# Speed up MinimalPolynomial

My Mathematica code runs slowly

MinimalPolynomial[Sqrt[2] + Sqrt[3]+ Sqrt[5]+ Sqrt[7]+ Sqrt[11]+ Sqrt[13], x]


runs slowly, but the Maple version

evala(Norm(convert(x-(sqrt(2)+sqrt(3)+sqrt(5)+sqrt(7)+sqrt(11)+sqrt(13)), RootOf)));


runs quite fast Is there a faster way do this in Mathematica?

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What is the answer in maple? –  Chenminqi Mar 29 at 15:21

GroebnerBasis[{x1+x2+x3+x4+x5+x6-x,x1^2-2,x2^2-3,x3^2-5,x4^2-7,x5^2-11,x6^2-13},x,{x1,x2,x3,x4,x5,x6}]

This will not in general give the minimal polynomial. Try it on sqrt(2)+sqrt(3)+sqrt(6) which clearly has a min poly of degree no larger than 4 since it lies in Q(sqrt(2),sqrt(3)). But GroebnerBasis[{x1+x2+x3-x, x1^2-2, x2^2-3, x3^2-6}, x, {x1,x2,x3}] gives a poly of degree 8. –  Daniel Lichtblau May 5 at 14:58