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[1e579c6] | 177 | return 0 == mpz_cmp((int_number) a, (int_number) b); |
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[255eaa] | 178 | } |
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| 179 | |
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[9bb5457] | 180 | BOOLEAN nrzGreater (number a,number b, const coeffs) |
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[255eaa] | 181 | { |
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[1e579c6] | 182 | return 0 < mpz_cmp((int_number) a, (int_number) b); |
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[255eaa] | 183 | } |
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| 184 | |
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[9bb5457] | 185 | BOOLEAN nrzGreaterZero (number k, const coeffs) |
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[b18621] | 186 | { |
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[675ce47] | 187 | return 0 < mpz_cmp_si((int_number) k, 0); |
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[b18621] | 188 | } |
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| 189 | |
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[bec902b] | 190 | int nrzDivComp(number a, number b, const coeffs r) |
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[255eaa] | 191 | { |
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[bec902b] | 192 | if (nrzDivBy(a, b, r)) |
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[91d286] | 193 | { |
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[bec902b] | 194 | if (nrzDivBy(b, a, r)) return 2; |
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[91d286] | 195 | return -1; |
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[04f365] | 196 | } |
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[bec902b] | 197 | if (nrzDivBy(b, a, r)) return 1; |
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[91d286] | 198 | return 0; |
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[255eaa] | 199 | } |
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| 200 | |
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[9bb5457] | 201 | BOOLEAN nrzDivBy (number a,number b, const coeffs) |
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[255eaa] | 202 | { |
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[8e56ad] | 203 | return mpz_divisible_p((int_number) a, (int_number) b) != 0; |
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[255eaa] | 204 | } |
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| 205 | |
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[bec902b] | 206 | number nrzDiv (number a,number b, const coeffs R) |
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[255eaa] | 207 | { |
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[1d03c4e] | 208 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[1e579c6] | 209 | mpz_init(erg); |
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[1d03c4e] | 210 | int_number r = (int_number) omAllocBin(gmp_nrz_bin); |
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| 211 | mpz_init(r); |
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[1e579c6] | 212 | mpz_tdiv_qr(erg, r, (int_number) a, (int_number) b); |
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[bec902b] | 213 | if (!nrzIsZero((number) r, R)) |
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[1e579c6] | 214 | { |
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[bca575c] | 215 | WerrorS("Division by non divisible element."); |
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| 216 | WerrorS("Result is without remainder."); |
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[1e579c6] | 217 | } |
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| 218 | mpz_clear(r); |
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[bac8611] | 219 | omFreeBin(r, gmp_nrz_bin); |
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[1e579c6] | 220 | return (number) erg; |
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[255eaa] | 221 | } |
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| 222 | |
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[9bb5457] | 223 | number nrzIntDiv (number a,number b, const coeffs) |
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[255eaa] | 224 | { |
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[1d03c4e] | 225 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[1e579c6] | 226 | mpz_init(erg); |
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| 227 | mpz_tdiv_q(erg, (int_number) a, (int_number) b); |
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| 228 | return (number) erg; |
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[255eaa] | 229 | } |
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| 230 | |
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[9bb5457] | 231 | number nrzIntMod (number a,number b, const coeffs) |
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[3231f3] | 232 | { |
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| 233 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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| 234 | mpz_init(erg); |
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| 235 | int_number r = (int_number) omAllocBin(gmp_nrz_bin); |
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| 236 | mpz_init(r); |
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| 237 | mpz_tdiv_qr(erg, r, (int_number) a, (int_number) b); |
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| 238 | mpz_clear(erg); |
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| 239 | return (number) r; |
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| 240 | } |
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| 241 | |
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[4d1ae5] | 242 | number nrzInvers (number c, const coeffs r) |
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[255eaa] | 243 | { |
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[bec902b] | 244 | if (!nrzIsUnit((number) c, r)) |
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[1e579c6] | 245 | { |
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[bca575c] | 246 | WerrorS("Non invertible element."); |
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[1e579c6] | 247 | return (number)0; //TODO |
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| 248 | } |
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[4d1ae5] | 249 | return nrzCopy(c,r); |
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[255eaa] | 250 | } |
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| 251 | |
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[9bb5457] | 252 | number nrzNeg (number c, const coeffs) |
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[255eaa] | 253 | { |
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[1d03c4e] | 254 | // nNeg inplace !!! |
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[a539ad] | 255 | mpz_mul_si((int_number) c, (int_number) c, -1); |
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| 256 | return c; |
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[255eaa] | 257 | } |
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| 258 | |
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[9bb5457] | 259 | number nrzMapMachineInt(number from, const coeffs /*src*/, const coeffs /*dst*/) |
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[d9301a] | 260 | { |
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[1d03c4e] | 261 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[d9301a] | 262 | mpz_init_set_ui(erg, (NATNUMBER) from); |
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| 263 | return (number) erg; |
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| 264 | } |
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| 265 | |
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[9bb5457] | 266 | number nrzMapZp(number from, const coeffs /*src*/, const coeffs /*dst*/) |
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[894f5b1] | 267 | { |
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[1d03c4e] | 268 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[894f5b1] | 269 | mpz_init_set_si(erg, (long) from); |
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| 270 | return (number) erg; |
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| 271 | } |
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| 272 | |
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[9bb5457] | 273 | number nrzMapQ(number from, const coeffs src, const coeffs /*dst*/) |
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[894f5b1] | 274 | { |
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[1d03c4e] | 275 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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[894f5b1] | 276 | mpz_init(erg); |
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[4d1ae5] | 277 | nlGMP(from, (number) erg, src); |
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[894f5b1] | 278 | return (number) erg; |
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| 279 | } |
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| 280 | |
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[85d8bee] | 281 | nMapFunc nrzSetMap(const coeffs src, const coeffs dst) |
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[255eaa] | 282 | { |
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[d9301a] | 283 | /* dst = currRing */ |
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[1cce47] | 284 | if (nCoeff_is_Ring_Z(src) || nCoeff_is_Ring_ModN(src) || nCoeff_is_Ring_PtoM(src)) |
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[d9301a] | 285 | { |
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[c14846c] | 286 | return ndCopyMap; //nrzCopyMap; |
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[d9301a] | 287 | } |
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[1cce47] | 288 | if (nCoeff_is_Ring_2toM(src)) |
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[d9301a] | 289 | { |
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| 290 | return nrzMapMachineInt; |
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| 291 | } |
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[1cce47] | 292 | if (nCoeff_is_Zp(src)) |
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[894f5b1] | 293 | { |
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| 294 | return nrzMapZp; |
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| 295 | } |
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[1cce47] | 296 | if (nCoeff_is_Q(src)) |
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[894f5b1] | 297 | { |
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| 298 | return nrzMapQ; |
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| 299 | } |
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[d9301a] | 300 | return NULL; // default |
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[255eaa] | 301 | } |
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| 302 | |
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| 303 | |
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| 304 | /* |
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| 305 | * set the exponent (allocate and init tables) (TODO) |
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| 306 | */ |
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| 307 | |
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[9bb5457] | 308 | void nrzSetExp(int, coeffs) |
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[255eaa] | 309 | { |
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| 310 | } |
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| 311 | |
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[9bb5457] | 312 | void nrzInitExp(int, coeffs) |
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[255eaa] | 313 | { |
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| 314 | } |
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| 315 | |
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| 316 | #ifdef LDEBUG |
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[9bb5457] | 317 | BOOLEAN nrzDBTest (number, const char *, const int, const coeffs) |
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[ec997eb] | 318 | { |
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| 319 | return TRUE;//TODO |
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| 320 | } |
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[255eaa] | 321 | #endif |
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| 322 | |
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[9bb5457] | 323 | void nrzWrite (number &a, const coeffs) |
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[255eaa] | 324 | { |
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[1e579c6] | 325 | char *s,*z; |
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| 326 | if (a==NULL) |
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| 327 | { |
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| 328 | StringAppendS("o"); |
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| 329 | } |
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| 330 | else |
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| 331 | { |
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[c81a40] | 332 | int l=mpz_sizeinbase((int_number) a, 10) + 2; |
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[1e579c6] | 333 | s=(char*)omAlloc(l); |
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| 334 | z=mpz_get_str(s,10,(int_number) a); |
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| 335 | StringAppendS(z); |
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| 336 | omFreeSize((ADDRESS)s,l); |
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| 337 | } |
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[255eaa] | 338 | } |
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| 339 | |
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[1e579c6] | 340 | /*2 |
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| 341 | * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc) |
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| 342 | */ |
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[a604c3] | 343 | static const char * nlEatLongC(char *s, mpz_ptr i) |
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[255eaa] | 344 | { |
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[3ad53dd] | 345 | const char * start=s; |
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| 346 | |
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[0959dc] | 347 | if (*s<'0' || *s>'9') |
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| 348 | { |
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| 349 | mpz_set_si(i,1); |
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| 350 | return s; |
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| 351 | } |
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[1e579c6] | 352 | while (*s >= '0' && *s <= '9') s++; |
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| 353 | if (*s=='\0') |
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[255eaa] | 354 | { |
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[1e579c6] | 355 | mpz_set_str(i,start,10); |
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| 356 | } |
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| 357 | else |
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| 358 | { |
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| 359 | char c=*s; |
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| 360 | *s='\0'; |
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| 361 | mpz_set_str(i,start,10); |
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| 362 | *s=c; |
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[255eaa] | 363 | } |
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| 364 | return s; |
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| 365 | } |
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| 366 | |
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[9bb5457] | 367 | const char * nrzRead (const char *s, number *a, const coeffs) |
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[255eaa] | 368 | { |
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[1d03c4e] | 369 | int_number z = (int_number) omAllocBin(gmp_nrz_bin); |
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[255eaa] | 370 | { |
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[1e579c6] | 371 | mpz_init(z); |
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[3ad53dd] | 372 | s = nlEatLongC((char *) s, z); |
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[255eaa] | 373 | } |
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[1e579c6] | 374 | *a = (number) z; |
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[255eaa] | 375 | return s; |
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| 376 | } |
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[ec997eb] | 377 | |
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[03f7b5] | 378 | void nrzCoeffWrite (const coeffs, BOOLEAN /*details*/) |
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[7a8011] | 379 | { |
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| 380 | PrintS("// characteristic : 0 (Integers)\n"); |
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| 381 | } |
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| 382 | |
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| 383 | |
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[9bb5457] | 384 | BOOLEAN nrzInitChar(coeffs r, void *) |
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[ec997eb] | 385 | { |
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[73a9ffb] | 386 | assume( getCoeffType(r) == ID ); |
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[613794] | 387 | r->nCoeffIsEqual = ndCoeffIsEqual; |
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| 388 | r->cfKillChar = ndKillChar; |
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[ec997eb] | 389 | r->cfMult = nrzMult; |
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| 390 | r->cfSub = nrzSub; |
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| 391 | r->cfAdd = nrzAdd; |
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| 392 | r->cfDiv = nrzDiv; |
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| 393 | r->cfIntDiv= nrzDiv; |
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| 394 | r->cfIntMod= nrzIntMod; |
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| 395 | r->cfExactDiv= nrzDiv; |
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| 396 | r->cfInit = nrzInit; |
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| 397 | r->cfSize = nrzSize; |
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| 398 | r->cfInt = nrzInt; |
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[7a8011] | 399 | //#ifdef HAVE_RINGS |
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| 400 | r->cfDivComp = nrzDivComp; // only for ring stuff |
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| 401 | r->cfIsUnit = nrzIsUnit; // only for ring stuff |
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| 402 | r->cfGetUnit = nrzGetUnit; // only for ring stuff |
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| 403 | r->cfExtGcd = nrzExtGcd; // only for ring stuff |
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| 404 | r->cfDivBy = nrzDivBy; // only for ring stuff |
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| 405 | //#endif |
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[ec997eb] | 406 | r->cfNeg = nrzNeg; |
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| 407 | r->cfInvers= nrzInvers; |
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| 408 | r->cfCopy = nrzCopy; |
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[ce1f78] | 409 | r->cfWriteLong = nrzWrite; |
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[ec997eb] | 410 | r->cfRead = nrzRead; |
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| 411 | r->cfGreater = nrzGreater; |
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| 412 | r->cfEqual = nrzEqual; |
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| 413 | r->cfIsZero = nrzIsZero; |
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| 414 | r->cfIsOne = nrzIsOne; |
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| 415 | r->cfIsMOne = nrzIsMOne; |
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| 416 | r->cfGreaterZero = nrzGreaterZero; |
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| 417 | r->cfPower = nrzPower; |
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| 418 | r->cfGcd = nrzGcd; |
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| 419 | r->cfLcm = nrzGcd; |
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| 420 | r->cfDelete= nrzDelete; |
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| 421 | r->cfSetMap = nrzSetMap; |
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[7a8011] | 422 | r->cfCoeffWrite = nrzCoeffWrite; |
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[ec997eb] | 423 | // debug stuff |
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| 424 | |
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| 425 | #ifdef LDEBUG |
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| 426 | r->cfDBTest=nrzDBTest; |
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| 427 | #endif |
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[9bb5457] | 428 | |
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[9306a01] | 429 | r->nNULL = 0; |
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[73a9ffb] | 430 | r->ch = 0; |
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[f0797c] | 431 | r->ringtype = 4; |
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[9306a01] | 432 | r->has_simple_Alloc=FALSE; |
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[9bb5457] | 433 | r->has_simple_Inverse=FALSE; |
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[5d594a9] | 434 | return FALSE; |
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[ec997eb] | 435 | } |
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| 436 | |
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[1e579c6] | 437 | #endif |
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