OFFSET
1,2
COMMENTS
Possible discriminants of the general normalized quintic polynomial x^5+b*x^4+c*x^3+d*x^2+e*x+f with b,c,d,e,f>=0
REFERENCES
Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.
MATHEMATICA
aa = {}; a = 1; Do[Print[f]; Do[Do[Do[Do[k = b^2 c^2 d^2 e^2 - 4 a c^3 d^2 e^2 - 4 b^3 d^3 e^2 + 18 a b c d^3 e^2 - 27 a^2 d^4 e^2 - 4 b^2 c^3 e^3 + 16 a c^4 e^3 + 18 b^3 c d e^3 - 80 a b c^2 d e^3 - 6 a b^2 d^2 e^3 + 144 a^2 c d^2 e^3 - 27 b^4 e^4 + 144 a b^2 c e^4 - 128 a^2 c^2 e^4 - 192 a^2 b d e^4 + 256 a^3 e^5 - 4 b^2 c^2 d^3 f + 16 a c^3 d^3 f + 16 b^3 d^4 f - 72 a b c d^4 f + 108 a^2 d^5 f + 18 b^2 c^3 d e f - 72 a c^4 d e f - 80 b^3 c d^2 e f + 356 a b c^2 d^2 e f + 24 a b^2 d^3 e f - 630 a^2 c d^3 e f - 6 b^3 c^2 e^2 f + 24 a b c^3 e^2 f + 144 b^4 d e^2 f - 746 a b^2 c d e^2 f + 560 a^2 c^2 d e^2 f + 1020 a^2 b d^2 e^2 f - 36 a b^3 e^3 f + 160 a^2 b c e^3 f - 1600 a^3 d e^3 f - 27 b^2 c^4 f^2 + 108 a c^5 f^2 + 144 b^3 c^2 d f^2 - 630 a b c^3 d f^2 - 128 b^4 d^2 f^2 + 560 a b^2 c d^2 f^2 + 825 a^2 c^2 d^2 f^2 - 900 a^2 b d^3 f^2 - 192 b^4 c e f^2 + 1020 a b^2 c^2 e f^2 - 900 a^2 c^3 e f^2 + 160 a b^3 d e f^2 - 2050 a^2 b c d e f^2 + 2250 a^3 d^2 e f^2 - 50 a^2 b^2 e^2 f^2 + 2000 a^3 c e^2 f^2 + 256 b^5 f^3 - 1600 a b^3 c f^3 + 2250 a^2 b c^2 f^3 + 2000 a^2 b^2 d f^3 - 3750 a^3 c d f^3 - 2500 a^3 b e f^3 + 3 125 a^4 f^4; If[k > 0 && k < 1000, AppendTo[aa, k]], {b, 0, 30}], {c, 0, 30}], {d, 0, 30}], {e, 0, 30}], {f, 0, 30}]; Union[aa] (*Artur Jasinski*)
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Apr 29 2008
STATUS
approved