1 | LIB "tst.lib"; |
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2 | tst_init(); |
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3 | |
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4 | ring r=2,(t,b,a,y),dp; |
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5 | ideal i=a2+tb,b4+b2+t; |
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6 | poly f=(y2+tb)*(y+b3+b2)*(y2+tb+t2); |
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7 | ideal I=i,f; |
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8 | char_series (I); |
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9 | |
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10 | kill r; |
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11 | |
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12 | ring r=2,(t,a,b,y),dp; |
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13 | ideal i=a2+tb,b4+b2+t; |
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14 | poly f=(y2+tb)*(y+b3+b2)*(y2+tb+t2); |
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15 | ideal I=i,f; |
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16 | char_series (I); |
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17 | |
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18 | kill r; |
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19 | |
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20 | ring r=2,(t,a,b,c,y),dp; |
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21 | ideal i=a2+tb,c2+c+b,b4+b2+t; |
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22 | poly f=(y2+tb)*(y2+b3+c+b)*(y+c+t)*(y2+tb+t2); |
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23 | ideal I=i,f; |
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24 | char_series (I); |
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25 | |
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26 | kill r; |
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27 | |
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28 | ring r=2,(t,a,b,c,y),dp; |
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29 | ideal i=a2+tb,c2+c+b,b4+b2+t; |
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30 | poly f=(y2+a)^8*(y2+b3+c+b)*(y+c+t)*(y2+tb+t2); |
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31 | ideal I=i,f; |
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32 | char_series (I); |
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33 | |
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34 | kill r; |
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35 | |
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36 | ring r=2,(t,a,b,c,y),dp; |
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37 | ideal i=a2+tb,c2+c+b,b4+b2+t; |
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38 | poly f=(y3+a)^8*(y2+b3+c+b)*(y+c+t)*(y2+tb+t2); |
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39 | ideal I=i,f; |
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40 | char_series (I); |
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41 | |
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42 | kill r; |
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43 | |
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44 | ring r=2,(t,b,a,c,y),dp; |
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45 | ideal i=a2+tb,c2+c+b,b4+b2+t; |
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46 | poly f=(y2+tb)*(y2+b3+c+b)*(y+c+t)*(y2+tb+t2); |
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47 | ideal I=i,f; |
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48 | char_series (I); |
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49 | |
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50 | kill r; |
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51 | |
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52 | ring r=2,(t,b,c,a,y),dp; |
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53 | ideal i=a2+tb,c2+c+b,b4+b2+t; |
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54 | poly f=(y2+tb)*(y2+b3+c+b)*(y+c+t)*(y2+tb+t2); |
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55 | ideal I=i,f; |
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56 | char_series (I); |
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57 | |
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58 | kill r; |
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59 | |
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60 | ring r=2,(t,a,c,b,y),dp; |
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61 | ideal i=a2+tb,c2+c+b,b4+b2+t; |
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62 | poly f=(y2+tb)*(y2+b3+c+b)*(y+c+t)*(y2+tb+t2); |
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63 | ideal I=i,f; |
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64 | char_series (I); |
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65 | |
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66 | kill r; |
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67 | |
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68 | ring r=2,(t,c,a,b,y),dp; |
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69 | ideal i=a2+tb,c2+c+b,b4+b2+t; |
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70 | poly f=(y2+tb)*(y2+b3+c+b)*(y+c+t)*(y2+tb+t2); |
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71 | ideal I=i,f; |
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72 | char_series (I); |
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73 | |
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74 | kill r; |
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75 | |
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76 | ring r=2,(t,c,b,a,y),dp; |
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77 | ideal i=a2+tb,c2+c+b,b4+b2+t; |
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78 | poly f=(y2+tb)*(y2+b3+c+b)*(y+c+t)*(y2+tb+t2); |
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79 | ideal I=i,f; |
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80 | char_series (I); |
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81 | |
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82 | kill r; |
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83 | |
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84 | ring r=2,(t,u,a,b,c,x,y,z),dp; |
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85 | ideal i=a2+tb, b4+b2+c, c2+tu; |
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86 | poly f=x8+t2x4+t4c; |
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87 | ideal I=i,f; |
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88 | char_series (I); |
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89 | |
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90 | kill r; |
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91 | |
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92 | ring r=2,(t,u,a,c,b,x,y,z),dp; |
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93 | ideal i=a2+tb, b4+b2+c, c2+tu; |
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94 | poly f=x8+t2x4+t4c; |
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95 | ideal I=i,f; |
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96 | char_series (I); |
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97 | |
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98 | kill r; |
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99 | |
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100 | ring r=2,(t,u,c,a,b,x,y,z),dp; |
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101 | ideal i=a2+tb, b4+b2+c, c2+tu; |
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102 | poly f=x8+t2x4+t4c; |
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103 | ideal I=i,f; |
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104 | char_series (I); |
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105 | |
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106 | kill r; |
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107 | |
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108 | ring r=2,(t,u,b,a,c,x,y,z),dp; |
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109 | ideal i=a2+tb, b4+b2+c, c2+tu; |
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110 | poly f=x8+t2x4+t4c; |
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111 | ideal I=i,f; |
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112 | char_series (I); |
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113 | |
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114 | kill r; |
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115 | |
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116 | ring r=2,(t,u,b,c,a,x,y,z),dp; |
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117 | ideal i=a2+tb, b4+b2+c, c2+tu; |
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118 | poly f=x8+t2x4+t4c; |
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119 | ideal I=i,f; |
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120 | char_series (I); |
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121 | |
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122 | kill r; |
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123 | |
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124 | ring r=2,(t,u,c,b,a,x,y,z),dp; |
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125 | ideal i=a2+tb, b4+b2+c, c2+tu; |
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126 | poly f=x8+t2x4+t4c; |
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127 | ideal I=i,f; |
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128 | char_series (I); |
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129 | |
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130 | kill r; |
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131 | |
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132 | ring r=2,(t,u,a,b,x),dp; |
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133 | ideal i=a2+t, b4+u; |
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134 | poly f=x8+(t+u)*x4+tu; |
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135 | ideal J= i,f; |
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136 | char_series (J); |
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137 | |
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138 | kill r; |
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139 | |
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140 | ring r=2,(t,u,b,a,x),dp; |
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141 | ideal i=a2+t, b4+u; |
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142 | poly f=x8+(t+u)*x4+tu; |
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143 | ideal J= i,f; |
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144 | char_series (J); |
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145 | |
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146 | kill r; |
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147 | |
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148 | ring r=3,(x1,x2,x3,x4,x5,y),lp; |
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149 | poly f6= ((y+x1*x3+x2+1)*(y+x3*x4+x1*x3)*(y^3+x3*x4+x1*x3)); |
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150 | ideal I=x1^2+1, x2^2+x1+1, x3^2+x2+1, x4^2+x3+x2+2; |
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151 | ideal K=I,f6; |
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152 | char_series (K); |
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153 | |
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154 | kill r; |
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155 | |
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156 | ring r=32003,(a,b,c,d,e,f,g,h),dp; |
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157 | ideal i= -1*a-1*d+e+f+h, |
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158 | -2*a^2+2*a*d+2*c*e+2*b*f-1*a-1, |
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159 | 3*a^3-3*a^2*d+3*c^2*e+3*b^2*f+3*a^2+4*a-1*d, |
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160 | 6*a^3-6*a^2*d+6*b*e*g+6*a^2-3*a*d+4*a-1*d, |
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161 | -4*a^4+4*a^3*d+4*c^3*e+4*b^3*f-6*a^3-10*a^2+4*a*d-1*a-1, |
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162 | -8*a^4+8*a^3*d+8*b*c*e*g-12*a^3+4*a^2*d-14*a^2+4*a*d-3*a-1, |
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163 | -12*a^4+12*a^3*d+12*b^2*e*g-18*a^3+12*a^2*d-14*a^2+8*a*d-1*a-1, |
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164 | 24*a^4-24*a^3*d+36*a^3-24*a^2*d+26*a^2-8*a*d+7*a+1; |
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165 | char_series (i); |
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166 | |
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167 | kill r; |
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168 | |
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169 | ring r=31991,(a,b,c,d),dp; |
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170 | ideal i= a*b*c-b*c*d-c*d*a-d*a*b, a^3-b^3-a^3*b^3+c^3+d^3, a*b+b*c+c*d+d*a, |
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171 | a^2, c*a*b+a*b+a+b; |
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172 | char_series (i); |
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173 | |
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174 | kill r; |
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175 | |
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176 | ring r=31991,(x,y,z),dp; |
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177 | ideal i= x^3-y^2, x^3-z^2, y^3-z^2; |
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178 | char_series (i); |
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179 | |
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180 | kill r; |
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181 | |
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182 | ring r=31991,(a,b,c,d,e,f),dp; |
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183 | ideal i=a*b*c+a*b+a*e,a-b*d*e,d*e*f+f,f-e,a-a*b; |
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184 | char_series (i); |
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185 | |
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186 | kill r; |
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187 | |
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188 | ring r=31991,(x,y,z),dp; |
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189 | ideal i=x^3-x^2+y^2, x-y^3, x*y*z+z^3; |
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190 | char_series (i); |
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191 | |
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192 | kill r; |
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193 | |
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194 | ring r=31991,(x,y,z,t),dp; |
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195 | ideal i= t^2+x*t^2-y*t-x*y*t+x*y+3*y, x*t+z-x*y, z*t-2*y^2-x*y-1; |
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196 | char_series (i); |
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197 | |
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198 | kill r; |
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199 | |
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200 | ring r=31991,(d,c,b,a),dp; |
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201 | ideal i= a*b*c-b*c*d-c*d*a-d*a*b, a^3-b^3-a^3*b^3+c^3+d^3, |
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202 | a*b+b*c+c*d+d*a, a^2, c*a*b+a*b+a+b; |
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203 | char_series (i); |
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204 | |
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205 | kill r; |
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206 | |
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207 | ring r=31991, (a,b,c,d,e,f,g,h,k,j), dp; |
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208 | ideal I= -j+a^2*b^2*c^2*d^2*e+a^2*b^2*c^2*d^2*f+a^2*b^2*c^2*d*e^2+2*a^2*b^2*c^2*d*e*f+a^2*b^2*c^2*d*f^2+a^2*b^2*c^2*e^2*f+a^2*b^2*c^2*e*f^2+a^2*d*h-b^2*f*g*c^2*e*k*g-h-k, |
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209 | 2*a*d*h+2*a*b^2*c^2*e*f^2+2*a*b^2*c^2*d*f^2+2*a*b^2*c^2*e^2*f+4*a*b^2*c^2*d*e*f+2*a*b^2*c^2*d^2*f+2*a*b^2*c^2*d*e^2+2*a*b^2*c^2*d^2*e, |
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210 | -2*b*c^2*e*f*g^2*k+2*a^2*b*c^2*e*f^2+2*a^2*b*c^2*d*f^2+2*a^2*b*c^2*e^2*f+4*a^2*b*c^2*d*e*f+2*a^2*b*c^2*d^2*f+2*a^2*b*c^2*d*e^2+2*a^2*b*c^2*d^2*e, |
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211 | -2*b^2*c*e*f*g^2*k+2*a^2*b^2*c*e*f^2+2*a^2*b^2*c*d*f^2+2*a^2*b^2*c*e^2*f+4*a^2*b^2*c*d*e*f+2*a^2*b^2*c*d^2*f+2*a^2*b^2*c*d*e^2+2*a^2*b^2*c*d^2*e, |
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212 | a^2*h+a^2*b^2*c^2*f^2+2*a^2*b^2*c^2*e*f+2*a^2*b^2*c^2*d*f+a^2*b^2*c^2*e^2+2*a^2*b^2*c^2*d*e, |
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213 | -b^2*c^2*f*g^2*k+a^2*b^2*c^2*f^2+2*a^2*b^2*c^2*e*f+2*a^2*b^2*c^2*d*f+2*a^2*b^2*c^2*d*e+a^2*b^2*c^2*d^2, |
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214 | -b^2*c^2*e*g^2*k+2*a^2*b^2*c^2*e*f+2*a^2*b^2*c^2*d*f+a^2*b^2*c^2*e^2+2*a^2*b^2*c^2*d*e+a^2*b^2*c^2*d^2, |
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215 | -2*b^2*c^2*e*f*g*k, |
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216 | a^2*d-1, |
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217 | -b^2*c^2*e*f*g^2-1; |
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218 | char_series (I); |
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219 | |
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220 | kill r; |
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221 | |
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222 | ring r= 31991, (a,b,c,d,e,f,g,h,i,j),dp; |
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223 | ideal I= |
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224 | -6*b*c^2*e*f*g^2+2*a^2*b*c^2*e*f^2+2*a^2*b*c^2*d*f^2+2*a^2*b*c^2*e^2*f+4*a^2*b*c^2*d*e*f+2*a^2*b*c^2*d^2*f+2*a^2*b*c^2*d*e^2+2*a^2*b*c^2*d^2*e, |
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225 | -j-b^2*c^2*e*f*g^2-1+a^2*d*h-h+a^2*b^2*c^2*e*f^2+a^2*b^2*c^2*d*f^2+a^2*b^2*c^2*e^2*f+2*a^2*b^2*c^2*d*e*f+a^2*b^2*c^2*d^2*f+a^2*b^2*c^2*d*e^2+a^2*b^2*c^2*d^2*e, |
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226 | -8*b^2*c*e*f*g^2+2*a^2*b^2*c*e*f^2+2*a^2*b^2*c*d*f^2+2*a^2*b^2*c*e^2*f+4*a^2*b^2*c*d*e*f+2*a^2*b^2*c*d^2*f+2*a^2*b^2*c*d*e^2+2*a^2*b^2*c*d^2*e, |
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227 | -16*b^2*c^2*e*f*g, |
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228 | -7*b^2*c^2*e*g^2+2*a^2*b^2*c^2*e*f+2*a^2*b^2*c^2*d*f+a^2*b^2*c^2*e^2+2*a^2*b^2*c^2*d*e+a^2*b^2*c^2*d^2, |
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229 | -6*b^2*c^2*f*g^2+a^2*b^2*c^2*f^2+2*a^2*b^2*c^2*e*f+2*a^2*b^2*c^2*d*f+2*a^2*b^2*c^2*d*e+a^2*b^2*c^2*d^2, |
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230 | a^2*d-1, |
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231 | -b^2*c^2*e*f*g^2-1, |
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232 | 2*a*d*h+2*a*b^2*c^2*e*f^2+2*a*b^2*c^2*d*f^2+2*a*b^2*c^2*e^2*f+4*a*b^2*c^2*d*e*f+2*a*b^2*c^2*d^2*f+2*a*b^2*c^2*d*e^2+2*a*b^2*c^2*d^2*e, |
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233 | a^2*h+a^2*b^2*c^2*f^2+2*a^2*b^2*c^2*e*f+2*a^2*b^2*c^2*d*f+a^2*b^2*c^2*e^2+2*a^2*b^2*c^2*d*e; |
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234 | char_series (I); |
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235 | |
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236 | kill r; |
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237 | |
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238 | ring r=31991,(a,b,c,x,y,z),dp; |
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239 | ideal I=a*(x+y+z)-(x-y-z), |
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240 | b*(x+z)-(x+y-z), |
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241 | c*(x-y+z)-(x+y); |
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242 | char_series (I); |
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243 | |
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244 | kill r; |
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245 | |
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246 | ring rr=31991,(a,b,c,d,e,f,g,h,j,k,l,m,n,o,p,q,r),dp; |
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247 | ideal I=d*k, |
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248 | e*g+d*j+c*k+l, |
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249 | b*h, |
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250 | e*l, |
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251 | b*f+b*g+a*h+d*h+b*k+h+o, |
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252 | a*f+d*f+a*g+d*g+c*h+e*h+b*j+a*k+d*k+b*l+f+g+k+m+n+q, |
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253 | c*f+e*f+c*g+e*g+a*j+d*j+c*k+e*k+a*l+d*l+j+l+p+r-1, |
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254 | c*j+e*j+c*l+e*l, |
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255 | e*j+c*l+2*e*l, |
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256 | e*f+e*g+d*j+c*k+2*e*k+a*l+2*d*l+l+r, |
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257 | d*f+d*g+e*h+a*k+2*d*k+b*l+k+q, |
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258 | d*h+b*k, |
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259 | e*k+d*l, |
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260 | 2*c*j+e*j+c*l, |
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261 | c*f+2*c*g+e*g+a*j+d*j+c*k+2*j+l+p, |
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262 | a*g+d*g+c*h+b*j+f+2*g+k+n, |
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263 | b*g+h, |
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264 | e*j+c*l, |
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265 | d*g+k; |
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266 | char_series (I); |
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267 | |
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268 | kill rr; |
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269 | |
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270 | ring rr=31991,(r,s,t,u,v,w,x,y,z),dp; |
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271 | ideal i= |
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272 | s*u+r*v, |
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273 | t*u+r*w, |
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274 | t*v+s*w, |
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275 | s*x+r*y, |
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276 | t*x+r*z, |
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277 | t*y+s*z, |
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278 | v*x+u*y, |
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279 | w*x+u*z, |
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280 | w*y+v*z; |
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281 | char_series (i); |
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282 | |
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283 | kill rr; |
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284 | |
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285 | ring r=31991,(a,b,c,d,e,f),dp; |
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286 | ideal i= |
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287 | a*d*e*f+3/2*b*e^2*f-1/2*c*e*f^2, |
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288 | a*d^2*f+5/4*b*d*e*f+1/4*c*d*f^2, |
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289 | a*d^2*e+3/4*b*d*e^2+7/4*c*d*e*f, |
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290 | a*c*d*e+3/2*b*c*e^2-1/2*c^2*e*f, |
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291 | a*c*d^2+5/4*b*c*d*e+1/4*c^2*d*f, |
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292 | a*b*d*f+3/2*b^2*e*f-1/2*b*c*f^2, |
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293 | a*b*d*e+3/4*b^2*e^2-a*c*d*f+1/2*b*c*e*f-1/4*c^2*f^2, |
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294 | a*b*d^2+3/4*b^2*d*e+7/4*b*c*d*f, |
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295 | a*b*c*d+3/2*b^2*c*e-1/2*b*c^2*f, |
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296 | a^2*d*f+5/4*a*b*e*f+1/4*a*c*f^2, |
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297 | a^2*d*e+3/4*a*b*e^2+7/4*a*c*e*f, |
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298 | a^2*d^2-9/16*b^2*e^2+2*a*c*d*f-9/8*b*c*e*f+7/16*c^2*f^2, |
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299 | a^2*c*d+5/4*a*b*c*e+1/4*a*c^2*f, |
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300 | a^2*b*d+3/4*a*b^2*e+7/4*a*b*c*f, |
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301 | b*c^3*d+1/4*c*d^3*e, |
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302 | b^2*c^2*e-1/3*b*c^3*f+2/3*c*d^2*e*f, |
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303 | b^2*c^2*d-1/2*a*d^4-3/8*b*d^3*e-1/8*c*d^3*f, |
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304 | b^3*c*e-1/3*b^2*c^2*f+2/3*b*d^2*e*f, |
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305 | b^3*c*d+3/4*b*d^3*f, |
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306 | a*c^3*e-1/3*c*d*e^3, |
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307 | a*c^3*d-3/4*b*c^3*e-1/2*c*d^2*e^2+1/4*c^4*f, |
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308 | a*b*c^2*f-c*d*e*f^2, |
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309 | a*b*c^2*e-c*d*e^2*f, |
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310 | a*b^2*c*f-b*d*e*f^2, |
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311 | a*b^3*f-3*b*d*f^3, |
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312 | a*b^3*d+3/4*b^4*e-1/4*b^3*c*f-3/2*b*d^2*f^2, |
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313 | a^2*c^2*e-2/3*a*d*e^3-1/2*b*e^4+1/6*c*e^3*f, |
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314 | a^2*b*c*f+3/2*b*e^2*f^2-1/2*c*e*f^3, |
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315 | a^2*b*c*e+3/2*b*e^3*f-1/2*c*e^2*f^2, |
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316 | a^2*b^2*f-2*a*d*f^3+3/2*b*e*f^3-1/2*c*f^4, |
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317 | a^3*c*e+4/3*a*e^3*f, |
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318 | a^3*b*f+4*a*e*f^3, |
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319 | a^4*d+3/4*a^3*b*e+1/4*a^3*c*f-2*a*e^2*f^2; |
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320 | char_series (i); |
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321 | |
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322 | kill r; |
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323 | |
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324 | ring r=31991,(x,y),dp; |
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325 | ideal i= x^2, x*y; |
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326 | char_series (i); |
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327 | |
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328 | tst_status(1); $ |
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