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SwinnertonDyerPoly    --    compute Swinnerton-Dyer polynomial with given roots

SwinnertonDyerPoly(x: RINGELEM, RootList: LIST of INT): RINGELEM

This function computes the Swinnerton-Dyer polynomial whose roots are the sum of all square-roots of the elements in RootList . The result is irreducible if RootList contains distinct prime numbers.

/**/  use QQ[x];
/**/  SwinnertonDyerPoly(x,[2,3]); --> roots are +/- sqrt(2) +/- sqrt(3)
x^4 -10*x^2 +1
/**/  SwinnertonDyerPoly(x, [2,2,2]);  -- you may also repeat the roots
x^8 -24*x^6 +120*x^4 -224*x^2 +144

See Also