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A240582
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Largest absolute value of coefficient in the expression for the discriminant of a generic polynomial of degree n.
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0
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1, 4, 27, 256, 3750, 77760, 1728720, 55494528, 1948916016, 146502720000, 9131329626090
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OFFSET
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1,2
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REFERENCES
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B. L. van der Waerden, Modern Algebra, Ungar, NY, Vol. I, 1953, pp. 82-83.
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LINKS
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EXAMPLE
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For n=3, f(x) = a x^3 + b x^2 + c x + d, discriminant = b^2 c^2 - 4 a c^3 - 4 b^3 d + 18 a b c d - 27 a^2 d^2. The largest absolute value of a coefficient is 27.
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MAPLE
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f := proc(n) local x, a, i; maxnorm(discrim(add(a[i]*x^i, i=0..n), x)) end: # Roman Pearce, Aug 29 2014
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MATHEMATICA
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n = 6;
Table[List @@ Discriminant[Sum[a[j] x^j, {j, 0, i}], x] /. a[_] -> 1 //
Abs // Max, {i, n}]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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