1 | LIB "arcAtPoint.lib"; |
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2 | LIB "tst.lib"; |
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3 | tst_init(); |
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4 | ring R=0,(x,y,z),dp; |
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5 | poly f=z4+y3-x2; |
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6 | // We obtain six families in Tr(i) for |
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7 | // i sufficiently large, and the following |
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8 | // corresponding sequences of |
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9 | // Nash multiplicities: |
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10 | // |
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11 | // a(1)=b(1)=c(1)^4-a(2)^2=0, |
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12 | // c(1)!=0,a(2)!=0 |
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13 | // from (2,2,1) ==> two families |
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14 | // |
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15 | // a(1)=b(1)=a(2)=c(1)=b(2)^3-a(3)^2=0, |
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16 | // b(2)!=0,a(3)!=0 from (2,2,2,1) |
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17 | // |
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18 | // a(1)=b(1)=c(1)=a(2)=b(2)=a(3) |
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19 | // =c(2)^4-a(4)^2=0, |
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20 | // c(2)!=0,a(4)!=0 |
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21 | // from (2,2,2,2,1) ==> two families |
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22 | // |
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23 | // a(1)=b(1)=c(1)=a(2)=b(2)=c(2)=a(3)=b(3) |
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24 | // =a(4)=a(5)=c(3)^4+b(4)^3-a(6)^2=0, |
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25 | // a(6)!=0,c(3)^4+b(4)^3!=0 |
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26 | // from (2,2,2,2,2,2,1) |
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27 | |
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28 | def S1=nashmult(f,6); |
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29 | setring S1; |
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30 | allsteps; |
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31 | |
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32 | |
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33 | setring R; |
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34 | // we allow only for positive integer |
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35 | // arguments |
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36 | def S2=nashmult(f,-6); |
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37 | |
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38 | //---------------------------------------- |
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39 | kill R; |
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40 | |
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41 | ring R=0,(x,y,z),dp; |
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42 | ideal I=x,y2,z3; |
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43 | ideal J=x2+y3; |
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44 | // J in I but I not in J |
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45 | |
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46 | equalJinI(I,J); |
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47 | |
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48 | ideal I1=x+y,xy,z; |
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49 | ideal J1=x2+y2,z2; |
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50 | // J1 in I1 but I1 not in J1 |
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51 | |
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52 | equalJinI(I1,J1); |
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53 | |
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54 | ideal I2=x,y,z; |
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55 | ideal J2=x+y,y+z,y; |
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56 | // I2==J2 |
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57 | |
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58 | equalJinI(I2,J2); |
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59 | |
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60 | |
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61 | kill R; |
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62 | //---------------------------------------- |
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63 | |
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64 | ring R=0,(a(1..3),b(1..3),c(1..3)),dp; |
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65 | ideal I=a(1)^3,a(2)^7,a(3),b(1)^34,b(2)*b(3),c(1)*a(1),c(3)^4; |
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66 | // I has generators |
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67 | // |
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68 | // I[1]=a(1)^3 |
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69 | // I[2]=a(2)^7 |
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70 | // I[3]=a(3) |
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71 | // I[4]=b(1)^34 |
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72 | // I[5]=b(2)*b(3) |
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73 | // I[6]=a(1)*c(1) |
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74 | // I[7]=c(3)^4 |
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75 | // |
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76 | // and replacing powers of variables by the |
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77 | // respective variables leads to an ideal |
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78 | // generated by |
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79 | // a(1),a(2),a(3),b(1),b(2)*b(3),a(1)*c(1),c(3) |
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80 | |
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81 | removepower(I); |
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82 | |
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83 | kill R; |
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84 | //---------------------------------------- |
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85 | |
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86 | ring R=0,(a(1..3),b(1..3),c(1..3)),dp; |
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87 | ideal I=a(1)^3,a(2)^7,a(3),b(1)^34,b(2)*b(3),c(1)*a(1),c(3)^4; |
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88 | |
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89 | // pairwise reduction of the generators of I gives |
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90 | // an ideal J (such that V(I)=V(J)) generated by |
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91 | // a(1),a(2),a(3),b(1),b(2)*b(3),c(3) |
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92 | |
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93 | idealsimplify(I,10); |
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94 | |
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95 | // .. but we admit only positive integer |
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96 | // arguments: |
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97 | |
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98 | idealsimplify(I,-10); |
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99 | |
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100 | tst_status(1);$ |
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