1 | // Test File for 'zeroset.lib" |
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2 | // rinvar.tst |
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3 | // |
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4 | // Implementation by : Thomas Bayer |
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5 | // Current Adress: |
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6 | // Institut fuer Informatik, Technische Universitaet Muenchen |
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7 | // www: http://wwwmayr.informatik.tu-muenchen.de/personen/bayert/ |
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8 | // email : bayert@in.tum.de |
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9 | // |
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10 | // Last change 10.12.2000 |
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11 | /////////////////////////////////////////////////////////////////////////////// |
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12 | |
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13 | LIB "tst.lib"; |
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14 | LIB "rinvar.lib"; |
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15 | |
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16 | tst_init(); |
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17 | tst_ignore("CVS ID $Id$"); |
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18 | |
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19 | |
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20 | // example 1 |
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21 | |
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22 | ring S = 0,(s(1..4), t(1..6)), dp; |
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23 | ideal G = s(1) - 1, s(2) - 2*s(3) - 3*s(4); |
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24 | ideal action = s(1)*t(1) + s(2)*t(2), s(1)*t(2), s(1)*t(3) + s(3)*t(4), s(1)*t(4), s(1)*t(5) + s(4)*t(6), s(1)*t(6); |
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25 | |
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26 | ideal inv = NullCone(G,action); |
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27 | inv; |
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28 | kill S; |
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29 | //tst_status(); |
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30 | |
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31 | |
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32 | // example 2 |
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33 | |
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34 | ring S = 0,(s(1..10), t(1..3)), dp; |
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35 | |
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36 | ideal G3 = s(7)+s(8)+s(9)-1,s(4)+s(5)+s(6)-1,s(3)+s(6)+s(9)-1,s(2)+s(5)+s(8)-1,s(1)-s(5)-s(6)-s(8)-s(9)+1,s(9)^2-s(9),s(8)*s(9),s(6)*s(9),s(8)^2-s(8),s(6)*s(8)+s(5)*s(9)-s(5)-s(6)-s(8)-s(9)+1,s(5)*s(8),s(6)^2-s(6),s(5)*s(6),s(5)^2-s(5); |
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37 | ideal G = G3, s(10)^3 - 1; |
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38 | ideal action = s(10)*(t(1)*s(1)+t(2)*s(2)+t(3)*s(3)),s(10)*(t(1)*s(4)+t(2)*s(5)+t(3)*s(6)),s(10)*(t(1)*s(7)+t(2)*s(8)+t(3)*s(9)); |
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39 | |
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40 | def T = InvariantRing(G,action); |
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41 | setring T; |
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42 | invars; |
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43 | groupid; |
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44 | |
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45 | kill S; |
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46 | kill T; |
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47 | //tst_status(); |
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48 | |
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49 | |
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50 | // example 3 |
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51 | |
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52 | ring S = 0,(s(1..4),x,y),dp; |
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53 | ideal action = s(1)*x+s(2)*y,s(3)*x+s(4)*y; |
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54 | ideal G =s(3)*s(4),s(2)*s(4),s(3)^2+s(4)^2-1,s(1)*s(3),s(2)^2+s(4)^2-1,s(1)*s(2),s(1)^2-s(4)^2,s(4)^3-s(4),s(1)*s(4)^2-s(1); |
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55 | |
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56 | def T = InvariantRing(G,action); |
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57 | setring T; |
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58 | invars; |
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59 | groupid; |
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60 | |
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61 | kill S; |
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62 | kill T; |
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63 | //tst_status(); |
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64 | |
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65 | // example 4 |
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66 | |
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67 | ring S = 0,(s(1..3), t(1..4)), dp; |
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68 | ideal G = s(1)^4-1, s(2)^4-1, s(3)^4-1; |
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69 | ideal action = s(1)^2*s(2)^2*s(3)^2*t(1), s(1)*s(2)^2*s(3)^2*t(2), s(1)^2*s(2)*s(3)^2*t(3), s(1)^2*s(2)^2*s(3)*t(4); |
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70 | |
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71 | def T = InvariantRing(G,action); |
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72 | setring T; |
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73 | invars; |
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74 | groupid; |
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75 | |
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76 | kill S; |
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77 | kill T; |
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78 | //tst_status(); |
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79 | |
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80 | |
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81 | // example 5 |
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82 | |
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83 | ring S = (0,a), (s(1..4),t(1..2)), dp; |
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84 | |
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85 | ideal action = s(1)*t(1)+s(2)*t(2),s(3)*t(1)+s(4)*t(2); |
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86 | ideal G = s(4)^5-s(4),s(3)*s(4),4*s(3)^4+(-4*a)*s(3)^3*s(4)^2+(-2*a+6)*s(3)^3*s(4)+(a-1)*s(3)^2*s(4)^3+(4*a-2)*s(3)^2*s(4)^2+(-a-5)*s(3)^2*s(4)+(-a+5)*s(3)*s(4)^3+6*s(3)*s(4)^2+(3*a+3)*s(3)*s(4)+4*s(4)^4-4,4*s(2)+4*s(3)^3+(-4*a)*s(3)^2*s(4)^2+(-2*a+6)*s(3)^2*s(4)+(a-1)*s(3)*s(4)^3+(4*a-2)*s(3)*s(4)^2+(-a-5)*s(3)*s(4),s(1)-s(4)^3; |
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87 | |
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88 | def T = InvariantRing(G,action); |
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89 | setring T; |
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90 | invars; |
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91 | groupid; |
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92 | |
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93 | kill S; |
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94 | kill T; |
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95 | //tst_status(); |
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96 | |
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97 | // example 6 |
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98 | |
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99 | ring S = 0, (s(1..16),y(1..4)), dp; |
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100 | |
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101 | ideal I1 = s(13)+s(14)+s(15)+s(16)-1,3*s(9)+3*s(10)+3*s(11)+3*s(12)+s(13)+s(14)+s(15)+s(16)-4,3*s(5)+3*s(6)+3*s(7)+3*s(8)+s(13)+s(14)+s(15)+s(16)-4,s(4)+s(8)+s(12)+s(16)-1,s(3)+s(7)+s(11)+s(15)-1,s(2)+s(6)+s(10)+s(14)-1,s(1)+s(5)+s(9)+s(13)-1,s(16)^2-s(16),s(15)*s(16),s(14)*s(16),s(12)*s(16),2*s(8)*s(16)+s(12)*s(16),s(15)^2-s(15),s(14)*s(15),s(11)*s(15),2*s(7)*s(15)+s(11)*s(15),s(14)^2-s(14),s(11)*s(14)+s(12)*s(14)+s(10)*s(15)+s(12)*s(15)+s(10)*s(16)+s(11)*s(16)-s(10)-s(11)-s(12)-s(14)-s(15)-s(16)+1,s(10)*s(14),s(7)*s(14)+s(8)*s(14)+s(6)*s(15)+s(8)*s(15)+s(6)*s(16)+s(7)*s(16)-s(6)-s(7)-s(8)-s(14)-s(15)-s(16)+1; |
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102 | ideal I2 = 2*s(6)*s(14)+s(10)*s(14),s(12)^2-s(12),s(11)*s(12)+s(15)*s(16),s(10)*s(12)+s(14)*s(16),s(8)*s(12)+s(8)*s(16)+s(12)*s(16),s(11)^2-s(11),s(10)*s(11)+s(14)*s(15),s(8)*s(11)+s(7)*s(12)+s(8)*s(15)+s(12)*s(15)+s(7)*s(16)+s(11)*s(16)-s(7)-s(8)-s(11)-s(12)-s(15)-s(16)+1,s(7)*s(11)+s(7)*s(15)+s(11)*s(15),s(10)^2-s(10),s(8)*s(10)+s(6)*s(12)+s(8)*s(14)+s(12)*s(14)+s(6)*s(16)+s(10)*s(16)-s(6)-s(8)-s(10)-s(12)-s(14)-s(16)+1,s(7)*s(10)+s(6)*s(11)+s(7)*s(14)+s(11)*s(14)+s(6)*s(15)+s(10)*s(15)-s(6)-s(7)-s(10)-s(11)-s(14)-s(15)+1,s(6)*s(10)+s(6)*s(14)+s(10)*s(14),s(8)^2-s(8),2*s(7)*s(8)+s(8)*s(11)+s(7)*s(12)+2*s(11)*s(12)+s(8)*s(15)+s(12)*s(15)+s(7)*s(16)+s(11)*s(16)+2*s(15)*s(16)-s(7)-s(8)-s(11)-s(12)-s(15)-s(16)+1; |
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103 | ideal I3 = 2*s(6)*s(8)+s(8)*s(10)+s(6)*s(12)+2*s(10)*s(12)+s(8)*s(14)+s(12)*s(14)+s(6)*s(16)+s(10)*s(16)+2*s(14)*s(16)-s(6)-s(8)-s(10)-s(12)-s(14)-s(16)+1,s(7)^2-s(7),2*s(6)*s(7)+s(7)*s(10)+s(6)*s(11)+2*s(10)*s(11)+s(7)*s(14)+s(11)*s(14)+s(6)*s(15)+s(10)*s(15)+2*s(14)*s(15)-s(6)-s(7)-s(10)-s(11)-s(14)-s(15)+1,s(6)^2-s(6),s(6)*s(12)*s(15)+s(6)*s(11)*s(16)-s(6)*s(11)-s(6)*s(12)+s(7)*s(14)+s(8)*s(14)+s(8)*s(15)+s(7)*s(16)-s(7)-s(8)-s(14)-s(15)-s(16)+1; |
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104 | ideal G = I1,I2,I3; |
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105 | |
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106 | ideal action = y(1)*s(1)+y(2)*s(2)+y(3)*s(3)+y(4)*s(4),y(1)*s(5)+y(2)*s(6)+y(3)*s(7)+y(4)*s(8), y(1)*s(9)+y(2)*s(10)+y(3)*s(11)+y(4)*s(12),y(1)*s(13)+y(2)*s(14)+y(3)*s(15)+y(4)*s(16); |
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107 | |
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108 | def T = InvariantRing(G,action); |
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109 | setring T; |
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110 | invars; |
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111 | groupid; |
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112 | |
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113 | kill S; |
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114 | kill T; |
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115 | |
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116 | |
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117 | |
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118 | // end |
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119 | |
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120 | tst_status(1);$ |
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