1 | ///////////////////////////////////////////////// |
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2 | version="version rwalk.lib 4.0.0.0 Jun_2013 "; // $Id$ |
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3 | category="Commutative Algebra"; |
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4 | |
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5 | info=" |
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6 | LIBRARY: rwalk.lib Groebner Walk Conversion Algorithms |
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7 | AUTHOR: Stephan Oberfranz |
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8 | |
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9 | PROCEDURES: |
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10 | rwalk(ideal[,intvec]); standard basis of ideal via randomwalk algorithm |
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11 | "; |
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12 | |
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13 | /*********************************** |
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14 | * Argument string for Random Walk * |
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15 | ***********************************/ |
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16 | static proc OrderStringalp_NP(string Wpal,list #) |
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17 | { |
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18 | int n= nvars(basering); |
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19 | string order_str = "dp"; |
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20 | |
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21 | int nP = 1; |
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22 | |
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23 | //Default: if size(#)=0, the Groebnerwalk algorithm and its developments compute a Groebner basis from "dp" to "lp" |
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24 | |
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25 | intvec curr_weight = system("Mivdp",n); //define (1,1,...,1) |
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26 | intvec target_weight = system("Mivlp",n); //define (1,0,...,0) |
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27 | |
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28 | if(size(#) != 0) |
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29 | { |
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30 | if(size(#) == 1) |
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31 | { |
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32 | if(typeof(#[1]) == "intvec") { |
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33 | curr_weight = #[1]; |
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34 | |
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35 | if(Wpal == "al"){ |
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36 | order_str = "(a("+string(#[1])+"),lp("+string(n) + "),C)"; |
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37 | } |
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38 | else { |
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39 | order_str = "(Wp("+string(#[1])+"),C)"; |
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40 | } |
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41 | } |
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42 | else { |
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43 | if(typeof(#[1]) == "int"){ |
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44 | nP = #[1]; |
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45 | } |
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46 | else { |
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47 | print("// ** the input must be \"(ideal, int)\" or "); |
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48 | print("// ** \"(ideal, intvec)\""); |
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49 | print("// ** a lex. GB will be computed from \"dp\" to \"lp\""); |
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50 | } |
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51 | } |
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52 | } |
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53 | else |
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54 | { |
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55 | if(size(#) == 2) |
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56 | { |
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57 | if(typeof(#[1]) == "intvec" and typeof(#[2]) == "int"){ |
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58 | curr_weight = #[1]; |
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59 | |
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60 | if(Wpal == "al"){ |
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61 | order_str = "(a("+string(#[1])+"),lp("+string(n) + "),C)"; |
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62 | } |
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63 | else { |
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64 | order_str = "(Wp("+string(#[1])+"),C)"; |
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65 | } |
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66 | } |
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67 | else{ |
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68 | if(typeof(#[1]) == "intvec" and typeof(#[2]) == "intvec"){ |
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69 | curr_weight = #[1]; |
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70 | target_weight = #[2]; |
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71 | |
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72 | if(Wpal == "al"){ |
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73 | order_str = "(a("+string(#[1])+"),lp("+string(n) + "),C)"; |
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74 | } |
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75 | else { |
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76 | order_str = "(Wp("+string(#[1])+"),C)"; |
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77 | } |
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78 | } |
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79 | else{ |
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80 | print("// ** the input must be \"(ideal,intvec,int)\" or "); |
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81 | print("// ** \"(ideal,intvec,intvec)\""); |
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82 | print("// ** and a lex. GB will be computed from \"dp\" to \"lp\""); |
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83 | } |
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84 | } |
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85 | } |
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86 | else { |
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87 | if(size(#) == 3) { |
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88 | if(typeof(#[1]) == "intvec" and typeof(#[2]) == "intvec" and |
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89 | typeof(#[3]) == "int") |
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90 | { |
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91 | curr_weight = #[1]; |
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92 | target_weight = #[2]; |
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93 | nP = #[3]; |
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94 | if(Wpal == "al"){ |
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95 | order_str = "(a("+string(#[1])+"),lp("+string(n) + "),C)"; |
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96 | } |
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97 | else { |
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98 | order_str = "(Wp("+string(#[1])+"),C)"; |
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99 | } |
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100 | } |
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101 | else{ |
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102 | print("// ** the input must be \"(ideal,intvec,intvec,int)\""); |
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103 | print("// ** and a lex. GB will be computed from \"dp\" to \"lp\""); |
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104 | |
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105 | } |
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106 | } |
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107 | else{ |
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108 | print("// ** The given input is wrong"); |
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109 | print("// ** and a lex. GB will be computed from \"dp\" to \"lp\""); |
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110 | } |
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111 | } |
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112 | } |
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113 | } |
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114 | |
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115 | list result; |
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116 | result[1] = nP; |
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117 | result[2] = order_str; |
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118 | result[3] = curr_weight; |
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119 | result[4] = target_weight; |
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120 | |
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121 | return(result); |
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122 | } |
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123 | |
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124 | /************************************ |
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125 | * Random Walk with perturbation * |
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126 | ************************************/ |
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127 | proc rwalk(ideal Go, int radius, int pert_deg, list #) |
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128 | "SYNTAX: rwalk(ideal i, int radius); |
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129 | rwalk(ideal i, int radius, intvec v, intvec w); |
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130 | TYPE: ideal |
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131 | PURPOSE: compute the standard basis of the ideal, calculated via |
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132 | the Random walk algorithm from the ordering |
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133 | \"(a(v),lp)\", \"dp\" or \"Dp\" |
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134 | to the ordering \"(a(w),lp)\" or \"(a(1,0,...,0),lp)\". |
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135 | SEE ALSO: std, stdfglm, groebner, gwalk, pwalk, fwalk, twalk, awalk1, awalk2 |
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136 | KEYWORDS: Groebner walk |
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137 | EXAMPLE: example rwalk; shows an example" |
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138 | { |
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139 | //-------------------- Initialize parameters ------------------------ |
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140 | list OSCTW = OrderStringalp_NP("al", #); |
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141 | string ord_str = OSCTW[2]; |
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142 | intvec curr_weight = OSCTW[3]; // original weight vector |
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143 | intvec target_weight = OSCTW[4]; // target weight vector |
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144 | kill OSCTW; |
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145 | option(redSB); |
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146 | |
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147 | //-------------------- Initialize parameters ------------------------ |
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148 | def xR = basering; |
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149 | execute("ring ostR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";"); |
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150 | def old_ring = basering; |
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151 | |
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152 | ideal G = fetch(xR, Go); |
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153 | G = system("Mrwalk", G, curr_weight, target_weight, radius, pert_deg); |
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154 | |
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155 | setring xR; |
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156 | kill Go; |
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157 | |
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158 | keepring basering; |
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159 | ideal result = fetch(old_ring, G); |
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160 | attrib(result,"isSB",1); |
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161 | return (result); |
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162 | } |
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163 | example |
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164 | { |
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165 | "EXAMPLE:"; echo = 2; |
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166 | // compute a Groebner basis of I w.r.t. lp. |
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167 | ring r = 32003,(z,y,x), lp; |
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168 | ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z; |
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169 | int radius = 1; |
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170 | int perturb_deg = 2; |
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171 | rwalk(I,radius,perturb_deg); |
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172 | } |
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173 | |
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174 | /************************************ |
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175 | * Fractal Walk with random element * |
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176 | ************************************/ |
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177 | proc frandwalk(ideal Go, int radius, list #) |
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178 | "SYNTAX: frwalk(ideal i, int radius); |
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179 | frwalk(ideal i, int radius, intvec v, intvec w); |
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180 | TYPE: ideal |
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181 | PURPOSE: compute the standard basis of the ideal w.r.t. the |
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182 | lexicographical ordering or a weighted-lex ordering, |
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183 | calculated via the fractal walk algorithm with random element. |
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184 | SEE ALSO: std, stdfglm, groebner, gwalk, pwalk, twalk, awalk1, awalk2 |
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185 | KEYWORDS: The fractal walk algorithm |
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186 | EXAMPLE: example frwalk; shows an example" |
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187 | { |
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188 | // we use ring with ordering (a(...),lp,C) |
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189 | list OSCTW = OrderStringalp_NP("al", #); |
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190 | |
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191 | string ord_str = OSCTW[2]; |
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192 | intvec curr_weight = OSCTW[3]; /* original weight vector */ |
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193 | intvec target_weight = OSCTW[4]; /* target weight vector */ |
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194 | kill OSCTW; |
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195 | option(redSB); |
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196 | def xR = basering; |
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197 | |
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198 | execute("ring ostR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";"); |
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199 | def old_ring = basering; |
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200 | //print("//** help ring = " + string(basering)); |
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201 | ideal G = fetch(xR, Go); |
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202 | |
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203 | G = system("Mfrwalk", G, curr_weight, target_weight, radius); |
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204 | |
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205 | setring xR; |
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206 | //kill Go; |
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207 | |
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208 | keepring basering; |
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209 | ideal result = fetch(old_ring, G); |
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210 | attrib(result,"isSB",1); |
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211 | return (result); |
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212 | } |
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213 | example |
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214 | { |
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215 | "EXAMPLE:"; echo = 2; |
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216 | ring r = 0,(z,y,x), lp; |
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217 | ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z; |
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218 | frandwalk(I,2); |
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219 | } |
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220 | |
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221 | /******************************************* |
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222 | * Tran Walk Algorithm with random element * |
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223 | *******************************************/ |
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224 | proc trwalk(ideal Go, int radius, int pert_deg, list #) |
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225 | "SYNTAX: trwalk(ideal i); |
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226 | trwalk(ideal i, intvec v, intvec w); |
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227 | TYPE: ideal |
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228 | PURPOSE: compute the standard basis of the ideal w.r.t. |
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229 | the ordering \"(a(w),lp)\" or \"(a(1,0,...,0),lp)\", |
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230 | calculated via the Tran algorithm with random element. |
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231 | SEE ALSO: std, stdfglm, groebner, gwalk, pwalk, fwalk, awalk1, awalk2 |
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232 | KEYWORDS: The Tran algorithm |
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233 | EXAMPLE: example trwalk; shows an example" |
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234 | { |
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235 | list L = OrderStringalp_NP("al", #); |
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236 | int nP = L[1]; |
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237 | |
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238 | // we use ring with ordering (a(...),lp,C) |
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239 | string ord_str = L[2]; |
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240 | intvec curr_weight = L[3]; |
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241 | intvec target_weight = L[4]; |
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242 | kill L; |
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243 | |
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244 | option(redSB); |
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245 | def xR = basering; |
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246 | |
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247 | execute("ring ostR = ("+charstr(xR)+"),("+varstr(xR)+"),"+ord_str+";"); |
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248 | def old_ring = basering; |
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249 | |
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250 | //print("//** help ring = " + string(basering)); |
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251 | ideal G = fetch(xR, Go); |
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252 | G = system("TranMrImprovwalk", G, curr_weight, target_weight, nP, radius, pert_deg); |
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253 | |
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254 | setring xR; |
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255 | //kill Go; |
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256 | |
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257 | keepring basering; |
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258 | ideal result = fetch(old_ring, G); |
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259 | attrib(result,"isSB",1); |
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260 | return (result); |
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261 | } |
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262 | example |
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263 | { |
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264 | "EXAMPLE:"; echo = 2; |
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265 | ring r = 32003,(z,y,x), lp; |
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266 | ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z; |
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267 | int radius = 2; |
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268 | int perturb_degree = 3; |
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269 | trwalk(I,radius,perturb_degree); |
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270 | } |
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