[6ba162] | 1 | // binomial.cc |
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| 2 | |
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| 3 | // implementation of class binomial |
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| 4 | |
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| 5 | #ifndef BINOMIAL_CC |
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| 6 | #define BINOMIAL_CC |
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| 7 | |
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[10b7a4] | 8 | #include <climits> |
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[6ba162] | 9 | #include "binomial__term_ordering.h" |
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| 10 | |
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| 11 | ///////////////////////// constructors and destructor ////////////////////// |
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| 12 | |
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| 13 | // For a better overview, the constructor code is separated for |
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| 14 | // NO_SUPPORT_DRIVEN_METHODS and SUPPORT_DRIVEN_METHODS. |
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| 15 | |
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| 16 | #ifdef NO_SUPPORT_DRIVEN_METHODS |
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| 17 | |
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| 18 | binomial::binomial(const short& number_of_variables) |
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| 19 | :_number_of_variables(number_of_variables) |
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| 20 | { |
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| 21 | exponent_vector=new Integer[_number_of_variables]; |
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| 22 | } |
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| 23 | |
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| 24 | |
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| 25 | |
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| 26 | |
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| 27 | binomial::binomial(const short& number_of_variables,const Integer* exponents) |
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| 28 | :_number_of_variables(number_of_variables) |
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| 29 | { |
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| 30 | |
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| 31 | // range check for rarely used constructors |
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| 32 | if(_number_of_variables<=0) |
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| 33 | { |
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| 34 | cerr<<"\nWARNING: binomial::binomial(const short&, const Integer*):\n" |
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| 35 | "argument out of range"<<endl; |
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| 36 | exponent_vector=NULL; |
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| 37 | // to avoid problems when deleting |
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| 38 | return; |
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| 39 | } |
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| 40 | |
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| 41 | // initialization |
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| 42 | exponent_vector=new Integer[_number_of_variables]; |
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| 43 | for(short i=0;i<_number_of_variables;i++) |
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| 44 | exponent_vector[i]=exponents[i]; |
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| 45 | } |
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| 46 | |
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| 47 | |
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| 48 | |
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| 49 | |
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| 50 | binomial::binomial(const short& number_of_variables,const Integer* exponents, |
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| 51 | const term_ordering& w) |
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| 52 | :_number_of_variables(number_of_variables) |
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| 53 | { |
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| 54 | |
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| 55 | // range check for rarely used constructors |
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| 56 | if(_number_of_variables<=0) |
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| 57 | { |
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| 58 | cerr<<"\nWARNING: binomial::binomial(const short&, const Integer*):\n" |
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| 59 | "argument out of range"<<endl; |
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| 60 | exponent_vector=NULL; |
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| 61 | // to avoid problems when deleting |
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| 62 | return; |
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| 63 | } |
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| 64 | |
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| 65 | exponent_vector=new Integer[_number_of_variables]; |
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| 66 | |
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| 67 | // determine head and tail |
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| 68 | if(w.compare_to_zero(exponents)>=0) |
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| 69 | for(short i=0;i<_number_of_variables;i++) |
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| 70 | exponent_vector[i]=exponents[i]; |
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| 71 | else |
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| 72 | for(short i=0;i<_number_of_variables;i++) |
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| 73 | exponent_vector[i]=-exponents[i]; |
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| 74 | |
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| 75 | } |
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| 76 | |
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| 77 | |
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| 78 | |
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| 79 | |
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| 80 | binomial::binomial(const binomial& b) |
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| 81 | :_number_of_variables(b._number_of_variables) |
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| 82 | { |
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| 83 | exponent_vector=new Integer[_number_of_variables]; |
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| 84 | for(short i=0;i<_number_of_variables;i++) |
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| 85 | exponent_vector[i]=b.exponent_vector[i]; |
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| 86 | } |
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| 87 | |
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| 88 | |
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| 89 | |
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| 90 | |
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| 91 | #endif // NO_SUPPORT_DRIVEN_METHODS |
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| 92 | |
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| 93 | |
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| 94 | |
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| 95 | |
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| 96 | #ifdef SUPPORT_DRIVEN_METHODS |
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| 97 | |
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| 98 | |
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| 99 | |
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| 100 | |
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| 101 | binomial::binomial(const short& number_of_variables) |
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| 102 | :_number_of_variables(number_of_variables),head_support(0),tail_support(0) |
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| 103 | { |
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| 104 | exponent_vector=new Integer[_number_of_variables]; |
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| 105 | } |
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| 106 | |
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| 107 | |
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| 108 | |
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| 109 | |
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| 110 | binomial::binomial(const short& number_of_variables, const Integer* exponents) |
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| 111 | :_number_of_variables(number_of_variables),head_support(0),tail_support(0) |
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| 112 | { |
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| 113 | |
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| 114 | // range check for rarely used constructors |
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| 115 | if(_number_of_variables<=0) |
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| 116 | { |
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| 117 | exponent_vector=NULL; |
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| 118 | // to avoid problems when deleting |
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| 119 | cerr<<"\nWARNING: binomial::binomial(const short&, const Integer*):\n" |
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| 120 | "argument out of range"<<endl; |
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| 121 | return; |
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| 122 | } |
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| 123 | |
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| 124 | exponent_vector=new Integer[_number_of_variables]; |
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| 125 | |
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| 126 | short size_of_support_vectors=CHAR_BIT*sizeof(unsigned long); |
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| 127 | // number of bits of a long int |
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| 128 | |
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| 129 | |
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| 130 | for(short i=0;i<_number_of_variables;i++) |
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| 131 | { |
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| 132 | |
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| 133 | #ifdef SUPPORT_VARIABLES_FIRST |
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| 134 | |
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| 135 | Integer actual_entry=exponents[i]; |
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| 136 | exponent_vector[i]=actual_entry; |
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| 137 | |
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| 138 | #endif // SUPPORT_VARIABLES_FIRST |
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| 139 | |
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| 140 | #ifdef SUPPORT_VARIABLES_LAST |
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| 141 | |
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| 142 | short j=_number_of_variables-1-i; |
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| 143 | Integer actual_entry=exponents[j]; |
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| 144 | exponent_vector[j]=actual_entry; |
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| 145 | |
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| 146 | #endif // SUPPORT_VARIABLES_LAST |
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| 147 | |
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| 148 | if(i<size_of_support_vectors) |
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[f07fec] | 149 | { |
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[6ba162] | 150 | // variable i is considered in the support vectors |
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| 151 | if(actual_entry>0) |
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| 152 | head_support|=(1<<i); |
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| 153 | // bit i of head_support is set to 1 (counting from 0) |
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[f07fec] | 154 | else if(actual_entry<0) |
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| 155 | tail_support|=(1<<i); |
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| 156 | // bit i of tail_support is set to 1 |
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| 157 | } |
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[6ba162] | 158 | } |
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| 159 | |
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| 160 | } |
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| 161 | |
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| 162 | |
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| 163 | |
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| 164 | |
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| 165 | binomial::binomial(const short& number_of_variables, const Integer* exponents, |
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| 166 | const term_ordering& w) |
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| 167 | :_number_of_variables(number_of_variables),head_support(0),tail_support(0) |
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| 168 | { |
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| 169 | // range check for rarely used constructors |
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| 170 | if(_number_of_variables<=0) |
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| 171 | { |
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| 172 | cerr<<"\nWARNING: binomial::binomial(const short&, const Integer*):\n" |
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| 173 | "argument out of range"<<endl; |
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| 174 | exponent_vector=NULL; |
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| 175 | // to avoid problems when deleting |
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| 176 | return; |
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| 177 | } |
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| 178 | |
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| 179 | |
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| 180 | exponent_vector=new Integer[_number_of_variables]; |
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| 181 | |
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| 182 | short size_of_support_vectors=CHAR_BIT*sizeof(unsigned long); |
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| 183 | // number of bits of a long int |
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| 184 | |
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| 185 | // determine head and tail |
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| 186 | short sign; |
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| 187 | if(w.compare_to_zero(exponents)>=0) |
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| 188 | sign=1; |
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| 189 | else |
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| 190 | sign=-1; |
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| 191 | |
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| 192 | |
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| 193 | for(short i=0;i<_number_of_variables;i++) |
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| 194 | { |
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| 195 | |
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| 196 | #ifdef SUPPORT_VARIABLES_FIRST |
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| 197 | |
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| 198 | Integer actual_entry=sign*exponents[i]; |
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| 199 | exponent_vector[i]=actual_entry; |
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| 200 | |
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| 201 | #endif // SUPPORT_VARIABLES_FIRST |
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| 202 | |
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| 203 | #ifdef SUPPORT_VARIABLES_LAST |
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| 204 | |
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| 205 | short j=_number_of_variables-1-i; |
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| 206 | Integer actual_entry=sign*exponents[j]; |
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| 207 | exponent_vector[j]=actual_entry; |
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| 208 | |
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| 209 | #endif // SUPPORT_VARIABLES_LAST |
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| 210 | |
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| 211 | if(i<size_of_support_vectors) |
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[f07fec] | 212 | { |
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[6ba162] | 213 | // variable i is considered in the support vectors |
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| 214 | if(actual_entry>0) |
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| 215 | head_support|=(1<<i); |
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| 216 | // bit i of head_support is set to 1 (counting from 0) |
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[f07fec] | 217 | else if(actual_entry<0) |
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| 218 | tail_support|=(1<<i); |
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| 219 | // bit i of tail_support is set to 1 |
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| 220 | } |
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[6ba162] | 221 | } |
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| 222 | |
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| 223 | } |
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| 224 | |
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| 225 | |
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| 226 | |
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| 227 | |
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| 228 | binomial::binomial(const binomial& b) |
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| 229 | :_number_of_variables(b._number_of_variables), |
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| 230 | head_support(b.head_support),tail_support(b.tail_support) |
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| 231 | { |
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| 232 | exponent_vector=new Integer[_number_of_variables]; |
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| 233 | for(short i=0;i<_number_of_variables;i++) |
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| 234 | exponent_vector[i]=b.exponent_vector[i]; |
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| 235 | } |
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| 236 | |
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| 237 | |
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| 238 | |
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| 239 | |
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| 240 | #endif // SUPPORT_DRIVEN_METHODS |
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| 241 | |
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| 242 | |
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| 243 | |
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| 244 | |
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| 245 | binomial::~binomial() |
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| 246 | { |
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| 247 | delete[] exponent_vector; |
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| 248 | } |
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| 249 | |
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| 250 | |
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| 251 | |
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| 252 | |
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| 253 | /////////////////// object information ///////////////////////////////////// |
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| 254 | |
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| 255 | |
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| 256 | |
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| 257 | |
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| 258 | short binomial::number_of_variables() const |
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| 259 | { |
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| 260 | return _number_of_variables; |
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| 261 | } |
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| 262 | |
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| 263 | |
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| 264 | |
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| 265 | |
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| 266 | short binomial::error_status() const |
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| 267 | { |
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| 268 | if(_number_of_variables<0) |
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| 269 | return _number_of_variables; |
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| 270 | return 0; |
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| 271 | } |
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| 272 | |
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| 273 | |
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| 274 | |
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| 275 | |
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| 276 | //////////////////// assignment and access operators //////////////////////// |
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| 277 | |
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| 278 | |
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| 279 | |
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| 280 | |
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| 281 | binomial& binomial::operator=(const binomial& b) |
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| 282 | { |
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| 283 | |
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| 284 | if(&b==this) |
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| 285 | return *this; |
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| 286 | |
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| 287 | |
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| 288 | #ifdef SUPPORT_DRIVEN_METHODS |
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| 289 | |
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| 290 | head_support=b.head_support; |
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| 291 | tail_support=b.tail_support; |
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| 292 | |
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| 293 | #endif // SUPPORT_DRIVEN_METHODS |
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| 294 | |
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| 295 | if(_number_of_variables!=b._number_of_variables) |
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| 296 | { |
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| 297 | delete[] exponent_vector; |
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| 298 | _number_of_variables=b._number_of_variables; |
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| 299 | |
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| 300 | if(_number_of_variables<=0) |
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| 301 | { |
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| 302 | cerr<<"\nWARNING: binomial& binomial::operator=(const binomial&):\n" |
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[88615db] | 303 | "assignment from corrupt binomial"<<endl; |
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[6ba162] | 304 | exponent_vector=NULL; |
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| 305 | return (*this); |
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| 306 | } |
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| 307 | |
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| 308 | exponent_vector=new Integer[_number_of_variables]; |
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| 309 | } |
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| 310 | |
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| 311 | for(short i=0;i<_number_of_variables;i++) |
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| 312 | exponent_vector[i]=b.exponent_vector[i]; |
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| 313 | |
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| 314 | return(*this); |
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| 315 | } |
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| 316 | |
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| 317 | |
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| 318 | |
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| 319 | |
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| 320 | Integer binomial::operator[](const short& i) const |
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| 321 | { |
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| 322 | return exponent_vector[i]; |
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| 323 | } |
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| 324 | |
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| 325 | |
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| 326 | |
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| 327 | |
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| 328 | //////////////////// comparison operators /////////////////////////////////// |
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| 329 | |
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| 330 | |
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| 331 | |
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| 332 | |
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| 333 | BOOLEAN binomial::operator==(const binomial& b) const |
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| 334 | { |
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| 335 | if(this == &b) |
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| 336 | return(TRUE); |
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| 337 | |
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| 338 | #ifdef SUPPORT_DRIVEN_METHODS |
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| 339 | |
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| 340 | if(head_support!=b.head_support) |
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| 341 | return(FALSE); |
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| 342 | if(tail_support!=b.tail_support) |
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| 343 | return(FALSE); |
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| 344 | |
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| 345 | #endif // SUPPORT_DRIVEN_METHODS |
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| 346 | |
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| 347 | for(short i=0;i<_number_of_variables;i++) |
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| 348 | if(exponent_vector[i]!=b.exponent_vector[i]) |
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| 349 | return(FALSE); |
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| 350 | return(TRUE); |
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| 351 | } |
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| 352 | |
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| 353 | |
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| 354 | |
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| 355 | |
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| 356 | BOOLEAN binomial::operator!=(const binomial& b) const |
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| 357 | { |
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| 358 | if(this == &b) |
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| 359 | return(FALSE); |
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| 360 | |
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| 361 | #ifdef SUPPORT_DRIVEN_METHODS |
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| 362 | |
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| 363 | if(head_support!=b.head_support) |
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| 364 | return(TRUE); |
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| 365 | if(tail_support!=b.tail_support) |
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| 366 | return(TRUE); |
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| 367 | |
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| 368 | #endif // SUPPORT_DRIVEN_METHODS |
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| 369 | |
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| 370 | for(short i=0;i<_number_of_variables;i++) |
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| 371 | if(exponent_vector[i]!=b.exponent_vector[i]) |
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| 372 | return(TRUE); |
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| 373 | return(FALSE); |
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| 374 | } |
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| 375 | |
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| 376 | |
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| 377 | |
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| 378 | |
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| 379 | // operators for efficient comparisons with the zero binomial (comp_value=0) |
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| 380 | |
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| 381 | BOOLEAN binomial::operator==(const Integer comp_value) const |
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| 382 | { |
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| 383 | |
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| 384 | #ifdef SUPPORT_DRIVEN_METHODS |
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| 385 | |
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| 386 | if(comp_value==0) |
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| 387 | { |
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| 388 | if(head_support!=0) |
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| 389 | return(FALSE); |
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| 390 | if(tail_support!=0) |
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| 391 | return(FALSE); |
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| 392 | } |
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| 393 | |
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| 394 | #endif // SUPPORT_DRIVEN_METHODS |
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| 395 | |
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| 396 | for(short i=0;i<_number_of_variables;i++) |
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| 397 | if(exponent_vector[i]!=comp_value) |
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| 398 | return(FALSE); |
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| 399 | return(TRUE); |
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| 400 | } |
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| 401 | |
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| 402 | |
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| 403 | |
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| 404 | |
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| 405 | BOOLEAN binomial::operator!=(const Integer comp_value) const |
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| 406 | { |
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| 407 | |
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| 408 | #ifdef SUPPORT_DRIVEN_METHODS |
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| 409 | |
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| 410 | if(comp_value==0) |
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| 411 | { |
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| 412 | if(head_support!=0) |
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| 413 | return(TRUE); |
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| 414 | if(tail_support!=0) |
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| 415 | return(TRUE); |
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| 416 | } |
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| 417 | |
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| 418 | #endif // SUPPORT_DRIVEN_METHODS |
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| 419 | |
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| 420 | for(short i=0;i<_number_of_variables;i++) |
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| 421 | if(exponent_vector[i]!=comp_value) |
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| 422 | return(TRUE); |
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| 423 | return(FALSE); |
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| 424 | } |
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| 425 | |
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| 426 | |
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| 427 | |
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| 428 | |
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| 429 | BOOLEAN binomial::operator<=(const Integer comp_value) const |
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| 430 | { |
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| 431 | |
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| 432 | #ifdef SUPPORT_DRIVEN_METHODS |
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| 433 | |
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| 434 | if(comp_value==0) |
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| 435 | if(head_support!=0) |
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| 436 | return(FALSE); |
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| 437 | |
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| 438 | #endif // SUPPORT_DRIVEN_METHODS |
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| 439 | |
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| 440 | for(short i=0;i<_number_of_variables;i++) |
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| 441 | if(exponent_vector[i]>comp_value) |
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| 442 | return(FALSE); |
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| 443 | return(TRUE); |
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| 444 | } |
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| 445 | |
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| 446 | |
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| 447 | |
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| 448 | |
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| 449 | BOOLEAN binomial::operator>=(const Integer comp_value) const |
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| 450 | { |
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| 451 | |
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| 452 | #ifdef SUPPORT_DRIVEN_METHODS |
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| 453 | |
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| 454 | if(comp_value==0) |
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| 455 | if(tail_support!=0) |
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| 456 | return(FALSE); |
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| 457 | |
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| 458 | #endif |
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| 459 | |
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| 460 | for(short i=0;i<_number_of_variables;i++) |
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| 461 | if(exponent_vector[i]<comp_value) |
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| 462 | return(FALSE); |
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| 463 | return(TRUE); |
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| 464 | } |
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| 465 | |
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| 466 | |
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| 467 | |
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| 468 | |
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| 469 | ////////////// basic routines for Buchbergers's algorithm ////////////////// |
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| 470 | |
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| 471 | |
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| 472 | |
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| 473 | |
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| 474 | Integer binomial::head_reductions_by(const binomial& b) const |
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| 475 | // Returns the number of possible reductions of the actual binomialŽs head |
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| 476 | // by the binomial b. This is the minimum of the quotients |
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| 477 | // exponent_vector[i]/b.exponent_vector[i] |
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| 478 | // where exponent_vector[i]>0 and b.exponent_vector[i]>0 |
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| 479 | // (0 if there are no such quotients). |
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| 480 | // A negative return value means b=0 or head(b)=1. |
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| 481 | { |
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| 482 | |
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| 483 | |
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| 484 | #ifdef NO_SUPPORT_DRIVEN_METHODS |
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| 485 | |
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| 486 | Integer result=-1; |
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| 487 | Integer new_result=-1; |
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| 488 | // -1 stands for infinitely many reductions |
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| 489 | |
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| 490 | for(short i=0;i<_number_of_variables;i++) |
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| 491 | // explicit sign tests for all components |
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| 492 | { |
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| 493 | Integer actual_b_component=b.exponent_vector[i]; |
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| 494 | |
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| 495 | if(actual_b_component>0) |
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| 496 | // else variable i is not involved in the head of b |
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| 497 | { |
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| 498 | Integer actual_component=exponent_vector[i]; |
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| 499 | |
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| 500 | if(actual_component<actual_b_component) |
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| 501 | return 0; |
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| 502 | |
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| 503 | new_result=(Integer) (actual_component/actual_b_component); |
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| 504 | |
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| 505 | // new_result>=1 |
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| 506 | if((new_result<result) || (result==-1)) |
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| 507 | // new (or first) minimum |
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| 508 | result=new_result; |
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| 509 | } |
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| 510 | } |
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| 511 | |
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| 512 | #endif // NO_SUPPORT_DRIVEN_METHODS |
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| 513 | |
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| 514 | |
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| 515 | #ifdef SUPPORT_DRIVEN_METHODS |
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| 516 | |
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| 517 | if((head_support&b.head_support)!=b.head_support) |
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| 518 | // head support of b not contained in head support, no reduction possible |
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| 519 | return 0; |
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| 520 | |
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| 521 | |
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| 522 | Integer result=-1; |
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| 523 | Integer new_result=-1; |
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| 524 | // -1 stands for infinitely many reductions |
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| 525 | |
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| 526 | |
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| 527 | short size_of_support_vectors=CHAR_BIT*sizeof(long); |
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| 528 | // number of bits of a long int |
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| 529 | if(size_of_support_vectors>_number_of_variables) |
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| 530 | size_of_support_vectors=_number_of_variables; |
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| 531 | // number of components of the support vectors |
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| 532 | |
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| 533 | |
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| 534 | #ifdef SUPPORT_VARIABLES_FIRST |
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| 535 | |
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| 536 | for(short i=0;i<size_of_support_vectors;i++) |
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| 537 | // test support variables |
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| 538 | |
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| 539 | if(b.head_support&(1<<i)) |
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| 540 | // bit i of b.head_support is 1 |
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| 541 | { |
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| 542 | new_result=(Integer) (exponent_vector[i]/b.exponent_vector[i]); |
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| 543 | // remember that exponent_vector[i]>0 ! |
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| 544 | // (head support contains that of b) |
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| 545 | |
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| 546 | if(new_result==0) |
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| 547 | // exponent_vector[i]<b.exponent_vector[i] |
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| 548 | return 0; |
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| 549 | |
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| 550 | // new_result>=1 |
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| 551 | if((new_result<result) || (result==-1)) |
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| 552 | // new (or first) minimum |
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| 553 | result=new_result; |
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| 554 | } |
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| 555 | |
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| 556 | |
---|
| 557 | for(short i=size_of_support_vectors;i<_number_of_variables;i++) |
---|
| 558 | // test non-support variables |
---|
| 559 | // from now on we need explicit sign tests |
---|
| 560 | { |
---|
| 561 | Integer actual_b_component=b.exponent_vector[i]; |
---|
| 562 | |
---|
| 563 | if(actual_b_component>0) |
---|
| 564 | // else variable i is not involved in the head of b |
---|
| 565 | { |
---|
| 566 | Integer actual_component=exponent_vector[i]; |
---|
| 567 | |
---|
| 568 | if(actual_component<actual_b_component) |
---|
| 569 | return 0; |
---|
| 570 | |
---|
| 571 | new_result=(Integer) (actual_component/actual_b_component); |
---|
| 572 | |
---|
| 573 | // new_result>=1 |
---|
| 574 | if((new_result<result) || (result==-1)) |
---|
| 575 | // new (or first) minimum |
---|
| 576 | result=new_result; |
---|
| 577 | } |
---|
| 578 | } |
---|
| 579 | |
---|
| 580 | #endif // SUPPORT_VARIABLES_FIRST |
---|
| 581 | |
---|
| 582 | |
---|
| 583 | #ifdef SUPPORT_VARIABLES_LAST |
---|
| 584 | |
---|
| 585 | for(short i=0;i<size_of_support_vectors;i++) |
---|
| 586 | // test support variables |
---|
| 587 | |
---|
| 588 | if(b.head_support&(1<<i)) |
---|
| 589 | // bit i of b.head_support is 1 |
---|
| 590 | { |
---|
| 591 | short j=_number_of_variables-1-i; |
---|
| 592 | new_result=(Integer) (exponent_vector[j]/ b.exponent_vector[j]); |
---|
| 593 | // remember that exponent_vector[_number_of_variables-1-i]>0 ! |
---|
| 594 | // (head support contains that of b) |
---|
| 595 | |
---|
| 596 | if(new_result==0) |
---|
| 597 | // exponent_vector[_number_of_variables-1-i] |
---|
| 598 | // <b.exponent_vector[_number_of_variables-1-i] |
---|
| 599 | return 0; |
---|
| 600 | |
---|
| 601 | // new_result>=1 |
---|
| 602 | if((new_result<result) || (result==-1)) |
---|
| 603 | // new (or first) minimum |
---|
| 604 | result=new_result; |
---|
| 605 | } |
---|
| 606 | |
---|
| 607 | |
---|
| 608 | for(short i=size_of_support_vectors;i<_number_of_variables;i++) |
---|
| 609 | // test non-support variables |
---|
| 610 | // from now on we need explicit sign tests |
---|
| 611 | { |
---|
| 612 | short j=_number_of_variables-1-i; |
---|
| 613 | Integer actual_b_component=b.exponent_vector[j]; |
---|
| 614 | |
---|
| 615 | if(actual_b_component>0) |
---|
| 616 | // else variable number_of_variables-1-i is not involved in the head of b |
---|
| 617 | { |
---|
| 618 | Integer actual_component=exponent_vector[j]; |
---|
| 619 | |
---|
| 620 | if(actual_component<actual_b_component) |
---|
| 621 | return 0; |
---|
| 622 | |
---|
| 623 | new_result=(Integer) (actual_component/actual_b_component); |
---|
| 624 | |
---|
| 625 | // new_result>=1 |
---|
| 626 | if((new_result<result) || (result==-1)) |
---|
| 627 | // new (or first) minimum |
---|
| 628 | result=new_result; |
---|
| 629 | } |
---|
| 630 | } |
---|
| 631 | |
---|
| 632 | #endif // SUPPORT_VARIABLES_LAST |
---|
| 633 | |
---|
| 634 | |
---|
| 635 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 636 | |
---|
| 637 | |
---|
| 638 | return(result); |
---|
| 639 | } |
---|
| 640 | |
---|
| 641 | |
---|
| 642 | |
---|
| 643 | |
---|
| 644 | Integer binomial::tail_reductions_by(const binomial& b) const |
---|
| 645 | // Returns the number of possible reductions of the actual binomialŽs tail |
---|
| 646 | // by the binomial b. This is the minimum of the quotients |
---|
| 647 | // - exponent_vector[i]/b.exponent_vector[i] |
---|
| 648 | // where exponent_vector[i]<0 and b.exponent_vector[i]>0 |
---|
| 649 | // (0 if there are no such quotients). |
---|
| 650 | // A negative return value means b=0 or head(b)=1. |
---|
| 651 | { |
---|
| 652 | |
---|
| 653 | |
---|
| 654 | #ifdef NO_SUPPORT_DRIVEN_METHODS |
---|
| 655 | |
---|
| 656 | Integer result=-1; |
---|
| 657 | Integer new_result=-1; |
---|
| 658 | // -1 stands for infinitely many reductions |
---|
| 659 | |
---|
| 660 | for(short i=0;i<_number_of_variables;i++) |
---|
| 661 | // explicit sign tests for all components |
---|
| 662 | { |
---|
| 663 | Integer actual_b_component=b.exponent_vector[i]; |
---|
| 664 | |
---|
| 665 | if(actual_b_component>0) |
---|
| 666 | // else variable i is not involved in the head of b |
---|
| 667 | { |
---|
| 668 | Integer actual_component=-exponent_vector[i]; |
---|
| 669 | |
---|
| 670 | if(actual_component<actual_b_component) |
---|
| 671 | return 0; |
---|
| 672 | |
---|
| 673 | new_result=(Integer) (actual_component/actual_b_component); |
---|
| 674 | |
---|
| 675 | // new_result>=1 |
---|
| 676 | if((new_result<result) || (result==-1)) |
---|
| 677 | // new (or first) minimum |
---|
| 678 | result=new_result; |
---|
| 679 | } |
---|
| 680 | } |
---|
| 681 | |
---|
| 682 | #endif // NO_SUPPORT_DRIVEN_METHODS |
---|
| 683 | |
---|
| 684 | |
---|
| 685 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 686 | |
---|
| 687 | if((tail_support&b.head_support)!=b.head_support) |
---|
| 688 | // head support of b not contained in tail support, no reduction possible |
---|
| 689 | return 0; |
---|
| 690 | |
---|
| 691 | |
---|
| 692 | Integer result=-1; |
---|
| 693 | Integer new_result=-1; |
---|
| 694 | // -1 stands for infinitely many reductions |
---|
| 695 | |
---|
| 696 | |
---|
| 697 | short size_of_support_vectors=CHAR_BIT*sizeof(long); |
---|
| 698 | // number of bits of a long int |
---|
| 699 | if(size_of_support_vectors>_number_of_variables) |
---|
| 700 | size_of_support_vectors=_number_of_variables; |
---|
| 701 | // number of components of the support vectors |
---|
| 702 | |
---|
| 703 | |
---|
| 704 | #ifdef SUPPORT_VARIABLES_FIRST |
---|
| 705 | |
---|
| 706 | for(short i=0;i<size_of_support_vectors;i++) |
---|
| 707 | // test support variables |
---|
| 708 | |
---|
| 709 | if(b.head_support&(1<<i)) |
---|
| 710 | // bit i of b.head_support is 1 |
---|
| 711 | { |
---|
| 712 | new_result=(Integer) (-exponent_vector[i]/b.exponent_vector[i]); |
---|
| 713 | // remember that exponent_vector[i]<0 ! |
---|
| 714 | // (tail support contains the head support of b) |
---|
| 715 | |
---|
| 716 | if(new_result==0) |
---|
| 717 | // -exponent_vector[i]<b.exponent_vector[i] |
---|
| 718 | return 0; |
---|
| 719 | |
---|
| 720 | // new_result>=1 |
---|
| 721 | if((new_result<result) || (result==-1)) |
---|
| 722 | // new (or first) minimum |
---|
| 723 | result=new_result; |
---|
| 724 | } |
---|
| 725 | |
---|
| 726 | |
---|
| 727 | for(short i=size_of_support_vectors;i<_number_of_variables;i++) |
---|
| 728 | // test non-support variables |
---|
| 729 | // from now on we need explicit sign tests |
---|
| 730 | { |
---|
| 731 | Integer actual_b_component=b.exponent_vector[i]; |
---|
| 732 | |
---|
| 733 | if(actual_b_component>0) |
---|
| 734 | // else variable i is not involved in the head of b |
---|
| 735 | { |
---|
| 736 | Integer actual_component=-exponent_vector[i]; |
---|
| 737 | |
---|
| 738 | if(actual_component<actual_b_component) |
---|
| 739 | return 0; |
---|
| 740 | |
---|
| 741 | new_result=(Integer) (actual_component/actual_b_component); |
---|
| 742 | |
---|
| 743 | // new_result>=1 |
---|
| 744 | if((new_result<result) || (result==-1)) |
---|
| 745 | // new (or first) minimum |
---|
| 746 | result=new_result; |
---|
| 747 | } |
---|
| 748 | } |
---|
| 749 | |
---|
| 750 | #endif // SUPPORT_VARIABLES_FIRST |
---|
| 751 | |
---|
| 752 | |
---|
| 753 | #ifdef SUPPORT_VARIABLES_LAST |
---|
| 754 | |
---|
| 755 | for(short i=0;i<size_of_support_vectors;i++) |
---|
| 756 | // test support variables |
---|
| 757 | |
---|
| 758 | if(b.head_support&(1<<i)) |
---|
| 759 | // bit i of b.head_support is 1 |
---|
| 760 | { |
---|
| 761 | short j=_number_of_variables-1-i; |
---|
| 762 | new_result=(Integer) (-exponent_vector[j] / b.exponent_vector[j]); |
---|
| 763 | // remember that exponent_vector[_number_of_variables-1-i]<0 ! |
---|
| 764 | // (tail support contains the head support of b) |
---|
| 765 | |
---|
| 766 | if(new_result==0) |
---|
| 767 | // -exponent_vector[_number_of_variables-1-i] |
---|
| 768 | // <b.exponent_vector[_number_of_variables-1-i] |
---|
| 769 | return 0; |
---|
| 770 | |
---|
| 771 | // new_result>=1 |
---|
| 772 | if((new_result<result) || (result==-1)) |
---|
| 773 | // new (or first) minimum |
---|
| 774 | result=new_result; |
---|
| 775 | } |
---|
| 776 | |
---|
| 777 | |
---|
| 778 | for(short i=size_of_support_vectors;i<_number_of_variables;i++) |
---|
| 779 | // test non-support variables |
---|
| 780 | // from now on we need explicit sign tests |
---|
| 781 | { |
---|
| 782 | short j=_number_of_variables-1-i; |
---|
| 783 | Integer actual_b_component=b.exponent_vector[j]; |
---|
| 784 | |
---|
| 785 | if(actual_b_component>0) |
---|
| 786 | // else variable number_of_variables-1-i is not involved in the head of b |
---|
| 787 | { |
---|
| 788 | Integer actual_component=-exponent_vector[j]; |
---|
| 789 | |
---|
| 790 | if(actual_component<actual_b_component) |
---|
| 791 | return 0; |
---|
| 792 | |
---|
| 793 | new_result=(Integer) (actual_component/actual_b_component); |
---|
| 794 | |
---|
| 795 | // new_result>=1 |
---|
| 796 | if((new_result<result) || (result==-1)) |
---|
| 797 | // new (or first) minimum |
---|
| 798 | result=new_result; |
---|
| 799 | } |
---|
| 800 | } |
---|
| 801 | |
---|
| 802 | #endif // SUPPORT_VARIABLES_LAST |
---|
| 803 | |
---|
| 804 | |
---|
| 805 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 806 | |
---|
| 807 | |
---|
| 808 | return(result); |
---|
| 809 | } |
---|
| 810 | |
---|
| 811 | |
---|
| 812 | |
---|
| 813 | |
---|
| 814 | int binomial::reduce_head_by(const binomial& b, const term_ordering& w) |
---|
| 815 | { |
---|
| 816 | Integer reduction_number=head_reductions_by(b); |
---|
| 817 | if(reduction_number<=0) |
---|
| 818 | return 0; |
---|
| 819 | |
---|
| 820 | for(short i=0;i<_number_of_variables;i++) |
---|
| 821 | exponent_vector[i]-=(reduction_number * b.exponent_vector[i]); |
---|
| 822 | // multiple reduction |
---|
| 823 | // reduction corresponds to subtraction of vectors |
---|
| 824 | |
---|
| 825 | short sign=w.compare_to_zero(exponent_vector); |
---|
| 826 | |
---|
| 827 | |
---|
| 828 | #ifdef NO_SUPPORT_DRIVEN_METHODS |
---|
| 829 | |
---|
| 830 | if(sign==0) |
---|
| 831 | // binomial reduced to zero |
---|
| 832 | return 2; |
---|
| 833 | |
---|
| 834 | for(short i=0;i<_number_of_variables;i++) |
---|
| 835 | exponent_vector[i]*=sign; |
---|
| 836 | |
---|
| 837 | #endif // NO_SUPPORT_DRIVEN_METHODS |
---|
| 838 | |
---|
| 839 | |
---|
| 840 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 841 | |
---|
| 842 | head_support=0; |
---|
| 843 | tail_support=0; |
---|
| 844 | |
---|
| 845 | if(sign==0) |
---|
| 846 | // binomial reduced to zero |
---|
| 847 | return 2; |
---|
| 848 | |
---|
| 849 | short size_of_support_vectors=CHAR_BIT*sizeof(unsigned long); |
---|
| 850 | |
---|
| 851 | |
---|
| 852 | // recompute the support vectors |
---|
| 853 | |
---|
| 854 | #ifdef SUPPORT_VARIABLES_FIRST |
---|
| 855 | |
---|
| 856 | for(short i=0;i<_number_of_variables;i++) |
---|
| 857 | { |
---|
| 858 | |
---|
| 859 | Integer& actual_entry=exponent_vector[i]; |
---|
| 860 | // to avoid unnecessary pointer arithmetic |
---|
| 861 | |
---|
| 862 | actual_entry*=sign; |
---|
| 863 | |
---|
| 864 | if(i<size_of_support_vectors) |
---|
| 865 | if(actual_entry>0) |
---|
| 866 | head_support|=(1<<i); |
---|
| 867 | else |
---|
| 868 | if(actual_entry<0) |
---|
| 869 | tail_support|=(1<<i); |
---|
| 870 | } |
---|
| 871 | |
---|
| 872 | #endif // SUPPORT_VARIABLES_FIRST |
---|
| 873 | |
---|
| 874 | |
---|
| 875 | #ifdef SUPPORT_VARIABLES_LAST |
---|
| 876 | |
---|
| 877 | for(short i=0;i<_number_of_variables;i++) |
---|
| 878 | { |
---|
| 879 | Integer& actual_entry=exponent_vector[_number_of_variables-1-i]; |
---|
| 880 | // to avoid unneccessary pointer arithmetic |
---|
| 881 | |
---|
| 882 | actual_entry*=sign; |
---|
| 883 | |
---|
| 884 | if(i<size_of_support_vectors) |
---|
[f07fec] | 885 | { |
---|
[6ba162] | 886 | if(actual_entry>0) |
---|
| 887 | head_support|=(1<<i); |
---|
[f07fec] | 888 | else if(actual_entry<0) |
---|
| 889 | tail_support|=(1<<i); |
---|
| 890 | } |
---|
[6ba162] | 891 | } |
---|
| 892 | |
---|
| 893 | #endif // SUPPORT_VARIABLES_LAST |
---|
| 894 | |
---|
| 895 | |
---|
| 896 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 897 | |
---|
| 898 | return 1; |
---|
| 899 | } |
---|
| 900 | |
---|
| 901 | |
---|
| 902 | |
---|
| 903 | |
---|
| 904 | int binomial::reduce_tail_by(const binomial& b, const term_ordering& w) |
---|
| 905 | { |
---|
| 906 | Integer reduction_number=tail_reductions_by(b); |
---|
| 907 | if(reduction_number<=0) |
---|
| 908 | return 0; |
---|
| 909 | |
---|
| 910 | for(short i=0;i<_number_of_variables;i++) |
---|
| 911 | exponent_vector[i]+=(reduction_number * b.exponent_vector[i]); |
---|
| 912 | // multiple reduction |
---|
| 913 | // reduction corresponds to addition of vectors |
---|
| 914 | |
---|
| 915 | // a tail reduction does not require a sign check |
---|
| 916 | |
---|
| 917 | |
---|
| 918 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 919 | |
---|
| 920 | head_support=0; |
---|
| 921 | tail_support=0; |
---|
| 922 | |
---|
| 923 | short size_of_support_vectors=CHAR_BIT*sizeof(unsigned long); |
---|
| 924 | |
---|
| 925 | |
---|
| 926 | // recompute the support vectors |
---|
| 927 | |
---|
| 928 | #ifdef SUPPORT_VARIABLES_FIRST |
---|
| 929 | |
---|
| 930 | for(short i=0;i<_number_of_variables;i++) |
---|
| 931 | { |
---|
| 932 | |
---|
| 933 | Integer& actual_entry=exponent_vector[i]; |
---|
| 934 | // to avoid unnecessary pointer arithmetic |
---|
| 935 | |
---|
| 936 | if(i<size_of_support_vectors) |
---|
[f07fec] | 937 | { |
---|
[6ba162] | 938 | if(actual_entry>0) |
---|
| 939 | head_support|=(1<<i); |
---|
[f07fec] | 940 | else if(actual_entry<0) |
---|
| 941 | tail_support|=(1<<i); |
---|
| 942 | } |
---|
[6ba162] | 943 | } |
---|
| 944 | |
---|
| 945 | #endif // SUPPORT_VARIABLES_FIRST |
---|
| 946 | |
---|
| 947 | |
---|
| 948 | #ifdef SUPPORT_VARIABLES_LAST |
---|
| 949 | |
---|
| 950 | for(short i=0;i<_number_of_variables;i++) |
---|
| 951 | { |
---|
| 952 | Integer& actual_entry=exponent_vector[_number_of_variables-1-i]; |
---|
| 953 | // to avoid unneccessary pointer arithmetic |
---|
| 954 | |
---|
| 955 | if(i<size_of_support_vectors) |
---|
[f07fec] | 956 | { |
---|
[6ba162] | 957 | if(actual_entry>0) |
---|
| 958 | head_support|=(1<<i); |
---|
[f07fec] | 959 | else if(actual_entry<0) |
---|
| 960 | tail_support|=(1<<i); |
---|
| 961 | } |
---|
[6ba162] | 962 | } |
---|
| 963 | |
---|
| 964 | #endif // SUPPORT_VARIABLES_LAST |
---|
| 965 | |
---|
| 966 | |
---|
| 967 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 968 | |
---|
| 969 | return 1; |
---|
| 970 | } |
---|
| 971 | |
---|
| 972 | |
---|
| 973 | |
---|
| 974 | |
---|
| 975 | binomial& S_binomial(const binomial& a, const binomial& b, |
---|
| 976 | const term_ordering& w) |
---|
| 977 | { |
---|
| 978 | binomial* S_bin=new binomial(a._number_of_variables); |
---|
| 979 | binomial& result=*S_bin; |
---|
| 980 | // Note that we allocate memory for the result binomial. We often use |
---|
| 981 | // pointers or references as argument and return types because the |
---|
| 982 | // generating binomials of an ideal are kept in lists. For the performance |
---|
| 983 | // of Buchberger's algorithm it it very important to avoid local copies |
---|
| 984 | // of binomials, so a lot of attention is paid on the choice of argument |
---|
| 985 | // and return types. As this choice is done in order to improve performance, |
---|
| 986 | // it might be a bad choice with respect to code reuse (there are some |
---|
| 987 | // dangerous constructions). |
---|
| 988 | |
---|
| 989 | for(short i=0;i<result._number_of_variables;i++) |
---|
| 990 | result.exponent_vector[i]=a.exponent_vector[i]-b.exponent_vector[i]; |
---|
| 991 | // The S-binomial corresponds to the vector difference. |
---|
| 992 | |
---|
| 993 | // compute head and tail |
---|
| 994 | short sign=w.compare_to_zero(result.exponent_vector); |
---|
| 995 | |
---|
| 996 | |
---|
| 997 | #ifdef NO_SUPPORT_DRIVEN_METHODS |
---|
| 998 | |
---|
| 999 | if(sign==0) |
---|
| 1000 | // binomial reduced to zero |
---|
| 1001 | return result; |
---|
| 1002 | |
---|
| 1003 | for(short i=0;i<result._number_of_variables;i++) |
---|
| 1004 | result.exponent_vector[i]*=sign; |
---|
| 1005 | |
---|
| 1006 | #endif // NO_SUPPORT_DRIVEN_METHODS |
---|
| 1007 | |
---|
| 1008 | |
---|
| 1009 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1010 | |
---|
| 1011 | result.head_support=0; |
---|
| 1012 | result.tail_support=0; |
---|
| 1013 | |
---|
| 1014 | if(sign==0) |
---|
| 1015 | // binomial reduced to zero |
---|
| 1016 | return result; |
---|
| 1017 | |
---|
| 1018 | short size_of_support_vectors=CHAR_BIT*sizeof(unsigned long); |
---|
| 1019 | |
---|
| 1020 | |
---|
| 1021 | // recompute the support vectors |
---|
| 1022 | |
---|
| 1023 | #ifdef SUPPORT_VARIABLES_FIRST |
---|
| 1024 | |
---|
| 1025 | for(short i=0;i<result._number_of_variables;i++) |
---|
| 1026 | { |
---|
| 1027 | |
---|
| 1028 | Integer& actual_entry=result.exponent_vector[i]; |
---|
| 1029 | // to avoid unnecessary pointer arithmetic |
---|
| 1030 | |
---|
| 1031 | actual_entry*=sign; |
---|
| 1032 | |
---|
| 1033 | if(i<size_of_support_vectors) |
---|
[f07fec] | 1034 | { |
---|
[6ba162] | 1035 | if(actual_entry>0) |
---|
| 1036 | result.head_support|=(1<<i); |
---|
[f07fec] | 1037 | else if(actual_entry<0) |
---|
| 1038 | result.tail_support|=(1<<i); |
---|
| 1039 | } |
---|
[6ba162] | 1040 | } |
---|
| 1041 | |
---|
| 1042 | #endif // SUPPORT_VARIABLES_FIRST |
---|
| 1043 | |
---|
| 1044 | |
---|
| 1045 | #ifdef SUPPORT_VARIABLES_LAST |
---|
| 1046 | |
---|
| 1047 | for(short i=0;i<result._number_of_variables;i++) |
---|
| 1048 | { |
---|
| 1049 | Integer& actual_entry=result.exponent_vector |
---|
| 1050 | [result._number_of_variables-1-i]; |
---|
| 1051 | // to avoid unneccessary pointer arithmetic |
---|
| 1052 | |
---|
| 1053 | actual_entry*=sign; |
---|
| 1054 | |
---|
| 1055 | if(i<size_of_support_vectors) |
---|
[f07fec] | 1056 | { |
---|
[6ba162] | 1057 | if(actual_entry>0) |
---|
| 1058 | result.head_support|=(1<<i); |
---|
[f07fec] | 1059 | else if(actual_entry<0) |
---|
[6ba162] | 1060 | result.tail_support|=(1<<i); |
---|
[f07fec] | 1061 | } |
---|
[6ba162] | 1062 | } |
---|
| 1063 | |
---|
| 1064 | #endif // SUPPORT_VARIABLES_LAST |
---|
| 1065 | |
---|
| 1066 | |
---|
| 1067 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 1068 | |
---|
| 1069 | |
---|
| 1070 | return result; |
---|
| 1071 | } |
---|
| 1072 | |
---|
| 1073 | |
---|
| 1074 | |
---|
| 1075 | |
---|
| 1076 | ///////////// criteria for unnecessary S-pairs /////////////////////////////// |
---|
| 1077 | |
---|
| 1078 | // The criteria are programmed in a way that tries to minimize pointer |
---|
| 1079 | // arithmetic. Therefore the code may appear a little bit inflated. |
---|
| 1080 | |
---|
| 1081 | |
---|
| 1082 | |
---|
| 1083 | |
---|
| 1084 | BOOLEAN relatively_prime(const binomial& a, const binomial& b) |
---|
| 1085 | { |
---|
| 1086 | |
---|
| 1087 | #ifdef NO_SUPPORT_DRIVEN_METHODS |
---|
| 1088 | |
---|
| 1089 | // look at all variables |
---|
| 1090 | for(short i=0;i<a._number_of_variables;i++) |
---|
| 1091 | if((a.exponent_vector[i]>0) && (b.exponent_vector[i]>0)) |
---|
| 1092 | return FALSE; |
---|
| 1093 | |
---|
| 1094 | return TRUE; |
---|
| 1095 | |
---|
| 1096 | #endif // NO_SUPPORT_DRIVEN_METHODS |
---|
| 1097 | |
---|
| 1098 | |
---|
| 1099 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1100 | |
---|
| 1101 | if((a.head_support & b.head_support)!=0) |
---|
| 1102 | // common support variable in the heads |
---|
| 1103 | return FALSE; |
---|
| 1104 | |
---|
| 1105 | // no common support variable in the heads, look at remaining variables |
---|
| 1106 | short size_of_support_vectors=CHAR_BIT*sizeof(unsigned long); |
---|
| 1107 | |
---|
| 1108 | |
---|
| 1109 | #ifdef SUPPORT_VARIABLES_FIRST |
---|
| 1110 | |
---|
| 1111 | for(short i=size_of_support_vectors;i<a._number_of_variables;i++) |
---|
| 1112 | if((a.exponent_vector[i]>0) && (b.exponent_vector[i]>0)) |
---|
| 1113 | return FALSE; |
---|
| 1114 | |
---|
| 1115 | return TRUE; |
---|
| 1116 | |
---|
| 1117 | #endif // SUPPORT_VARIABLES_FIRST |
---|
| 1118 | |
---|
| 1119 | |
---|
| 1120 | #ifdef SUPPORT_VARIABLES_LAST |
---|
| 1121 | |
---|
| 1122 | for(short i=a._number_of_variables-1-size_of_support_vectors;i>=0;i--) |
---|
| 1123 | if((a.exponent_vector[i]>0) && (b.exponent_vector[i]>0)) |
---|
| 1124 | return FALSE; |
---|
| 1125 | |
---|
| 1126 | return TRUE; |
---|
| 1127 | |
---|
| 1128 | #endif // SUPPORT_VARIABLES_LAST |
---|
| 1129 | |
---|
| 1130 | |
---|
| 1131 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 1132 | |
---|
| 1133 | } |
---|
| 1134 | |
---|
| 1135 | |
---|
| 1136 | |
---|
| 1137 | |
---|
| 1138 | BOOLEAN M(const binomial& a, const binomial& b, const binomial& c) |
---|
| 1139 | // Returns TRUE iff lcm(head(a),head(c)) divides properly lcm(head(b),head(c)). |
---|
| 1140 | // This is checked by comparing the positive components of the exponent |
---|
| 1141 | // vectors. |
---|
| 1142 | { |
---|
| 1143 | |
---|
| 1144 | |
---|
| 1145 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1146 | |
---|
| 1147 | long b_or_c=b.head_support|c.head_support; |
---|
| 1148 | |
---|
| 1149 | if((a.head_support|b_or_c) != b_or_c) |
---|
| 1150 | return FALSE; |
---|
| 1151 | // The support of lcm(head(a),head(c)) equals the union of the head supports |
---|
| 1152 | // of a and c. The above condition verifies if the support of |
---|
| 1153 | // lcm(head(a),head(c)) is contained in the support of lcm(head(b),head(c)) |
---|
| 1154 | // by checking if head a involves a variable that is not involved in |
---|
| 1155 | // head(b) or head(c). |
---|
| 1156 | |
---|
| 1157 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 1158 | |
---|
| 1159 | |
---|
| 1160 | BOOLEAN properly=FALSE; |
---|
| 1161 | |
---|
| 1162 | for(short i=0;i<a._number_of_variables;i++) |
---|
| 1163 | { |
---|
| 1164 | Integer a_exponent=a.exponent_vector[i]; |
---|
| 1165 | Integer b_exponent=b.exponent_vector[i]; |
---|
| 1166 | Integer c_exponent=c.exponent_vector[i]; |
---|
| 1167 | Integer m1=MAXIMUM(a_exponent,c_exponent); |
---|
| 1168 | Integer m2=MAXIMUM(b_exponent,c_exponent); |
---|
| 1169 | |
---|
| 1170 | if(m1>0) |
---|
| 1171 | { |
---|
| 1172 | if(m1>m2) |
---|
| 1173 | return FALSE; |
---|
| 1174 | if(m1<m2) |
---|
| 1175 | properly=TRUE; |
---|
| 1176 | } |
---|
| 1177 | } |
---|
| 1178 | |
---|
| 1179 | return properly; |
---|
| 1180 | } |
---|
| 1181 | |
---|
| 1182 | |
---|
| 1183 | |
---|
| 1184 | |
---|
| 1185 | BOOLEAN F(const binomial& a, const binomial& b, const binomial& c) |
---|
| 1186 | // verifies if lcm(head(a),head(c))=lcm(head(b),head(c)) |
---|
| 1187 | { |
---|
| 1188 | |
---|
| 1189 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1190 | |
---|
| 1191 | if((a.head_support|c.head_support)!=(b.head_support|c.head_support)) |
---|
| 1192 | return FALSE; |
---|
| 1193 | // The above condition verifies if the support of lcm(head(a),head(c)) |
---|
| 1194 | // equals the support of lcm(head(b),head(c)). |
---|
| 1195 | |
---|
| 1196 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 1197 | |
---|
| 1198 | for(short i=0;i<a._number_of_variables;i++) |
---|
| 1199 | { |
---|
| 1200 | Integer a_exponent=a.exponent_vector[i]; |
---|
| 1201 | Integer b_exponent=b.exponent_vector[i]; |
---|
| 1202 | Integer c_exponent=c.exponent_vector[i]; |
---|
| 1203 | Integer m1=MAXIMUM(a_exponent,c_exponent); |
---|
| 1204 | Integer m2=MAXIMUM(b_exponent,c_exponent); |
---|
| 1205 | |
---|
| 1206 | if((m1!=m2) && (m1>0 || m2>0)) |
---|
| 1207 | return FALSE; |
---|
| 1208 | } |
---|
| 1209 | |
---|
| 1210 | return TRUE; |
---|
| 1211 | } |
---|
| 1212 | |
---|
| 1213 | |
---|
| 1214 | |
---|
| 1215 | |
---|
| 1216 | BOOLEAN B(const binomial& a, const binomial& b, const binomial& c) |
---|
| 1217 | // verifies if head(a) divides lcm(head(b),head(c)) and |
---|
| 1218 | // lcm(head(a),head(b))!=lcm(head(b),head(c))!=lcm(head(a),head(c)) |
---|
| 1219 | { |
---|
| 1220 | |
---|
| 1221 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1222 | |
---|
| 1223 | long a_or_b=a.head_support|b.head_support; |
---|
| 1224 | long a_or_c=a.head_support|c.head_support; |
---|
| 1225 | long b_or_c=b.head_support|c.head_support; |
---|
| 1226 | |
---|
| 1227 | if((a.head_support & b_or_c)!=a.head_support) |
---|
| 1228 | return FALSE; |
---|
| 1229 | // The above condition verifies if the support of head(a) is contained in |
---|
| 1230 | // the support of lcm(head(b),head(c)). |
---|
| 1231 | |
---|
| 1232 | if( (a_or_c != b_or_c) && (a_or_b != b_or_c)) |
---|
| 1233 | // Then the inequality conditions are guaranteed... |
---|
| 1234 | { |
---|
| 1235 | for(short i=0;i<a._number_of_variables;i++) |
---|
| 1236 | { |
---|
| 1237 | Integer b_exponent=b.exponent_vector[i]; |
---|
| 1238 | Integer c_exponent=c.exponent_vector[i]; |
---|
| 1239 | |
---|
| 1240 | if(a.exponent_vector[i]>MAXIMUM(b_exponent,c_exponent)) |
---|
| 1241 | return FALSE; |
---|
| 1242 | } |
---|
| 1243 | |
---|
| 1244 | return (TRUE); |
---|
| 1245 | } |
---|
| 1246 | |
---|
| 1247 | |
---|
| 1248 | if(a_or_b != b_or_c) |
---|
| 1249 | // Then the first inequality conditions is guaranteed... |
---|
| 1250 | // Verifie only the second. |
---|
| 1251 | { |
---|
| 1252 | BOOLEAN not_equal=FALSE; |
---|
| 1253 | |
---|
| 1254 | for(short i=0;i<a._number_of_variables;i++) |
---|
| 1255 | { |
---|
| 1256 | Integer a_exponent=a.exponent_vector[i]; |
---|
| 1257 | Integer b_exponent=b.exponent_vector[i]; |
---|
| 1258 | Integer c_exponent=c.exponent_vector[i]; |
---|
| 1259 | Integer m=MAXIMUM(b_exponent, c_exponent); |
---|
| 1260 | |
---|
| 1261 | if(a_exponent>m) |
---|
| 1262 | return FALSE; |
---|
| 1263 | |
---|
| 1264 | if(MAXIMUM(a_exponent,c_exponent) != m) |
---|
| 1265 | not_equal=TRUE; |
---|
| 1266 | } |
---|
| 1267 | return(not_equal); |
---|
| 1268 | } |
---|
| 1269 | |
---|
| 1270 | |
---|
| 1271 | if( a_or_c != b_or_c ) |
---|
| 1272 | // Then the second inequality conditions is guaranteed... |
---|
| 1273 | // Verifie only the first. |
---|
| 1274 | { |
---|
| 1275 | BOOLEAN not_equal=FALSE; |
---|
| 1276 | |
---|
| 1277 | for(short i=0;i<a._number_of_variables;i++) |
---|
| 1278 | { |
---|
| 1279 | Integer a_exponent=a.exponent_vector[i]; |
---|
| 1280 | Integer b_exponent=b.exponent_vector[i]; |
---|
| 1281 | Integer c_exponent=c.exponent_vector[i]; |
---|
| 1282 | Integer m=MAXIMUM(b_exponent, c_exponent); |
---|
| 1283 | |
---|
| 1284 | if(a_exponent > m) |
---|
| 1285 | return FALSE; |
---|
| 1286 | |
---|
| 1287 | if(MAXIMUM(a_exponent,b_exponent) != m) |
---|
| 1288 | not_equal=TRUE; |
---|
| 1289 | } |
---|
| 1290 | return(not_equal); |
---|
| 1291 | } |
---|
| 1292 | |
---|
| 1293 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 1294 | |
---|
| 1295 | |
---|
| 1296 | BOOLEAN not_equal_1=FALSE; |
---|
| 1297 | BOOLEAN not_equal_2=FALSE; |
---|
| 1298 | |
---|
| 1299 | for(short i=0;i<a._number_of_variables;i++) |
---|
| 1300 | { |
---|
| 1301 | Integer a_exponent=a.exponent_vector[i]; |
---|
| 1302 | Integer b_exponent=b.exponent_vector[i]; |
---|
| 1303 | Integer c_exponent=c.exponent_vector[i]; |
---|
| 1304 | Integer m=MAXIMUM(b_exponent, c_exponent); |
---|
| 1305 | |
---|
| 1306 | if(a_exponent > m) |
---|
| 1307 | return FALSE; |
---|
| 1308 | |
---|
| 1309 | if(MAXIMUM(a_exponent,b_exponent) != m) |
---|
| 1310 | not_equal_1=TRUE; |
---|
| 1311 | if(MAXIMUM(a_exponent,c_exponent) != m) |
---|
| 1312 | not_equal_2=TRUE; |
---|
| 1313 | } |
---|
| 1314 | |
---|
| 1315 | return (not_equal_1 && not_equal_2); |
---|
| 1316 | |
---|
| 1317 | } |
---|
| 1318 | |
---|
| 1319 | |
---|
| 1320 | |
---|
| 1321 | |
---|
| 1322 | BOOLEAN second_crit(const binomial& a, const binomial& b, |
---|
| 1323 | const binomial& c) |
---|
| 1324 | // verifies if head(a) divides lcm(head(b),head(c)) |
---|
| 1325 | { |
---|
| 1326 | |
---|
| 1327 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1328 | |
---|
| 1329 | if((a.head_support & (b.head_support|c.head_support))!=a.head_support) |
---|
| 1330 | return FALSE; |
---|
| 1331 | // The above condition verifies if the support of head(a) is contained in |
---|
| 1332 | // the support of lcm(head(b),head(c)) |
---|
| 1333 | |
---|
| 1334 | #endif // SUPPORT_DRIVEN_METHODS. |
---|
| 1335 | |
---|
| 1336 | for(short i=0;i<a._number_of_variables;i++) |
---|
| 1337 | { |
---|
| 1338 | Integer b_exponent=b.exponent_vector[i]; |
---|
| 1339 | Integer c_exponent=c.exponent_vector[i]; |
---|
| 1340 | |
---|
| 1341 | if(a.exponent_vector[i]>MAXIMUM(b_exponent,c_exponent)) |
---|
| 1342 | return FALSE; |
---|
| 1343 | } |
---|
| 1344 | |
---|
| 1345 | return (TRUE); |
---|
| 1346 | } |
---|
| 1347 | |
---|
| 1348 | |
---|
| 1349 | |
---|
| 1350 | |
---|
| 1351 | //////// special routines needed by the IP-algorithms /////////////////////// |
---|
| 1352 | |
---|
| 1353 | |
---|
| 1354 | |
---|
| 1355 | |
---|
| 1356 | BOOLEAN binomial::involves_elimination_variables(const term_ordering& w) |
---|
| 1357 | { |
---|
| 1358 | // The use of support information would require the distinction of various |
---|
| 1359 | // cases here (relation between the number of variables to eliminate |
---|
| 1360 | // and the number of support variables) and be quite difficult. |
---|
| 1361 | // It is doubtful if this would improve performance. |
---|
| 1362 | // As this function is not used in BuchbergerŽs algorithm (and therefore |
---|
| 1363 | // rather rarely), I renounce to implement this. |
---|
| 1364 | |
---|
| 1365 | for(short i=0;i<w.number_of_elimination_variables();i++) |
---|
| 1366 | // elimination variables are always the last ones |
---|
| 1367 | if(exponent_vector[_number_of_variables-1-i]!=0) |
---|
| 1368 | return TRUE; |
---|
| 1369 | |
---|
| 1370 | return FALSE; |
---|
| 1371 | } |
---|
| 1372 | |
---|
| 1373 | |
---|
| 1374 | |
---|
| 1375 | |
---|
| 1376 | BOOLEAN binomial::drop_elimination_variables(const term_ordering& w) |
---|
| 1377 | { |
---|
| 1378 | _number_of_variables-=w.number_of_elimination_variables(); |
---|
| 1379 | // dangerous (no compatibility check)!! |
---|
| 1380 | |
---|
| 1381 | // copy components of interest to save memory |
---|
| 1382 | // the leading term has to be recomputed!! |
---|
| 1383 | |
---|
| 1384 | Integer *aux=exponent_vector; |
---|
| 1385 | exponent_vector=new Integer[_number_of_variables]; |
---|
| 1386 | |
---|
| 1387 | if(w.weight(aux)>=0) |
---|
| 1388 | for(short i=0;i<_number_of_variables;i++) |
---|
| 1389 | exponent_vector[i]=aux[i]; |
---|
| 1390 | else |
---|
| 1391 | for(short i=0;i<_number_of_variables;i++) |
---|
| 1392 | exponent_vector[i]=-aux[i]; |
---|
| 1393 | |
---|
| 1394 | delete[] aux; |
---|
| 1395 | |
---|
| 1396 | |
---|
| 1397 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1398 | |
---|
| 1399 | // Recompute head and tail. |
---|
| 1400 | // Normally, this routine is only called for binomials that do not involve |
---|
| 1401 | // the variables to eliminate. But if SUPPORT_VARIABLES_LAST is enabled, |
---|
| 1402 | // the support changes in spite of this. Therefore, the support is |
---|
| 1403 | // recomputed... For the same reasons as mentionned in the preceeding |
---|
| 1404 | // routine, the existing support information is not used. |
---|
| 1405 | |
---|
| 1406 | head_support=0; |
---|
| 1407 | tail_support=0; |
---|
| 1408 | short size_of_support_vectors=CHAR_BIT*sizeof(unsigned long); |
---|
| 1409 | if(size_of_support_vectors>_number_of_variables) |
---|
| 1410 | size_of_support_vectors=_number_of_variables; |
---|
| 1411 | |
---|
| 1412 | |
---|
| 1413 | #ifdef SUPPORT_VARIABLES_FIRST |
---|
| 1414 | |
---|
| 1415 | for(short i=0;i<size_of_support_vectors;i++) |
---|
| 1416 | { |
---|
| 1417 | Integer actual_entry=exponent_vector[i]; |
---|
| 1418 | if(actual_entry>0) |
---|
| 1419 | head_support|=(1<<i); |
---|
[f07fec] | 1420 | else if(actual_entry[i]<0) |
---|
| 1421 | tail_support|=(1<<i); |
---|
[6ba162] | 1422 | } |
---|
| 1423 | |
---|
| 1424 | #endif // SUPPORT_VARIABLES_FIRST |
---|
| 1425 | |
---|
| 1426 | |
---|
| 1427 | #ifdef SUPPORT_VARIABLES_LAST |
---|
| 1428 | |
---|
| 1429 | for(short i=0;i<size_of_support_vectors;i++) |
---|
| 1430 | { |
---|
| 1431 | Integer actual_entry=exponent_vector[_number_of_variables-1-i]; |
---|
| 1432 | if(actual_entry>0) |
---|
| 1433 | head_support|=(1<<i); |
---|
[f07fec] | 1434 | else if(actual_entry<0) |
---|
| 1435 | tail_support|=(1<<i); |
---|
[6ba162] | 1436 | } |
---|
| 1437 | |
---|
| 1438 | #endif // SUPPORT_VARIABLES_LAST |
---|
| 1439 | |
---|
| 1440 | |
---|
| 1441 | #endif // SUPPORT_DRIVEN_METHODS |
---|
[ce3dda] | 1442 | return TRUE; |
---|
[6ba162] | 1443 | |
---|
| 1444 | } |
---|
| 1445 | |
---|
| 1446 | |
---|
| 1447 | |
---|
| 1448 | |
---|
| 1449 | BOOLEAN binomial::drop_last_weighted_variable(const term_ordering& w) |
---|
| 1450 | { |
---|
| 1451 | _number_of_variables--; |
---|
| 1452 | // dangerous!! |
---|
| 1453 | |
---|
| 1454 | // copy components of interest to save memory |
---|
| 1455 | // the leading term has to be recomputed!! |
---|
| 1456 | |
---|
| 1457 | Integer *aux=exponent_vector; |
---|
| 1458 | exponent_vector=new Integer[_number_of_variables]; |
---|
| 1459 | |
---|
| 1460 | short last_weighted_variable=w.number_of_weighted_variables()-1; |
---|
| 1461 | aux[last_weighted_variable]=0; |
---|
| 1462 | // set last component to zero, so it cannot influence the weight |
---|
| 1463 | |
---|
| 1464 | if(w.weight(aux)>=0) |
---|
| 1465 | { |
---|
| 1466 | for(short i=0;i<last_weighted_variable;i++) |
---|
| 1467 | exponent_vector[i]=aux[i]; |
---|
| 1468 | for(short i=last_weighted_variable;i<_number_of_variables;i++) |
---|
| 1469 | exponent_vector[i]=aux[i+1]; |
---|
| 1470 | } |
---|
| 1471 | else |
---|
| 1472 | { |
---|
| 1473 | for(short i=0;i<last_weighted_variable;i++) |
---|
| 1474 | exponent_vector[i]=-aux[i]; |
---|
| 1475 | for(short i=last_weighted_variable;i<_number_of_variables;i++) |
---|
| 1476 | exponent_vector[i]=-aux[i+1]; |
---|
| 1477 | } |
---|
| 1478 | |
---|
| 1479 | delete[] aux; |
---|
| 1480 | |
---|
| 1481 | |
---|
| 1482 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1483 | |
---|
| 1484 | // Recompute head and tail. |
---|
| 1485 | // Normally, this routine is only called for binomials that do not involve |
---|
| 1486 | // the variable to be dropped. But if SUPPORT_VARIABLES_LAST is enabled, |
---|
| 1487 | // the support changes in spite of this. Therefore, the support is |
---|
| 1488 | // recomputed... For the same reasons as mentionned in the preceeding |
---|
| 1489 | // routines, the existing support information is not used. |
---|
| 1490 | |
---|
| 1491 | head_support=0; |
---|
| 1492 | tail_support=0; |
---|
| 1493 | short size_of_support_vectors=CHAR_BIT*sizeof(unsigned long); |
---|
| 1494 | if(size_of_support_vectors>_number_of_variables) |
---|
| 1495 | size_of_support_vectors=_number_of_variables; |
---|
| 1496 | |
---|
| 1497 | |
---|
| 1498 | #ifdef SUPPORT_VARIABLES_FIRST |
---|
| 1499 | |
---|
| 1500 | for(short i=0;i<size_of_support_vectors;i++) |
---|
| 1501 | { |
---|
| 1502 | Integer actual_entry=exponent_vector[i]; |
---|
| 1503 | if(actual_entry>0) |
---|
| 1504 | head_support|=(1<<i); |
---|
[f07fec] | 1505 | else if(actual_entry<0) |
---|
| 1506 | tail_support|=(1<<i); |
---|
[6ba162] | 1507 | } |
---|
| 1508 | |
---|
| 1509 | #endif // SUPPORT_VARIABLES_FIRST |
---|
| 1510 | |
---|
| 1511 | |
---|
| 1512 | #ifdef SUPPORT_VARIABLES_LAST |
---|
| 1513 | |
---|
| 1514 | for(short i=0;i<size_of_support_vectors;i++) |
---|
| 1515 | { |
---|
| 1516 | Integer actual_entry=exponent_vector[_number_of_variables-1-i]; |
---|
| 1517 | if(actual_entry>0) |
---|
| 1518 | head_support|=(1<<i); |
---|
[f07fec] | 1519 | else if(actual_entry<0) |
---|
| 1520 | tail_support|=(1<<i); |
---|
[6ba162] | 1521 | } |
---|
| 1522 | |
---|
| 1523 | #endif // SUPPORT_VARIABLES_LAST |
---|
| 1524 | |
---|
| 1525 | #endif // SUPPORT_DRIVEN_METHODS |
---|
[ce3dda] | 1526 | return TRUE; |
---|
[6ba162] | 1527 | } |
---|
| 1528 | |
---|
| 1529 | |
---|
| 1530 | |
---|
| 1531 | |
---|
| 1532 | int binomial::adapt_to_term_ordering(const term_ordering& w) |
---|
| 1533 | { |
---|
| 1534 | |
---|
| 1535 | if(w.compare_to_zero(exponent_vector)<0) |
---|
| 1536 | { |
---|
| 1537 | // then exchange head and tail |
---|
| 1538 | for(short i=0;i<_number_of_variables;i++) |
---|
| 1539 | exponent_vector[i]*=(-1); |
---|
| 1540 | |
---|
| 1541 | |
---|
| 1542 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1543 | |
---|
| 1544 | unsigned long swap=head_support; |
---|
| 1545 | head_support=tail_support; |
---|
| 1546 | tail_support=swap; |
---|
| 1547 | |
---|
| 1548 | #endif |
---|
| 1549 | |
---|
| 1550 | |
---|
| 1551 | return -1; |
---|
| 1552 | // binomial changed |
---|
| 1553 | } |
---|
| 1554 | |
---|
| 1555 | else |
---|
| 1556 | return 1; |
---|
| 1557 | // binomial unchanged |
---|
| 1558 | } |
---|
| 1559 | |
---|
| 1560 | |
---|
| 1561 | |
---|
| 1562 | |
---|
| 1563 | binomial& binomial::swap_variables(const short& i, const short& j) |
---|
| 1564 | { |
---|
| 1565 | |
---|
| 1566 | |
---|
| 1567 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1568 | |
---|
| 1569 | // First adjust head_support and tail_support. |
---|
| 1570 | |
---|
| 1571 | short size_of_support_vectors=CHAR_BIT*sizeof(unsigned long); |
---|
| 1572 | if(size_of_support_vectors>_number_of_variables) |
---|
| 1573 | size_of_support_vectors=_number_of_variables; |
---|
| 1574 | |
---|
| 1575 | |
---|
| 1576 | #ifdef SUPPORT_VARIABLES_FIRST |
---|
| 1577 | |
---|
| 1578 | if(i<size_of_support_vectors) |
---|
| 1579 | // else i is no support variable |
---|
| 1580 | { |
---|
| 1581 | if(exponent_vector[j]>0) |
---|
| 1582 | // bit i will be 1 in the new head_support, 0 in the new tail_support |
---|
| 1583 | { |
---|
| 1584 | head_support|=(1<<i); |
---|
| 1585 | // bit i is set to 1 |
---|
| 1586 | |
---|
| 1587 | tail_support&=~(1<<i); |
---|
| 1588 | // bit i is set to 0 |
---|
| 1589 | // (in the complement ~(1<<i) all bits are 1 except from bit i) |
---|
| 1590 | } |
---|
| 1591 | |
---|
| 1592 | if(exponent_vector[j]==0) |
---|
| 1593 | // bit i will be 0 in the new head_support, 0 in the new tail_support |
---|
| 1594 | { |
---|
| 1595 | head_support&=~(1<<i); |
---|
| 1596 | // bit i is set to 0 |
---|
| 1597 | |
---|
| 1598 | tail_support&=~(1<<i); |
---|
| 1599 | // bit i is set to 0 |
---|
| 1600 | } |
---|
| 1601 | |
---|
| 1602 | if(exponent_vector[j]<0) |
---|
| 1603 | // bit i will be 0 in the new head_support, 1 in the new tail_support |
---|
| 1604 | { |
---|
| 1605 | head_support&=~(1<<i); |
---|
| 1606 | // bit i is set to 0 |
---|
| 1607 | |
---|
| 1608 | tail_support|=(1<<i); |
---|
| 1609 | // bit i is set to 1 |
---|
| 1610 | } |
---|
| 1611 | } |
---|
| 1612 | |
---|
| 1613 | |
---|
| 1614 | if(j<size_of_support_vectors) |
---|
| 1615 | // else j is no support variable |
---|
| 1616 | { |
---|
| 1617 | if(exponent_vector[i]>0) |
---|
| 1618 | // bit j will be 1 in the new head_support, 0 in the new tail_support |
---|
| 1619 | { |
---|
| 1620 | head_support|=(1<<j); |
---|
| 1621 | // bit j is set to 1 |
---|
| 1622 | |
---|
| 1623 | tail_support&=~(1<<j); |
---|
| 1624 | // bit j is set to 0 |
---|
| 1625 | // (in the complement ~(1<<j) all bits are 1 except from bit j) |
---|
| 1626 | } |
---|
| 1627 | |
---|
| 1628 | if(exponent_vector[i]==0) |
---|
| 1629 | // bit j will be 0 in the new head_support, 0 in the new tail_support |
---|
| 1630 | { |
---|
| 1631 | head_support&=~(1<<j); |
---|
| 1632 | // bit j is set to 0 |
---|
| 1633 | |
---|
| 1634 | tail_support&=~(1<<j); |
---|
| 1635 | // bit j is set to 0 |
---|
| 1636 | } |
---|
| 1637 | |
---|
| 1638 | if(exponent_vector[i]<0) |
---|
| 1639 | // bit j will be 0 in the new head_support, 1 in the new tail_support |
---|
| 1640 | { |
---|
| 1641 | head_support&=~(1<<j); |
---|
| 1642 | // bit j is set to 0 |
---|
| 1643 | |
---|
| 1644 | tail_support|=(1<<j); |
---|
| 1645 | // bit j is set to 1 |
---|
| 1646 | } |
---|
| 1647 | } |
---|
| 1648 | |
---|
| 1649 | #endif // SUPPORT_VARIABLES_FIRST |
---|
| 1650 | |
---|
| 1651 | |
---|
| 1652 | #ifdef SUPPORT_VARIABLES_LAST |
---|
| 1653 | |
---|
| 1654 | // Using SUPPORT_VARIABLES_LAST, bit k of the support vectors |
---|
| 1655 | // corresponds to exponent_vector[_number_of_variables-1-k], |
---|
| 1656 | // hence bit _number_of_variables-1-i to exponent_vector[i]. |
---|
| 1657 | |
---|
| 1658 | if(i>=_number_of_variables-size_of_support_vectors) |
---|
| 1659 | // else i is no support variable |
---|
| 1660 | { |
---|
| 1661 | if(exponent_vector[j]>0) |
---|
| 1662 | // bit _number_of_variables-1-i will be 1 in the new head_support, |
---|
| 1663 | // 0 in the new tail_support |
---|
| 1664 | { |
---|
| 1665 | short k=_number_of_variables-1-i; |
---|
| 1666 | |
---|
| 1667 | head_support|=(1<<k); |
---|
| 1668 | // bit _number_of_variables-1-i is set to 1 |
---|
| 1669 | |
---|
| 1670 | tail_support&=~(1<<k); |
---|
| 1671 | // bit _number_of_variables-1-i is set to 0 |
---|
| 1672 | // (in the complement ~(1<<(_number_of_variables-1-i)) all bits are 1 |
---|
| 1673 | // except from bit _number_of_variables-1-i) |
---|
| 1674 | } |
---|
| 1675 | |
---|
| 1676 | if(exponent_vector[j]==0) |
---|
| 1677 | // bit _number_of_variables-1-i will be 0 in the new head_support, |
---|
| 1678 | // 0 in the new tail_support |
---|
| 1679 | { |
---|
| 1680 | short k=_number_of_variables-1-i; |
---|
| 1681 | |
---|
| 1682 | head_support&=~(1<<k); |
---|
| 1683 | // bit _number_of_variables-1-i is set to 0 |
---|
| 1684 | |
---|
| 1685 | tail_support&=~(1<<k); |
---|
| 1686 | // bit _number_of_variables-1-i is set to 0 |
---|
| 1687 | } |
---|
| 1688 | |
---|
| 1689 | if(exponent_vector[j]<0) |
---|
| 1690 | // bit _number_of_variables-1-i will be 0 in the new head_support, |
---|
| 1691 | // 1 in the new tail_support |
---|
| 1692 | { |
---|
| 1693 | short k=_number_of_variables-1-i; |
---|
| 1694 | |
---|
| 1695 | head_support&=~(1<<k); |
---|
| 1696 | // bit _number_of_variables-1-i is set to 0 |
---|
| 1697 | |
---|
| 1698 | tail_support|=(1<<k); |
---|
| 1699 | // bit _number_of_variables-1-i is set to 1 |
---|
| 1700 | } |
---|
| 1701 | } |
---|
| 1702 | |
---|
| 1703 | |
---|
| 1704 | if(j>=_number_of_variables-size_of_support_vectors) |
---|
| 1705 | // else j is no support variable |
---|
| 1706 | { |
---|
| 1707 | if(exponent_vector[i]>0) |
---|
| 1708 | // bit _number_of_variables-1-j will be 1 in the new head_support, |
---|
| 1709 | // 0 in the new tail_support |
---|
| 1710 | { |
---|
| 1711 | short k=_number_of_variables-1-j; |
---|
| 1712 | |
---|
| 1713 | head_support|=(1<<k); |
---|
| 1714 | // bit _number_of_variables-1-j is set to 1 |
---|
| 1715 | |
---|
| 1716 | tail_support&=~(1<<k); |
---|
| 1717 | // bit _number_of_variables-1-j is set to 0 |
---|
| 1718 | // (in the complement ~(1<<(_number_of_variables-1-j)) all bits are 1 |
---|
| 1719 | // except from bit _number_of_variables-1-j) |
---|
| 1720 | } |
---|
| 1721 | |
---|
| 1722 | if(exponent_vector[i]==0) |
---|
| 1723 | // bit _number_of_variables-1-j will be 0 in the new head_support, |
---|
| 1724 | // 0 in the new tail_support |
---|
| 1725 | { |
---|
| 1726 | short k=_number_of_variables-1-j; |
---|
| 1727 | |
---|
| 1728 | head_support&=~(1<<k); |
---|
| 1729 | // bit _number_of_variables-1-j is set to 0 |
---|
| 1730 | |
---|
| 1731 | tail_support&=~(1<<k); |
---|
| 1732 | // bit _number_of_variables-1-j is set to 0 |
---|
| 1733 | } |
---|
| 1734 | |
---|
| 1735 | if(exponent_vector[i]<0) |
---|
| 1736 | // bit _number_of_variables-1-j will be 0 in the new head_support, |
---|
| 1737 | // 1 in the new tail_support |
---|
| 1738 | { |
---|
| 1739 | short k=_number_of_variables-1-j; |
---|
| 1740 | |
---|
| 1741 | head_support&=~(1<<k); |
---|
| 1742 | // bit _number_of_variables-1-j is set to 0 |
---|
| 1743 | |
---|
| 1744 | tail_support|=(1<<k); |
---|
| 1745 | // bit _number_of_variables-1-j is set to 1 |
---|
| 1746 | } |
---|
| 1747 | } |
---|
| 1748 | |
---|
| 1749 | #endif // SUPPORT_VARIABLES_LAST |
---|
| 1750 | |
---|
| 1751 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 1752 | |
---|
| 1753 | |
---|
| 1754 | // Now swap the components. |
---|
| 1755 | |
---|
| 1756 | Integer swap=exponent_vector[j]; |
---|
| 1757 | exponent_vector[j]=exponent_vector[i]; |
---|
| 1758 | exponent_vector[i]=swap; |
---|
| 1759 | |
---|
| 1760 | return *this; |
---|
| 1761 | |
---|
| 1762 | } |
---|
| 1763 | |
---|
| 1764 | binomial& binomial::flip_variable(const short& i) |
---|
| 1765 | { |
---|
| 1766 | |
---|
| 1767 | if(exponent_vector[i]==0) |
---|
| 1768 | // binomial does not involve variable to flip |
---|
| 1769 | return *this; |
---|
| 1770 | |
---|
| 1771 | |
---|
| 1772 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1773 | |
---|
| 1774 | // First adjust head_support and tail_support. |
---|
| 1775 | |
---|
| 1776 | short size_of_support_vectors=CHAR_BIT*sizeof(unsigned long); |
---|
| 1777 | if(size_of_support_vectors>_number_of_variables) |
---|
| 1778 | size_of_support_vectors=_number_of_variables; |
---|
| 1779 | |
---|
| 1780 | |
---|
| 1781 | #ifdef SUPPORT_VARIABLES_FIRST |
---|
| 1782 | |
---|
| 1783 | if(i<size_of_support_vectors) |
---|
| 1784 | // else i is no support variable |
---|
| 1785 | { |
---|
| 1786 | if(exponent_vector[i]>0) |
---|
| 1787 | // variable i will be moved from head to tail |
---|
| 1788 | { |
---|
| 1789 | head_support&=~(1<<i); |
---|
| 1790 | // bit i is set to 0 |
---|
| 1791 | |
---|
| 1792 | tail_support|=(1<<i); |
---|
| 1793 | // bit i is set to 1 |
---|
| 1794 | } |
---|
| 1795 | |
---|
| 1796 | else |
---|
| 1797 | // variable i will be moved from tail to head |
---|
| 1798 | // remember that exponent_vector[i]!=0 |
---|
| 1799 | { |
---|
| 1800 | tail_support&=~(1<<i); |
---|
| 1801 | // bit i is set to 0 |
---|
| 1802 | |
---|
| 1803 | head_support|=(1<<i); |
---|
| 1804 | // bit i is set to 1 |
---|
| 1805 | } |
---|
| 1806 | } |
---|
| 1807 | #endif // SUPPORT_VARIABLES_FIRST |
---|
| 1808 | |
---|
| 1809 | #ifdef SUPPORT_VARIABLES_LAST |
---|
| 1810 | |
---|
| 1811 | // Using SUPPORT_VARIABLES_LAST, bit k of the support vectors |
---|
| 1812 | // corresponds to exponent_vector[_number_of_variables-1-k], |
---|
| 1813 | // hence bit _number_of_variables-1-i to exponent_vector[i]. |
---|
| 1814 | |
---|
| 1815 | if(i>=_number_of_variables-size_of_support_vectors) |
---|
| 1816 | // else i is no support variable |
---|
| 1817 | { |
---|
| 1818 | if(exponent_vector[i]>0) |
---|
| 1819 | // variable i will be moved from head to tail |
---|
| 1820 | { |
---|
| 1821 | short k=_number_of_variables-1-i; |
---|
| 1822 | |
---|
| 1823 | head_support&=~(1<<k); |
---|
| 1824 | // bit _number_of_variables-1-i is set to 0 |
---|
| 1825 | |
---|
| 1826 | tail_support|=(1<<k); |
---|
| 1827 | // bit _number_of_variables-1-i is set to 1 |
---|
| 1828 | |
---|
| 1829 | } |
---|
| 1830 | |
---|
| 1831 | else |
---|
| 1832 | // variable i will be moved from tail to head |
---|
| 1833 | { |
---|
| 1834 | short k=_number_of_variables-1-i; |
---|
| 1835 | |
---|
| 1836 | tail_support&=~(1<<k); |
---|
| 1837 | // bit _number_of_variables-1-i is set to 0 |
---|
| 1838 | |
---|
| 1839 | head_support|=(1<<k); |
---|
| 1840 | // bit _number_of_variables-1-i is set to 1 |
---|
| 1841 | |
---|
| 1842 | } |
---|
| 1843 | } |
---|
| 1844 | #endif // SUPPORT_VARIABLES_LAST |
---|
| 1845 | |
---|
| 1846 | |
---|
| 1847 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 1848 | |
---|
| 1849 | // Now flip the variable. |
---|
| 1850 | |
---|
| 1851 | exponent_vector[i]*=-1; |
---|
[056089] | 1852 | return *this; |
---|
[6ba162] | 1853 | } |
---|
| 1854 | |
---|
| 1855 | ////////////////////////// output ///////////////////////////////////////// |
---|
| 1856 | |
---|
| 1857 | void binomial::print() const |
---|
| 1858 | { |
---|
| 1859 | printf("("); |
---|
| 1860 | for(short i=0;i<_number_of_variables-1;i++) |
---|
| 1861 | printf("%6d,",exponent_vector[i]); |
---|
| 1862 | printf("%6d)\n",exponent_vector[_number_of_variables-1]); |
---|
| 1863 | } |
---|
| 1864 | |
---|
| 1865 | void binomial::print_all() const |
---|
| 1866 | { |
---|
| 1867 | print(); |
---|
| 1868 | |
---|
| 1869 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1870 | |
---|
| 1871 | printf("head: %ld, tail %ld\n",head_support,tail_support); |
---|
| 1872 | |
---|
| 1873 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 1874 | } |
---|
| 1875 | |
---|
| 1876 | void binomial::print(FILE* output) const |
---|
| 1877 | { |
---|
| 1878 | fprintf(output,"("); |
---|
| 1879 | for(short i=0;i<_number_of_variables-1;i++) |
---|
| 1880 | fprintf(output,"%6d,",exponent_vector[i]); |
---|
| 1881 | fprintf(output,"%6d)\n",exponent_vector[_number_of_variables-1]); |
---|
| 1882 | } |
---|
| 1883 | |
---|
| 1884 | void binomial::print_all(FILE* output) const |
---|
| 1885 | { |
---|
| 1886 | print(output); |
---|
| 1887 | |
---|
| 1888 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1889 | |
---|
| 1890 | fprintf(output,"head: %ld, tail %ld\n",head_support,tail_support); |
---|
| 1891 | |
---|
| 1892 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 1893 | } |
---|
| 1894 | |
---|
| 1895 | void binomial::print(ofstream& output) const |
---|
| 1896 | { |
---|
| 1897 | output<<"("; |
---|
| 1898 | for(short i=0;i<_number_of_variables-1;i++) |
---|
| 1899 | output<<setw(6)<<exponent_vector[i]<<","; |
---|
| 1900 | output<<setw(6)<<exponent_vector[_number_of_variables-1]<<")"<<endl; |
---|
| 1901 | } |
---|
| 1902 | |
---|
| 1903 | void binomial::print_all(ofstream& output) const |
---|
| 1904 | { |
---|
| 1905 | print(output); |
---|
| 1906 | |
---|
| 1907 | #ifdef SUPPORT_DRIVEN_METHODS |
---|
| 1908 | |
---|
| 1909 | output<<"head: "<<setw(16)<<head_support<<", tail: "<<setw(16) |
---|
| 1910 | <<tail_support<<endl; |
---|
| 1911 | |
---|
| 1912 | #endif // SUPPORT_DRIVEN_METHODS |
---|
| 1913 | } |
---|
| 1914 | |
---|
| 1915 | void binomial::format_print(ofstream& output) const |
---|
| 1916 | { |
---|
| 1917 | for(short i=0;i<_number_of_variables;i++) |
---|
| 1918 | output<<setw(6)<<exponent_vector[i]; |
---|
| 1919 | output<<endl; |
---|
| 1920 | } |
---|
| 1921 | |
---|
| 1922 | #endif // BINOMIAL_CC |
---|