| 1 | LIB "tst.lib"; |
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| 2 | tst_init(); |
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| 3 | |
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| 4 | LIB "primdecint.lib"; |
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| 5 | |
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| 6 | ring R1 = integer,(a,b,c,d,e,f,g),dp; |
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| 7 | ideal I = 2*3,a2+2de+2cf+2bg+a, 2ab+e2+2df+2cg+b, |
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| 8 | b2+2ac+2ef+2dg+c, 2bc+2ad+f2+2eg+d, |
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| 9 | c2+2bd+2ae+2fg+e, 2cd+2be+2af+g2+f, d2+2ce+2bf+2ag+g; |
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| 10 | primdecZ(I,1); |
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| 11 | primdecZ(I,3); |
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| 12 | |
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| 13 | |
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| 14 | ring R3 = integer,(w,z,y,x),dp; |
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| 15 | ideal I = 2*3*181*32003, xzw+(-y^2+y)*z^2, (-x^2+x)*w^2+yzw, |
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| 16 | ((y^4-2*y^3+y^2)*x-y^4+y^3)*z^3,y2z2w+(-y*4+2*y^3-y^2)*z3; |
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| 17 | primdecZ(I,1); |
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| 18 | primdecZ(I,3); |
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| 19 | |
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| 20 | ring R5 = integer,(x,y,z),dp; |
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| 21 | ideal I = 2*13*181*32003, x2-y2-z2, xy-z2, y3+xz2-yz2+2z3+xy-z2, |
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| 22 | -y2z2+2z4+x2-y2+z2, y3z9+3y2z10+3yz11+z12-y2z2+2z4; |
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| 23 | primdecZ(I,1); |
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| 24 | primdecZ(I,3); |
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| 25 | |
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| 26 | ring R7 = integer,(x,y,z),dp; |
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| 27 | ideal I = 2^4*3*5*7*11*13*17, x2-y2-(z+2)^2, xy-(z+2)^2, |
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| 28 | y3+x*(z+2)^2-y*(z+2)^2+2*(z+2)^3+xy-(z+2)^2, |
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| 29 | -y^2*(z+2)^2+2*(z+2)^4+x2-y2+(z+2)^2, |
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| 30 | y3z9+3y2z10+3yz11+z12-y2z2+2z4; |
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| 31 | primdecZ(I,1); |
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| 32 | primdecZ(I,2); |
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| 33 | primdecZ(I,3); |
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| 34 | primdecZ(I,4); |
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| 35 | |
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| 36 | ring R8 = integer,(x,y,z),dp; |
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| 37 | ideal I = x2-y2-(z+2)^2, xy-(z+2)^2, |
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| 38 | y3+x*(z+2)^2-y*(z+2)^2+2*(z+2)^3+xy-(z+2)^2, |
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| 39 | -y^2*(z+2)^2+2*(z+2)^4+x2-y2+(z+2)^2, |
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| 40 | y3z9+3y2z10+3yz11+z12-y2z2+2z4; |
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| 41 | primdecZ(I,1); |
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| 42 | primdecZ(I,3); |
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| 43 | |
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| 44 | ring R9 = integer,(w,z,y,x),dp; |
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| 45 | ideal I = 2*3*5*630, ((y^2-y)*x-y^3+y^2)*z^2, (x-y)*zw, |
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| 46 | (x-y^2)*zw+(-y^2+y)*z^2, (-x^2+x)*w^2+(-yx+y)*zw; |
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| 47 | primdecZ(I,1); |
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| 48 | primdecZ(I,3); |
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| 49 | |
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| 50 | ring R10 = integer,(w,z,y,x),dp; |
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| 51 | ideal I = 2*3*5*1260, -yxzw+(-y^2+y)*z^2, (-x^2+x)*w^2-yxzw, |
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| 52 | ((-y^2+y)*x-y^3+2*y^2-y)*z^3, |
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| 53 | (y^2-y)*z^2*w+(-y^2+y)*z^2*w+(-y^2+y)*z^3; |
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| 54 | primdecZ(I,1); |
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| 55 | primdecZ(I,3); |
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| 56 | |
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| 57 | ring R11 = integer,(w,z,y,x),dp; |
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| 58 | ideal I = (4*y^2*x^2+(4*y^3+4*y^2-y)*x-y^2-y)*z^2, |
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| 59 | (x+y+1)*zw+(-4*y^2*x-4*y^3-4*y^2)*z^2, |
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| 60 | (-x-2*y^2 - 2*y - 1)*zw + (8*y^3*x + 8*y^4 + 8*y^3 + 2*y^2+y)*z^2, |
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| 61 | ((y^3 + y^2)*x - y^2 - y)*z^2, |
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| 62 | (y +1)*zw + (-y^3 -y^2)*z^2, |
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| 63 | (x + 1)*zw +(- y^2 -y)*z^2, |
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| 64 | (x^2 +x)*w^2 + (-yx - y)*zw; |
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| 65 | primdecZ(I,1); |
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| 66 | primdecZ(I,2); |
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| 67 | primdecZ(I,3); |
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| 68 | primdecZ(I,4); |
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| 69 | |
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| 70 | ring R12 = integer,(w,z,y,x),dp; |
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| 71 | ideal I = 2*3*181*72, |
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| 72 | ((y^3 + y^2)*x - y^2 - y)*z^2, |
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| 73 | (y + 1)*zw + (-y^3 -y^2)*z^2, |
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| 74 | (x + 1)*zw + (-y^2 -y)*z^2, (x^2 + x)*w^2 + (-yx - y)*zw; |
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| 75 | primdecZ(I,1); |
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| 76 | primdecZ(I,3); |
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| 77 | |
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| 78 | ring R14 = integer,(x(1),x(2),x(3),x(4)),dp; |
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| 79 | ideal I = 181*49^2, x(4)^4, x(1)*x(4)^3, x(1)*x(2)*x(4)^2, |
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| 80 | x(2)^2*x(4)^2, x(2)^2*x(3)*x(4), x(1)*x(2)*x(3)*x(4), |
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| 81 | x(1)*x(3)^2*x(4), x(3)^3*x(4); |
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| 82 | primdecZ(I,1); |
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| 83 | primdecZ(I,3); |
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| 84 | |
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| 85 | ring R15 = integer,(x,y,z),dp; |
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| 86 | ideal I = 32003*181*64, |
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| 87 | ((z^2-z)*y^2 + (z^2 -z)*y)*x, |
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| 88 | (z*y^3 + z*y^2)*x, |
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| 89 | (y^4 - y^2)*x, |
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| 90 | (z^2 - z)*y*x^2, |
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| 91 | (y^3 - y^2)*x^2, |
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| 92 | (z^3 - z^2)*x^4 + (2*z^3 -2*z^2)*x^3 + (z^3 -z^2)*x^2, |
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| 93 | z*y^2*x^2; |
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| 94 | primdecZ(I,1); |
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| 95 | primdecZ(I,3); |
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| 96 | |
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| 97 | ring R16 = integer,(x(1),x(2),x(3),x(4),x(5)),dp; |
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| 98 | ideal I = x(5)^5, x(1)*x(5)^4, x(1)*x(2)*x(5)^3, x(2)^2*x(5)^3, |
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| 99 | x(2)^2*x(3)*x(5)^2, x(1)*x(2)*x(3)*x(5)^2, x(1)*x(3)^2*x(5)^2, |
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| 100 | x(3)^3*x(5)^2, x(3)^3*x(4)*x(5), x(1)*x(3)^2*x(4)*x(5), |
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| 101 | x(1)*x(2)*x(3)*x(4)*x(5), x(2)^2*x(3)*x(4)*x(5), |
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| 102 | x(2)^2*x(4)^2*x(5), x(1)*x(2)*x(4)^2*x(5), x(1)*x(4)^3*x(5), |
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| 103 | x(4)^4*x(5); |
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| 104 | I = intersectZ(I,ideal(64*181,x(1)^2)); |
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| 105 | I; |
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| 106 | primdecZ(I,1); |
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| 107 | primdecZ(I,2); |
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| 108 | primdecZ(I,3); |
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| 109 | primdecZ(I,4); |
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| 110 | |
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| 111 | ring R17 = integer,(x,y,z),dp; |
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| 112 | ideal I = 374, (z+2)^8-140z6+2622*(z+2)^4-1820*(z+2)^2+169, |
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| 113 | 17y*(z+2)^4-374*y*(z+2)^2+221y+2z7-281z5+5240z3-3081z, |
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| 114 | 204y2+136yz3-3128yz+z6-149z4+2739z2+117, |
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| 115 | 17xz4-374xz2+221x+2z7-281z5+5240z3-3081z, |
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| 116 | 136xy-136xz-136yz+2z6-281z4+5376z2-3081, |
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| 117 | 204x2+136xz3-3128xz+z6-149z4+2739z2+117; |
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| 118 | primdecZ(I,1); |
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| 119 | primdecZ(I,3); |
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| 120 | |
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| 121 | ring R24 = integer,(a,b,c,d,e,f,g,h,j),dp; |
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| 122 | ideal I = 2*3*5*7*11*13*17, a+2b+c-d+g, f2gh-a, efg-c, fg2j-b, |
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| 123 | a+b+c+f+g-1, 3ad+3bd+2cd+df+dg-a-2b-c-g; |
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| 124 | primdecZ(I,1); |
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| 125 | primdecZ(I,3); |
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| 126 | |
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| 127 | ring R25 = integer,(s,r,b,u,v,w,x,y,z),dp; |
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| 128 | ideal I = 2*3*5*7*11*13*17*19*23, su+bv, ru+bw, rv+sw, sx+by, rx+bz, |
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| 129 | ry+sz, vx+uy, wx+uz, wy+vz; |
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| 130 | primdecZ(I,1); |
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| 131 | primdecZ(I,3); |
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| 132 | |
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| 133 | tst_status(1);$ |
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