1 | LIB "tst.lib"; |
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2 | tst_init(); |
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3 | |
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4 | //EXAMPLES SHEET |
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5 | LIB"JMSConst.lib"; |
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6 | |
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7 | //Example 1 |
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8 | ring r=0, (x,y,z),rp; |
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9 | ideal Borid=z^5,z^4*y,z^3*y^2,z^2*y^3,z^4*x, z^3*y*x, z^2*y^2*x, z*y^4,z*y^3*x, z^3*x^2, z^2*y*x^2, z*y^2*x^2, y^5; |
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10 | JMarkedScheme(Borid,r); |
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11 | //152 equations |
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12 | |
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13 | //Example 2 |
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14 | ring r=0, (x,y,z),rp; |
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15 | ideal Borid=z^4*y,z^3*y^2,z^2*y^3,z^4*x, z^3*y*x, z^2*y^2*x, z*y^4,z*y^3*x, z^3*x^2, z^2*y*x^2, z*y^2*x^2, y^5; |
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16 | JMarkedScheme(Borid,r); |
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17 | //In this example Borid is not a Borel ideal, so the procedure returns the expected error message and the result is the empty list |
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18 | |
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19 | |
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20 | //Example 3 |
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21 | ring r=0, (x(0..3)), rp; |
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22 | ideal Borid=x(3)^2, x(3)*x(2),x(2)^2,x(3)*x(1),x(2)*x(1),x(1)^3; |
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23 | JMarkedScheme(Borid,r); |
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24 | //40 equations |
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25 | |
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26 | //Example 4 |
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27 | ring r=0, (x,y,z),rp; |
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28 | ideal Borid=xy,y^2,xz,yz,z^2; |
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29 | JMarkedScheme(Borid,r); |
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30 | //6 equations |
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31 | |
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32 | |
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33 | //Example 5 |
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34 | ring r=0, (z,y,x),rp; |
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35 | ideal Borid=x^4,x^3*y,x^2*y^2,x*y^3,z*x^3,x^2*y*z, x*y^2*z,y^5; |
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36 | JMarkedScheme(Borid,r); |
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37 | // 80 equations |
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38 | |
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39 | |
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40 | //Example 6 |
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41 | ring r=0, (z,y,x),rp; |
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42 | ideal Borid=yz,z^2,x*y^2,y^3,x^4,x^3*y,x^3*z; |
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43 | JMarkedScheme(Borid,r); |
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44 | // This is not a Borel ideal. |
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45 | |
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46 | |
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47 | //Example 7 |
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48 | ring r=0, (x,y,z),rp; |
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49 | ideal Borid=z,y^6,x^3*y^5; |
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50 | JMarkedScheme(Borid,r); |
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51 | // 10 equations. |
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52 | |
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53 | //Example 8 |
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54 | ring r=0, (x,y,z),rp; |
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55 | ideal Borid=yz, z^2, y^3, xy^2; |
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56 | JMarkedScheme(Borid,r); |
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57 | //13 equations |
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58 | |
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59 | //Example 9 |
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60 | ring r=0, (x,y,z),rp; |
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61 | ideal Borid=yz, z^2, y^3, x^2*z; |
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62 | JMarkedScheme(Borid,r); |
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63 | // 12 equations |
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64 | |
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65 | //Example 10 |
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66 | ring r=0,(x,z,y),rp; |
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67 | ideal Borid=yz, z^2, y^3, x^2*z; |
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68 | JMarkedScheme(Borid,r); |
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69 | // This is not a Borel ideal. |
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70 | |
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71 | //Example 11 |
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72 | ring r=0,(z,y,x),rp; |
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73 | ideal Borid=x^2,xy,y^2,xz; |
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74 | JMarkedScheme(Borid,r); |
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75 | // 8 equations. |
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76 | |
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77 | //Example 12 |
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78 | ring r=0,(w,z,y,x),rp; |
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79 | ideal Borid=x^2,xy,y^2,xz,yz,z^3,xw^2,yw^2; |
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80 | JMarkedScheme(Borid,r); |
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81 | // 55 equations. |
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82 | |
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83 | //Example 13 |
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84 | ring r=0, (x(0..5)),rp; |
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85 | ideal Bu=x(1)^2*x(2),x(1)^2*x(3),x(1)^2*x(4),x(1)^2*x(5),x(0)*x(2)^2,x(1)*x(2)^2,x(2)^3,x(2)^2*x(3),x(2)^2*x(4),x(2)^2*x(5),x(0)*x(2)*x(3),x(1)*x(2)*x(3),x(2)*x(3)^2,x(2)*x(3)*x(4),x(2)*x(3)*x(5),x(0)*x(3)^2,x(1)*x(3)^2,x(3)^3,x(3)^2*x(4),x(3)^2*x(5),x(0)*x(2)*x(4),x(1)*x(2)*x(4),x(2)*x(4)^2,x(2)*x(4)*x(5),x(0)*x(3)*x(4),x(1)*x(3)*x(4),x(3)*x(4)^2,x(3)*x(4)*x(5),x(0)*x(4)^2,x(1)*x(4)^2,x(4)^3,x(4)^2*x(5),x(0)*x(2)*x(5),x(1)*x(2)*x(5),x(2)*x(5)^2,x(0)*x(3)*x(5),x(1)*x(3)*x(5),x(3)*x(5)^2,x(0)*x(4)*x(5),x(1)*x(4)*x(5),x(4)*x(5)^2,x(0)*x(5)^2,x(1)*x(5)^2,x(5)^3; |
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86 | list L=sort(Bu); |
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87 | ideal Borid=L[1]+ideal(x(1)^4); |
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88 | JMarkedScheme(Borid,r); |
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89 | // 1860 equations. This is not really fast, requiring 2 or 3 minutes. |
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90 | |
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91 | |
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92 | |
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93 | //Example 14 |
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94 | ring r=0,(z,y,x),rp; |
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95 | ideal Borid=x^2,xy,y^3,xz^3; |
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96 | JMarkedScheme(Borid,r); |
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97 | // 12 equations. |
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98 | |
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99 | |
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100 | //Example 15 |
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101 | ring r=0,(x,y),rp; |
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102 | ideal Borid=xy,y^2; |
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103 | JMarkedScheme(Borid,r); |
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104 | // 1 equation, namely (-c(2)-c(1)^2). |
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105 | |
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106 | example BorelCheck; |
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107 | example JMarkedScheme; |
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108 | |
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109 | tst_status(1);$ |
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