| 1 | // -*- c++ -*- |
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| 2 | //***************************************************************************** |
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| 3 | /** @file cf_cyclo.cc |
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| 4 | * |
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| 5 | * @author Martin Lee |
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| 6 | * @date 29.01.2010 |
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| 7 | * |
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| 8 | * Compute cyclotomic polynomials and factorize integers by brute force |
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| 9 | * |
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| 10 | * @par Copyright: |
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| 11 | * (c) by The SINGULAR Team, see LICENSE file |
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| 12 | * |
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| 13 | * @internal |
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| 14 | * @version \$Id$ |
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| 15 | * |
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| 16 | **/ |
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| 17 | //***************************************************************************** |
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| 18 | |
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| 19 | #include "config.h" |
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| 20 | |
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| 21 | #include "canonicalform.h" |
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| 22 | #include "cf_primes.h" |
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| 23 | #include "cf_util.h" |
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| 24 | #include "cf_assert.h" |
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| 25 | |
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| 26 | #ifdef HAVE_NTL |
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| 27 | #include <NTL/ZZ.h> |
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| 28 | #endif |
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| 29 | |
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| 30 | |
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| 31 | /// integer factorization using table look-ups, |
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| 32 | /// function may fail if integer contains primes which exceed the largest prime |
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| 33 | /// in our table |
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| 34 | int* integerFactorizer (const long integer, int& length, bool& fail) |
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| 35 | { |
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| 36 | ASSERT (integer != 0 && integer != 1 && integer != -1, |
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| 37 | "non-zero non-unit expected"); |
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| 38 | int* result=NULL; |
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| 39 | length= 0; |
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| 40 | fail= false; |
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| 41 | int i= integer; |
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| 42 | if (integer < 0) |
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| 43 | i = -integer; |
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| 44 | |
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| 45 | int exp= 0; |
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| 46 | while ((i != 1) && (i%2 == 0)) |
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| 47 | { |
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| 48 | i /= 2; |
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| 49 | exp++; |
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| 50 | } |
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| 51 | if (exp != 0) |
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| 52 | { |
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| 53 | result= new int [exp]; |
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| 54 | for (int k= 0; k < exp; k++) |
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| 55 | result[k]= 2; |
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| 56 | length += exp; |
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| 57 | } |
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| 58 | if (i == 1) return result; |
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| 59 | |
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| 60 | long j= 0; |
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| 61 | exp= 0; |
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| 62 | int* buf; |
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| 63 | int next_prime; |
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| 64 | while ((i != 1) && (j < 31937)) |
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| 65 | { |
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| 66 | next_prime= cf_getPrime (j); |
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| 67 | while ((i != 1) && (i%next_prime == 0)) |
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| 68 | { |
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| 69 | i /= next_prime; |
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| 70 | exp++; |
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| 71 | } |
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| 72 | if (exp != 0) |
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| 73 | { |
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| 74 | buf= result; |
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| 75 | result= new int [length + exp]; |
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| 76 | for (int k= 0; k < length; k++) |
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| 77 | result [k]= buf[k]; |
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| 78 | for (int k= 0; k < exp; k++) |
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| 79 | result [k + length]= next_prime; |
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| 80 | length += exp; |
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| 81 | } |
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| 82 | exp= 0; |
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| 83 | j++; |
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| 84 | } |
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| 85 | if (j >= 31397) |
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| 86 | fail= true; |
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| 87 | ASSERT (j < 31397, "integer factorizer ran out of primes"); //sic |
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| 88 | return result; |
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| 89 | } |
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| 90 | |
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| 91 | /// make prime factorization distinct |
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| 92 | static inline |
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| 93 | int* makeDistinct (int* factors, const int factors_length, int& length) |
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| 94 | { |
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| 95 | length= 1; |
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| 96 | int* result= new int [length]; |
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| 97 | int* buf; |
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| 98 | result[0]= factors [0]; |
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| 99 | for (int i= 1; i < factors_length; i++) |
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| 100 | { |
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| 101 | if (factors[i - 1] != factors[i]) |
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| 102 | { |
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| 103 | buf= result; |
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| 104 | result= new int [length + 1]; |
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| 105 | for (int j= 0; j < length; j++) |
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| 106 | result[j]= buf [j]; |
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| 107 | result[length]= factors[i]; |
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| 108 | length++; |
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| 109 | } |
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| 110 | } |
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| 111 | return result; |
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| 112 | } |
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| 113 | |
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| 114 | /// compute the n-th cyclotomic polynomial, |
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| 115 | /// function may fail if integer_factorizer fails to factorize n |
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| 116 | CanonicalForm cyclotomicPoly (int n, bool& fail) |
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| 117 | { |
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| 118 | fail= false; |
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| 119 | Variable x= Variable (1); |
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| 120 | CanonicalForm result= x - 1; |
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| 121 | if (n == 1) |
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| 122 | return result; |
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| 123 | int* prime_factors; |
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| 124 | int prime_factors_length; |
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| 125 | int distinct_factors_length; |
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| 126 | prime_factors= integerFactorizer (n, prime_factors_length, fail); |
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| 127 | int* distinct_factors= makeDistinct (prime_factors, prime_factors_length, |
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| 128 | distinct_factors_length); |
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| 129 | if (fail) |
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| 130 | return 1; |
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| 131 | CanonicalForm buf; |
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| 132 | int prod= 1; |
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| 133 | for (int i= 0; i < distinct_factors_length; i++) |
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| 134 | { |
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| 135 | result= result (power (x, distinct_factors[i]), x)/result; |
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| 136 | prod *= distinct_factors[i]; |
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| 137 | } |
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| 138 | return result (power (x, n/prod), x); |
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| 139 | } |
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| 140 | |
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| 141 | #ifdef HAVE_NTL |
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| 142 | /// checks if alpha is a primitive element, alpha is assumed to be an algebraic |
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| 143 | /// variable over some finite prime field |
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| 144 | bool isPrimitive (const Variable& alpha, bool& fail) |
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| 145 | { |
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| 146 | int p= getCharacteristic(); |
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| 147 | CanonicalForm mipo= getMipo (alpha); |
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| 148 | int order= ipower(p, degree(mipo)) - 1; |
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| 149 | CanonicalForm cyclo= cyclotomicPoly (order, fail); |
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| 150 | if (fail) |
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| 151 | return false; |
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| 152 | if (mod(cyclo, mipo (Variable(1), alpha)) == 0) |
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| 153 | return true; |
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| 154 | else |
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| 155 | return false; |
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| 156 | } |
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| 157 | |
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| 158 | #endif |
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