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 in a rational function field K(t_1, .., t_s) with |
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6 | * transcendental variables t_1, ..., t_s, where s >= 1. |
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7 | * Denoting the implemented coeffs object by cf, then these numbers |
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8 | * are represented as quotients of polynomials living in the |
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9 | * polynomial ring K[t_1, .., t_s] represented by cf->extring. |
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10 | * |
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11 | * An element of K(t_1, .., t_s) may have numerous representations, |
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12 | * due to the possibility of common polynomial factors in the |
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13 | * numerator and denominator. This problem is handled by a |
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14 | * cancellation heuristic: Each number "knows" its complexity |
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15 | * which is 0 if and only if common factors have definitely been |
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16 | * cancelled, and some positive integer otherwise. |
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17 | * Each arithmetic operation of two numbers with complexities c1 |
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18 | * and c2 will result in a number of complexity c1 + c2 + some |
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19 | * penalty (specific for each arithmetic operation; see constants |
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20 | * in the *.h file). Whenever the resulting complexity exceeds a |
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21 | * certain threshold (see constant in the *.h file), then the |
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22 | * cancellation heuristic will call 'factory' to compute the gcd |
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23 | * and cancel it out in the given number. (This definite cancel- |
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24 | * lation will also be performed at the beginning of ntWrite, |
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25 | * ensuring that any output is free of common factors. |
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26 | * For the special case of K = Q (i.e., when computing over the |
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27 | * rationals), this definite cancellation procedure will also take |
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28 | * care of nested fractions: If there are fractional coefficients |
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29 | * in the numerator or denominator of a number, then this number |
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30 | * is being replaced by a quotient of two polynomials over Z, or |
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31 | * - if the denominator is a constant - by a polynomial over Q. |
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32 | * |
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33 | * TODO: the description above needs a major update!!! |
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34 | */ |
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35 | #define TRANSEXT_PRIVATES |
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36 | |
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37 | #include "config.h" |
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38 | #include <misc/auxiliary.h> |
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39 | |
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40 | #include <omalloc/omalloc.h> |
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41 | |
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42 | #include <reporter/reporter.h> |
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43 | |
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44 | #include <coeffs/coeffs.h> |
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45 | #include <coeffs/numbers.h> |
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46 | #include <coeffs/longrat.h> |
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47 | |
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48 | #include <polys/monomials/ring.h> |
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49 | #include <polys/monomials/p_polys.h> |
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50 | #include <polys/simpleideals.h> |
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51 | |
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52 | #ifdef HAVE_FACTORY |
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53 | #include <polys/clapsing.h> |
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54 | #include <polys/clapconv.h> |
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55 | #include <factory/factory.h> |
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56 | #endif |
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57 | |
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58 | #include <polys/ext_fields/transext.h> |
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59 | #include <polys/prCopy.h> |
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60 | |
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61 | #include <polys/PolyEnumerator.h> |
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62 | |
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63 | |
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64 | /* constants for controlling the complexity of numbers */ |
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65 | #define ADD_COMPLEXITY 1 /**< complexity increase due to + and - */ |
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66 | #define MULT_COMPLEXITY 2 /**< complexity increase due to * and / */ |
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67 | #define BOUND_COMPLEXITY 10 /**< maximum complexity of a number */ |
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68 | |
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69 | /// TRUE iff num. represents 1 |
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70 | #define NUMIS1(f) (p_IsOne(NUM(f), cf->extRing)) |
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71 | |
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72 | #define COM(f) f->complexity |
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73 | |
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74 | |
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75 | #ifdef LDEBUG |
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76 | #define ntTest(a) assume(ntDBTest(a,__FILE__,__LINE__,cf)) |
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77 | BOOLEAN ntDBTest(number a, const char *f, const int l, const coeffs r); |
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78 | #else |
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79 | #define ntTest(a) do {} while (0) |
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80 | #endif |
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81 | |
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82 | /// Our own type! |
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83 | static const n_coeffType ID = n_transExt; |
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84 | |
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85 | /* polynomial ring in which the numerators and denominators of our |
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86 | numbers live */ |
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87 | #define ntRing cf->extRing |
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88 | |
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89 | /* coeffs object in which the coefficients of our numbers live; |
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90 | * methods attached to ntCoeffs may be used to compute with the |
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91 | * coefficients of our numbers, e.g., use ntCoeffs->nAdd to add |
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92 | * coefficients of our numbers */ |
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93 | #define ntCoeffs cf->extRing->cf |
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94 | |
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95 | |
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96 | omBin fractionObjectBin = omGetSpecBin(sizeof(fractionObject)); |
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97 | |
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98 | /// forward declarations |
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99 | BOOLEAN ntGreaterZero(number a, const coeffs cf); |
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100 | BOOLEAN ntGreater(number a, number b, const coeffs cf); |
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101 | BOOLEAN ntEqual(number a, number b, const coeffs cf); |
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102 | BOOLEAN ntIsOne(number a, const coeffs cf); |
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103 | BOOLEAN ntIsMOne(number a, const coeffs cf); |
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104 | BOOLEAN ntIsZero(number a, const coeffs cf); |
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105 | number ntInit(long i, const coeffs cf); |
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106 | int ntInt(number &a, const coeffs cf); |
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107 | number ntNeg(number a, const coeffs cf); |
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108 | number ntInvers(number a, const coeffs cf); |
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109 | number ntAdd(number a, number b, const coeffs cf); |
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110 | number ntSub(number a, number b, const coeffs cf); |
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111 | number ntMult(number a, number b, const coeffs cf); |
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112 | number ntDiv(number a, number b, const coeffs cf); |
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113 | void ntPower(number a, int exp, number *b, const coeffs cf); |
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114 | number ntCopy(number a, const coeffs cf); |
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115 | void ntWriteLong(number &a, const coeffs cf); |
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116 | void ntWriteShort(number &a, const coeffs cf); |
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117 | number ntRePart(number a, const coeffs cf); |
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118 | number ntImPart(number a, const coeffs cf); |
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119 | number ntGetDenom(number &a, const coeffs cf); |
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120 | number ntGetNumerator(number &a, const coeffs cf); |
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121 | number ntGcd(number a, number b, const coeffs cf); |
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122 | number ntLcm(number a, number b, const coeffs cf); |
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123 | int ntSize(number a, const coeffs cf); |
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124 | void ntDelete(number * a, const coeffs cf); |
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125 | void ntCoeffWrite(const coeffs cf, BOOLEAN details); |
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126 | number ntIntDiv(number a, number b, const coeffs cf); |
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127 | const char * ntRead(const char *s, number *a, const coeffs cf); |
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128 | static BOOLEAN ntCoeffIsEqual(const coeffs cf, n_coeffType n, void * param); |
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129 | |
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130 | void heuristicGcdCancellation(number a, const coeffs cf); |
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131 | void definiteGcdCancellation(number a, const coeffs cf, |
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132 | BOOLEAN simpleTestsHaveAlreadyBeenPerformed); |
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133 | void handleNestedFractionsOverQ(fraction f, const coeffs cf); |
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134 | |
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135 | #ifdef LDEBUG |
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136 | BOOLEAN ntDBTest(number a, const char *f, const int l, const coeffs cf) |
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137 | { |
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138 | assume(getCoeffType(cf) == ID); |
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139 | |
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140 | if (IS0(a)) return TRUE; |
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141 | |
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142 | const fraction t = (fraction)a; |
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143 | |
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144 | const poly num = NUM(t); |
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145 | assume(num != NULL); /**< t != 0 ==> numerator(t) != 0 */ |
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146 | assume( _p_Test(num, ntRing,1) ); |
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147 | |
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148 | const poly den = DEN(t); |
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149 | |
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150 | if (den != NULL) // !DENIS1(f) |
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151 | { |
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152 | assume( _p_Test(den, ntRing,1) ); |
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153 | |
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154 | if(p_IsConstant(den, ntRing) && (n_IsOne(pGetCoeff(den), ntRing->cf))) |
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155 | { |
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156 | Print("?/1 in %s:%d\n",f,l); |
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157 | return FALSE; |
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158 | } |
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159 | |
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160 | if( !n_GreaterZero(pGetCoeff(den), ntRing->cf) ) |
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161 | { |
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162 | Print("negative sign of DEN. of a fraction in %s:%d\n",f,l); |
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163 | return FALSE; |
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164 | } |
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165 | |
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166 | // test that den is over integers!? |
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167 | |
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168 | } else |
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169 | { // num != NULL // den == NULL |
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170 | |
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171 | // if( COM(t) != 0 ) |
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172 | // { |
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173 | // Print("?//NULL with non-zero complexity: %d in %s:%d\n", COM(t), f, l); |
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174 | // return FALSE; |
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175 | // } |
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176 | // test that nume is over integers!? |
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177 | } |
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178 | return TRUE; |
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179 | } |
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180 | #endif |
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181 | |
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182 | /* returns the bottom field in this field extension tower; if the tower |
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183 | is flat, i.e., if there is no extension, then r itself is returned; |
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184 | as a side-effect, the counter 'height' is filled with the height of |
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185 | the extension tower (in case the tower is flat, 'height' is zero) */ |
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186 | static coeffs nCoeff_bottom(const coeffs r, int &height) |
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187 | { |
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188 | assume(r != NULL); |
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189 | coeffs cf = r; |
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190 | height = 0; |
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191 | while (nCoeff_is_Extension(cf)) |
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192 | { |
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193 | assume(cf->extRing != NULL); assume(cf->extRing->cf != NULL); |
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194 | cf = cf->extRing->cf; |
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195 | height++; |
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196 | } |
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197 | return cf; |
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198 | } |
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199 | |
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200 | BOOLEAN ntIsZero(number a, const coeffs cf) |
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201 | { |
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202 | ntTest(a); // !!! |
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203 | return (IS0(a)); |
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204 | } |
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205 | |
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206 | void ntDelete(number * a, const coeffs cf) |
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207 | { |
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208 | ntTest(*a); // !!! |
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209 | fraction f = (fraction)(*a); |
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210 | if (IS0(f)) return; |
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211 | p_Delete(&NUM(f), ntRing); |
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212 | if (!DENIS1(f)) p_Delete(&DEN(f), ntRing); |
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213 | omFreeBin((ADDRESS)f, fractionObjectBin); |
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214 | *a = NULL; |
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215 | } |
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216 | |
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217 | BOOLEAN ntEqual(number a, number b, const coeffs cf) |
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218 | { |
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219 | ntTest(a); |
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220 | ntTest(b); |
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221 | |
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222 | /// simple tests |
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223 | if (a == b) return TRUE; |
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224 | if ((IS0(a)) && (!IS0(b))) return FALSE; |
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225 | if ((IS0(b)) && (!IS0(a))) return FALSE; |
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226 | |
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227 | /// cheap test if gcd's have been cancelled in both numbers |
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228 | fraction fa = (fraction)a; |
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229 | fraction fb = (fraction)b; |
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230 | if ((COM(fa) == 1) && (COM(fb) == 1)) |
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231 | { |
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232 | poly f = p_Add_q(p_Copy(NUM(fa), ntRing), |
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233 | p_Neg(p_Copy(NUM(fb), ntRing), ntRing), |
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234 | ntRing); |
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235 | if (f != NULL) { p_Delete(&f, ntRing); return FALSE; } |
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236 | if (DENIS1(fa) && DENIS1(fb)) return TRUE; |
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237 | if (DENIS1(fa) && !DENIS1(fb)) return FALSE; |
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238 | if (!DENIS1(fa) && DENIS1(fb)) return FALSE; |
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239 | f = p_Add_q(p_Copy(DEN(fa), ntRing), |
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240 | p_Neg(p_Copy(DEN(fb), ntRing), ntRing), |
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241 | ntRing); |
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242 | if (f != NULL) { p_Delete(&f, ntRing); return FALSE; } |
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243 | return TRUE; |
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244 | } |
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245 | |
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246 | /* default: the more expensive multiplication test |
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247 | a/b = c/d <==> a*d = b*c */ |
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248 | poly f = p_Copy(NUM(fa), ntRing); |
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249 | if (!DENIS1(fb)) f = p_Mult_q(f, p_Copy(DEN(fb), ntRing), ntRing); |
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250 | poly g = p_Copy(NUM(fb), ntRing); |
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251 | if (!DENIS1(fa)) g = p_Mult_q(g, p_Copy(DEN(fa), ntRing), ntRing); |
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252 | poly h = p_Add_q(f, p_Neg(g, ntRing), ntRing); |
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253 | if (h == NULL) return TRUE; |
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254 | else |
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255 | { |
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256 | p_Delete(&h, ntRing); |
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257 | return FALSE; |
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258 | } |
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259 | } |
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260 | |
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261 | number ntCopy(number a, const coeffs cf) |
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262 | { |
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263 | ntTest(a); // !!! |
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264 | if (IS0(a)) return NULL; |
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265 | fraction f = (fraction)a; |
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266 | poly g = p_Copy(NUM(f), ntRing); |
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267 | poly h = NULL; if (!DENIS1(f)) h = p_Copy(DEN(f), ntRing); |
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268 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
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269 | NUM(result) = g; |
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270 | DEN(result) = h; |
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271 | COM(result) = COM(f); |
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272 | ntTest((number)result); |
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273 | return (number)result; |
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274 | } |
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275 | |
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276 | /// TODO: normalization of a!? |
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277 | number ntGetNumerator(number &a, const coeffs cf) |
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278 | { |
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279 | ntTest(a); |
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280 | definiteGcdCancellation(a, cf, FALSE); |
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281 | |
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282 | if (IS0(a)) return NULL; |
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283 | |
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284 | fraction f = (fraction)a; |
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285 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
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286 | |
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287 | const BOOLEAN denis1= DENIS1 (f); |
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288 | |
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289 | if (getCoeffType (ntCoeffs) == n_Q && !denis1) |
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290 | handleNestedFractionsOverQ (f, cf); |
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291 | |
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292 | if (getCoeffType (ntCoeffs) == n_Q && denis1) |
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293 | { |
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294 | assume( DEN (f) == NULL ); |
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295 | |
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296 | number g; |
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297 | // TODO/NOTE: the following should not be necessary (due to |
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298 | // Hannes!) as NUM (f) should be over Z!!! |
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299 | CPolyCoeffsEnumerator itr(NUM(f)); |
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300 | |
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301 | |
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302 | n_ClearDenominators(itr, g, ntRing->cf); |
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303 | |
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304 | if( !n_GreaterZero(g, ntRing->cf) ) |
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305 | { |
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306 | NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :((( |
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307 | g = n_Neg(g, ntRing->cf); |
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308 | } |
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309 | |
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310 | // g should be a positive integer now! |
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311 | assume( n_GreaterZero(g, ntRing->cf) ); |
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312 | |
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313 | if( !n_IsOne(g, ntRing->cf) ) |
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314 | { |
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315 | DEN (f) = p_NSet(g, ntRing); // update COM(f)??? |
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316 | COM (f) ++; |
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317 | assume( DEN (f) != NULL ); |
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318 | } |
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319 | else |
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320 | n_Delete(&g, ntRing->cf); |
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321 | |
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322 | ntTest(a); |
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323 | } |
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324 | |
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325 | // Call ntNormalize instead of above?!? |
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326 | |
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327 | NUM (result) = p_Copy (NUM (f), ntRing); // ??? |
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328 | DEN (result) = NULL; |
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329 | COM (result) = 0; |
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330 | |
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331 | ntTest((number)result); |
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332 | return (number)result; |
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333 | } |
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334 | |
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335 | /// TODO: normalization of a!? |
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336 | number ntGetDenom(number &a, const coeffs cf) |
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337 | { |
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338 | ntTest(a); |
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339 | definiteGcdCancellation(a, cf, FALSE); |
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340 | fraction f = (fraction)a; |
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341 | |
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342 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
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343 | DEN (result)= NULL; |
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344 | COM (result)= 0; |
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345 | |
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346 | |
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347 | const BOOLEAN denis1 = DENIS1 (f); |
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348 | |
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349 | if( IS0(f) || (denis1 && getCoeffType (ntCoeffs) != n_Q) ) // */1 or 0 |
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350 | { |
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351 | NUM (result)= p_One(ntRing); |
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352 | ntTest((number)result); |
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353 | return (number)result; |
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354 | } |
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355 | |
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356 | if (!denis1) // */* / Q |
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357 | { |
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358 | assume( DEN (f) != NULL ); |
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359 | |
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360 | if (getCoeffType (ntCoeffs) == n_Q) |
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361 | handleNestedFractionsOverQ (f, cf); |
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362 | |
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363 | ntTest(a); |
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364 | |
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365 | if( DEN (f) != NULL ) // is it ?? // 1 now??? |
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366 | { |
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367 | assume( !p_IsOne(DEN (f), ntRing) ); |
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368 | |
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369 | NUM (result) = p_Copy (DEN (f), ntRing); |
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370 | ntTest((number)result); |
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371 | return (number)result; |
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372 | } |
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373 | // NUM (result) = p_One(ntRing); // NOTE: just in order to be sure... |
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374 | } |
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375 | |
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376 | // */1 / Q |
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377 | assume( getCoeffType (ntCoeffs) == n_Q ); |
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378 | assume( DEN (f) == NULL ); |
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379 | |
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380 | number g; |
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381 | // poly num= p_Copy (NUM (f), ntRing); // ??? |
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382 | |
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383 | |
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384 | // TODO/NOTE: the following should not be necessary (due to |
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385 | // Hannes!) as NUM (f) should be over Z!!! |
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386 | CPolyCoeffsEnumerator itr(NUM(f)); |
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387 | |
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388 | n_ClearDenominators(itr, g, ntRing->cf); // may return -1 :((( |
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389 | |
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390 | if( !n_GreaterZero(g, ntRing->cf) ) |
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391 | { |
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392 | // NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :((( |
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393 | // g = n_Neg(g, ntRing->cf); |
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394 | NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :((( |
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395 | g = n_Neg(g, ntRing->cf); |
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396 | } |
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397 | |
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398 | // g should be a positive integer now! |
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399 | assume( n_GreaterZero(g, ntRing->cf) ); |
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400 | |
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401 | if( !n_IsOne(g, ntRing->cf) ) |
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402 | { |
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403 | assume( n_GreaterZero(g, ntRing->cf) ); |
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404 | assume( !n_IsOne(g, ntRing->cf) ); |
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405 | |
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406 | DEN (f) = p_NSet(g, ntRing); // update COM(f)??? |
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407 | assume( DEN (f) != NULL ); |
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408 | COM (f) ++; |
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409 | |
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410 | NUM (result)= p_Copy (DEN (f), ntRing); |
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411 | } |
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412 | else |
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413 | { // common denom == 1? |
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414 | NUM (result)= p_NSet(g, ntRing); // p_Copy (DEN (f), ntRing); |
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415 | // n_Delete(&g, ntRing->cf); |
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416 | } |
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417 | |
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418 | // if (!p_IsConstant (num, ntRing) && pNext(num) != NULL) |
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419 | // else |
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420 | // g= p_GetAllDenom (num, ntRing); |
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421 | // result= (fraction) ntSetMap (ntRing->cf, cf) (g, ntRing->cf, cf); |
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422 | |
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423 | ntTest((number)result); |
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424 | return (number)result; |
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425 | } |
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426 | |
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427 | BOOLEAN ntIsOne(number a, const coeffs cf) |
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428 | { |
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429 | ntTest(a); // !!! |
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430 | definiteGcdCancellation(a, cf, FALSE); |
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431 | fraction f = (fraction)a; |
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432 | return (f!=NULL) && DENIS1(f) && NUMIS1(f); |
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433 | } |
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434 | |
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435 | BOOLEAN ntIsMOne(number a, const coeffs cf) |
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436 | { |
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437 | ntTest(a); |
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438 | definiteGcdCancellation(a, cf, FALSE); |
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439 | fraction f = (fraction)a; |
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440 | if ((f==NULL) || (!DENIS1(f))) return FALSE; |
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441 | poly g = NUM(f); |
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442 | if (!p_IsConstant(g, ntRing)) return FALSE; |
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443 | return n_IsMOne(p_GetCoeff(g, ntRing), ntCoeffs); |
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444 | } |
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445 | |
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446 | /// this is in-place, modifies a |
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447 | number ntNeg(number a, const coeffs cf) |
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448 | { |
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449 | ntTest(a); |
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450 | if (!IS0(a)) |
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451 | { |
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452 | fraction f = (fraction)a; |
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453 | NUM(f) = p_Neg(NUM(f), ntRing); |
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454 | } |
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455 | ntTest(a); |
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456 | return a; |
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457 | } |
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458 | |
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459 | number ntImPart(number a, const coeffs cf) |
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460 | { |
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461 | ntTest(a); |
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462 | return NULL; |
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463 | } |
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464 | |
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465 | number ntInit_bigint(number longratBigIntNumber, const coeffs src, const coeffs cf) |
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466 | { |
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467 | assume( cf != NULL ); |
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468 | |
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469 | const ring A = cf->extRing; |
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470 | |
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471 | assume( A != NULL ); |
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472 | |
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473 | const coeffs C = A->cf; |
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474 | |
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475 | assume( C != NULL ); |
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476 | |
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477 | number n = n_Init_bigint(longratBigIntNumber, src, C); |
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478 | |
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479 | if ( n_IsZero(n, C) ) |
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480 | { |
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481 | n_Delete(&n, C); |
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482 | return NULL; |
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483 | } |
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484 | |
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485 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
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486 | |
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487 | number den = n_GetDenom(n, C); |
---|
488 | |
---|
489 | assume( n_GreaterZero(den, C) ); |
---|
490 | |
---|
491 | if( n_IsOne(den, C) ) |
---|
492 | { |
---|
493 | NUM(result) = p_NSet(n, A); |
---|
494 | DEN(result) = NULL; |
---|
495 | n_Delete(&den, C); |
---|
496 | } else |
---|
497 | { |
---|
498 | DEN(result) = p_NSet(den, A); |
---|
499 | NUM(result) = p_NSet(n_GetNumerator(n, C), A); |
---|
500 | n_Delete(&n, C); |
---|
501 | } |
---|
502 | |
---|
503 | COM(result) = 0; |
---|
504 | |
---|
505 | ntTest((number)result); |
---|
506 | |
---|
507 | return (number)result; |
---|
508 | } |
---|
509 | |
---|
510 | |
---|
511 | number ntInit(long i, const coeffs cf) |
---|
512 | { |
---|
513 | if (i != 0) |
---|
514 | { |
---|
515 | poly p=p_ISet(i, ntRing); |
---|
516 | if (p!=NULL) |
---|
517 | { |
---|
518 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
519 | NUM(result) = p; |
---|
520 | //DEN(result) = NULL; // done by omAlloc0Bin |
---|
521 | //COM(result) = 0; // done by omAlloc0Bin |
---|
522 | ntTest((number)result); |
---|
523 | return (number)result; |
---|
524 | } |
---|
525 | } |
---|
526 | return NULL; |
---|
527 | } |
---|
528 | |
---|
529 | |
---|
530 | /// takes over p! |
---|
531 | number ntInit(poly p, const coeffs cf) |
---|
532 | { |
---|
533 | if (p == NULL) return NULL; |
---|
534 | |
---|
535 | number g; |
---|
536 | // TODO/NOTE: the following should not be necessary (due to |
---|
537 | // Hannes!) as NUM (f) should be over Z!!! |
---|
538 | CPolyCoeffsEnumerator itr(p); |
---|
539 | |
---|
540 | n_ClearDenominators(itr, g, ntRing->cf); |
---|
541 | |
---|
542 | if( !n_GreaterZero(g, ntRing->cf) ) |
---|
543 | { |
---|
544 | p = p_Neg(p, ntRing); // Ugly :((( |
---|
545 | g = n_Neg(g, ntRing->cf); |
---|
546 | } |
---|
547 | |
---|
548 | // g should be a positive integer now! |
---|
549 | assume( n_GreaterZero(g, ntRing->cf) ); |
---|
550 | |
---|
551 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
552 | |
---|
553 | if( !n_IsOne(g, ntRing->cf) ) |
---|
554 | { |
---|
555 | DEN (f) = p_NSet(g, ntRing); |
---|
556 | // COM (f) ++; // update COM(f)??? |
---|
557 | assume( DEN (f) != NULL ); |
---|
558 | } |
---|
559 | else |
---|
560 | { |
---|
561 | DEN(f) = NULL; |
---|
562 | n_Delete(&g, ntRing->cf); |
---|
563 | } |
---|
564 | |
---|
565 | NUM(f) = p; |
---|
566 | COM(f) = 0; |
---|
567 | |
---|
568 | ntTest((number)f); |
---|
569 | return (number)f; |
---|
570 | } |
---|
571 | |
---|
572 | int ntInt(number &a, const coeffs cf) |
---|
573 | { |
---|
574 | ntTest(a); |
---|
575 | if (IS0(a)) return 0; |
---|
576 | definiteGcdCancellation(a, cf, FALSE); |
---|
577 | fraction f = (fraction)a; |
---|
578 | if (!DENIS1(f)) return 0; |
---|
579 | |
---|
580 | const poly aAsPoly = NUM(f); |
---|
581 | |
---|
582 | if(aAsPoly == NULL) |
---|
583 | return 0; |
---|
584 | |
---|
585 | if (!p_IsConstant(aAsPoly, ntRing)) |
---|
586 | return 0; |
---|
587 | |
---|
588 | assume( aAsPoly != NULL ); |
---|
589 | |
---|
590 | return n_Int(p_GetCoeff(aAsPoly, ntRing), ntCoeffs); |
---|
591 | } |
---|
592 | |
---|
593 | /* This method will only consider the numerators of a and b, without |
---|
594 | cancelling gcd's before. |
---|
595 | Moreover it may return TRUE only if one or both numerators |
---|
596 | are zero or if their degrees are equal. Then TRUE is returned iff |
---|
597 | coeff(numerator(a)) > coeff(numerator(b)); |
---|
598 | In all other cases, FALSE will be returned. */ |
---|
599 | BOOLEAN ntGreater(number a, number b, const coeffs cf) |
---|
600 | { |
---|
601 | ntTest(a); |
---|
602 | ntTest(b); |
---|
603 | number aNumCoeff = NULL; int aNumDeg = -1; |
---|
604 | number aDenCoeff = NULL; int aDenDeg = -1; |
---|
605 | number bNumCoeff = NULL; int bNumDeg = -1; |
---|
606 | number bDenCoeff = NULL; int bDenDeg = -1; |
---|
607 | if (!IS0(a)) |
---|
608 | { |
---|
609 | fraction fa = (fraction)a; |
---|
610 | aNumDeg = p_Totaldegree(NUM(fa), ntRing); |
---|
611 | aNumCoeff = p_GetCoeff(NUM(fa), ntRing); |
---|
612 | if (DEN(fa)!=NULL) |
---|
613 | { |
---|
614 | aDenDeg = p_Totaldegree(DEN(fa), ntRing); |
---|
615 | aDenCoeff=p_GetCoeff(DEN(fa),ntRing); |
---|
616 | } |
---|
617 | } |
---|
618 | else return !(ntGreaterZero (b,cf)); |
---|
619 | if (!IS0(b)) |
---|
620 | { |
---|
621 | fraction fb = (fraction)b; |
---|
622 | bNumDeg = p_Totaldegree(NUM(fb), ntRing); |
---|
623 | bNumCoeff = p_GetCoeff(NUM(fb), ntRing); |
---|
624 | if (DEN(fb)!=NULL) |
---|
625 | { |
---|
626 | bDenDeg = p_Totaldegree(DEN(fb), ntRing); |
---|
627 | bDenCoeff=p_GetCoeff(DEN(fb),ntRing); |
---|
628 | } |
---|
629 | } |
---|
630 | else return ntGreaterZero(a,cf); |
---|
631 | if (aNumDeg-aDenDeg > bNumDeg-bDenDeg) return TRUE; |
---|
632 | if (aNumDeg-aDenDeg < bNumDeg-bDenDeg) return FALSE; |
---|
633 | number aa; |
---|
634 | number bb; |
---|
635 | if (bDenCoeff==NULL) aa=n_Copy(aNumCoeff,ntRing->cf); |
---|
636 | else aa=n_Mult(aNumCoeff,bDenCoeff,ntRing->cf); |
---|
637 | if (aDenCoeff==NULL) bb=n_Copy(bNumCoeff,ntRing->cf); |
---|
638 | else bb=n_Mult(bNumCoeff,aDenCoeff,ntRing->cf); |
---|
639 | BOOLEAN rr= n_Greater(aa, bb, ntCoeffs); |
---|
640 | n_Delete(&aa,ntRing->cf); |
---|
641 | n_Delete(&bb,ntRing->cf); |
---|
642 | return rr; |
---|
643 | } |
---|
644 | |
---|
645 | /* this method will only consider the numerator of a, without cancelling |
---|
646 | the gcd before; |
---|
647 | returns TRUE iff the leading coefficient of the numerator of a is > 0 |
---|
648 | or the leading term of the numerator of a is not a |
---|
649 | constant */ |
---|
650 | BOOLEAN ntGreaterZero(number a, const coeffs cf) |
---|
651 | { |
---|
652 | ntTest(a); |
---|
653 | if (IS0(a)) return FALSE; |
---|
654 | fraction f = (fraction)a; |
---|
655 | poly g = NUM(f); |
---|
656 | return (n_GreaterZero(p_GetCoeff(g, ntRing), ntCoeffs) || |
---|
657 | (!p_LmIsConstant(g, ntRing))); |
---|
658 | } |
---|
659 | |
---|
660 | void ntCoeffWrite(const coeffs cf, BOOLEAN details) |
---|
661 | { |
---|
662 | assume( cf != NULL ); |
---|
663 | |
---|
664 | const ring A = cf->extRing; |
---|
665 | |
---|
666 | assume( A != NULL ); |
---|
667 | assume( A->cf != NULL ); |
---|
668 | |
---|
669 | n_CoeffWrite(A->cf, details); |
---|
670 | |
---|
671 | // rWrite(A); |
---|
672 | |
---|
673 | const int P = rVar(A); |
---|
674 | assume( P > 0 ); |
---|
675 | |
---|
676 | Print("// %d parameter : ", P); |
---|
677 | |
---|
678 | for (int nop=0; nop < P; nop ++) |
---|
679 | Print("%s ", rRingVar(nop, A)); |
---|
680 | |
---|
681 | assume( A->qideal == NULL ); |
---|
682 | |
---|
683 | PrintS("\n// minpoly : 0\n"); |
---|
684 | |
---|
685 | /* |
---|
686 | PrintS("// Coefficients live in the rational function field\n"); |
---|
687 | Print("// K("); |
---|
688 | for (int i = 0; i < rVar(ntRing); i++) |
---|
689 | { |
---|
690 | if (i > 0) PrintS(" "); |
---|
691 | Print("%s", rRingVar(i, ntRing)); |
---|
692 | } |
---|
693 | PrintS(") with\n"); |
---|
694 | PrintS("// K: "); n_CoeffWrite(cf->extRing->cf); |
---|
695 | */ |
---|
696 | } |
---|
697 | |
---|
698 | number ntAdd(number a, number b, const coeffs cf) |
---|
699 | { |
---|
700 | ntTest(a); |
---|
701 | ntTest(b); |
---|
702 | if (IS0(a)) return ntCopy(b, cf); |
---|
703 | if (IS0(b)) return ntCopy(a, cf); |
---|
704 | |
---|
705 | fraction fa = (fraction)a; |
---|
706 | fraction fb = (fraction)b; |
---|
707 | |
---|
708 | poly g = p_Copy(NUM(fa), ntRing); |
---|
709 | if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing); |
---|
710 | poly h = p_Copy(NUM(fb), ntRing); |
---|
711 | if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing); |
---|
712 | g = p_Add_q(g, h, ntRing); |
---|
713 | |
---|
714 | if (g == NULL) return NULL; |
---|
715 | |
---|
716 | poly f; |
---|
717 | if (DENIS1(fa) && DENIS1(fb)) f = NULL; |
---|
718 | else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing); |
---|
719 | else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing); |
---|
720 | else /* both denom's are != 1 */ f = p_Mult_q(p_Copy(DEN(fa), ntRing), |
---|
721 | p_Copy(DEN(fb), ntRing), |
---|
722 | ntRing); |
---|
723 | |
---|
724 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
725 | NUM(result) = g; |
---|
726 | DEN(result) = f; |
---|
727 | COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY; |
---|
728 | heuristicGcdCancellation((number)result, cf); |
---|
729 | |
---|
730 | // ntTest((number)result); |
---|
731 | |
---|
732 | return (number)result; |
---|
733 | } |
---|
734 | |
---|
735 | number ntSub(number a, number b, const coeffs cf) |
---|
736 | { |
---|
737 | ntTest(a); |
---|
738 | ntTest(b); |
---|
739 | if (IS0(a)) return ntNeg(ntCopy(b, cf), cf); |
---|
740 | if (IS0(b)) return ntCopy(a, cf); |
---|
741 | |
---|
742 | fraction fa = (fraction)a; |
---|
743 | fraction fb = (fraction)b; |
---|
744 | |
---|
745 | poly g = p_Copy(NUM(fa), ntRing); |
---|
746 | if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing); |
---|
747 | poly h = p_Copy(NUM(fb), ntRing); |
---|
748 | if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing); |
---|
749 | g = p_Add_q(g, p_Neg(h, ntRing), ntRing); |
---|
750 | |
---|
751 | if (g == NULL) return NULL; |
---|
752 | |
---|
753 | poly f; |
---|
754 | if (DENIS1(fa) && DENIS1(fb)) f = NULL; |
---|
755 | else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing); |
---|
756 | else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing); |
---|
757 | else /* both den's are != 1 */ f = p_Mult_q(p_Copy(DEN(fa), ntRing), |
---|
758 | p_Copy(DEN(fb), ntRing), |
---|
759 | ntRing); |
---|
760 | |
---|
761 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
762 | NUM(result) = g; |
---|
763 | DEN(result) = f; |
---|
764 | COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY; |
---|
765 | heuristicGcdCancellation((number)result, cf); |
---|
766 | // ntTest((number)result); |
---|
767 | return (number)result; |
---|
768 | } |
---|
769 | |
---|
770 | number ntMult(number a, number b, const coeffs cf) |
---|
771 | { |
---|
772 | ntTest(a); // !!!? |
---|
773 | ntTest(b); // !!!? |
---|
774 | |
---|
775 | if (IS0(a) || IS0(b)) return NULL; |
---|
776 | |
---|
777 | fraction fa = (fraction)a; |
---|
778 | fraction fb = (fraction)b; |
---|
779 | |
---|
780 | const poly g = pp_Mult_qq(NUM(fa), NUM(fb), ntRing); |
---|
781 | |
---|
782 | if (g == NULL) return NULL; // may happen due to zero divisors??? |
---|
783 | |
---|
784 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
785 | |
---|
786 | NUM(result) = g; |
---|
787 | |
---|
788 | const poly da = DEN(fa); |
---|
789 | const poly db = DEN(fb); |
---|
790 | |
---|
791 | |
---|
792 | if (db == NULL) |
---|
793 | { |
---|
794 | // b = ? // NULL |
---|
795 | |
---|
796 | if(da == NULL) |
---|
797 | { // both fa && fb are ?? // NULL! |
---|
798 | assume (da == NULL && db == NULL); |
---|
799 | DEN(result) = NULL; |
---|
800 | COM(result) = 0; |
---|
801 | } |
---|
802 | else |
---|
803 | { |
---|
804 | assume (da != NULL && db == NULL); |
---|
805 | DEN(result) = p_Copy(da, ntRing); |
---|
806 | COM(result) = COM(fa) + MULT_COMPLEXITY; |
---|
807 | heuristicGcdCancellation((number)result, cf); |
---|
808 | } |
---|
809 | } else |
---|
810 | { // b = ?? / ?? |
---|
811 | if (da == NULL) |
---|
812 | { // a == ? // NULL |
---|
813 | assume( db != NULL && da == NULL); |
---|
814 | DEN(result) = p_Copy(db, ntRing); |
---|
815 | COM(result) = COM(fb) + MULT_COMPLEXITY; |
---|
816 | heuristicGcdCancellation((number)result, cf); |
---|
817 | } |
---|
818 | else /* both den's are != 1 */ |
---|
819 | { |
---|
820 | assume (da != NULL && db != NULL); |
---|
821 | DEN(result) = pp_Mult_qq(da, db, ntRing); |
---|
822 | COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY; |
---|
823 | heuristicGcdCancellation((number)result, cf); |
---|
824 | } |
---|
825 | } |
---|
826 | |
---|
827 | // ntTest((number)result); |
---|
828 | |
---|
829 | return (number)result; |
---|
830 | } |
---|
831 | |
---|
832 | number ntDiv(number a, number b, const coeffs cf) |
---|
833 | { |
---|
834 | ntTest(a); |
---|
835 | ntTest(b); |
---|
836 | if (IS0(a)) return NULL; |
---|
837 | if (IS0(b)) WerrorS(nDivBy0); |
---|
838 | |
---|
839 | fraction fa = (fraction)a; |
---|
840 | fraction fb = (fraction)b; |
---|
841 | |
---|
842 | poly g = p_Copy(NUM(fa), ntRing); |
---|
843 | if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing); |
---|
844 | |
---|
845 | if (g == NULL) return NULL; /* may happen due to zero divisors */ |
---|
846 | |
---|
847 | poly f = p_Copy(NUM(fb), ntRing); |
---|
848 | if (!DENIS1(fa)) f = p_Mult_q(f, p_Copy(DEN(fa), ntRing), ntRing); |
---|
849 | |
---|
850 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
851 | NUM(result) = g; |
---|
852 | if (!n_GreaterZero(pGetCoeff(f),ntRing->cf)) |
---|
853 | { |
---|
854 | g=p_Neg(g,ntRing); |
---|
855 | f=p_Neg(f,ntRing); |
---|
856 | NUM(result) = g; |
---|
857 | } |
---|
858 | if (!p_IsConstant(f,ntRing) || !n_IsOne(pGetCoeff(f),ntRing->cf)) |
---|
859 | { |
---|
860 | DEN(result) = f; |
---|
861 | } |
---|
862 | COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY; |
---|
863 | heuristicGcdCancellation((number)result, cf); |
---|
864 | // ntTest((number)result); |
---|
865 | return (number)result; |
---|
866 | } |
---|
867 | |
---|
868 | /* 0^0 = 0; |
---|
869 | for |exp| <= 7 compute power by a simple multiplication loop; |
---|
870 | for |exp| >= 8 compute power along binary presentation of |exp|, e.g. |
---|
871 | p^13 = p^1 * p^4 * p^8, where we utilise that |
---|
872 | p^(2^(k+1)) = p^(2^k) * p^(2^k); |
---|
873 | intermediate cancellation is controlled by the in-place method |
---|
874 | heuristicGcdCancellation; see there. |
---|
875 | */ |
---|
876 | void ntPower(number a, int exp, number *b, const coeffs cf) |
---|
877 | { |
---|
878 | ntTest(a); |
---|
879 | |
---|
880 | /* special cases first */ |
---|
881 | if (IS0(a)) |
---|
882 | { |
---|
883 | if (exp >= 0) *b = NULL; |
---|
884 | else WerrorS(nDivBy0); |
---|
885 | } |
---|
886 | else if (exp == 0) { *b = ntInit(1, cf); return;} |
---|
887 | else if (exp == 1) { *b = ntCopy(a, cf); return;} |
---|
888 | else if (exp == -1) { *b = ntInvers(a, cf); return;} |
---|
889 | |
---|
890 | int expAbs = exp; if (expAbs < 0) expAbs = -expAbs; |
---|
891 | |
---|
892 | /* now compute a^expAbs */ |
---|
893 | number pow; number t; |
---|
894 | if (expAbs <= 7) |
---|
895 | { |
---|
896 | pow = ntCopy(a, cf); |
---|
897 | for (int i = 2; i <= expAbs; i++) |
---|
898 | { |
---|
899 | t = ntMult(pow, a, cf); |
---|
900 | ntDelete(&pow, cf); |
---|
901 | pow = t; |
---|
902 | heuristicGcdCancellation(pow, cf); |
---|
903 | } |
---|
904 | } |
---|
905 | else |
---|
906 | { |
---|
907 | pow = ntInit(1, cf); |
---|
908 | number factor = ntCopy(a, cf); |
---|
909 | while (expAbs != 0) |
---|
910 | { |
---|
911 | if (expAbs & 1) |
---|
912 | { |
---|
913 | t = ntMult(pow, factor, cf); |
---|
914 | ntDelete(&pow, cf); |
---|
915 | pow = t; |
---|
916 | heuristicGcdCancellation(pow, cf); |
---|
917 | } |
---|
918 | expAbs = expAbs / 2; |
---|
919 | if (expAbs != 0) |
---|
920 | { |
---|
921 | t = ntMult(factor, factor, cf); |
---|
922 | ntDelete(&factor, cf); |
---|
923 | factor = t; |
---|
924 | heuristicGcdCancellation(factor, cf); |
---|
925 | } |
---|
926 | } |
---|
927 | ntDelete(&factor, cf); |
---|
928 | } |
---|
929 | |
---|
930 | /* invert if original exponent was negative */ |
---|
931 | if (exp < 0) |
---|
932 | { |
---|
933 | t = ntInvers(pow, cf); |
---|
934 | ntDelete(&pow, cf); |
---|
935 | pow = t; |
---|
936 | } |
---|
937 | *b = pow; |
---|
938 | ntTest(*b); |
---|
939 | } |
---|
940 | |
---|
941 | /* assumes that cf represents the rationals, i.e. Q, and will only |
---|
942 | be called in that case; |
---|
943 | assumes furthermore that f != NULL and that the denominator of f != 1; |
---|
944 | generally speaking, this method removes denominators in the rational |
---|
945 | coefficients of the numerator and denominator of 'a'; |
---|
946 | more concretely, the following normalizations will be performed, |
---|
947 | where t^alpha denotes a monomial in the transcendental variables t_k |
---|
948 | (1) if 'a' is of the form |
---|
949 | (sum_alpha a_alpha/b_alpha * t^alpha) |
---|
950 | ------------------------------------- |
---|
951 | (sum_beta c_beta/d_beta * t^beta) |
---|
952 | with integers a_alpha, b_alpha, c_beta, d_beta, then both the |
---|
953 | numerator and the denominator will be multiplied by the LCM of |
---|
954 | the b_alpha's and the d_beta's (if this LCM is != 1), |
---|
955 | (2) if 'a' is - e.g. after having performed step (1) - of the form |
---|
956 | (sum_alpha a_alpha * t^alpha) |
---|
957 | ----------------------------- |
---|
958 | (sum_beta c_beta * t^beta) |
---|
959 | with integers a_alpha, c_beta, and with a non-constant denominator, |
---|
960 | then both the numerator and the denominator will be divided by the |
---|
961 | GCD of the a_alpha's and the c_beta's (if this GCD is != 1), |
---|
962 | (3) if 'a' is - e.g. after having performed steps (1) and (2) - of the |
---|
963 | form |
---|
964 | (sum_alpha a_alpha * t^alpha) |
---|
965 | ----------------------------- |
---|
966 | c |
---|
967 | with integers a_alpha, and c != 1, then 'a' will be replaced by |
---|
968 | (sum_alpha a_alpha/c * t^alpha); |
---|
969 | this procedure does not alter COM(f) (this has to be done by the |
---|
970 | calling procedure); |
---|
971 | modifies f */ |
---|
972 | void handleNestedFractionsOverQ(fraction f, const coeffs cf) |
---|
973 | { |
---|
974 | assume(nCoeff_is_Q(ntCoeffs)); |
---|
975 | assume(!IS0(f)); |
---|
976 | assume(!DENIS1(f)); |
---|
977 | |
---|
978 | if (!p_IsConstant(DEN(f), ntRing)) |
---|
979 | { /* step (1); see documentation of this procedure above */ |
---|
980 | p_Normalize(NUM(f), ntRing); |
---|
981 | p_Normalize(DEN(f), ntRing); |
---|
982 | number lcmOfDenominators = n_Init(1, ntCoeffs); |
---|
983 | number c; number tmp; |
---|
984 | poly p = NUM(f); |
---|
985 | /* careful when using n_Lcm!!! It computes the lcm of the numerator |
---|
986 | of the 1st argument and the denominator of the 2nd!!! */ |
---|
987 | while (p != NULL) |
---|
988 | { |
---|
989 | c = p_GetCoeff(p, ntRing); |
---|
990 | tmp = n_Lcm(lcmOfDenominators, c, ntCoeffs); |
---|
991 | n_Delete(&lcmOfDenominators, ntCoeffs); |
---|
992 | lcmOfDenominators = tmp; |
---|
993 | pIter(p); |
---|
994 | } |
---|
995 | p = DEN(f); |
---|
996 | while (p != NULL) |
---|
997 | { |
---|
998 | c = p_GetCoeff(p, ntRing); |
---|
999 | tmp = n_Lcm(lcmOfDenominators, c, ntCoeffs); |
---|
1000 | n_Delete(&lcmOfDenominators, ntCoeffs); |
---|
1001 | lcmOfDenominators = tmp; |
---|
1002 | pIter(p); |
---|
1003 | } |
---|
1004 | if (!n_IsOne(lcmOfDenominators, ntCoeffs)) |
---|
1005 | { /* multiply NUM(f) and DEN(f) with lcmOfDenominators */ |
---|
1006 | NUM(f) = p_Mult_nn(NUM(f), lcmOfDenominators, ntRing); |
---|
1007 | p_Normalize(NUM(f), ntRing); |
---|
1008 | DEN(f) = p_Mult_nn(DEN(f), lcmOfDenominators, ntRing); |
---|
1009 | p_Normalize(DEN(f), ntRing); |
---|
1010 | } |
---|
1011 | n_Delete(&lcmOfDenominators, ntCoeffs); |
---|
1012 | if (!p_IsConstant(DEN(f), ntRing)) |
---|
1013 | { /* step (2); see documentation of this procedure above */ |
---|
1014 | p = NUM(f); |
---|
1015 | number gcdOfCoefficients = n_Copy(p_GetCoeff(p, ntRing), ntCoeffs); |
---|
1016 | pIter(p); |
---|
1017 | while ((p != NULL) && (!n_IsOne(gcdOfCoefficients, ntCoeffs))) |
---|
1018 | { |
---|
1019 | c = p_GetCoeff(p, ntRing); |
---|
1020 | tmp = n_Gcd(c, gcdOfCoefficients, ntCoeffs); |
---|
1021 | n_Delete(&gcdOfCoefficients, ntCoeffs); |
---|
1022 | gcdOfCoefficients = tmp; |
---|
1023 | pIter(p); |
---|
1024 | } |
---|
1025 | p = DEN(f); |
---|
1026 | while ((p != NULL) && (!n_IsOne(gcdOfCoefficients, ntCoeffs))) |
---|
1027 | { |
---|
1028 | c = p_GetCoeff(p, ntRing); |
---|
1029 | tmp = n_Gcd(c, gcdOfCoefficients, ntCoeffs); |
---|
1030 | n_Delete(&gcdOfCoefficients, ntCoeffs); |
---|
1031 | gcdOfCoefficients = tmp; |
---|
1032 | pIter(p); |
---|
1033 | } |
---|
1034 | if (!n_IsOne(gcdOfCoefficients, ntCoeffs)) |
---|
1035 | { /* divide NUM(f) and DEN(f) by gcdOfCoefficients */ |
---|
1036 | number inverseOfGcdOfCoefficients = n_Invers(gcdOfCoefficients, |
---|
1037 | ntCoeffs); |
---|
1038 | NUM(f) = p_Mult_nn(NUM(f), inverseOfGcdOfCoefficients, ntRing); |
---|
1039 | p_Normalize(NUM(f), ntRing); |
---|
1040 | DEN(f) = p_Mult_nn(DEN(f), inverseOfGcdOfCoefficients, ntRing); |
---|
1041 | p_Normalize(DEN(f), ntRing); |
---|
1042 | n_Delete(&inverseOfGcdOfCoefficients, ntCoeffs); |
---|
1043 | } |
---|
1044 | n_Delete(&gcdOfCoefficients, ntCoeffs); |
---|
1045 | } |
---|
1046 | } |
---|
1047 | if (p_IsConstant(DEN(f), ntRing) && |
---|
1048 | (!n_IsOne(p_GetCoeff(DEN(f), ntRing), ntCoeffs))) |
---|
1049 | { /* step (3); see documentation of this procedure above */ |
---|
1050 | number inverseOfDen = n_Invers(p_GetCoeff(DEN(f), ntRing), ntCoeffs); |
---|
1051 | NUM(f) = p_Mult_nn(NUM(f), inverseOfDen, ntRing); |
---|
1052 | n_Delete(&inverseOfDen, ntCoeffs); |
---|
1053 | p_Delete(&DEN(f), ntRing); |
---|
1054 | DEN(f) = NULL; |
---|
1055 | } |
---|
1056 | |
---|
1057 | /* Now, due to the above computations, DEN(f) may have become the |
---|
1058 | 1-polynomial which needs to be represented by NULL: */ |
---|
1059 | if ((DEN(f) != NULL) && |
---|
1060 | p_IsConstant(DEN(f), ntRing) && |
---|
1061 | n_IsOne(p_GetCoeff(DEN(f), ntRing), ntCoeffs)) |
---|
1062 | { |
---|
1063 | p_Delete(&DEN(f), ntRing); DEN(f) = NULL; |
---|
1064 | } |
---|
1065 | |
---|
1066 | if( DEN(f) != NULL ) |
---|
1067 | if( !n_GreaterZero(pGetCoeff(DEN(f)), ntCoeffs) ) |
---|
1068 | { |
---|
1069 | NUM(f) = p_Neg(NUM(f), ntRing); |
---|
1070 | DEN(f) = p_Neg(DEN(f), ntRing); |
---|
1071 | } |
---|
1072 | |
---|
1073 | ntTest((number)f); // TODO! |
---|
1074 | } |
---|
1075 | |
---|
1076 | /* modifies a */ |
---|
1077 | void heuristicGcdCancellation(number a, const coeffs cf) |
---|
1078 | { |
---|
1079 | // ntTest(a); // !!!!???? |
---|
1080 | if (IS0(a)) return; |
---|
1081 | |
---|
1082 | fraction f = (fraction)a; |
---|
1083 | if (DENIS1(f) || NUMIS1(f)) { COM(f) = 0; ntTest(a); return; } |
---|
1084 | |
---|
1085 | assume( DEN(f) != NULL ); |
---|
1086 | |
---|
1087 | /* check whether NUM(f) = DEN(f), and - if so - replace 'a' by 1 */ |
---|
1088 | if (p_EqualPolys(NUM(f), DEN(f), ntRing)) |
---|
1089 | { /* numerator and denominator are both != 1 */ |
---|
1090 | p_Delete(&NUM(f), ntRing); NUM(f) = p_ISet(1, ntRing); |
---|
1091 | p_Delete(&DEN(f), ntRing); DEN(f) = NULL; |
---|
1092 | COM(f) = 0; |
---|
1093 | } else |
---|
1094 | { |
---|
1095 | if (COM(f) > BOUND_COMPLEXITY) |
---|
1096 | definiteGcdCancellation(a, cf, TRUE); |
---|
1097 | |
---|
1098 | // TODO: check if it is enough to put the following into definiteGcdCancellation?! |
---|
1099 | if( DEN(f) != NULL ) |
---|
1100 | if( !n_GreaterZero(pGetCoeff(DEN(f)), ntCoeffs) ) |
---|
1101 | { |
---|
1102 | NUM(f) = p_Neg(NUM(f), ntRing); |
---|
1103 | DEN(f) = p_Neg(DEN(f), ntRing); |
---|
1104 | } |
---|
1105 | } |
---|
1106 | |
---|
1107 | |
---|
1108 | ntTest(a); // !!!!???? |
---|
1109 | } |
---|
1110 | |
---|
1111 | /// modifies a |
---|
1112 | void definiteGcdCancellation(number a, const coeffs cf, |
---|
1113 | BOOLEAN simpleTestsHaveAlreadyBeenPerformed) |
---|
1114 | { |
---|
1115 | ntTest(a); // !!!! |
---|
1116 | |
---|
1117 | fraction f = (fraction)a; |
---|
1118 | |
---|
1119 | if (!simpleTestsHaveAlreadyBeenPerformed) |
---|
1120 | { |
---|
1121 | if (IS0(a)) return; |
---|
1122 | if (DENIS1(f) || NUMIS1(f)) { COM(f) = 0; return; } |
---|
1123 | |
---|
1124 | /* check whether NUM(f) = DEN(f), and - if so - replace 'a' by 1 */ |
---|
1125 | if (p_EqualPolys(NUM(f), DEN(f), ntRing)) |
---|
1126 | { /* numerator and denominator are both != 1 */ |
---|
1127 | p_Delete(&NUM(f), ntRing); NUM(f) = p_ISet(1, ntRing); |
---|
1128 | p_Delete(&DEN(f), ntRing); DEN(f) = NULL; |
---|
1129 | COM(f) = 0; |
---|
1130 | ntTest(a); // !!!! |
---|
1131 | return; |
---|
1132 | } |
---|
1133 | } |
---|
1134 | |
---|
1135 | #ifdef HAVE_FACTORY |
---|
1136 | /* Note that, over Q, singclap_gcd will remove the denominators in all |
---|
1137 | rational coefficients of pNum and pDen, before starting to compute |
---|
1138 | the gcd. Thus, we do not need to ensure that the coefficients of |
---|
1139 | pNum and pDen live in Z; they may well be elements of Q\Z. */ |
---|
1140 | /* singclap_gcd destroys its arguments; we hence need copies: */ |
---|
1141 | poly pGcd = singclap_gcd(p_Copy(NUM(f), ntRing), p_Copy(DEN(f), ntRing), cf->extRing); |
---|
1142 | if (p_IsConstant(pGcd, ntRing) && |
---|
1143 | n_IsOne(p_GetCoeff(pGcd, ntRing), ntCoeffs)) |
---|
1144 | { /* gcd = 1; nothing to cancel; |
---|
1145 | Suppose the given rational function field is over Q. Although the |
---|
1146 | gcd is 1, we may have produced fractional coefficients in NUM(f), |
---|
1147 | DEN(f), or both, due to previous arithmetics. The next call will |
---|
1148 | remove those nested fractions, in case there are any. */ |
---|
1149 | if (nCoeff_is_Zp(ntCoeffs) && p_IsConstant (DEN (f), ntRing)) |
---|
1150 | { |
---|
1151 | NUM (f) = p_Div_nn (NUM (f), p_GetCoeff (DEN(f),ntRing), ntRing); |
---|
1152 | //poly newNum= singclap_pdivide (NUM(f), DEN (f), ntRing); |
---|
1153 | //p_Delete(&NUM (f), ntRing); |
---|
1154 | //NUM (f)= newNum; |
---|
1155 | p_Delete(&DEN (f), ntRing); |
---|
1156 | DEN (f) = NULL; |
---|
1157 | COM (f) = 0; |
---|
1158 | } else if (nCoeff_is_Q(ntCoeffs)) handleNestedFractionsOverQ(f, cf); |
---|
1159 | } |
---|
1160 | else |
---|
1161 | { /* We divide both NUM(f) and DEN(f) by the gcd which is known |
---|
1162 | to be != 1. */ |
---|
1163 | poly newNum = singclap_pdivide(NUM(f), pGcd, ntRing); |
---|
1164 | p_Delete(&NUM(f), ntRing); |
---|
1165 | NUM(f) = newNum; |
---|
1166 | poly newDen = singclap_pdivide(DEN(f), pGcd, ntRing); |
---|
1167 | p_Delete(&DEN(f), ntRing); |
---|
1168 | DEN(f) = newDen; |
---|
1169 | if (p_IsConstant(DEN(f), ntRing) && |
---|
1170 | n_IsOne(p_GetCoeff(DEN(f), ntRing), ntCoeffs)) |
---|
1171 | { |
---|
1172 | /* DEN(f) = 1 needs to be represented by NULL! */ |
---|
1173 | p_Delete(&DEN(f), ntRing); |
---|
1174 | newDen = NULL; |
---|
1175 | } |
---|
1176 | else |
---|
1177 | { /* Note that over Q, by cancelling the gcd, we may have produced |
---|
1178 | fractional coefficients in NUM(f), DEN(f), or both. The next |
---|
1179 | call will remove those nested fractions, in case there are |
---|
1180 | any. */ |
---|
1181 | if (nCoeff_is_Q(ntCoeffs)) handleNestedFractionsOverQ(f, cf); |
---|
1182 | } |
---|
1183 | } |
---|
1184 | COM(f) = 0; |
---|
1185 | p_Delete(&pGcd, ntRing); |
---|
1186 | |
---|
1187 | if( DEN(f) != NULL ) |
---|
1188 | if( !n_GreaterZero(pGetCoeff(DEN(f)), ntCoeffs) ) |
---|
1189 | { |
---|
1190 | NUM(f) = p_Neg(NUM(f), ntRing); |
---|
1191 | DEN(f) = p_Neg(DEN(f), ntRing); |
---|
1192 | } |
---|
1193 | #endif /* HAVE_FACTORY */ |
---|
1194 | |
---|
1195 | ntTest(a); // !!!! |
---|
1196 | } |
---|
1197 | |
---|
1198 | // NOTE: modifies a |
---|
1199 | void ntWriteLong(number &a, const coeffs cf) |
---|
1200 | { |
---|
1201 | ntTest(a); |
---|
1202 | definiteGcdCancellation(a, cf, FALSE); |
---|
1203 | if (IS0(a)) |
---|
1204 | StringAppendS("0"); |
---|
1205 | else |
---|
1206 | { |
---|
1207 | fraction f = (fraction)a; |
---|
1208 | // stole logic from napWrite from kernel/longtrans.cc of legacy singular |
---|
1209 | BOOLEAN omitBrackets = p_IsConstant(NUM(f), ntRing); |
---|
1210 | if (!omitBrackets) StringAppendS("("); |
---|
1211 | p_String0Long(NUM(f), ntRing, ntRing); |
---|
1212 | if (!omitBrackets) StringAppendS(")"); |
---|
1213 | if (!DENIS1(f)) |
---|
1214 | { |
---|
1215 | StringAppendS("/"); |
---|
1216 | omitBrackets = p_IsConstant(DEN(f), ntRing); |
---|
1217 | if (!omitBrackets) StringAppendS("("); |
---|
1218 | p_String0Long(DEN(f), ntRing, ntRing); |
---|
1219 | if (!omitBrackets) StringAppendS(")"); |
---|
1220 | } |
---|
1221 | } |
---|
1222 | ntTest(a); // !!!! |
---|
1223 | } |
---|
1224 | |
---|
1225 | // NOTE: modifies a |
---|
1226 | void ntWriteShort(number &a, const coeffs cf) |
---|
1227 | { |
---|
1228 | ntTest(a); |
---|
1229 | definiteGcdCancellation(a, cf, FALSE); |
---|
1230 | if (IS0(a)) |
---|
1231 | StringAppendS("0"); |
---|
1232 | else |
---|
1233 | { |
---|
1234 | fraction f = (fraction)a; |
---|
1235 | // stole logic from napWrite from kernel/longtrans.cc of legacy singular |
---|
1236 | BOOLEAN omitBrackets = p_IsConstant(NUM(f), ntRing); |
---|
1237 | if (!omitBrackets) StringAppendS("("); |
---|
1238 | p_String0Short(NUM(f), ntRing, ntRing); |
---|
1239 | if (!omitBrackets) StringAppendS(")"); |
---|
1240 | if (!DENIS1(f)) |
---|
1241 | { |
---|
1242 | StringAppendS("/"); |
---|
1243 | omitBrackets = p_IsConstant(DEN(f), ntRing); |
---|
1244 | if (!omitBrackets) StringAppendS("("); |
---|
1245 | p_String0Short(DEN(f), ntRing, ntRing); |
---|
1246 | if (!omitBrackets) StringAppendS(")"); |
---|
1247 | } |
---|
1248 | } |
---|
1249 | ntTest(a); |
---|
1250 | } |
---|
1251 | |
---|
1252 | const char * ntRead(const char *s, number *a, const coeffs cf) |
---|
1253 | { |
---|
1254 | poly p; |
---|
1255 | const char * result = p_Read(s, p, ntRing); |
---|
1256 | if (p == NULL) *a = NULL; |
---|
1257 | else *a = ntInit(p, cf); |
---|
1258 | return result; |
---|
1259 | } |
---|
1260 | |
---|
1261 | void ntNormalize (number &a, const coeffs cf) |
---|
1262 | { |
---|
1263 | if ((a!=NULL)) |
---|
1264 | { |
---|
1265 | definiteGcdCancellation(a, cf, FALSE); |
---|
1266 | if ((DEN(a)!=NULL) |
---|
1267 | &&(!n_GreaterZero(pGetCoeff(DEN(a)),ntRing->cf))) |
---|
1268 | { |
---|
1269 | NUM(a)=p_Neg(NUM(a),ntRing); |
---|
1270 | DEN(a)=p_Neg(DEN(a),ntRing); |
---|
1271 | } |
---|
1272 | } |
---|
1273 | ntTest(a); // !!!! |
---|
1274 | } |
---|
1275 | |
---|
1276 | /* expects *param to be castable to TransExtInfo */ |
---|
1277 | static BOOLEAN ntCoeffIsEqual(const coeffs cf, n_coeffType n, void * param) |
---|
1278 | { |
---|
1279 | if (ID != n) return FALSE; |
---|
1280 | TransExtInfo *e = (TransExtInfo *)param; |
---|
1281 | /* for rational function fields we expect the underlying |
---|
1282 | polynomial rings to be IDENTICAL, i.e. the SAME OBJECT; |
---|
1283 | this expectation is based on the assumption that we have properly |
---|
1284 | registered cf and perform reference counting rather than creating |
---|
1285 | multiple copies of the same coefficient field/domain/ring */ |
---|
1286 | if (ntRing == e->r) |
---|
1287 | return TRUE; |
---|
1288 | |
---|
1289 | // NOTE: Q(a)[x] && Q(a)[y] should better share the _same_ Q(a)... |
---|
1290 | if( rEqual(ntRing, e->r, TRUE) ) |
---|
1291 | { |
---|
1292 | rDelete(e->r); |
---|
1293 | return TRUE; |
---|
1294 | } |
---|
1295 | |
---|
1296 | return FALSE; |
---|
1297 | } |
---|
1298 | |
---|
1299 | number ntLcm(number a, number b, const coeffs cf) |
---|
1300 | { |
---|
1301 | ntTest(a); |
---|
1302 | ntTest(b); |
---|
1303 | fraction fb = (fraction)b; |
---|
1304 | if ((b==NULL)||(DEN(fb)==NULL)) return ntCopy(a,cf); |
---|
1305 | #ifdef HAVE_FACTORY |
---|
1306 | fraction fa = (fraction)a; |
---|
1307 | /* singclap_gcd destroys its arguments; we hence need copies: */ |
---|
1308 | poly pa = p_Copy(NUM(fa), ntRing); |
---|
1309 | poly pb = p_Copy(DEN(fb), ntRing); |
---|
1310 | |
---|
1311 | /* Note that, over Q, singclap_gcd will remove the denominators in all |
---|
1312 | rational coefficients of pa and pb, before starting to compute |
---|
1313 | the gcd. Thus, we do not need to ensure that the coefficients of |
---|
1314 | pa and pb live in Z; they may well be elements of Q\Z. */ |
---|
1315 | poly pGcd = singclap_gcd(pa, pb, cf->extRing); |
---|
1316 | if (p_IsConstant(pGcd, ntRing) && |
---|
1317 | n_IsOne(p_GetCoeff(pGcd, ntRing), ntCoeffs)) |
---|
1318 | { /* gcd = 1; return pa*pb*/ |
---|
1319 | p_Delete(&pGcd,ntRing); |
---|
1320 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
1321 | NUM(result) = pp_Mult_qq(NUM(fa),DEN(fb),ntRing); |
---|
1322 | |
---|
1323 | ntTest((number)result); // !!!! |
---|
1324 | |
---|
1325 | return (number)result; |
---|
1326 | } |
---|
1327 | |
---|
1328 | |
---|
1329 | /* return pa*pb/gcd */ |
---|
1330 | poly newNum = singclap_pdivide(NUM(fa), pGcd, ntRing); |
---|
1331 | p_Delete(&pGcd,ntRing); |
---|
1332 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
1333 | NUM(result) = p_Mult_q(p_Copy(DEN(fb),ntRing),newNum,ntRing); |
---|
1334 | ntTest((number)result); // !!!! |
---|
1335 | return (number)result; |
---|
1336 | |
---|
1337 | #else |
---|
1338 | Print("// factory needed: transext.cc:ntLcm\n"); |
---|
1339 | return NULL; |
---|
1340 | #endif /* HAVE_FACTORY */ |
---|
1341 | return NULL; |
---|
1342 | } |
---|
1343 | |
---|
1344 | number ntGcd(number a, number b, const coeffs cf) |
---|
1345 | { |
---|
1346 | ntTest(a); |
---|
1347 | ntTest(b); |
---|
1348 | if (a==NULL) return ntCopy(b,cf); |
---|
1349 | if (b==NULL) return ntCopy(a,cf); |
---|
1350 | #ifdef HAVE_FACTORY |
---|
1351 | fraction fa = (fraction)a; |
---|
1352 | fraction fb = (fraction)b; |
---|
1353 | /* singclap_gcd destroys its arguments; we hence need copies: */ |
---|
1354 | poly pa = p_Copy(NUM(fa), ntRing); |
---|
1355 | poly pb = p_Copy(NUM(fb), ntRing); |
---|
1356 | |
---|
1357 | /* Note that, over Q, singclap_gcd will remove the denominators in all |
---|
1358 | rational coefficients of pa and pb, before starting to compute |
---|
1359 | the gcd. Thus, we do not need to ensure that the coefficients of |
---|
1360 | pa and pb live in Z; they may well be elements of Q\Z. */ |
---|
1361 | poly pGcd = singclap_gcd(pa, pb, cf->extRing); |
---|
1362 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
1363 | NUM(result) = pGcd; |
---|
1364 | ntTest((number)result); // !!!! |
---|
1365 | return (number)result; |
---|
1366 | #else |
---|
1367 | Print("// factory needed: transext.cc:ntGcd\n"); |
---|
1368 | return NULL; |
---|
1369 | #endif /* HAVE_FACTORY */ |
---|
1370 | } |
---|
1371 | |
---|
1372 | int ntSize(number a, const coeffs cf) |
---|
1373 | { |
---|
1374 | ntTest(a); |
---|
1375 | if (IS0(a)) return -1; |
---|
1376 | /* this has been taken from the old implementation of field extensions, |
---|
1377 | where we computed the sum of the degrees and the numbers of terms in |
---|
1378 | the numerator and denominator of a; so we leave it at that, for the |
---|
1379 | time being */ |
---|
1380 | fraction f = (fraction)a; |
---|
1381 | poly p = NUM(f); |
---|
1382 | int noOfTerms = 0; |
---|
1383 | int numDegree = 0; |
---|
1384 | while (p != NULL) |
---|
1385 | { |
---|
1386 | noOfTerms++; |
---|
1387 | int d = 0; |
---|
1388 | for (int i = 1; i <= rVar(ntRing); i++) |
---|
1389 | d += p_GetExp(p, i, ntRing); |
---|
1390 | if (d > numDegree) numDegree = d; |
---|
1391 | pIter(p); |
---|
1392 | } |
---|
1393 | int denDegree = 0; |
---|
1394 | if (!DENIS1(f)) |
---|
1395 | { |
---|
1396 | p = DEN(f); |
---|
1397 | while (p != NULL) |
---|
1398 | { |
---|
1399 | noOfTerms++; |
---|
1400 | int d = 0; |
---|
1401 | for (int i = 1; i <= rVar(ntRing); i++) |
---|
1402 | d += p_GetExp(p, i, ntRing); |
---|
1403 | if (d > denDegree) denDegree = d; |
---|
1404 | pIter(p); |
---|
1405 | } |
---|
1406 | } |
---|
1407 | ntTest(a); // !!!! |
---|
1408 | return numDegree + denDegree + noOfTerms; |
---|
1409 | } |
---|
1410 | |
---|
1411 | number ntInvers(number a, const coeffs cf) |
---|
1412 | { |
---|
1413 | ntTest(a); |
---|
1414 | if (IS0(a)) |
---|
1415 | { |
---|
1416 | WerrorS(nDivBy0); |
---|
1417 | return NULL; |
---|
1418 | } |
---|
1419 | fraction f = (fraction)a; |
---|
1420 | assume( f != NULL ); |
---|
1421 | |
---|
1422 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
1423 | |
---|
1424 | assume( NUM(f) != NULL ); |
---|
1425 | const poly den = DEN(f); |
---|
1426 | |
---|
1427 | if (den == NULL) |
---|
1428 | NUM(result) = p_One(ntRing); |
---|
1429 | else |
---|
1430 | NUM(result) = p_Copy(den, ntRing); |
---|
1431 | |
---|
1432 | if( !NUMIS1(f) ) |
---|
1433 | { |
---|
1434 | poly num_f=NUM(f); |
---|
1435 | BOOLEAN neg= !n_GreaterZero(pGetCoeff(num_f),ntRing->cf); |
---|
1436 | if (neg) |
---|
1437 | { |
---|
1438 | num_f=p_Neg(p_Copy(num_f, ntRing), ntRing); |
---|
1439 | NUM(result)=p_Neg(NUM(result), ntRing); |
---|
1440 | } |
---|
1441 | else |
---|
1442 | { |
---|
1443 | num_f=p_Copy(num_f, ntRing); |
---|
1444 | } |
---|
1445 | DEN(result) = num_f; |
---|
1446 | COM(result) = COM(f); |
---|
1447 | if (neg) |
---|
1448 | { |
---|
1449 | if (p_IsOne(num_f, ntRing)) |
---|
1450 | { |
---|
1451 | DEN(result)=NULL; |
---|
1452 | COM(result) = 0; |
---|
1453 | p_Delete(&num_f,ntRing); |
---|
1454 | } |
---|
1455 | } |
---|
1456 | } |
---|
1457 | else |
---|
1458 | { |
---|
1459 | DEN(result) = NULL; |
---|
1460 | COM(result) = 0; |
---|
1461 | } |
---|
1462 | ntTest((number)result); // !!!! |
---|
1463 | return (number)result; |
---|
1464 | } |
---|
1465 | |
---|
1466 | /* assumes that src = Q, dst = Q(t_1, ..., t_s) */ |
---|
1467 | number ntMap00(number a, const coeffs src, const coeffs dst) |
---|
1468 | { |
---|
1469 | if (n_IsZero(a, src)) return NULL; |
---|
1470 | assume(n_Test(a, src)); |
---|
1471 | assume(src == dst->extRing->cf); |
---|
1472 | return ntInit(p_NSet(n_Copy(a, src), dst->extRing), dst); |
---|
1473 | } |
---|
1474 | |
---|
1475 | /* assumes that src = Z/p, dst = Q(t_1, ..., t_s) */ |
---|
1476 | number ntMapP0(number a, const coeffs src, const coeffs dst) |
---|
1477 | { |
---|
1478 | if (n_IsZero(a, src)) return NULL; |
---|
1479 | assume(n_Test(a, src)); |
---|
1480 | /* mapping via intermediate int: */ |
---|
1481 | int n = n_Int(a, src); |
---|
1482 | number q = n_Init(n, dst->extRing->cf); |
---|
1483 | if (n_IsZero(q, dst->extRing->cf)) |
---|
1484 | { |
---|
1485 | n_Delete(&q, dst->extRing->cf); |
---|
1486 | return NULL; |
---|
1487 | } |
---|
1488 | return ntInit(p_NSet(q, dst->extRing), dst); |
---|
1489 | } |
---|
1490 | |
---|
1491 | /* assumes that either src = Q(t_1, ..., t_s), dst = Q(t_1, ..., t_s), or |
---|
1492 | src = Z/p(t_1, ..., t_s), dst = Z/p(t_1, ..., t_s) */ |
---|
1493 | number ntCopyMap(number a, const coeffs cf, const coeffs dst) |
---|
1494 | { |
---|
1495 | // if (n_IsZero(a, cf)) return NULL; |
---|
1496 | |
---|
1497 | ntTest(a); |
---|
1498 | |
---|
1499 | if (IS0(a)) return NULL; |
---|
1500 | |
---|
1501 | const ring rSrc = cf->extRing; |
---|
1502 | const ring rDst = dst->extRing; |
---|
1503 | |
---|
1504 | if( rSrc == rDst ) |
---|
1505 | return ntCopy(a, dst); // USUALLY WRONG! |
---|
1506 | |
---|
1507 | fraction f = (fraction)a; |
---|
1508 | poly g = prCopyR(NUM(f), rSrc, rDst); |
---|
1509 | |
---|
1510 | poly h = NULL; |
---|
1511 | |
---|
1512 | if (!DENIS1(f)) |
---|
1513 | h = prCopyR(DEN(f), rSrc, rDst); |
---|
1514 | |
---|
1515 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
1516 | |
---|
1517 | NUM(result) = g; |
---|
1518 | DEN(result) = h; |
---|
1519 | COM(result) = COM(f); |
---|
1520 | assume(n_Test((number)result, dst)); |
---|
1521 | return (number)result; |
---|
1522 | } |
---|
1523 | |
---|
1524 | number ntCopyAlg(number a, const coeffs cf, const coeffs dst) |
---|
1525 | { |
---|
1526 | assume( n_Test(a, cf) ); |
---|
1527 | if (n_IsZero(a, cf)) return NULL; |
---|
1528 | |
---|
1529 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
1530 | // DEN(f) = NULL; COM(f) = 0; |
---|
1531 | NUM(f) = prCopyR((poly)a, cf->extRing, dst->extRing); |
---|
1532 | assume(n_Test((number)f, dst)); |
---|
1533 | return (number)f; |
---|
1534 | } |
---|
1535 | |
---|
1536 | /* assumes that src = Q, dst = Z/p(t_1, ..., t_s) */ |
---|
1537 | number ntMap0P(number a, const coeffs src, const coeffs dst) |
---|
1538 | { |
---|
1539 | assume( n_Test(a, src) ); |
---|
1540 | if (n_IsZero(a, src)) return NULL; |
---|
1541 | // int p = rChar(dst->extRing); |
---|
1542 | number q = nlModP(a, src, dst->extRing->cf); |
---|
1543 | |
---|
1544 | if (n_IsZero(q, dst->extRing->cf)) |
---|
1545 | { |
---|
1546 | n_Delete(&q, dst->extRing->cf); |
---|
1547 | return NULL; |
---|
1548 | } |
---|
1549 | |
---|
1550 | poly g = p_NSet(q, dst->extRing); |
---|
1551 | |
---|
1552 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
1553 | NUM(f) = g; // DEN(f) = NULL; COM(f) = 0; |
---|
1554 | assume(n_Test((number)f, dst)); |
---|
1555 | return (number)f; |
---|
1556 | } |
---|
1557 | |
---|
1558 | /* assumes that src = Z/p, dst = Z/p(t_1, ..., t_s) */ |
---|
1559 | number ntMapPP(number a, const coeffs src, const coeffs dst) |
---|
1560 | { |
---|
1561 | assume( n_Test(a, src) ); |
---|
1562 | if (n_IsZero(a, src)) return NULL; |
---|
1563 | assume(src == dst->extRing->cf); |
---|
1564 | poly p = p_One(dst->extRing); |
---|
1565 | p_SetCoeff(p, n_Copy(a, src), dst->extRing); |
---|
1566 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
1567 | NUM(f) = p; DEN(f) = NULL; COM(f) = 0; |
---|
1568 | assume(n_Test((number)f, dst)); |
---|
1569 | return (number)f; |
---|
1570 | } |
---|
1571 | |
---|
1572 | /* assumes that src = Z/u, dst = Z/p(t_1, ..., t_s), where u != p */ |
---|
1573 | number ntMapUP(number a, const coeffs src, const coeffs dst) |
---|
1574 | { |
---|
1575 | assume( n_Test(a, src) ); |
---|
1576 | if (n_IsZero(a, src)) return NULL; |
---|
1577 | /* mapping via intermediate int: */ |
---|
1578 | int n = n_Int(a, src); |
---|
1579 | number q = n_Init(n, dst->extRing->cf); |
---|
1580 | poly p; |
---|
1581 | if (n_IsZero(q, dst->extRing->cf)) |
---|
1582 | { |
---|
1583 | n_Delete(&q, dst->extRing->cf); |
---|
1584 | return NULL; |
---|
1585 | } |
---|
1586 | p = p_One(dst->extRing); |
---|
1587 | p_SetCoeff(p, q, dst->extRing); |
---|
1588 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
1589 | NUM(f) = p; DEN(f) = NULL; COM(f) = 0; |
---|
1590 | assume(n_Test((number)f, dst)); |
---|
1591 | return (number)f; |
---|
1592 | } |
---|
1593 | |
---|
1594 | nMapFunc ntSetMap(const coeffs src, const coeffs dst) |
---|
1595 | { |
---|
1596 | /* dst is expected to be a rational function field */ |
---|
1597 | assume(getCoeffType(dst) == ID); |
---|
1598 | |
---|
1599 | if( src == dst ) return ndCopyMap; |
---|
1600 | |
---|
1601 | int h = 0; /* the height of the extension tower given by dst */ |
---|
1602 | coeffs bDst = nCoeff_bottom(dst, h); /* the bottom field in the tower dst */ |
---|
1603 | coeffs bSrc = nCoeff_bottom(src, h); /* the bottom field in the tower src */ |
---|
1604 | |
---|
1605 | /* for the time being, we only provide maps if h = 1 and if b is Q or |
---|
1606 | some field Z/pZ: */ |
---|
1607 | if (h==0) |
---|
1608 | { |
---|
1609 | if (nCoeff_is_Q(src) && nCoeff_is_Q(bDst)) |
---|
1610 | return ntMap00; /// Q --> Q(T) |
---|
1611 | if (nCoeff_is_Zp(src) && nCoeff_is_Q(bDst)) |
---|
1612 | return ntMapP0; /// Z/p --> Q(T) |
---|
1613 | if (nCoeff_is_Q(src) && nCoeff_is_Zp(bDst)) |
---|
1614 | return ntMap0P; /// Q --> Z/p(T) |
---|
1615 | if (nCoeff_is_Zp(src) && nCoeff_is_Zp(bDst)) |
---|
1616 | { |
---|
1617 | if (src->ch == dst->ch) return ntMapPP; /// Z/p --> Z/p(T) |
---|
1618 | else return ntMapUP; /// Z/u --> Z/p(T) |
---|
1619 | } |
---|
1620 | } |
---|
1621 | if (h != 1) return NULL; |
---|
1622 | if ((!nCoeff_is_Zp(bDst)) && (!nCoeff_is_Q(bDst))) return NULL; |
---|
1623 | |
---|
1624 | /* Let T denote the sequence of transcendental extension variables, i.e., |
---|
1625 | K[t_1, ..., t_s] =: K[T]; |
---|
1626 | Let moreover, for any such sequence T, T' denote any subsequence of T |
---|
1627 | of the form t_1, ..., t_w with w <= s. */ |
---|
1628 | |
---|
1629 | if ((!nCoeff_is_Zp(bSrc)) && (!nCoeff_is_Q(bSrc))) return NULL; |
---|
1630 | |
---|
1631 | if (nCoeff_is_Q(bSrc) && nCoeff_is_Q(bDst)) |
---|
1632 | { |
---|
1633 | if (rVar(src->extRing) > rVar(dst->extRing)) |
---|
1634 | return NULL; |
---|
1635 | |
---|
1636 | for (int i = 0; i < rVar(src->extRing); i++) |
---|
1637 | if (strcmp(rRingVar(i, src->extRing), rRingVar(i, dst->extRing)) != 0) |
---|
1638 | return NULL; |
---|
1639 | |
---|
1640 | if (src->type==n_transExt) |
---|
1641 | return ntCopyMap; /// Q(T') --> Q(T) |
---|
1642 | else |
---|
1643 | return ntCopyAlg; |
---|
1644 | } |
---|
1645 | |
---|
1646 | if (nCoeff_is_Zp(bSrc) && nCoeff_is_Zp(bDst)) |
---|
1647 | { |
---|
1648 | if (rVar(src->extRing) > rVar(dst->extRing)) |
---|
1649 | return NULL; |
---|
1650 | |
---|
1651 | for (int i = 0; i < rVar(src->extRing); i++) |
---|
1652 | if (strcmp(rRingVar(i, src->extRing), rRingVar(i, dst->extRing)) != 0) |
---|
1653 | return NULL; |
---|
1654 | |
---|
1655 | if (src->type==n_transExt) |
---|
1656 | return ntCopyMap; /// Z/p(T') --> Z/p(T) |
---|
1657 | else |
---|
1658 | return ntCopyAlg; |
---|
1659 | } |
---|
1660 | |
---|
1661 | return NULL; /// default |
---|
1662 | } |
---|
1663 | #if 0 |
---|
1664 | nMapFunc ntSetMap_T(const coeffs src, const coeffs dst) |
---|
1665 | { |
---|
1666 | nMapFunc n=ntSetMap(src,dst); |
---|
1667 | if (n==ntCopyAlg) printf("n=ntCopyAlg\n"); |
---|
1668 | else if (n==ntCopyMap) printf("n=ntCopyMap\n"); |
---|
1669 | else if (n==ntMapUP) printf("n=ntMapUP\n"); |
---|
1670 | else if (n==ntMap0P) printf("n=ntMap0P\n"); |
---|
1671 | else if (n==ntMapP0) printf("n=ntMapP0\n"); |
---|
1672 | else if (n==ntMap00) printf("n=ntMap00\n"); |
---|
1673 | else if (n==NULL) printf("n=NULL\n"); |
---|
1674 | else printf("n=?\n"); |
---|
1675 | return n; |
---|
1676 | } |
---|
1677 | #endif |
---|
1678 | |
---|
1679 | void ntKillChar(coeffs cf) |
---|
1680 | { |
---|
1681 | if ((--cf->extRing->ref) == 0) |
---|
1682 | rDelete(cf->extRing); |
---|
1683 | } |
---|
1684 | #ifdef HAVE_FACTORY |
---|
1685 | number ntConvFactoryNSingN( const CanonicalForm n, const coeffs cf) |
---|
1686 | { |
---|
1687 | if (n.isZero()) return NULL; |
---|
1688 | poly p=convFactoryPSingP(n,ntRing); |
---|
1689 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
1690 | NUM(result) = p; |
---|
1691 | //DEN(result) = NULL; // done by omAlloc0Bin |
---|
1692 | //COM(result) = 0; // done by omAlloc0Bin |
---|
1693 | ntTest((number)result); |
---|
1694 | return (number)result; |
---|
1695 | } |
---|
1696 | CanonicalForm ntConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs cf ) |
---|
1697 | { |
---|
1698 | ntTest(n); |
---|
1699 | if (IS0(n)) return CanonicalForm(0); |
---|
1700 | |
---|
1701 | fraction f = (fraction)n; |
---|
1702 | return convSingPFactoryP(NUM(f),ntRing); |
---|
1703 | } |
---|
1704 | #endif |
---|
1705 | |
---|
1706 | static int ntParDeg(number a, const coeffs cf) |
---|
1707 | { |
---|
1708 | ntTest(a); |
---|
1709 | if (IS0(a)) return -1; |
---|
1710 | fraction fa = (fraction)a; |
---|
1711 | return cf->extRing->pFDeg(NUM(fa),cf->extRing); |
---|
1712 | } |
---|
1713 | |
---|
1714 | /// return the specified parameter as a number in the given trans.ext. |
---|
1715 | static number ntParameter(const int iParameter, const coeffs cf) |
---|
1716 | { |
---|
1717 | assume(getCoeffType(cf) == ID); |
---|
1718 | |
---|
1719 | const ring R = cf->extRing; |
---|
1720 | assume( R != NULL ); |
---|
1721 | assume( 0 < iParameter && iParameter <= rVar(R) ); |
---|
1722 | |
---|
1723 | poly p = p_One(R); p_SetExp(p, iParameter, 1, R); p_Setm(p, R); |
---|
1724 | |
---|
1725 | // return (number) p; |
---|
1726 | |
---|
1727 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
1728 | NUM(f) = p; |
---|
1729 | DEN(f) = NULL; |
---|
1730 | COM(f) = 0; |
---|
1731 | |
---|
1732 | ntTest((number)f); |
---|
1733 | |
---|
1734 | return (number)f; |
---|
1735 | } |
---|
1736 | |
---|
1737 | /// if m == var(i)/1 => return i, |
---|
1738 | int ntIsParam(number m, const coeffs cf) |
---|
1739 | { |
---|
1740 | ntTest(m); |
---|
1741 | assume(getCoeffType(cf) == ID); |
---|
1742 | |
---|
1743 | const ring R = cf->extRing; |
---|
1744 | assume( R != NULL ); |
---|
1745 | |
---|
1746 | fraction f = (fraction)m; |
---|
1747 | |
---|
1748 | if( DEN(f) != NULL ) |
---|
1749 | return 0; |
---|
1750 | |
---|
1751 | return p_Var( NUM(f), R ); |
---|
1752 | } |
---|
1753 | |
---|
1754 | struct NTNumConverter |
---|
1755 | { |
---|
1756 | static inline poly convert(const number& n) |
---|
1757 | { |
---|
1758 | // suitable for trans. ext. numbers that are fractions of polys |
---|
1759 | return NUM((fraction)n); // return the numerator |
---|
1760 | } |
---|
1761 | }; |
---|
1762 | |
---|
1763 | |
---|
1764 | static void ntClearContent(ICoeffsEnumerator& numberCollectionEnumerator, number& c, const coeffs cf) |
---|
1765 | { |
---|
1766 | assume(cf != NULL); |
---|
1767 | assume(getCoeffType(cf) == ID); |
---|
1768 | // all coeffs are given by fractions of polynomails over integers!!! |
---|
1769 | // without denominators!!! |
---|
1770 | |
---|
1771 | const ring R = cf->extRing; |
---|
1772 | assume(R != NULL); |
---|
1773 | const coeffs Q = R->cf; |
---|
1774 | assume(Q != NULL); |
---|
1775 | assume(nCoeff_is_Q(Q)); |
---|
1776 | |
---|
1777 | |
---|
1778 | numberCollectionEnumerator.Reset(); |
---|
1779 | |
---|
1780 | if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial? |
---|
1781 | { |
---|
1782 | c = ntInit(1, cf); |
---|
1783 | return; |
---|
1784 | } |
---|
1785 | |
---|
1786 | // all coeffs are given by integers after returning from this routine |
---|
1787 | |
---|
1788 | // part 1, collect product of all denominators /gcds |
---|
1789 | poly cand = NULL; |
---|
1790 | |
---|
1791 | do |
---|
1792 | { |
---|
1793 | number &n = numberCollectionEnumerator.Current(); |
---|
1794 | |
---|
1795 | ntNormalize(n, cf); |
---|
1796 | |
---|
1797 | fraction f = (fraction)n; |
---|
1798 | |
---|
1799 | assume( f != NULL ); |
---|
1800 | |
---|
1801 | const poly den = DEN(f); |
---|
1802 | |
---|
1803 | assume( den == NULL ); // ?? / 1 ? |
---|
1804 | |
---|
1805 | const poly num = NUM(f); |
---|
1806 | |
---|
1807 | if( cand == NULL ) |
---|
1808 | cand = p_Copy(num, R); |
---|
1809 | else |
---|
1810 | cand = singclap_gcd(cand, p_Copy(num, R), R); // gcd(cand, num) |
---|
1811 | |
---|
1812 | if( p_IsConstant(cand, R) ) |
---|
1813 | break; |
---|
1814 | } |
---|
1815 | while( numberCollectionEnumerator.MoveNext() ) ; |
---|
1816 | |
---|
1817 | |
---|
1818 | // part2: all coeffs = all coeffs * cand |
---|
1819 | if( cand != NULL ) |
---|
1820 | { |
---|
1821 | if( !p_IsConstant(cand, R) ) |
---|
1822 | { |
---|
1823 | c = ntInit(cand, cf); |
---|
1824 | numberCollectionEnumerator.Reset(); |
---|
1825 | while (numberCollectionEnumerator.MoveNext() ) |
---|
1826 | { |
---|
1827 | number &n = numberCollectionEnumerator.Current(); |
---|
1828 | const number t = ntDiv(n, c, cf); // TODO: rewrite!? |
---|
1829 | ntDelete(&n, cf); |
---|
1830 | n = t; |
---|
1831 | } |
---|
1832 | } // else NUM (result) = p_One(R); |
---|
1833 | else { p_Delete(&cand, R); cand = NULL; } |
---|
1834 | } |
---|
1835 | |
---|
1836 | // Quick and dirty fix for constant content clearing: consider numerators??? |
---|
1837 | CRecursivePolyCoeffsEnumerator<NTNumConverter> itr(numberCollectionEnumerator); // recursively treat the NUM(numbers) as polys! |
---|
1838 | number cc; |
---|
1839 | |
---|
1840 | n_ClearContent(itr, cc, Q); |
---|
1841 | number g = ntInit(p_NSet(cc, R), cf); |
---|
1842 | |
---|
1843 | if( cand != NULL ) |
---|
1844 | { |
---|
1845 | number gg = ntMult(g, c, cf); |
---|
1846 | ntDelete(&g, cf); |
---|
1847 | ntDelete(&c, cf); c = gg; |
---|
1848 | } else |
---|
1849 | c = g; |
---|
1850 | ntTest(c); |
---|
1851 | } |
---|
1852 | |
---|
1853 | static void ntClearDenominators(ICoeffsEnumerator& numberCollectionEnumerator, number& c, const coeffs cf) |
---|
1854 | { |
---|
1855 | assume(cf != NULL); |
---|
1856 | assume(getCoeffType(cf) == ID); // both over Q(a) and Zp(a)! |
---|
1857 | // all coeffs are given by fractions of polynomails over integers!!! |
---|
1858 | |
---|
1859 | numberCollectionEnumerator.Reset(); |
---|
1860 | |
---|
1861 | if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial? |
---|
1862 | { |
---|
1863 | c = ntInit(1, cf); |
---|
1864 | return; |
---|
1865 | } |
---|
1866 | |
---|
1867 | // all coeffs are given by integers after returning from this routine |
---|
1868 | |
---|
1869 | // part 1, collect product of all denominators /gcds |
---|
1870 | poly cand = NULL; |
---|
1871 | |
---|
1872 | const ring R = cf->extRing; |
---|
1873 | assume(R != NULL); |
---|
1874 | |
---|
1875 | const coeffs Q = R->cf; |
---|
1876 | assume(Q != NULL); |
---|
1877 | // assume(nCoeff_is_Q(Q)); |
---|
1878 | |
---|
1879 | do |
---|
1880 | { |
---|
1881 | number &n = numberCollectionEnumerator.Current(); |
---|
1882 | |
---|
1883 | ntNormalize(n, cf); |
---|
1884 | |
---|
1885 | fraction f = (fraction)ntGetDenom (n, cf); |
---|
1886 | |
---|
1887 | assume( f != NULL ); |
---|
1888 | |
---|
1889 | const poly den = NUM(f); |
---|
1890 | |
---|
1891 | if( den == NULL ) // ?? / 1 ? |
---|
1892 | continue; |
---|
1893 | |
---|
1894 | if( cand == NULL ) |
---|
1895 | cand = p_Copy(den, R); |
---|
1896 | else |
---|
1897 | { |
---|
1898 | // cand === LCM( cand, den )!!!! |
---|
1899 | // NOTE: maybe it's better to make the product and clearcontent afterwards!? |
---|
1900 | // TODO: move the following to factory? |
---|
1901 | poly gcd = singclap_gcd(p_Copy(cand, R), p_Copy(den, R), R); // gcd(cand, den) is monic no mater leading coeffs! :(((( |
---|
1902 | if (nCoeff_is_Q (Q)) |
---|
1903 | { |
---|
1904 | number LcGcd= n_Gcd (p_GetCoeff (cand, R), p_GetCoeff(den, R), Q); |
---|
1905 | gcd = p_Mult_nn(gcd, LcGcd, R); |
---|
1906 | n_Delete(&LcGcd,Q); |
---|
1907 | } |
---|
1908 | // assume( n_IsOne(pGetCoeff(gcd), Q) ); // TODO: this may be wrong... |
---|
1909 | cand = p_Mult_q(cand, p_Copy(den, R), R); // cand *= den |
---|
1910 | const poly t = singclap_pdivide( cand, gcd, R ); // cand' * den / gcd(cand', den) |
---|
1911 | p_Delete(&cand, R); |
---|
1912 | p_Delete(&gcd, R); |
---|
1913 | cand = t; |
---|
1914 | } |
---|
1915 | } |
---|
1916 | while( numberCollectionEnumerator.MoveNext() ); |
---|
1917 | |
---|
1918 | if( cand == NULL ) |
---|
1919 | { |
---|
1920 | c = ntInit(1, cf); |
---|
1921 | return; |
---|
1922 | } |
---|
1923 | |
---|
1924 | c = ntInit(cand, cf); |
---|
1925 | |
---|
1926 | numberCollectionEnumerator.Reset(); |
---|
1927 | |
---|
1928 | number d = NULL; |
---|
1929 | |
---|
1930 | while (numberCollectionEnumerator.MoveNext() ) |
---|
1931 | { |
---|
1932 | number &n = numberCollectionEnumerator.Current(); |
---|
1933 | number t = ntMult(n, c, cf); // TODO: rewrite!? |
---|
1934 | ntDelete(&n, cf); |
---|
1935 | |
---|
1936 | ntNormalize(t, cf); // TODO: needed? |
---|
1937 | n = t; |
---|
1938 | |
---|
1939 | fraction f = (fraction)t; |
---|
1940 | assume( f != NULL ); |
---|
1941 | |
---|
1942 | const poly den = DEN(f); |
---|
1943 | |
---|
1944 | if( den != NULL ) // ?? / ?? ? |
---|
1945 | { |
---|
1946 | assume( p_IsConstant(den, R) ); |
---|
1947 | assume( pNext(den) == NULL ); |
---|
1948 | |
---|
1949 | if( d == NULL ) |
---|
1950 | d = n_Copy(pGetCoeff(den), Q); |
---|
1951 | else |
---|
1952 | { |
---|
1953 | number g = n_Lcm(d, pGetCoeff(den), Q); |
---|
1954 | n_Delete(&d, Q); d = g; |
---|
1955 | } |
---|
1956 | } |
---|
1957 | } |
---|
1958 | |
---|
1959 | if( d != NULL ) |
---|
1960 | { |
---|
1961 | numberCollectionEnumerator.Reset(); |
---|
1962 | while (numberCollectionEnumerator.MoveNext() ) |
---|
1963 | { |
---|
1964 | number &n = numberCollectionEnumerator.Current(); |
---|
1965 | fraction f = (fraction)n; |
---|
1966 | |
---|
1967 | assume( f != NULL ); |
---|
1968 | |
---|
1969 | const poly den = DEN(f); |
---|
1970 | |
---|
1971 | if( den == NULL ) // ?? / 1 ? |
---|
1972 | NUM(f) = p_Mult_nn(NUM(f), d, R); |
---|
1973 | else |
---|
1974 | { |
---|
1975 | assume( p_IsConstant(den, R) ); |
---|
1976 | assume( pNext(den) == NULL ); |
---|
1977 | |
---|
1978 | number ddd = n_Div(d, pGetCoeff(den), Q); // but be an integer now!!! |
---|
1979 | NUM(f) = p_Mult_nn(NUM(f), ddd, R); |
---|
1980 | n_Delete(&ddd, Q); |
---|
1981 | |
---|
1982 | p_Delete(&DEN(f), R); |
---|
1983 | DEN(f) = NULL; // TODO: check if this is needed!? |
---|
1984 | } |
---|
1985 | |
---|
1986 | assume( DEN(f) == NULL ); |
---|
1987 | } |
---|
1988 | |
---|
1989 | NUM(c) = p_Mult_nn(NUM(c), d, R); |
---|
1990 | n_Delete(&d, Q); |
---|
1991 | } |
---|
1992 | |
---|
1993 | |
---|
1994 | ntTest(c); |
---|
1995 | } |
---|
1996 | |
---|
1997 | BOOLEAN ntInitChar(coeffs cf, void * infoStruct) |
---|
1998 | { |
---|
1999 | |
---|
2000 | assume( infoStruct != NULL ); |
---|
2001 | |
---|
2002 | TransExtInfo *e = (TransExtInfo *)infoStruct; |
---|
2003 | |
---|
2004 | assume( e->r != NULL); // extRing; |
---|
2005 | assume( e->r->cf != NULL); // extRing->cf; |
---|
2006 | assume( e->r->qideal == NULL ); |
---|
2007 | |
---|
2008 | assume( cf != NULL ); |
---|
2009 | assume(getCoeffType(cf) == ID); // coeff type; |
---|
2010 | |
---|
2011 | ring R = e->r; |
---|
2012 | assume(R != NULL); |
---|
2013 | |
---|
2014 | R->ref ++; // increase the ref.counter for the ground poly. ring! |
---|
2015 | |
---|
2016 | cf->extRing = R; |
---|
2017 | /* propagate characteristic up so that it becomes |
---|
2018 | directly accessible in cf: */ |
---|
2019 | cf->ch = R->cf->ch; |
---|
2020 | cf->factoryVarOffset = R->cf->factoryVarOffset + rVar(R); |
---|
2021 | |
---|
2022 | cf->cfGreaterZero = ntGreaterZero; |
---|
2023 | cf->cfGreater = ntGreater; |
---|
2024 | cf->cfEqual = ntEqual; |
---|
2025 | cf->cfIsZero = ntIsZero; |
---|
2026 | cf->cfIsOne = ntIsOne; |
---|
2027 | cf->cfIsMOne = ntIsMOne; |
---|
2028 | cf->cfInit = ntInit; |
---|
2029 | cf->cfInit_bigint = ntInit_bigint; |
---|
2030 | cf->cfInt = ntInt; |
---|
2031 | cf->cfNeg = ntNeg; |
---|
2032 | cf->cfAdd = ntAdd; |
---|
2033 | cf->cfSub = ntSub; |
---|
2034 | cf->cfMult = ntMult; |
---|
2035 | cf->cfDiv = ntDiv; |
---|
2036 | cf->cfExactDiv = ntDiv; |
---|
2037 | cf->cfPower = ntPower; |
---|
2038 | cf->cfCopy = ntCopy; |
---|
2039 | cf->cfWriteLong = ntWriteLong; |
---|
2040 | cf->cfRead = ntRead; |
---|
2041 | cf->cfNormalize = ntNormalize; |
---|
2042 | cf->cfDelete = ntDelete; |
---|
2043 | cf->cfSetMap = ntSetMap; |
---|
2044 | cf->cfGetDenom = ntGetDenom; |
---|
2045 | cf->cfGetNumerator = ntGetNumerator; |
---|
2046 | cf->cfRePart = ntCopy; |
---|
2047 | cf->cfImPart = ntImPart; |
---|
2048 | cf->cfCoeffWrite = ntCoeffWrite; |
---|
2049 | #ifdef LDEBUG |
---|
2050 | cf->cfDBTest = ntDBTest; |
---|
2051 | #endif |
---|
2052 | cf->cfGcd = ntGcd; |
---|
2053 | cf->cfLcm = ntLcm; |
---|
2054 | cf->cfSize = ntSize; |
---|
2055 | cf->nCoeffIsEqual = ntCoeffIsEqual; |
---|
2056 | cf->cfInvers = ntInvers; |
---|
2057 | cf->cfIntDiv = ntDiv; |
---|
2058 | cf->cfKillChar = ntKillChar; |
---|
2059 | |
---|
2060 | if( rCanShortOut(ntRing) ) |
---|
2061 | cf->cfWriteShort = ntWriteShort; |
---|
2062 | else |
---|
2063 | cf->cfWriteShort = ntWriteLong; |
---|
2064 | |
---|
2065 | #ifndef HAVE_FACTORY |
---|
2066 | PrintS("// Warning: The 'factory' module is not available.\n"); |
---|
2067 | PrintS("// Hence gcd's cannot be cancelled in any\n"); |
---|
2068 | PrintS("// computed fraction!\n"); |
---|
2069 | #else |
---|
2070 | cf->convFactoryNSingN =ntConvFactoryNSingN; |
---|
2071 | cf->convSingNFactoryN =ntConvSingNFactoryN; |
---|
2072 | #endif |
---|
2073 | cf->cfParDeg = ntParDeg; |
---|
2074 | |
---|
2075 | cf->iNumberOfParameters = rVar(R); |
---|
2076 | cf->pParameterNames = R->names; |
---|
2077 | cf->cfParameter = ntParameter; |
---|
2078 | |
---|
2079 | if( nCoeff_is_Q(R->cf) ) |
---|
2080 | cf->cfClearContent = ntClearContent; |
---|
2081 | |
---|
2082 | cf->cfClearDenominators = ntClearDenominators; |
---|
2083 | |
---|
2084 | return FALSE; |
---|
2085 | } |
---|