1 | ring h2=32003,(t,x,y,z),dp; |
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2 | ideal i= |
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3 | 2t3x5y2z+x2t5y+2x2y, |
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4 | 2y3z2x+3z2t6x2y+9y2t3z, |
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5 | 2t5z+y3x2t+z2t3y2x5; |
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6 | intvec e=weight(i); |
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7 | e; |
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8 | //ring r=32003,(a,b,c,d),wp(e[1],e[2],e[3],e[4]); |
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9 | //map f=h2,a,b,c,d; |
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10 | //ideal k=f(i); |
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11 | //ideal k0=std(k); |
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12 | //"//size "+string(size(k0))+ |
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13 | //", dim "+string(dim(k0))+", mult "+string(mult(k0))+ |
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14 | //", lastdeg "+string(ord(k0[size(k0)])); |
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15 | //kill r; |
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16 | kill h2,e; |
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17 | ring s6=32003,(x,y,z),dp; |
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18 | int a =6; |
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19 | int b =8; |
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20 | int c =10; |
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21 | int alpha =5; |
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22 | int beta= 5; |
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23 | int t= 0; |
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24 | poly f =x^a+y^b+z^c+x^alpha*y^(beta-5)+x^(alpha-2)*y^(beta-3); |
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25 | f=f+x^(alpha-3)*y^(beta-4)*z^2+x^(alpha-4)*y^(beta-4)*(y^2+t*x)^2; |
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26 | ideal i= jacob(f); |
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27 | i=i,f; |
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28 | intvec e=weight(i); |
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29 | e; |
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30 | //ring r=32003,(u,v,w),wp(e[1],e[2],e[3]); |
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31 | //map f=s6,u,v,w; |
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32 | //ideal k=f(i); |
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33 | //ideal k0=std(k); |
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34 | //"//size "+string(size(k0))+ |
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35 | //", dim "+string(dim(k0))+", mult "+string(mult(k0))+ |
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36 | //", lastdeg "+string(ord(k0[size(k0)])); |
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37 | //kill r; |
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38 | kill s6,e,a,b,c,alpha,beta,t; |
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39 | |
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40 | ring s12=32003,(x,y,z,w),dp; |
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41 | ideal i0=x2-z10-z20,xy3-z10-z30,y6-xy3w40; |
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42 | ideal i=interred(i0^3); |
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43 | intvec e=weight(i); |
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44 | e; |
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45 | //ring r=32003,(u,v,a,b),wp(e[1],e[2],e[3],e[4]); |
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46 | //map f=s12,u,v,a,b; |
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47 | //ideal k=f(i); |
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48 | //ideal k0=std(k); |
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49 | //"//size "+string(size(k0))+ |
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50 | //", dim "+string(dim(k0))+", mult "+string(mult(k0))+ |
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51 | //", lastdeg "+string(ord(k0[size(k0)])); |
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52 | //kill r; |
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53 | kill s12,e; |
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54 | |
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55 | ring pa= 32003,(k,h,g,f,e,d,c,b,a),dp; |
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56 | ideal i0= af2-f5,bg2-f4g,c3-f3gh,k-fgh3,df-fh4,ef-h5; |
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57 | ideal i=i0^2; |
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58 | intvec E=weight(i); |
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59 | E; |
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60 | //ring r=32003,(u,v,w,x,y,z,l,m,n), |
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61 | //wp(e[1],e[2],e[3],e[4],e[5],e[6],e[7],e[8],e[9]); |
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62 | //map g=pa,u,v,w,x,y,z,l,m,n; |
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63 | //ideal k0=g(i); |
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64 | //ideal j=std(k0); |
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65 | //"//size "+string(size(j))+ |
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66 | //", dim "+string(dim(j))+", mult "+string(mult(j))+ |
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67 | //", lastdeg "+string(ord(j[size(j)])); |
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68 | //kill r; |
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69 | kill pa,E; |
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70 | |
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71 | ring r5=32003,(a,b,c,d,e),dp; |
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72 | ideal i = |
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73 | 47b6+94b3c2-71b3e2+91ab3-22b4+47c4+71b3d-67b3e-71c2e2-2e4+91b3+91ac2-22bc2 |
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74 | +71c2d-67c2e-21ae2-80be2+4de2+82e3+53a2-23ab-47b2+91c2+21ad+80bd-2d2+55ae+18be |
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75 | -82de-26e2+106a-23b+21d+55e+53, |
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76 | -98b6-196b3c2+4b3e2-54ab3-81b4-98c4-4b3d-87b3e+4c2e2-51e4-54b3-54ac2-81bc2 |
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77 | -4c2d-87c2e+22be2+102de2+92e3-28a2-53ab+70b2-54c2-22bd-51d2+86ae+27be-92de+73e2 |
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78 | -56a-53b+86e-28, |
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79 | 49b6+98b3c2-49b3e2-54ab3+90b4+49c4+49b3d+57b3e-49c2e2-21e4-54b3-54ac2+90bc2 |
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80 | +49c2d+57c2e+18ae2-67be2+42de2-23e3+26a2-50ab+28b2-54c2-18ad+67bd-21d2-74ae+2be |
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81 | +23de+58e2+52a-50b-18d-74e+26, |
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82 | 34b6+68b3c2-74b3e2-30ab3-56b4+34c4+74b3d+21b3e-74c2e2+9e4-30b3-30ac2-56bc2 |
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83 | +74c2d+21c2e-77ae2+66be2-18de2-26e3-69a2+38ab+26b2-30c2+77ad-66bd+9d2+50ae+29be |
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84 | +26de-121e2-138a+38b+77d+50e-69, |
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85 | -29b6-58b3c2+68b3e2+28ab3+89b4-29c4-68b3d-52b3e+68c2e2+13e4+28b3+28ac2+89bc2 |
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86 | -68c2d-52c2e-17ae2+87be2-26de2+32e3-100a2-41ab-75b2+28c2+17ad-87bd+13d2+79ae- |
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87 | 87be-32de+33e2-200a-41b+17d+79e-100; |
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88 | intvec E=weight(i); |
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89 | E; |
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90 | //ring r=32003,(u,v,w,x,y),wp(e[1],e[2],e[3],e[4],e[5]); |
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91 | //map g=r5,u,v,w,x,y; |
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92 | //ideal k0=g(i); |
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93 | //ideal j=std(k0); |
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94 | //"//size "+string(size(j))+ |
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95 | //", dim "+string(dim(j))+", mult "+string(mult(j))+ |
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96 | //", lastdeg "+string(ord(j[size(j)])); |
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97 | //kill r; |
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98 | kill r5,E; |
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99 | |
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100 | ring p1=32003,(t,x,y,z,a,b,c,d,e),dp; |
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101 | ideal i = |
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102 | -y82a+x32z23, |
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103 | x45-y13z21b, |
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104 | y33z12-z41c, |
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105 | -y33z12d+z22, |
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106 | x5y17z22e-1, |
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107 | xyzt-1; |
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108 | intvec ew=weight(i); |
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109 | ew; |
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110 | //ring r=32003,(s,u,v,w,h,l,m,n,o), |
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111 | //wp(ew[1],ew[2],ew[3],ew[4],ew[5],ew[6],ew[7],ew[8],ew[9]); |
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112 | //map g=p1,s,u,v,w,h,l,m,n,o; |
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113 | //ideal k0=g(i); |
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114 | //ideal j=std(k0); |
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115 | //size(j); |
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116 | //ord(j[size(j)]); |
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117 | //kill r; |
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118 | kill p1,ew; |
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119 | |
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120 | test(9); |
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121 | option(weightM); |
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122 | ring vc= 32003,(x,y,z,t),ds; |
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123 | degBound=1; |
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124 | ideal i= |
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125 | 49y5-9y4+41x2z+12y3+33y2+11y+73t, |
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126 | 33y4+21x2y+17x2z+63y3+11xy+77y2+91y+1t, |
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127 | 26y2+44xz+12y+9t; |
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128 | ideal k=i^2; |
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129 | ideal j = std(k); |
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130 | //"//size "+string(size(j))+ |
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131 | //", dim "+string(dim(j))+", mult "+string(mult(j))+ |
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132 | //", lastdeg "+string(ord(j[size(j)])); |
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133 | degBound=0; |
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134 | kill vc; |
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135 | |
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136 | int N=3; |
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137 | ring ra3=32003,x(1..N),ds; |
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138 | ideal i0= |
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139 | -7*x(1)^6-49*x(1)^5*x(2)+16*x(1)^4*x(2)^2+27*x(1)^3*x(2)^3- |
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140 | 38*x(1)^2*x(2)^4+60*x(1)*x(2)^5+70*x(2)^6-28*x(1)^5*x(3)+85*x(1)^4*x(2)*x(3)+ |
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141 | 69*x(1)^3*x(2)^2*x(3)-13*x(1)^2*x(2)^3*x(3)-65*x(1)*x(2)^4*x(3)+51*x(2)^5*x(3)- |
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142 | 70*x(1)^4*x(3)^2+37*x(1)^3*x(2)*x(3)^2+89*x(1)^2*x(2)^2*x(3)^2- |
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143 | 82*x(1)*x(2)^3*x(3)^2+6*x(2)^4*x(3)^2-67*x(1)^3*x(3)^3+19*x(1)^2*x(2)*x(3)^3- |
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144 | 12*x(1)*x(2)^2*x(3)^3-81*x(2)^3*x(3)^3+33*x(1)^2*x(3)^4-98*x(1)*x(2)*x(3)^4+ |
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145 | 51*x(2)^2*x(3)^4+11*x(1)*x(3)^5+11*x(2)*x(3)^5-39*x(3)^6, |
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146 | 5*x(1)^6-17*x(1)^5*x(2)-62*x(1)^4*x(2)^2+41*x(1)^3*x(2)^3-85*x(1)^2*x(2)^4+ |
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147 | 57*x(1)*x(2)^5-52*x(2)^6+80*x(1)^5*x(3)+19*x(1)^4*x(2)*x(3)- |
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148 | 72*x(1)^3*x(2)^2*x(3)-34*x(1)^2*x(2)^3*x(3)-46*x(1)*x(2)^4*x(3)- |
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149 | 6*x(2)^5*x(3)-33*x(1)^4*x(3)^2+44*x(1)^3*x(2)*x(3)^2-23*x(1)^2*x(2)^2*x(3)^2- |
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150 | 60*x(1)*x(2)^3*x(3)^2+64*x(2)^4*x(3)^2+26*x(1)^3*x(3)^3-84*x(1)^2*x(2)*x(3)^3+ |
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151 | 35*x(1)*x(2)^2*x(3)^3-91*x(2)^3*x(3)^3-93*x(1)^2*x(3)^4+22*x(1)*x(2)*x(3)^4+ |
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152 | 99*x(2)^2*x(3)^4-36*x(1)*x(3)^5+5*x(2)*x(3)^5+46*x(3)^6, |
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153 | -32*x(1)^6-73*x(1)^5*x(2)-43*x(1)^4*x(2)^2-55*x(1)^3*x(2)^3-83*x(1)^2*x(2)^4- |
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154 | 50*x(1)*x(2)^5-74*x(2)^6-56*x(1)^5*x(3)+79*x(1)^4*x(2)*x(3)+ |
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155 | 86*x(1)^3*x(2)^2*x(3)-27*x(1)^2*x(2)^3*x(3)+28*x(1)*x(2)^4*x(3)+71*x(2)^5*x(3)+ |
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156 | 77*x(1)^4*x(3)^2-71*x(1)^3*x(2)*x(3)^2-63*x(1)^2*x(2)^2*x(3)^2- |
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157 | 22*x(1)*x(2)^3*x(3)^2+17*x(2)^4*x(3)^2+58*x(1)^3*x(3)^3+31*x(1)^2*x(2)*x(3)^3+ |
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158 | 19*x(1)*x(2)^2*x(3)^3-36*x(2)^3*x(3)^3-15*x(1)^2*x(3)^4-9*x(1)*x(2)*x(3)^4+ |
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159 | 42*x(2)^2*x(3)^4-61*x(1)*x(3)^5-67*x(2)*x(3)^5+31*x(3)^6; |
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160 | ring r=32003,(a,b,c),ds; |
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161 | map ff=ra3,a+b2,b2-c3,c; |
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162 | ideal i=ff(i0); |
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163 | ideal j=std(i); |
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164 | //"//size "+string(size(j))+ |
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165 | //", dim "+string(dim(j))+", mult "+string(mult(j))+ |
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166 | //", lastdeg "+string(ord(j[size(j)])); |
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167 | kill ra3,r,N; |
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168 | |
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169 | ring r1=32003,(t,x,y,z),ds; |
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170 | ideal i= |
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171 | 5t3x2z+2t2y3x5, |
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172 | 7y+4x2y+y2x+2zt, |
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173 | 3tz+3yz2+2yz4; |
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174 | ideal j=std(i); |
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175 | //"//size "+string(size(j))+ |
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176 | //", dim "+string(dim(j))+", mult "+string(mult(j))+ |
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177 | //", lastdeg "+string(ord(j[size(j)])); |
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178 | kill r1; |
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179 | |
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180 | ring r2=32003,(x,y,z),ds; |
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181 | poly p1 = 1x3y2+21328x5y+10667x2y4+21328x2yz3+10666xy6+10667y9; |
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182 | poly p2 = 1x2y2z2+3z8; |
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183 | poly p3 = 5x4y2+4xy5+2x2y2z3+1y7+11x10; |
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184 | ideal i=p1,p2,p3; |
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185 | ideal j=std(i); |
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186 | //"//size "+string(size(j))+ |
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187 | //", dim "+string(dim(j))+", mult "+string(mult(j))+ |
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188 | //", lastdeg "+string(ord(j[size(j)])); |
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189 | kill r2; |
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190 | |
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191 | ring r12=32003,(x,y,z,w),ds; |
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192 | ideal i=x2-z10-z20,xy3-z10-z30,y6-xy3w40; |
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193 | ideal j=std(i); |
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194 | //"//size "+string(size(j))+ |
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195 | //", dim "+string(dim(j))+", mult "+string(mult(j))+ |
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196 | //", lastdeg "+string(ord(j[size(j)])); |
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197 | kill r12; |
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198 | |
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199 | ring r17=32003,(x,y,z),ds; |
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200 | ideal i= |
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201 | 1x3+1y4+2xz3+1z5+32000x4y2+2z6+3z7, |
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202 | 1xz3+32001x4y2+1z6+2z7, |
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203 | 9x3z2+18x2z5+31998z7+12x4y2z2+42x2z6+40x3y2z4+7z9+24x3y2z5, |
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204 | 31999y3z3+31991x6y+32x3y5+32001x4yz3, |
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205 | 12xy3z2+6x5yz2+24y3z5+20x4yz4+56y3z6+12x4yz5; |
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206 | ideal j=std(i); |
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207 | //"//size "+string(size(j))+ |
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208 | //", dim "+string(dim(j))+", mult "+string(mult(j))+ |
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209 | //", lastdeg "+string(ord(j[size(j)])); |
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210 | kill r17; |
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211 | |
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212 | ring r18=32003,(t,x,y,z),ds; |
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213 | ideal i= |
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214 | 4t2z+6z3t+3z3+tz, |
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215 | 5t2z7y3x+5x2z4t3y+3t7, |
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216 | 6zt2y+2x8+6z2y2t+2y5; |
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217 | ideal j=std(i); |
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218 | //"//size "+string(size(j))+ |
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219 | //", dim "+string(dim(j))+", mult "+string(mult(j))+ |
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220 | //", lastdeg "+string(ord(j[size(j)])); |
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221 | kill r18; |
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222 | |
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223 | ring r5=32003,(x,y,z),ds; |
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224 | int a=7; |
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225 | poly f =xyz*(x+y+z)^2 +(x+y+z)^3 +x^a+y^a+z^a; |
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226 | ideal i= jacob(f); |
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227 | test(-9); |
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228 | ideal j=std(i); |
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229 | //"//size "+string(size(j))+ |
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230 | //", dim "+string(dim(j))+", mult "+string(mult(j))+ |
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231 | //", lastdeg "+string(ord(j[size(j)])); |
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232 | kill r5; |
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233 | LIB "tst.lib";tst_status(1);$ |
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