why don't you give me the exact groebner basics?

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sebastiano della gatta
i have these equations:
f1n=121*c1^4 - 5984*c1^3*c3 + 242*c1^2*c2^2 - 43736*c1^2*c2*c3 + 5984*c1^2*c2 - 412446*c1^2*c3^2 + 242*c1^2 + 5984*c1*c2^2*c3 + 43736*c1*c2^2 - 1293600*c1*c2*c3 + 5984*c1*c3^3 - 43736*c1*c3^2 - 5984*c1*c3 + 121*c2^4 - 5984*c2^3 + 242*c2^2*c3^2 + 647042*c2^2 - 5984*c2*c3^2 + 43736*c2*c3 + 5984*c2 + 121*c3^4 + 242*c3^2 + 121;
f2n=308*c1^4 - 2310*c1^3*c2 + 153426*c1^3*c3 + 2332*c1^2*c2^2 - 191264*c1^2*c2*c3 - 172926*c1^2*c2 + 43460*c1^2*c3^2 - 7062*c1^2*c3 + 616*c1^2 + 8674*c1*c2^2*c3 + 358298*c1*c2^2 - 23262*c1*c2*c3^2 - 82256*c1*c2*c3 - 44214*c1*c2 + 197518*c1*c3^3 - 141152*c1*c3^2 + 3582*c1*c3 + 2024*c2^4 - 28174*c2^3 + 4048*c2^2*c3^2 - 44214*c2^2*c3 + 122960*c2^2 - 197518*c2*c3^2 + 141152*c2*c3 - 3582*c2 + 2024*c3^4 - 2310*c3^3 + 2332*c3^2 - 2310*c3 + 308;
f3n=- 11*c1^3*c2 + 1021*c1^3*c3 + 1132*c1^2*c2*c3 - 1021*c1^2*c2 - 119*c1^2*c3 - 11*c1*c2^3 + 1039*c1*c2^2*c3 - 1132*c1*c2^2 + 97*c1*c2*c3^2 + 97*c1*c2 + 1021*c1*c3^3 + 1039*c1*c3 - 1039*c2^3 - 119*c2^2*c3 - 1021*c2*c3^2 - 1132*c2*c3 - 1039*c2 - 11*c3^3 - 11*c3;
I have to do the groebner bases of these equations, an equation should come out only in c3 of degree 64, one in c1 and c3 of degree 63 and one in c2 and c3 of degree 63, but I get 4 equations of degree 57. Why?

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