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| 2 | ring r = (0,a2,b2,a1,b1,c1,c2,a3,b3,c3,a4,b4,c4),(e,f,t,s,y1,y2,y3,y4,s0,s1,s2,k1,k2,k3),dp; |
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| 3 | poly fs0 = - a1*s0*e + b1*y1 + c4*y4; |
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| 4 | poly fs2 = c2*y2 - a3*s2*f + b3*y3; |
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| 5 | poly fy1 = a1*s0*e - (b1+c1)*y1; |
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| 6 | poly fy2 = a2*s1*e - (b2+c2)*y2; |
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| 7 | poly fy3 = a3*s2*f - (b3+c3)*y3; |
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| 8 | poly fy4 = a4*s1*f - (b4+c4)*y4; |
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| 9 | poly ls = s0+s1+s2+y1+y2+y3+y4-k1; |
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| 10 | poly le = e+y1+y2-k2; |
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| 11 | poly lf = f+y3+y4-k3; |
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| 12 | ideal i = fs0,fs2,fy1,fy2,fy3,fy4; |
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| 13 | option(redSB); |
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| 14 | poly ii1=(c2)*y2+(-c3)*y3; |
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| 15 | poly ii2=(-c1)*y1+(c4)*y4; |
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| 16 | poly ii3=(a3)*f*s2+(-b3-c3)*y3; |
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| 17 | poly ii4=(b3*a4+c3*a4)*y3*s1+(-a3*b4-a3*c4)*y4*s2; |
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| 18 | poly ii5=(a4)*f*s1+(-b4-c4)*y4; |
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| 19 | poly ii6=(a2*c2)*e*s1+(-b2*c3-c2*c3)*y3; |
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| 20 | poly ii7=(-b2*a1*c1*c3-a1*c1*c2*c3)*y3*s0+(a2*b1*c2*c4+a2*c1*c2*c4)*y4*s1; |
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| 21 | poly ii8=(-a1*c1)*e*s0+(b1*c4+c1*c4)*y4; |
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| 22 | poly ii9=(-b2*c3*a4-c2*c3*a4)*f*y3+(a2*c2*b4+a2*c2*c4)*e*y4; |
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| 23 | poly ii10=(a2*c2*a3*b4+a2*c2*a3*c4)*e*y4*s2+(-b2*b3*c3*a4-b2*c3^2*a4-c2*b3*c3*a4-c2*c3^2*a4)*y3^2; |
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| 24 | poly ii11=(a2*b1*c2*b3*a4*c4+a2*b1*c2*c3*a4*c4+a2*c1*c2*b3*a4*c4+a2*c1*c2*c3*a4*c4)*y4*s1^2+(-b2*a1*c1*a3*c3*b4-b2*a1*c1*a3*c3*c4-a1*c1*c2*a3*c3*b4-a1*c1*c2*a3*c3*c4)*y4*s0*s2; |
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| 25 | poly ii12=y1+y2+y3+y4+s0+s1+s2-k1; |
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| 26 | poly ii13=e+y1+y2-k2; |
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| 27 | poly ii14=f+y3+y4-k3; |
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| 28 | ideal ii = ii1,ii2,ii3,ii4,ii5,ii6,ii7,ii8,ii9,ii10,ii11,ii12,ii13,ii14,e*t-1,f*s-1; |
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| 29 | ideal jj = std(ii); |
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| 30 | jj; |
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| 31 | ideal ky=eliminate(jj,y1*y2*y3*y4); |
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| 32 | ideal kef=eliminate(jj,e*f*t*s); |
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