1 | ring r=(32003,a),x,dp; |
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2 | poly f=a; |
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3 | f; |
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4 | f; |
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5 | f+f; |
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6 | f=1; |
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7 | f; |
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8 | f-f; |
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9 | f=a; |
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10 | f+1-1; |
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11 | f=a^2+1; |
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12 | f; |
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13 | f; |
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14 | poly g=f; |
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15 | g; |
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16 | f=a2-a^2+3a4; |
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17 | f; |
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18 | r; |
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19 | minpoly=a^2+1; |
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20 | r; |
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21 | f; |
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22 | f=f+0; |
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23 | f; |
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24 | f=f+1-1; |
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25 | f; |
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26 | ring rr=(0,a),x,dp; |
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27 | poly f=a; |
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28 | f; |
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29 | f; |
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30 | f+f; |
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31 | f=1; |
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32 | f; |
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33 | f=a^2+1; |
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34 | f; |
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35 | f; |
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36 | poly g=f; |
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37 | g; |
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38 | f=a2-a^2+3a4; |
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39 | f; |
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40 | rr; |
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41 | minpoly=a^2-1; |
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42 | rr; |
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43 | f; |
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44 | f=f+0; |
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45 | f; |
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46 | f=f+1-1; |
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47 | f; |
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48 | kill rr; |
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49 | ring rr=(0,a,b),x,dp; |
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50 | poly f=a2b; |
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51 | f; |
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52 | f=b2a; |
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53 | f; |
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54 | f=a2b2-b2a2+a^2*b^2-a^2*b2; |
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55 | f; |
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56 | kill rr; |
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57 | ring r=(32003,a),x,dp; |
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58 | short=1; |
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59 | poly f=a; |
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60 | f; |
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61 | f; |
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62 | f+f; |
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63 | f=1; |
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64 | f; |
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65 | f-f; |
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66 | f=a; |
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67 | f+1-1; |
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68 | f=a^2+1; |
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69 | f; |
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70 | f; |
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71 | poly g=f; |
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72 | g; |
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73 | f=a2-a^2+3a4; |
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74 | f; |
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75 | r; |
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76 | minpoly=a^2-1; |
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77 | r; |
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78 | f; |
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79 | f=f+0; |
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80 | f; |
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81 | f=f+1-1; |
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82 | f; |
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83 | ring rr=(0,a),x,dp; |
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84 | short=1; |
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85 | poly f=a; |
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86 | f; |
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87 | f; |
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88 | f+f; |
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89 | f=1; |
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90 | f; |
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91 | f=a^2+1; |
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92 | f; |
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93 | f; |
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94 | poly g=f; |
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95 | g; |
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96 | f=a2-a^2+3a4; |
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97 | f; |
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98 | rr; |
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99 | minpoly=a^2-1; |
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100 | rr; |
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101 | f; |
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102 | f=f+0; |
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103 | f; |
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104 | f=f+1-1; |
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105 | f; |
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106 | kill rr; |
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107 | ring rr=(0,a,b),x,dp; |
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108 | short=1; |
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109 | poly f=a2b; |
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110 | f; |
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111 | f=b2a; |
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112 | f; |
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113 | f=a2b2-b2a2+a^2*b^2-a^2*b2; |
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114 | f; |
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115 | |
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116 | kill rr,r; |
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117 | //----------------------------------------------------------- |
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118 | ring s1=(0,a),(x,y,z,w),dp; |
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119 | ideal i0=(a2-1)*x2-z10-z20,(a+1)*xy3-z10-z30,y6-(a+1)*xy3w40; |
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120 | ideal i = std(i0); |
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121 | i; |
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122 | |
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123 | ring s2=(0,a),(x,y,z,w),dp; |
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124 | minpoly=8a4+1; |
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125 | ideal j0=(a2-1)*x2-z10-z20,(a+1)*xy3-z10-z30,y6-(a+1)*xy3w40; |
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126 | ideal j = std(j0); |
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127 | j; |
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128 | |
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129 | ring s3=(32003,a),(x,y,z,w),dp; |
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130 | ideal k0=(a2-1)*x2-z10-z20,(a+1)*xy3-z10-z30,y6-(a+1)*xy3w40; |
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131 | ideal k = std(k0); |
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132 | k; |
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133 | |
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134 | ring s4=(32003,a),(x,y,z,w),dp; |
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135 | minpoly=8a4+1; |
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136 | ideal l0=(a2-1)*x2-z10-z20,(a+1)*xy3-z10-z30,y6-(a+1)*xy3w40; |
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137 | ideal l = std(l0); |
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138 | l; |
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139 | |
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140 | kill s1,s2,s3,s4; |
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141 | |
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142 | ring r1=(0,a),(x,y,z),dp; |
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143 | minpoly=4a4+1; |
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144 | poly f0=3a2-3; |
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145 | poly g0=2a+2; |
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146 | poly h=4a4+3a3+2a2+a; |
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147 | poly f=f0*h; |
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148 | poly g=g0*h; |
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149 | poly f1=f/g; |
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150 | poly g1=g/f; |
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151 | f; |
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152 | g; |
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153 | f1; |
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154 | g1; |
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155 | (3/2*a-3/2)*(-8/15*a^3-8/15*a^2-8/15*a-8/15); |
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156 | newline; |
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157 | |
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158 | ring r2=(0,a),(x,y,z),dp; |
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159 | poly f0=3a2-3; |
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160 | poly g0=2a+2; |
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161 | poly h=4a4+3a3+2a2+a; |
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162 | poly f=f0*h; |
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163 | poly g=g0*h; |
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164 | poly f1=f/g; |
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165 | poly g1=g/f; |
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166 | f; |
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167 | g; |
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168 | f1; |
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169 | g1; |
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170 | g/(0*a); |
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171 | newline; |
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172 | |
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173 | ring r3=(32003,a),(x,y,z),dp; |
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174 | poly f0=3a2-3; |
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175 | poly g0=2a+2; |
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176 | poly h=4a4+3a3+2a2+a; |
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177 | poly f=f0*h; |
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178 | poly g=g0*h; |
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179 | poly f1=f/g; |
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180 | poly g1=g/f; |
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181 | f; |
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182 | g; |
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183 | f1; |
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184 | g1; |
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185 | newline; |
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186 | |
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187 | ring r4=(32003,a),(x,y,z),dp; |
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188 | minpoly=4a4+1; |
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189 | poly f0=3a2-3; |
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190 | poly g0=2a+2; |
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191 | poly h=4a4+3a3+2a2+a; |
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192 | poly f=f0*h; |
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193 | poly g=g0*h; |
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194 | poly f1=f/g; |
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195 | poly g1=g/f; |
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196 | f; |
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197 | g; |
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198 | f1; |
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199 | g1; |
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200 | (-16000*a+16000)*(2133*a^3+2133*a^2+2133*a+2133); |
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201 | newline; |
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202 | |
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203 | kill r1,r2,r3,r4; |
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204 | |
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205 | ring w2=(0,i),(u,v),dp; |
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206 | poly g=(i-1/3)^10; |
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207 | ring w1=(0,i),(x,y),dp; |
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208 | minpoly=i2+1; |
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209 | poly f=(i-1/3)^10; |
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210 | map q=w2,x,y; |
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211 | poly h=q(g); |
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212 | h=h*(1); |
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213 | f; |
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214 | h; |
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215 | h-f; |
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216 | poly f1=(6i+8)^10; |
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217 | poly f2=(6i-8)^10; |
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218 | f2*f1; |
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219 | newline; |
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220 | |
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221 | kill w2; |
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222 | LIB "tst.lib";tst_status(1);$ |
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